Journal of Chromatogaphy Library
-
Volume 6
ISOTACHOPHORESIS Theory, Instrumentation and Applications
JOURNAL O F CHROMATOGRAPHY LIBRARY Volume 1 Chromatography of Antibiotics by G. H. Wagman and M. J. Weinstein Volume 2 Extraction Chromatography edited by T. Braun and G . Ghersini Volume 3 Liquid Column Chromatography. A Survey of Modern Techniques and Applications edited by Z . Deyl, K. Macek and J. Janak Volume 4 Detectors in Gas Chromatography by J. SevEik Volume 5 Instrumental Liquid Chromatography. A Practical Manual on High-Performance Liquid Chromatographic Methods by N. A. Parris Volume 6 Isotachophoresis. Theory, Instrumentation and Applications by F. M. Everaerts, J. L. Beckers and Th. P. E. M. Verheggen Volume 7 Chemical Derivatization in Liquid Chromatography by J. F. Lawrence and R. W. Frei Volume 8 Chromatography of Steroids by E. Heftmann
Journal of Chromatography Library - Volume 6
ISOTACHOPHORESIS Theory, Instrumentation and Applications
Frans M. Everaerts Department of Instrumental Analysis, Eindhoven University of Technology, Eindhoven
Jo L. Beckers Eijkhagen College, Schaesberg
The0 P.E.M. Verheggen Department of Instrumental Analysis, Eindhoven University of Technology, Eindhoven
ELSEVIER SCIENTIFIC PUBLISHING COMPANY AMSTERDAM - OXFORD - NEW YORK 1976
ELSEVIER SCIENTIFIC PUBLISHING COMPANY 335 Jan van Galenstraat P.O.Box 211, Amsterdam, The Netherlands
Distributors for the United States and Canada: ELSEVIER/NORTH-HOLLAND INC. 52,Vanderbilt Avenue New York, N.Y. 10017
Library of Congress Calaloging in Publication Data
Everaerts, Frans M 1941Isotachophoresis : theory, instrumentation, and applications. (Journal of chromatography library ; vo 6) Includes bibliographies and index. 1. Electrophoresis. I. Beckers, Jo L., joint author. 11. Verheggen, Theo P. E. M., joint author. 111. Title. TV. Series. QD79.EaE93 543 ’ .087 7644834 fSBN
0-444-41430-4
Copyright 0 1976 by Elsevier Scientific Publishing Company, Amsterdam All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Elsevier Scientific Publishing Company, Jan van Galenstraat 335, Amsterdam Printed in The Netherlands
Dedicated to Pr0f.Dr.h. A.I.M. Keulemans, for providing the possibility of developing this analytical separation technique in his Department of Instrumental Analysis, University of Technology, Eindhoven.
This Page Intentionally Left Blank
Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.Historicalreview ........................................................... Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Historical review ......................................................... References ...............................................................
XI11 1 1 1 4
THEORY 2 . Principles of electrophoretic techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary........ ..................................................... 2.1.Introduction .......................................................... 2.2. Principle of zone electrophoresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Principle of moving-boundary electrophoresis ................................. 2.4. Principle of isotachophoresis .............................................. 2.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2. Simplified model for isotachophoresis: ................................. 2.4.3. Concentration adaptation ........................................... 2.4.4. Some isotachophcrograms ........................................... 2.5. Principle of isoelectric focusing ............................................ 2.6.Discussicin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.Conceptofmobility ......................................................... Summary ................................................................ 3.1.Introduction .......................................................... 3.2. Interpretation of electrophoretic migration ................................... 3.3. Ionic mobility and ionic equivalent conductivity ............................... 3.4. Effective ionic mobility .................................................. 3.4.1. Partial dissociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1.1. Protolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....... 3.4.1.2. Complex formation .......................................... 3.4.2. Relaxation and electrophoretic retardation .............................. 3.5. Determination of ionic mobilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1. Relationship between volume and ionic mobility ......................... 3.5.2. Relationship between entropy and ionic mobility ......................... 3.5.3.Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . Mathematical model for isotachophoresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. General equations ...................................................... 4.2.1. Equilibrium equations .............................................. 4.2.2. Electroneutrality equations .......................................... 4.2.3. Mass balances for all ionic species . . . . . . . . . . . 4.2.4. Modified Ohm’s law ...................... 4.2.5. Parameters and equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Mathematical model for the steady state in isotachophoresis ..................... 4.3.1. Concept of isotachophoretic separation ................................. 4.3.2. Mathematical model of isotachophoresis ................................ 4.3.2.1. Equilibrium equations ....................................... 4.3.2.2. The isotachophoretic condition ................................
I 7 7 I 9 13 13 15 18 20 23 24 21 21 21 21
29 31 32 33 33 36 31 31 39 40 40 41 41 41 43 45 41 48 51 51
55 55 58 58 58
VIII
CONTENTS
4.3.2.3. Mass balance of the buffer .................................... 4.3.2.4. Principle of electroneutrality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2.5. Modified Ohm’s law .... 4.3.3. Computer program for calculation of the steady state ...................... 4.3.3.1. Computation procedure ...................................... 4.3.3.2. Iteration procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3.3. Discussion ..................................... 4.4. Validity of the isotachophoretic model ...................................... 4.4.1. Introduction ..................................................... 4.4.2. Influence of diffusion on the zone boundaries ........................... 4.4.3. Influence of axial and radial temperature differences ...................... 4.4.4. Influence of activity coefficients ..................................... 4.5. Check of the isotachophoretic model ....................................... References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59 60 61 62 62 62 69 69 69 74 75 76 76 81
.................................................
83 83 83 84 84 87 87 89 92 93 96 99 99 99 99 99 100 100 113
5 . Choice of electrolyte systems
Summary ................................................................ 5.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1. General remarks .................................................. 5.2. Choice of the solvent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1. Methanol as a solvent .............................................. 5.2.1.1. Comparative behaviour with water .............................. 5.2.1.2. Determination of pK values in methanolic solutions ................ 5.3. Choice of the buffering counter ionic species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Choice of the pH of the leading electrolyte ................................... 5.5. Choice of the terminating and leading ionic species ............................. 5.6. Additions to the electrolyte solutions ............................... 5.6.1. Stabilizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.2. Surface-active chemicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.3. Reference materiall~foridentificationandi~e~ifi~atio~~~ calibration of concentrations . . . . . . . 5.6.4. Spacers and carriers .................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.Discussion ............................................................ 5.8.Examples ............................................................ References . ..........................................................
INSTRUMENTATION
6 . Detection systems
................................................
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 .1. Universal detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2. Specific detectors ....................................... 6.1.3. Combinations of universal and specific detectors ......................... 6.2. Thermometric recording . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
..................................................
6.2.3. Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.4. Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.5. Conclusion ............................... ................... ................... 6.3. High-frequency conductivity detection . . . . . . . . . . . . . . 6.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2.Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Conductivity detection . . . . . . . . . . . ............................... 6.4.1. Introduction . . . .................... ........................
117 117 117 118 118 119 119 119 119 125 126 129 130 130 131 133 133
CONTENTS 6.4.2. The d.c. method of resistance determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.3. The d.c.-a.c. converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.4. The a.c. method of resistance determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.5. Conductivity probe with equiplanar-mounted sensing electrodes . . . . . . . . . . . . . 6.5. UV absorption meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.2. Construction of the UV source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.3. UV detector in combination with a non-modulated UV source . . . . . . . . . . . . . . . 6.5.4. UV detector in combination with a modulated UV source . . . . . . . . . . . . . . . . . . 6.5.5.UVcell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.6. Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6. Additives to the electrolytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.2. Effect of additives on the electroendosmotic flow ......................... 6.6.3. Effect of additives on the micro-sensing electrodes ........................ 6.6.4.Additives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7. Coating of the micro-sensing electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7.2. Experimental . . . . . . . . . . . . . .................................. 6.8. Detection limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8.2.Experimental .................................................... 6.9.Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 . Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Injection systems ...................... ............................. 7.2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2.Four-way tap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3. Six-way valve . . . . . . . . . . . . .................................... 7.2.4. Injection block . . . . . . . . . . . . . . . . . . .............................. 7.2.5. Simplified injection block . . .................................... 7.3. Counter electrode compartments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2. Cylindrical counter electrode compartment ............................. 7.3.3. Counter electrode compartment with flat membrane ....................... 7.4.Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.2. Narrow-bore tube surrounded with a water-jacket ......................... 7.4.3. Narrow-bore tube thermostated with an aluminium block . . . . . . . . . . . . . . . . . . . 7.4.4. Equipment with high-resolution detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5. Counter flow of electrolyte . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.2. Counter flow with level regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.3. Counter flow with light-dependent resistor regulation ...................... 7.5.4. Counter flow with direct control on the pumping mechanism via the power supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.5. Counter flow with no regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.6. Counter flow regulated by the cur -stabilized power supply; the membrane pump . . . . . . . . . . . . . ..................................
IX 135 140 143 143 153 153 155 159 161 164 165 171 171 171 174 180 191 191 191 193 193 196 199 201 203 203 203 203 203 204 205 208 211 211 211 213 215 217 217 219 221 224 230 230 231 233 237 238 24 1
X
CONTENTS
APPLICATIONS 8.Introduction ............................................................... Summary ................................................................ 8.Introduction ............................................................
249 249 249
9 .Practical aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary ................................................................ 9.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2. Disturbances caused by hydrogen and hydroxyl ions ............................ 9.2.1. Disturbances from the terminator zone in unbuffered systems . . . . . . . . . . . . . . . 9.2.1.1. HI-MI boundary ........................................... 9.2.1.2. MI-MI, boundary . . . .................................... 9.2.2. Disturbances from the leading zone in unbuffered systems . . . . . . . . . . . . . . . . . . 9.2.3. Disturbances due to the presence of hydrogen and hydroxyl ions in buffered systems ......................................................... 9.3. Disturbances due to the presence of carbon dioxide ............................ 9.4. Enforced isotachophoresis ............................................... 9.4.1. Disc electrophoresis ................................................ 9.5. Water as terminator ..................................................... 9.6. Purification of the terminator ............................................. 9.7. Conversion of data measured with different detectors ........................... References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
260 263 264 265 267 268 210 271
10. Quantitative aspects ........................................................ Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1.Introduction ......................................................... 10.2.Theoretical .......................................................... 10.3. Thermometric measurements ............................................ 10.3.1. Reproducibility ................................................. 10.3.2. Calibration constant ............................................. 10.4. Conductimetric measurements ........................................... 10.4.1. Reproducibility ................................................. 10.4.2. Calibration constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.Conclusion ........................................................... References ...............................................................
273 213 273 214 215 275 215 219 279 280 281 282
11. Separation of cationic species in aqueous solutions ................................ Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1. Separation of cationic species in aqueous solutions using a thermocouple as detector . . 11.1.1. The system WHCl ............................................... 11.1.2. The system WHIO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3. The system WKAC ............................................... 11.1.4. The system WKCAC ............................................. 11.1.5. The system WKDIT .............................................. 11.2. Separation of cationic species in water and deuterium oxide using a conductivity detector (a.c. method) and a UV absorption detector (256 nm) ...................
283 283 283 285 286 288 289 293
12. Separation of anionic species in aqueous solutions ................................. Summary ................................................................. 12.1. Separation of anionic species in aqueous solut'ions using a thermometric detector . . . . . 12.1.1. Operational system histidine/histidine hydrochloride (pH 6) . . . . . . . . . . . . . . . 12.1.2. Operational system imidazole/imidazole hydrochloride (pH 7) . . . . . . . . . . . . . 12.2. Separation of anionic species in aqueous solutions using a conductivity detector (a.c. method) and a UV absorption detector (256 nm) ............................. 12.2.1. Introduction ...................................................
253 253 253 253 253 254 254 257
293 295 295 295 295 296 300 300
XI
CONTENTS
.....................................
301
13. Amino acids, peptides and proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary ....................... ........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1.Amino acids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1.2. Separation at low pH values in aqueous systems ........................ 13.1.3. Separation at high pH values in aqueous systems ........................ 13.1.4. Separation by use of complex formation ........................... 13.1.5. Separation in aqueous propanal solutions ............................. 13.2. Separation of proteins in ampholyte gradients ............................... 13.2.1. Introduction ................................................... 13.2.2. Experimental ................................................... 13.3. Separation of small peptides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3.1. Introduction ................................................... 13.3.2. Experimental .................................................. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
311 311 311 311 312 312 318 319 322 322 325 335 335 336 336
............................ 14. Separation of nucleotides in aqueous systems . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1.1ntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2. Separation using a thermometric detector ................................... 14.3. Separation using a conductivity detector (ax . method) and a UV absorption detector (256 nm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
337 337 337 337
15. Enzymatic reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...... 15.1.Introduction ......................................................... 15.2. Enzymatic conversion of glucose (fructose) into glucose-6-phosphate (fructosedphosphate) with hexokinase from yeast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.3. Enzymatic conversion of pyruvate into lactate with lactate dehydrogenase from pigheart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
347 347 347
....................... 16.Separations in non-aqueous systems. . . . . . . . . . . . . . . . . Summary .................................... ................ 16.1.Introduction ......................................................... 16.2. Separation of anionic species in methanol using a thermometric detector . . . . . . . . . . . 16.3. Separation of cationic species in methanol using a thermometric detector . . . . . . . . . . . . 16.3.1. The operational system MHCl ...................................... 16.3.2. The operational system MKAC ..................................... 16.3.3. The operational system MTMAAC .................................. 16.4. Experiments in aqueous methanolic systems using a conductimetric detector (a.c. method) and W absorption detector (256 nm) .........................
361 361 361 362 364 365 367 373 373
17. Counter flow of electrolyte .................................................. Summary ........................................................... 17.1. lntroduction ......................................................... 17.2.Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.3.Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
375 375 375 378 384 384
12.2.2. Applications
...........
342
348 355 360
APPENDICES A. Simplified model of moving-boundary electrophoresis for the measurement of effective mobilities ................................................................
387
XI1
CONTENTS
A.1.inrroduction .......................................................... A.2. Model of moving-boundary electrophoresis .................................. A.2.1. Electroneutrality equations ......................................... A.2.2. Modified Ohm’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2.3. Mass balances for all cationic species . . . . . . . . . . . . . . . A.3. Procedure of computation ............................................... A.4.Experimental ................................................ A.5.Discussion ............................................................ References ........................................................... ~
B. Diameter of the narrow-bore tube, applied for separation C. Literature
...............
......................................................... Symbols and abbreviations ..................................................... Symbols ................................................................. Subscripts ............................................................... Superscripts .............................................................. Examples ................................................................ Abbreviations ............................................................. Subjectindex ...............................................................
387 387 388 388 388 389 390 392 394 395 397 409 409 410 411 411 411 413
It is very well known that charged particles move under the influence of an electric field. Because the final velocity of such particles depends on numerous parameters, many scientists through several decades have applied t h s phenomenon to the characterization and separation of a variety of charged particles, with a wide range of molecular weights, both for analytical and preparative purposes. Because the vital components of electrophoretic equipment need to be made of insulating materials, in the early days it was a handicap for the further development of electrophoretic instrumentation that modern insulating materials such as Perspex, PTFE and fluoroethylene polymer were not available. Moreover, sensitive detection systems had not been developed, so that the minimum detectable amount was rather high in comparison with some other separation techniques. After World War 11, the chemical industry began t o show considerable interest in the development of chromatographic separation techniques for the analysis of hydrocarbons and other (complex) organic compounds. It may have bezn due to this development that the materials for the construction of the vital parts of the electrophoretic equipment, including the detectors, rapidly became available. Moreover, in the same period the electronics industry also underwent a phenomenal expansion. Although this book is devoted mainly to isotachophoresis, with which all kind of charged molecules can be separated (as is shown in the Section Applications), the instrument described can be used for other types of electrophoretic separations. Three main aspects of isotachophoresis are covered, in three different sections. In the first section, the theory of the isotachophoretic separation technique is given, and other electrophoretic techniques are briefly described. For isotachophoresis, both a simplified and a more complicated model are given. The latter model results in a computer program suitable for the qualitative and quantitative interpretation of the analytical results. In the Section Instrumentation, several detectors and the “isotachophoretic” equipment are described. Also, a means is described of formulating a simplified model rapidly, because for many problems simplified equipment is adequate. Moreover, not much cheap equipment is commercially available yet. In the last section, possible fields of application are considered. Analytical conditions (so-called operational systems) are presented and results are given in the form of both automatically recorded isotachopherograms and tables. The data in these tables can be used for the qualitative interpretation of isotachophoretic analyses. Because all of the values given were derived directly under the operational conditions considered, they cannot be used for the calculation of, for example, mobilities at infinite concentration. All of the isotachophoretic zones have a well defined temperature, pH and composition of the electrolytes present, and these are constant in a chosen operational system but are different from each other. For further theoretical approaches, corrections need to be made. In the Appendices, a method is described for mobility determinations, the influence of the diameter of the narrow-bore tube is dealt with and a list of relevant papers concerning isotachophoresis is given. Each section can be used almost independently by scientists interested in fundamental aspects, by research groups who intend t o construct an instrument and by scientists whose main interest is in the analytical aspects.
XIV
PREFACE
In this book, most of the results given summarize about 12 years research, performed with a variety of instruments. Not only the authors but also the research students, who worked in the electrophoresis research group contributed to the development of this technique. In particular, we thank Ir. M. Geurts, who developed most of the electronic circuits described, and Ir. F. Mikkers, who helped greatly in the collection of many of the data presented and in the work with tKe instrument equipped with the UV absorption detector and the a.c. conductivity detector. Eindhoven
Schaesberg Eindhoven
FRANS M. EVERAERTS JO L. BECKERS THEO P.E.M. VEI~HEGGEN
Chapter 1
Historical review SUMMARY
Mens ugitat molem*
1. HISTORICAL REVIEW In the middle of the nineteenth century, Wiedeman [ 1 , 2 ] and Buff [3] reported on the phenomenon that charged particles migrate in a solution when an electric field is applied. Later experiments, carried out by Lodge [4] and Whetham [S, 61 , were the basis on which Kohlrausch [7] developed a theory of ionic migration. With the equation that he derived, all electrophoretic principles can be described**, including zone electrophoresis, moving-boundary electrophoresis and isotachophoresis. The discovery by Hardy [8,9] that many biocolloids, such as proteins, show characteristic mobilities that depend largely on the pH of the electrolyte solution in which the analysis is performed, greatly stimulated interest in electrophoretic work. The characterization of such substances on the basis of their electrophoretic properties, especially the p l points, increased interest in electrophoretic separation techniques. As an early example, the work of Michaelis [ 101 can be considered. He found that enzymes can be characterized on the basis of their isoelectric points, measured in migration experiments performed at various pH values; this work, of course, was carried out before pure enzymes were available. Although at first the terms cataphoresis and electrophoresis were introduced in order to indicate the migration of charged colloidal particles and the term ionophoresis was reserved for substances of lower molecular weight, nowadays most workers use the term electrophoresis to describe the migration of charged particles in aqueous and non-aqueous stabilized and free solutions. Perhaps owing to the major interest in compounds such as proteins and enzymes, or because high-resolution detectors had not been developed, most attention was paid to only one of the basic principles, as already described by Kohlrausch [7] , namely zone electrophoresis and few reports dealing with the other principles were published. It is a fact that substances such as proteins need appropriate stabilization by electrolytes, as discussed in Chapter 13. It was not until about 1923 that a principle of electrophoresis other than zone electrophoresis was described. Kendall and Crittenden [ 1I ] succeeded in separating rare *Motto, University of Technology, Eindhoven.
**In Chapter 2, isoelectric focusing is also briefly described because it is a separation technique that has many similarities with electrophoretic techniques, although once separated the charged particles do not migrate if the amphiprotic compounds have reached their isoelectric points (the overall charge is zero).
1
2
HISTORICAL REVIEW
earth metals and some simple acids by, as they called it, the ‘ion migration method’, which was, in fact, isotachophoresis. He stated that the ions not only separate, but also adapt their concentrations to the concentration of the first zone according to the Kohlrausch [7] regulating function, the ‘beharrliche Funktion’. It was also Kendall [ 12) who considered that it is necessary to be able to follow the separation in some convenient way and suggested that a coloured ion, with an effective mobility intermediate between those of the ions of interest, could be used. The end of the experiment could, by the addition of this coloured ion, easily be determined without the need for a detector. Kendall also suggested that other detection methods are possible, e.g., utilizing thermometric and conductivity detectors, and pointed out that, especially when analyzing metals, spectroscopic detection can easily be used. Finally, when appropriate, the measurement of the radioactivity can be used to obtain qualitative and quantitative information. The experiments in which he attempted to separate 35 Cl from 37Cl, as proposed by Lindemann [ 131 , failed, even when very long analysis times were used. Other isotopes also could not be separated. The ‘movingboundary method‘ of MacInnes and Longsworth [ 141 , which was used for the determination of transport numbers, was also based on the Kohlrausch [7] theory. For about 10 years, little relevant work was carried out on electrophoretic techniques other than zone electrophoresis, then in 1942 Martin [ 151 separated chloride, acetate, aspartate and glutamate by isotachophoresis, which he called ‘displacement electrophoresis’, because it was so similar to the displacement technique in chromatography. There was a further gap until 1953, when a paper was published by Longsworth [16], who realized the importance of Kendall’s work. In a Tiselius moving-boundary apparatus, he introduced a mixture of cations (Ca2’, Ba” and Mg2+)between two other zones, called the leading solution and the trailing solution. Once separated, the effective mobilities decrease on going from the leading solution towards the trailing solution. Detection via Schlieren scanning patterns showed very clearly the sharpness of the boundaries between the consecutive zones. Longsworth introduced a counter flow of electrolyte, because the separation chamber in a Tiselius apparatus is very short, and adjusted it in such a way that the zones remained in the detection region until they were separated. He also found that a steady state was reached, once the components were separated. The importance of the pH of the trailing solution was recognized. The work of Poulik [17] is important, although he was not aware that he was working along the lines of the Kohlrausch [7] regulating function. Kaimakov and Fiks [ 181 reported on experiments carried out in an electrophoretic equipment, the separation chamber being filled with quartz sand so as to eliminate convection problems. The separation chamber was initially filled with an electrolyte, called an indicator electrolyte, that was different from the test solutions. Again, their results showed that a decreasing sequence of mobilities was obtained once the steady Ftate had been reached. They also used a counter flow of electrolyte. Transport numbers were measured by Kaimakov [I91 and Konstantinov and Kaimakov [20]. Konstantinov et al. 121,221 extended the work of Hartley [23] and Gordon and Kay [24]. Konstantinov and Oshurkova [25,26] in 1963 described an analytical application based on the ‘moving-boundary method’. Their separation chamber was a narrow-bore tube of I.D. 0.1 mm and a wall thickness of 0.05 mm. Measurements of the refractive index of the various zones by photographic methods gave a recording of the zone boundaries.
HISTORICAL REVIEW
3
Independently in 1963, Everaerts [27] started, together with Martin, work that finally resulted in the appearance of this book on isotachophoresis. As Martin [ 151 , he used the term ‘displacement electrophoresis’. He performed the analysis in a narrow-bore tube of Pyrex glass of I.D. 0.5 mm and an O.D. of 0.8 mm. In order to prevent hydrodynamic flow between the two electrode compartments through the narrow-bore tube, caused by differences in levels, this tube was filled with an electrolyte the viscosity of which was increased up to 100 CPby addition of a watersoluble linear polymer, e.g., hydroxyethylcellulose. This polymer was purified by shaking it with a mixed-bed ion exchanger. A thermocouple (30-pm copper-25-pm constantan) was used as the detector. Independently, and unaware of this work, Kaimakov and Sharkov [28] reported on the use of microthermistors to detect zone boundaries. In 1964, Ornstein [29] and Davis [30] introduced disc electrophoresis. They placed a protein mixture between an electrolyte with an anion of low effective mobility and an electrolyte with an anion with a high effective mobility. Owing to the concentration phenomenon of isotachophoresis, the proteins are stacked in narrow zones between the two electrolytes (‘steady-state stacking’). The zones, however, are so narrow that even a high-resolution detector cannot detect them. Therefore, in the second stage of the analysis, the principle of zone electrophoresis was used, which allowed every protein to move at a different velocity. Cross-linked polyacrylamide was used as a stabilizing medium and as a molecular sieve. The mobilities of the proteins could be controlled, moreover, by varying the pore size in the gel. Ornstein [29] derived several equations, with which it was possible to calculate the mobilities and the pH values of the electrolyte systems. In 1966, Vesterrnark [31] introduced a new term, ‘cons electrophoresis’, for the electrophoretic technique that makes use of Kohlrausch’s regulating function [7] . Vestermark also used the spacer technique. In 1966, Preetz [32] gave a theoretical treatment of the use of a counter flow of electrolyte in isotachophoretic systems. In 1967, Preetz and Pfeifer [33] described an instrument that was specially designed for measurements of potential gradients and ion concentrations. Preetz also performed analyses in narrow-bore tubes. A further development was the continuous counter flow equipment described by Preetz and Pfeifer [34]. Based on work of Everaerts [35] and Martin and Everaerts [36], Verheggen and Everaerts built an instrument and introduced the technique in Bergstr6m’s department at the Karolinska Institute, Stockholm, Sweden, in 1968. This was the basis of the commercial production of isotachophoretic equipment, produced by LKB Produkter AB in Bromma, Sweden. In 1969, Everaerts and Verheggen introduced the technique at the Charles University in Prague, Czechoslovakia, in Vacik’s research group. Up to 1970, several names had been used for similar electrophoretic techniques, including ion migration method, Kendall [ 121 (1928); moving-boundary method, MacInnes and Longsworth [ 141 (1932); displacement electrophoresis, Martin [ 151 (1942) and Everaerts [27] (1964); steady-state stacking, Ornstein [29] (1964); cons electrophoresis, Vestermark [31] (1966); and ionophoresis, Preetz [32] (1966). Together with Haglund [37], a group of research workers in the field introduced a new name, based upon an important phenomenon of the electrophoretic technique, namely the identical velocities of the sample zones in the steady state: isotacho-electro-phoresis*, or isotachophoresis for short. *r
LOO =
equal; ~ 0 1 x 0= ~velocity; @peeueorc = to be dragged.
4
HISTORICAL REVIEW
It is very difficult to summarize the individual contributions of the various scientists to the development of the technique after 1970. In Appendix B, we give an almost complete list of the relevant papers on the subject. Of all the papers, special note is made of two, in which new types of operational detector were described, representing landmarks in the development of isotachophoresis. In 1970, Arlinger and Routs [38] introduced an operational UV absorption detector, and in 1972, Verheggen et al. [39] introduced an operational conductivity detector.
REFERENCES 1 G. Wiedeman, Pogg. Ann., 99 (1856) 197. 2 G. Wiedeman, Pogg. Ann., 104 (1858) 166. 3 H. Buff, Ann. Chem. Pharm., 105 (1858) 168. 4 0. Lodge, Brit. Ass. Advan. Sci., Rep., 56 (1886) 389. 5 W.C.D. Whetham, Phil. Trans. Roy. SOC. London, Ser. A , 184 (1893) 337. 6 W.C.D. Whetham,PhiI. Trans. Roy. SOC.London, Ser. A , 186 (1895) 507. 7 F. Kohlrausch,Ann. Phys. (Leipzig), 62 (1897) 209. 8 W.B. Hardy, Proc. Roy. Soc. London. 66 (1900) 110. 9 W.B. Hardy, J. Physiol. (London), 33 (1905) 251. 10 L. Michaelis, Biochem. Z., 16 (1909) 81. 11 J. Kendall and E.D. Crittenden, Proc. Nut. Acad. Sci. US.,9 (1923) 75. 12 J. Kendall, Science, 67 (1928) 163. 1 3 A. Lindemann, Proc. Roy. Soc., Ser. A, 99 (1921) 102. 14 D.A. MacInnes and L.G. Longsworth, Chem. Rev., 11 (1932) 171. 15 A.J.P. Martin, unpublished results, 1942. 16 L.G. Longsworth, Nut. Bur. Stand. (US.). Circ., No. 524 (1953) 59. 17 M.D. Poulik, Nature (London), 180 (1957) 1477. 18 E.A. Kaimakov, and V.B. Fiks, Rum. J. Phys. Chem., 35 (1961) 873. 19 E.A. Kairnakov, Russ. J. Phys. Chem., 36 (1961) 436. 20 B.P. Konstantinov and E.A. Kaimakov, Rum. J. Phys. Chem., 36 (1962) 437. 21 B.P. Konstantinov, E.A. Kaimakov and N.L. Varshovskaya, Russ. J. Phys. Chem., 36 (1962) 535. 22 B.P. Konstantinov, E.A. Kaimakov and N.L. Varshovskaya, Russ. J. Phys. Chem., 36 (1962) 540. 23 G.S. Hartley, Trans. Faraday SOC.,30 (1934) 648. 24 A.R. Gordon and R.L. Kay, J. Chem. Phys., 21 (1953) 131. 25 B.P. Konstantinov and O.V. Oshurkova, Dokl. Akad. Nauk. SSSR, 148 (1963) 1110. 26 B.P. Konstantinov and O.V. Oshurkova, Sov. Phys.-Tech. Phys., 11 (1966) 693. 27 F.M. Everaerts, Graduation Rep., University of Technology, Eindhoven, 1964. 28 E.A. Kaimakov and V.I. Sharkov, Russ. J. Phys. Chem., 38 (1964) 893. 29 L. Ornstein, Ann. N. Y. Acad. Sci., 121 (1964) 321. 30 B.J. Davis, Ann. N. Y. Acad. Sci., 121 (1964) 404. 3 1 A. Vestermark, Cons Electrophoresis: An Experimental Study, unpublished results, 1966. 32 W. Preetz, Tdanta, 13 (1966) 1649. 33 W. Preetz and H.L. Pfeifer, Talanta, 14 (1967) 143. 34 W. Preetz and H.L. Pfeifer, Anal. a i m . Acta, 38 (1967) 255. 35 F.M. Everaerts, Thesis, University of Technology, Eindhoven, 1968. 36 A.J.P. Martin and F.M. Everaerts,Anal. Chim. Acta, 38 (1967) 233. 37 H. Haglund, Sci. Tools, 17 (1970) 2. 38 L. Arlinger and R.J. Routs, Sci. Tools, 17 (1970) 21. 39 Th. P.E.M. Verheggen, E.C. van Ballegooijen, C.H. Massen and F.M. Everaerts, J. Chromatogr., 64 (1972) 185.
THEORY
This Page Intentionally Left Blank
Chapter 2
Principles of electrophoretic techniques SUMMARY The principles of the four main types of electrophoresis, viz., zone electrophoresis, moving-boundary electrophoresis, isotachophoresis and isoelectric focusing, are described and a simplified mathematical model for isotachophoresis is given. The characteristics of these four main types are compared.
2.1. INTRODUCTION As already described in the Preface, ionic species will move, under the influence of an applied electric field, E, with a velocity, v , of
v=mE
(2-1)
where m is the effective mobility of the ionic species, which depends on several factors that will be discussed in Chapter 3. Differences in effective mobilities cause differences in velocities and, by utilizing, this effect, the ionic species can be separated. Separation techniques based on this principle are called electrophoretic techniques, which can be divided into three main types, viz., zone electrophoresis, moving-boundary electrophoresis and isotachophoresis. In isoelectric focusing, ionic species are not separated according to differences in mobilities, differences in PIvalues determining whether they can be separated. In the steady state, ionic species do not migrate. Because the ionic species migrate electrophoretically in order to attain that steady state, isoelectric focusing can also be considered to be an electrophoretic technique; hence four main types of electrophoresis can be distinguished. In principle, all of these electrophoretic techniques can be carried out in any electrophoretic equipment. Such an instrument generally consists of five units, viz.,the anode and cathode compartments, the separation chamber, the injection system and the detector. In this chapter, the principles of the four main types of electrophoresis are discussed briefly, the most attention being paid, of course, to isotachophoresis.
2.2. PRINCIPLE OF ZONE ELECTROPHORESIS For the description of the principle of zone electrophoresis, we shall consider a narrowbore tube as the separation chamber, which is connected with the anode and cathode compartments. The distinguishing feature of all zone electrophoretic systems is that the whole system (anode and cathode compartments and the separation chamber) is filled with one electrolyte, the so-called background or supporting electrolyte, which carries the
PRINCIPLES OF ELECTROPHORETIC TECHNIQUES
8
electric current and generally has a buffering capacity. The sample (a mixture of anionic and cationic species) is introduced into the system in this background electrolyte. In general, the concentration of this background electrolyte is high compared with that of the sample ionic species and therefore it provides a constant pH and voltage gradient in the whole system. The ionic species of the background electrolyte have a certain effective mobility and, when an electric current is passed through the system, these ionic species will migrate with specific velocities, cations migrating towards the cathode and anions towards the anode. The sample ionic species also migrate under the influence of the applied electric field, each ionic species having a characteristic velocity, depending on the conditions chosen. Because of the high concentration of the background electrolyte, the influence of the sample ionic species on the voltage gradient and pH is negligible and therefore all sample ionic species migrate with constant velocity in time, resulting in a flow of ions of the background electrolyte accompanied by a flow of sample ions. The ionic species of the sample will be separated after some time if the differences in effective mobilities are sufficiently great. Owing to the diffusion, the peaks are wide (tailing), and adsorption phenomena can cause further tailing. Often detection is effected by a specific method, e.g., measurement of the colour of the sample ionic species. Quantitative information can be obtained by measuring the intensity of the colour due to the reaction products, while qualitative information (identification) is obtained from the migration distance. Just as in paper chromatography, for example, here the R , values can be used for identification in standardised systems, where R, is defined as the migration distance (Z) of the ionic species in question related to the migration distance of a standard ionic species:
R,
= 'ionic species 'standard
A disadvantage of such a detection method is that the detection takes place after the separation procedure. In addition to the extra steps required and the long time involved, disturbances such as diffusion in the various zones often occur. In Fig.2.1, the separation of a mixture of anionic species A, B and C and a cationic species D is shown. The background electrolyte consists of an anionic species Q and a cationic species P. In Fig.2. la, the whole system is filled with the background electrolyte and the sample is injected. In Fig.2.lb, all ionic species of the sample are separated. The migration distances are l A , I, I , and I, respectively. The R , values relative to the anionic species C would be R,(A) =-'A and R,(B) = IB 'C
In Fig.2.2, the voltage gradients, temperatures and pH values for some zones are shown. The background electrolyte containing sample ionic species with low effective mobilities shows a higher voltage gradient over the zone than that for rapid ionic species. This influence is small for high concentrations of the background electrolyte and nearly constant pH and voltage gradients can be expected in practice. In this instance, a specific means of detection must be used (see Chapter 6). This method can be compared with elution chromatography.
9
MOVINGBOUNDARY ELECTROPHORESIS
a
S
/
b
P O
\
S
0
I I
I I I
L
L _
/ a
_I I
I I
I
/ A
J
Fig. 1. Electrophoretic separation of the anionic species A, B and C and -..e cationic species D along the lines of zone electrophoresis. All compartments are filled with the electrolyte PQ-.The distances l A , I g , lc and I,, can be used for the determination of the ionic species A , B, C and D. (a), Sample injection; (b), all ionic species of the sample are separated.
2.3. PRINClPLE OF MOVING-BOUNDARY ELECTROPHORESIS We shall first consider the separation of anionic species according to the method of Tiselius. In Fig.2.3a, the anionic species to be separated, mixed with a buffer solution, fill the lower part of a U-tube while the upper part is filled with the buffer solution. If an electric current is passed through such a system, the anionic species migrate in the direction of the anode and, after some time, a partial separation occurs. Two series of mixed zones are obtained; in front of the original zone are present the zones A and A + B and behind the original zone are present B+C and C (see Fig.2.3b), if the effective mobilities of the ionic species A, B and C decrease in the order mA > m B > mc. It is also possible to carry out moving-boundary electrophoretic experiments in the following way. Anionic species can be separated by using a narrow-bore tube as the separation chamber, connected with anode and cathode compartments. The anode compartment and narrow-bore tube are filled with an electrolyte, the anionic species of which is chosen to be more mobile than the anionic species to be separated. The sample is introduced into the cathode compartment (see Fig.2.4a). The anionic species migrate towards the anode, and the sample anions can never pass the anionic species of the leading electrolyte because its effective mobility is higher. The mobilities of the
PRINCIPLES OF ELECTROPHORETIC TECHNIQUES
10
E
T
PH
I l
I
I
Fig.2.2. Electric field strength (E), temperature ( T ) and pH in the different zones of the zone electrophoretic separation procedure. Theoretically, the zones show small differences in the electric field strength and temperature. The dotted lines are exaggerated. No general means of detection can be applied, e.g., conductimetric or thermometric. X refers to, the position in the separation chamber.
anionic species of the sample differ, however, so that some of them will migrate forward. Thus a situation as shown in Fig.2.4b will be obtained after some time. Substance A, which is more mobile than the other substances of the sample, is partially separated from
11
MOVINGBOUNDARY ELECTROPHORESIS
0
0
0
buffer
butter
buffer
n r
0
iuf ter
A
-
-C B+C
A+B A+B+C
A+B+C
a
b
Fig.2.3. Separation according to the Tiselius moving-boundary principle. In (a), the lower tube is filled with a mixture of the anions A , B and C. Specific buffers need to be applied for optimal separation. In (b), it is shown that zones exist on both the front and rear sides, vii., A, A + B and A+B+C, and A + B t C , B t C and C, respectively.
B and C. Substance B, mixed with A, forms the second sample zone after the pure A zone. The third zone contains the mixture A t B+C. This method can be compared with frontal analysis in chromatography. In movingboundary electrophoresis, the zones generally contain more ionic species of the sample. The composition of the sample plays an important role in the determination of the concentrations, pH values and conductivities of the different zones. This situation contrasts with that in isotachophoresis, where all of these quantities are independent of the quantitative composition of the sample. A quantitative description of this method is given in Section 4.2. As will be clear after the description of isotachophoresis, the first zone in moving-boundary electrophoresis has a self-correcting effect, so that the first boundary will be sharp. All other zones are not sharp, although this influence is generally smaller than in zone electrophoresis. In Appendix A, a method is given with which effective mobilities can be measured by using moving-boundary electrophoresis. Fig.2.4 shows the temperature, voltage gradients and electrical resistances for the different zones. All of these quantities show similar relationships.
PRINCIPLES OF ELECTROPHORETIC TECHNIQUES
12
1
U
I
1 I
I
I
I
I
I
t
I I I
I
E , 1,R.
I I I
I
I
I
I
I
L
A
A+B
A+B+ C
t-
X
Fig.2.4. (a) Separation according to the moving-boundary principle. The sample anions A + B + C are introduced into the cathode compartment. The separation chamber and the anode compartment are filled with a leading electrolyte, a suitable choice of counter ion needs to be made, because it determines the pH at which the analysis is performed. After some time, a partial separation is obtained, which is shown schematically in (b). The electric field strength Q, electric resistance ( R ) and temperature ( r ) are shown schematically for the different zones.
ISOTACHOPHORESIS
13
2.4. PRINCIPLE OF iSOTACHOPHORESIS 2.4.1. Introduction
We shall consider here the separation of anionic species in narrow-bore tubes. For the separation of anionic species, the narrow-bore tube and anode compartment are filled with the so-called leading electrolyte, the anions of which must have a mobility that is higher than that of any of the sample anionic species. The cations of the leading electrolyte must have a buffering capacity at the pH at which the analyses will be performed. The cathode compartment is filled with the terminating electrolyte, the anions of w h c h must have a mobility that is lower than that of any of the sample anionic species. The sample is introduced between the leading and terminating electrolyte, e.g., by means of a sample tap or a micro-syringe. #en an electric current is passed through such a system (see Fig.2.5a), a uniform electric field strength over the sample zone occurs and hence each sample anionic species will have a different migration velocity according to eqn. 2.1. The sample anionic species with the highest effective mobility will run forwards and those with lower mobilities will remain behind. Hence, both in front of and behind the original sample zone, the movingboundary procedure results in two series of mixed zones (comparable with the Tiselius method). In the series of mixed zones, the sample anionic species are arranged in order of their decreasing effective mobilities (see Fig.2.5b), The anionic species of the leading electrolyte can never be passed by sample anions, because its effective mobility is chosen so as t o be higher. Similarly, the terminating anions can never pass the anionic species of the sample. In this way, the sample zones are sandwiched between the leading and terminating electrolyte. In the mixed zones of the sample (see Fig.2.5b), the separation continues and, after some time, when the separation is complete, a series of zones is obtained in which each zone contains only one anionic species of the sample if no anionic species with identical effective mobilities are present in the sample. Of course, this series of zones is still sandwiched between leading and terminating electrolyte (see Fig.2.5~). The first sample zone contains the anionic species of the sample with the highest effective mobility, the last zone that with the lowest effective mobility. After this stage, no further changes t o the system occur and a steady state has been reached. In such a case, we can speak of an isotachophoretic separated system. (Of course, one or more unmixable ‘mixed zones’, i.e., zones that contain one or more anionic species with identical effective mobilities, may still be present.) In this state, all of the zones must run connected together, in contrast to zone electrophoresis, where all zones release. Here the zones cannot release as there is no background electrolyte that can support the electric current (a requirement for the solvent is that its self-conductance must be negligible; see section 5.2 .)* . *If it is assumed that the zones release, then the concentration of the ionic species at that position will decrease, the electric field strength will increase (working at a constant current density) and hence the migration velocity of the ionic species involved will be higher. Therefore, finally these ionic species will reach the preceding zone.
PRINCIPLES OF ELECTROPHORETIC TECHNIQUES
14
b
0
L
C , conatant
,,,
Fig.2.5. Separation of a mixture of anions according to the isotachophoretic principle. The sample A+B+C is introduced between the leading anionic species L and the terminating anionic species T. A suitable cationic species is chosen as the buffering counter ion. The original conditions are shown in (a). After some time (b), some mixed zones are obtained according to the moving boundary principle. Finally (c), all anionic species of the sample are separated and all zones contain only one anionic species of the sample (‘ideal case’).
For this steady state, all zones must have identical migration velocities, determined by the migration velocity of the anionic species of the leading electrolyte. Considering the zones L, A, B, C and T (see Figure 2 . 5 ~ ) :
v, = V A = V B = vc = VT or
m,E, = mAEA = mBEB= m,Ec
= mTET
Eqn. 2.4 will be called the ‘isotachophoretic condition’ and it is characteristic of isotachophoretic separations.
(2.4)
ISOTACHOPHORESIS
15
As the anionic species are arranged in order of decreasing effective mobilities*, i.e., > mT, the electric field strengths increase on the rear side. Working at a constant current density, the product EI (a measure for the heat production) also increases on the rear side and therefore the temperatures increase in the preceding zones. In Figs.2.6~and 2.6d, the electric field strengths and temperatures are shown for the zones of Fig.2.6a. In Fig.2.6b, the variation of potential with position in the tube is shown. The increase in the voltage gradients in the consecutive zones induces two important characteristics of isotachophoretic systems. The first characteristic is the ‘self-correction’ of the zone boundaries. When a zone has attained the steady state, the boundary will not broaden further, which again is in contrast to zone electrophoresis, where the peaks are unsharp and broad owing to adsorption and diffusion phenomena. This effect can easily be understood. If an ion remains behind in a zone with a higher electric field strength, then it will acquire a hgher migration velocity according to eqn. 2.1, until it reaches its own zone. If it diffuses into a preceding zone, where the electric field strength is lower than the value that corresponds to its velocity, its velocity will decrease and it will be overtaken by its proper zone*. The second characteristic is the increase in temperature in the preceding zones, and by this feature the zones can be detected with a thermometric detector. In order to obtain a better understanding of isotachophoresis, we now give a much simplified model and subsequently some isotachopherograms, obtained with several detection systems, are shown and discussed in order to facilitate the understanding of later chapters.
mL > mA > mg > mc
2.4.2. Simplified model for isotachophoresis Let us first consider a boundary between two connected zones, containing anionic species A and B with mA > m B .The influence of diffusion, etc., will be neglected. Suppose the counter ionic species Q are similar in both zones and have a constant mobility mQ , all ions are monovalent and fully ionized and the influence of the presence of H and OH- ions can be neglected. Working at a constant current density, the following equations can be derived: (a) According to the principle of electroneutrality, the amounts of positive and negative ions in both zones must be identical, so
The subscripts indicate the ionic species and the zone, e.g., cA,l represents the concentration of anionic species A in the first zone. (b) According to the isotachophoretic condition, the zones must have identical *If not too large pH shifts occur in the consecutive zones considered (see Chapter 9).
PRINCIPLES OF ELECTROPHORETIC TECHNIQUES
16
V
-X
-X
dl
I
T
/
\
I
Fig.2.6. Graphical representation of potential V (b), electric field strength E (c) and temperature T (d) for the different zones, moving in the steady state of an isotachophoretic analysis (a). X = Position in the narrow-bore tube where the analysis is performed; s = position of introduction of sample.
17
ISOTACHOPHORESIS
velocities, so that v1
=v2
(c) According to Ohm’s law: I = constant = E l hl
= E2
(2.10)
h2
and the conductivities of the zones can be written as
+ mQ)
A1 = C A , ~ ~ A F + C Q , ~ ~ Q F = ~ A , ~ F ( ~ A
(2.1 1) (2.12)
(2.13)
(2.14) Replacing El lE2 with mBlm, according to eqn. 2.9: (2.15) From e q n 2.15. it can be seen that the concentration of all zones is determined by the concentration of the leading electrolyte, and depends on the mobilities of the ionic species concerned. In Chapter 4, a more accurate model will be derived, with corrections for the influence of pH, different temperatures in the zones, buffering counter ionic species, the pK values of the ionic species present, etc. Although the model here is greatly simplified, it can be stated that the concentrations in the zones are constant in a given system and that the ionic concentrations decrease to the rear side. The concentrations do not depend on the composition of the sample. If the sample is very dilute, then during analyses by other techniques (e.g., zone electrophoresis and gas chromatography), the concentrations will be further decreased. In isotachophoresis, however, the concentration always attains a value fixed by the composition of the leading electrolyte. Therefore, isotachophoresis is sometimes used with other techniques in order t o concentrate the sample in narrow zones. For example, in disc electrophoresis, the first stage in the analysis involves concentration of the sample
18
PRINCIPLES OF ELECTROPHORETICTECHNIQUES
by the so-called ‘stacking electrophoresis’*. The importance of this phenomenon is clear when it is realized that, because the concentrations in the zones are constant, the length of a zone (the distance between two differential signals) is a direct measure of the concentration of the sample ionic species. 2.4.3. Concentration adaptation
If zones migrate, they must have a concentration that is fixed by the preceding zones according to Ohm’s law, and we call them ‘adapted zones’. The effects on changes in concentration during an isotachophoretic analysis are shown in Figs.2.7a-2.7f for the separation of a mixture of anionic species A and B, introduced between the leading electrolyte L and the terminating electrolyte T. In Fig.2.7a, the original situation is shown. A mixture of A and B (Ao +Bo) is introduced between the leading ions L and the terminating ions T I . Of course, the zone A. +Bo is not adapted to L according Ohm’s law, and nor is zone T I . In Fig.2.7b, the situation is shown after a certain time, where the leading zone L has migrated over a certain distance, its concentration remaining constant, however. According to all movingboundary procedures, a zone containing the anionic species A is formed and the concentration in this zone A l is adapted to zone L. The mixed zone A+B that has passed the original boundary is also adapted. But behind the original boundary, the originzl mixture A. +Bo is present, still not adapted. Behind that zone A. +Bo, a zone B1 is formed that contains only the anionic species B and this zone is adapted to the zone A. + Bo. Also, the migrated zone Tz is adapted to zone A. +B,. In Fig.2.7c, the original mixture A. +B, has disappeared, but now there are two zones B, one adapted to the leading zone L(Bz) and one still adapted to the non-existing original zone A. + Bo. In Fig.2.7d, the terminator has passed the original boundary and from this time also a zone T3 exists, already adapted to the leading zone L. At this moment, three T zones exist, viz., a zone T3 adapted to the leading zone L, a zone T2 adapted to the non-existing zone A. +Bo and the original zone T I **. In Fig.2.7e, the same situationisshown, the mixed zone A + B being much smaller. In Fig.2.7f, the mixed-zone A+B has disappeared, ie.,anionic species A and B are separated. Three T zones still exist, marking the spot where the sample was introduced. It is important to understand this procedure, although we shall not take this effect into account, because it is of no importance at the position of detection, as the original boundaries do not move and never reach the position of detection. In fact, we can never detect these zones with electrophoretic equipment, as will be discussed later***. These three zones do not remain sharp, because the ‘self-correcting’ effect, characteristic of isotachophoresis, does not occur in these zones. *It should be noted that the proteins in the ‘stack‘ can be easily denatured, because the conditions are not ideal for proteins, as indicated in Chapter 1 3 where the separation of proteins is considered. **In the separation chamber, all zones are now adapted to the composition of the leading zone, although mixed zones are still present. If a counter flow of electrolyte (as described in section 7.5.5) is to be applied, it should be applied at this moment, because the zone of the terminating electrolyte, which has passed the boundary occupied originally by the sample, has already attained its isotachophoretic velocity. Even if 100%counter flow of electrolyte occurs, neither the sample zone nor the zone of the terminating electrolyte is flushed back. ***No scanning device has yet been constructed.
ISOTACHOPHORESIS
19
d.t I
X
’.t -X
Fig.2.7. Changes in concentrations for the different zones in an isotachophoretic analysis. The sample is a mixture of A + B (original concentration A,+B,). The sample is introduced between the leading electrolyte L and the terminating electrolyte T.Theoretically, three different zones, marking the terminator concentrations T,,T , and T,, are finally obtained, in addition to the zones of the sample species to be analyzed. For further explanation, see text. s = position of introduction of sample; R = increasing electric resistance; X = position in the separation chamber.
20
PRINCIPLES OF ELECTROPHORETIC TECHNIQUES
2.4.4. Some isotachopherograms In order to detect the zones in isotachophoretic separations, several detection methods can be used, some of which are described in the section Instrumentation (Chapters 6 and 7). In order to understand the isotachopherograms shown in later chapters, some of them are discussed here, although only a brief description will be given. The first isotachopherograrn (see Fig.2.8) was obtained by means of a thermocouple. As explained in section 2.4, the temperatures of the proceeding zones increase and these temperatures can be measured by means of a thermometric detector, e.g., a thermocouple (made of 15-pm constantan and 25-pm copper wire). A signal as shown in Fig.2.8 is obtained. The construction of the thermocouple is described in the section Instrumentation. In Fig.2.8, the differential of the linear trace is also given. This signal marks the zone boundaries more clearly. The distance between two differential signal peaks is a measure of the zone length and hence it is a measure of the amount of the ionic species in that zone, because the concentration of the ionic species in that zone is constant for a given operational system. The step heights to be measured on the linear trace of the thermocouple signal are a measure of the conductivity in that zone and are also a measure of the effective mobilities of the ionic species in the zones. Hence the step height can be used for the identification of the ionic species in the sample. For recording the isotachopherogram shown in Fig.2.8, a potential recorder with zero suppression was used, which is advantageous for the accurate determination of the various step heights, but may confuse the information if one is not familiar with it. Under the conditions chosen, the step heights h l and h2 are characteristic of the tetramethylammonium and the ammonium ion, respectively. It should be noted that h l and h2 refer to the temperature of the chloride zone, which is also constant under the conditions chosen. The data presented later (Chapters 11 and 12) are referred to the thermocouple signal at 0 PA. [Note that, e.g., in gas chromatography, the distances are a measure of the identification (retention times) and the peak areas are commonly a measure of the amounts present.] Fig.2.9 shows an isotachopherogram for the separation of some anions. The experiments were carried out in the operational system at pH 6 (Table 12.1). The analyses were performed in equipment that is described in section 7.4.4,using the two highresolution detectors: a conductimeter (a.c. method)* and a UV absorption detector (256 nm). The linear trace from the conductivity detector, as in the linear trace from a thermocouple detector, is a measure of the conductivities of the zones. Hence it is a measure of the effective mobilities of the ionic species in the zones and characterizes the ionic species. The ‘step heights’ that can be found in the linear trace can be used for the identification of the various ionic species in a well defined operational system. All of the step heights, as described in the section Applications (Chapters 8-17), refer t o the conductivity of the zone of the leading electrolyte, which is-adjusted to ‘zero’ with the electronic device described in Chapter 6 (Fig.6.18). The differential of the linear signal *For the difference between the a s . method, using a conductivity detector, and the d.c. method, using a potential gradient detector, see Chapter 6 .
ISOTACHOPHORESIS
21
t
Fig.2.8. Isotachopherogram of the separation of some cations in the operational system listed in Table 16.1 (methanol was used as the solvent), obtained by using a thermometric detector. For further explanation, see text. 1 = H’ (leading ion); 2 = (CHJ,N+; 3 = NH:; 4 = K+; 5 = Na+;6: Li,; 7 = Mn2+; 8 = Cuz+; 9=CdZ’ (terminating ion). h,=Step height (qualitative information) of the tetramethylammonium ion; h , = step height of the ammonium ion. These step heights are referred to the ‘temperature’ of the zone of the leading ion and x , and x , are a measure of these quantities. T = temperature; i = time.
of the conductivity detector is also given in order to mark the zones, as the zone length is a measure that can be used for quantitative determinations. .4s the signals from W absorption detector depend on the absorption properties of the ionic species in the zones (not depending on the conditions of the leading electrolyte), one cannot always obtain quantitative and qualitative information from w h c h the ionic species can be defined. It will be clear that the combination of two high-resolution detectors will give the maximum amount of information in isotachophoretic separations.
PRINCIPLES OF ELECTROPHORETIC TECHNIQUES
22 4-
’7i -
I nI
3
-. __
a
,
3
0
?
ISOELECTRIC FOCUSING
23
The four isotachophoretic separations shown in Fig.2.9. were obtained under identical conditions, Le., stabilised electric current (70 PA), operational system, thermostating (22°C) and speed of the recorder chart paper (6 cm/min). The isotachopherograms show that the step heights in the linear traces from the conductivity and UV absorption detectors are not influenced by the sample size, that a quantitative determination of the ionic species is possible and that the mutual influence of the various ionic species is zero. In Fig.2.9A, the difference in zone lengths is due to the fact that the pyrazole-3,5dicarboxylate has a greater electric charge than the acetate at the pH of the operational system chosen. In Fig.2.9B, it can be seen that both zone lengths increase as the amounts of the components increase.
2.5. PRINCIPLE OF ISOELECTRIC FOCUSING Amphiprotic substances (e.g., proteins), which contain acidic and basic groups in their molecules, have a so-called isoelectric point, pl, which is the pH value at which they have no net charge. At this pH, they are present mainly in the form of a zwitter-ion. In solution, with a pH equal to the p l value of the amphiprotic substances, they do not migrate when they are placed in an electric field. At higher pH, they lose protons and become negatively charged, so that they will then migrate towards the anode if an electric field is applied. At lower pH, their net charges will be positive and consequently they 4 1 migrate towards the cathode. The basic principle of isoelectric focusing is that a buffer gradient is used such that the pH in the separation chamber increases from one side to the other, the lowest pH being obtained at the anode and the highest pH at the cathode. When a mixture of amphiprotic substances is introduced into such a system, all substances d 1 acquire different net charges according to their p1 values and hence will have different mobilities. On applying an electric field across the system, each substance will migrate towards that position where the pH is equal to its pI value. For example, if a protein is introduced at a pH higher than its p1 value, it becomes negatively charged, migrates towards the anode, in which direction the pH decreases, and reaches finally the position where the pH is equal to its p1 value. At this position, its net charge is zero and its velocity decreases to zero. By isoelectric focusing, all substances in the sample will be concentrated into narrow zones. Because plvalues are characteristic of, for instance, proteins, they can be separated by this means; proteins with pldifferences of 0.02 pH unit have been successfully separated. Fig.2.9. Isotachopherogram of the separation of some anions in the operational system at pH 6 (Table 12.1). R =increasing electric resistance;A =increasing UV absorption; ?=time. 1 =Chloride; 2=pyrazole-3,5dicarboxylate;+acetate; 4=glutamate. A, 10 nmole of acetic acid and 10 nmob of pyrazole-3,5-dicarboxylateinjected (note the difference in step length, due to the difference in charge of the ionic species): B, 20 nmole of acetic acid and 20 nmole of pyrazole-3,5-dicarboxylate injected; C, 10 nmole of acetic acid and 20 nmole of pyrazole-3,5dicarboxylate injected; D, 20 nmole of acetic acid and 10 nmole of pyrazole-3,5-dicarboxylateinjected. A conductimetric (ax. method) and a UV absorption (256 nm) detector were used. The step heights are constant (qualitative information), while the distance between the peaks (= length of the corresponding step) varies (quantitative information).
24
PRINCIPLES OF ELECTROPHORETIC TECHNIQUES
s
a
0
L
pH
4
5
IffCREASlNO
7
6
8
c pH
INCRPASINO
Fig.2.10. Separation of the amphiprotic substances A, B and C with PIvalues of 4, 6 and 8, respectively, by isoelectric focusing. The amphiprotic substances are eventually concentrated into narrow zones where the pH of the buffer gradient is equal to the PIvalue of the amphiprotic substance in each instance. (a), Sample introduction; (b), separation of A, B and C. s = position of introduction of sample.
In Fig.2.10, t h s situation is shown for the separation of three substances with pf values of 4,6 and 8, respectively. The substances A, B and C are introduced at a pH of 6, Le. the net charge of A is negative (pH is higher than its pZ value), the net charge of B is zero (pH = pf) and the net charge of C is positive (pH is lower than its pf value). Substance A will migrate towards the anode until it reaches a pH of 4, substance B stays at the position where pH = 6 and substance C migrates towards the cathode until it reaches a pH of 8. After a certain time, A, B and C are separated and concentrated into narrow zones with pH values of 4 , 6 and 8, respectively. Further information on equipment, performances, carrier ampholytes, etc. is given in detad in the literature.
2.6. DISCUSSION
In the preceding sections, the four main types of electrophoresis have been described, and in Fig.2.11 their characteristics are summarized. In each instance a sample is introduced (at an injection point X) that consists of two anionic species B and C and one
DISCUSSION
25
Fig.2.11. Survey of the four main electrophoretic techniques: (a) zone electrophoresis; (b) movingboundary electrophoresis; (c) isotachophoresis; (d) isoelectric focusing. X indicates the position where the sample is usually introduced. For further information, see text.
cationic species D. h Fig.2.11a, the situation in a zone electrophoretic system after a certain time is shown. The background electrolyte AE is present in the whole system, and the anionic species B and C have migrated in the direction of the anode. Anionic species B, which has a higher mobility, has covered a greater migration length. Cationic
26
PRINCIPLES OF ELECTROPHORETIC TECHNIQUES
species D has migrated in the direction of the cathode. Fig.2.1 l b shows the movingboundary procedure. The sample mixture is introduced into the cathode compartment and the leading electrolyte AE fills the separation chamber and the anode compartment. The cationic species D thus remains in the cathode compartment and the anionic species B and C, partially separated, migrate behind the leading electrolyte AE. Note that the pure zone B and the mixed zone B+C have the counter ionic species of the leading electrolyte E. The first boundary (with a velocity V , ) is sharp (according to the isotachophoretic condition), whereas the separation boundary (with a velocity V*) is not sharp, as in zone electrophoresis. The zone velocities v* and V1 are different. Fig.2.1 l c shows the separation procedure for an isotachophoretic system. The sample is introduced between the leading electrolyte AE and the terminating solution TE. The anionic species B and C are separated and migrate between the terminator T and the leading ion A. All zones have equal velocities, and contain the same counter ionic species E. The cationic species D of the sample has migrated to the cathode. In Fig.2.1 I d , the sample is introduced in an isoelectric focusing system. The point of injection is not important. The ionic species are eventually separated according to their plvalues and are concentrated on spots where the pH values are identical with their p l values, their net charges and velocities then being zero. B and C have migrated towards the anode (lower pH) while the cationic species D has migrated towards the cathode (higher pH). Only amphiprotic substances can be separated by this method.
Chapter 3
Concept of mobility SUMMARY Electrophoretic migration is discussed and the ionic mobility is defined. The relationship between equivalent conductance and ionic mobility is shown, the concept of effective mobility is described and the influence of partial dissociation, relaxation and the retardation effect on the effective mobility is discussed. Some approaches are suggested for the determination of unknown mobilities.
3.1. INTRODUCTION
The concept of mobility plays an important role in electrophoretic techniques, as differences in effective mobilities determine whether or not ionic species can be separated. The concentrations and the voltage gradients of the different zones, related to the parameters of the leading zone, are also fixed by the effective mobilities. In this chapter, the concept of mobility is discussed. We do not intend to give here a complete survey of all of the mathematical theories proposed and experiments carried out on this subject, which have been described in various papers. We will consider mobility only so far as is necessary in order to understand and use the theory of electrophoresis. Further, some approaches will be given with which unknown ionic mobilities can be estimated by relationships with other parameters.
3.2. INTERPRETATION OF ELECTROPHORETICMIGRATION
If an electric field is applied to an electrolyte solution, charged particles will move and a stationary state will be reached in which the velocity of the particles, in the direction of the field, is constant with time. In this state, there are four different forces acting on a particle, called F I ,F 2 ,F3 and F4 (see Fig.3.1). F1 is a force exerted on the charge of the particle and can be denoted by
F, = q E
(3.1)
where E is the electric field strength. F2 is a friction force, which Stokes determined for a rigid spherical particle as
F2 = -f,v
= -6nqrv
(3-2)
where v is the electrophoretic velocity, r is the radius of the particle, q is the viscosity of the solvent andf, is the friction factor. For a non-spherical particle,f, is still proportional to Q, but a correction factor has to be introduced so as to allow for-the sizeTshape and orientation of the particle. 21
CONCEPT OF MOBILITY
28
Fig.3.1. Forces acting on a positively charged particle, which moves under an electric field, E , can be represented by F, ,Fz , F3 and F A .The originally symmetrical, in this instance negatively charged, ionic atmosphere(1) is shifted due to the electric field E(2). For further explanation, see text.
The forces F3 and F4 are due to the presence of oppositely charged particles, forming a so-called ionic atmosphere. For F 3 , the electric field exerts a force on the ions of the ionic atmosphere, which is transferred to the molecules of the solvent. The particles considered do not move through a stationary solvent, but through a solvent flowing in the opposite direction, so that the net velocity is decreased. This effect is called the ‘electrophoretic retardation’. F4 represents the ‘relaxation effect’. The distribution of ions in the vicinity of the particles is deformed when an electric field is applied, because the particles move away from the centre of the ionic atmosphere. The Coulomb forces between the ions tend to re-build the ‘atmosphere’ in its ‘proper’ place, which takes a finite time called the relaxation time. Hence, the centre of the ionic atmosphere of the particle constantly lags behind the centre of the particle in the stationary state, resulting in an electrical force on the charge of the particle. This force is called the relaxation effect. For the stationary state, the sum of these forces must be zero, so that
FI
+F2
+F3 +F4 = O
(3 -3)
01
or
From eqn. 3.5, the influence of electrophoretic retardation, the relaxation effect, the shape, charge and radius of the particle and the influence of the solvent on the electrophoretic migration velocity can be understood. In the next section, the relationship between ionic conductance and migration velocity is considered and the absolute ionic mobility is defined.
29
IONIC MOBILITY AND IONIC EQUIVALENT CONDUCTIVITY
3.3. IONIC MOBIUTY AND IONIC EQUIVALENT CONDUCTIVITY
We speak of an 'equivalent weight' of an electrolyte if, for complete dissociation, the total amounts of positive and negative charges are eN and -eN respectively, where N is Avogadro's number and e is the electronic charge. For example, one equivalent weight of potassium fluoride gives, for complete dissociation, one Avogadro's number of K’and of F ions. The conductance of such an amount of electrolyte is the conductance measured in a conductance cell with electrodes 1 cm apart and with such cross-sections that the volume of solution between the electrodes will contain exactly one equivalent of the electrolyte. This conductance is known as the 'equivalent conductance' and is denoted by A*. Kohlrausch showed that at a f n e d temperature the relationship between the equivalent conductance of an electrolyte and the square root of the concentration is nearly linear, especially for very low concentrations and strong electrolytes. At infinite dilution, the equivalent conductances can be interpreted in terms of ionic contributions, whereby the contribution of an ion is independent of the other ionic species of the electrolyte (the influence of retardation and relaxation effects can be neglected, as no ionic atmosphere is present at infinite dilution). At infinite dilution, we can therefore write
A: = Ax’
+ Ax-
(3.6)
where Ax’ and Ax- are the equivalent ionic conductivities of the anions and cations, respectively, and A: is the equivalent conductance, all at infinite dilution. If a voltage V is applied t o a cell as mentioned above (see Fig.3.2) a current I flows through the cell: I = V/R or I = VA*
(3.7)
Assuming that such a cell contains one equivalent of the electrolyte, N/z' positive and N/z- negative ions are present, where z’ and z- are the valences of the positive and negative ions, respectively. If the velocities of the ions are represented by’ v and v-, respectively, the positive ions present in volume B and the negative ions present in volume C (see Fig.3.2) will have passed the cross-section A in 1 sec. Because the cell is I cm in length, this means that the volumes B and C will contain v+/l and v-/l parts of the total amount of the positive and negative ions of the cell, w h c h is
v’(N/z’)
positive ions and v - ( N / z - ) negative ions
(3.9)
The currents corresponding to these flow rates are obtained by multiplying by the ionic charges ez' and ez- and by this:
r' = ez' ’ v (IV/z+)= e Nu+= Fv'
(3.10a)
r = ez-
(3. lob)
v- ( N / z - ) = eNv-
= Fv-
At infinite dilution, combination of eqns. 3.8 and 3.10 gives
CONCEPT OF MOBILITY
30
Fig.3.2. Conductance cell with electrodes 1 cm apart. For further explanation, see text.
(3.1 la) (3.1 Ib) The average velocity with which an ion moves under the influence of a potential of 1V is called the ionic mobility, and the ionic mobility a t infinite dilution is called the
absolute ionic mobility. Thus, (3.12) It can be concluded from eqn. 3.12 that absolute ionic mobilities can be calculated by dividing the equivalent ionic conductivities at infinite dilution by the Faraday constant. The equivalent ionic conductivities can be obtained measuring the transport numbers. As the transport numbers give the fractions of the total current carried by each ion, ie., the fraction of the total conductance that each ion contributes, we can write
hg+= t,'A,*
(3.13a)
and A,*- = ti A:
(3.13b)
where t = transport number. Data for conductances and transport numbers in order to
EFFECTIVE IONIC MOBILITY
31
obtain A*" and A*- for the calculations of the ionic mobilities at concentrations other than infinite dilution cannot be properly used, because the law of independent migration of the ions is invalid and the conductance is really a property of the electrolyte rather than of the individual ions of the electrolyte. This means that the ionic conductivities (and hence ionic mobilities) of a chloride ion in 1N calcium chloride solution and in 1 N sodium chloride solution are different. In such instances a correction must be made for the influence of relaxation and retardation effects and for incomplete dissociation (ion pair formation). Also, for "weak" electrolytes it is sometimes very difficult to obtain correct values for the equivalent ionic conductances at zero concentration (infinite dilution). For such solutions, we can calculate the correct values from the ionic contributions of strong electrolytes at infinite dilution. For example: A,*(HAc) = A,*(NaAc) + A: (Ha)- A,*(NaCl)
(3.14)
because the right-hand side can be interpreted as AX+ (N2) + A-: =
Ar(H+ +)A-:
(Ac- ) + Ag"(H)
+A-:
(Ac-) = A;f'(HAc)
(GI-) - A x ' (Na') -A,*-
(a-) (3.15)
This procedure is not valid at concentrations other than zero, but in practice it can be used in order to obtain conductivities and mobilities at concentrations other than zero. In fact, corrections for the differences in relaxation and retardation effects and ion pair formation in electrolytes are neglected and i t can be used only as a rough approximation.
3.4. EFFECTIVE IONIC MOBILITY The absolute ionic mobility, m:, is defined as the average velocity of an ion per unit of electric field strength at infinite dilution. This absolute ionic mobility is a characteristic constant for every ionic species in a certain solvent and is proportional to the equivalent conductance at zero concentration: A,*=AE'fX:-
=(m,'+m;)F
(3.16)
In practice, we are not working at infinite dilution and the influence of other ionic species present in an electrolyte solution cannot be neglected. The effective mobility of an ionic species is related to the absolute mobility. Corrections have to be made for influences such as the electrophoretic retardation and the relaxation effect, as described by Onsager (see ref. 1). By using the Onsager equation, a correction can be made for ion-ion interactions. Another influence is the effect of partial dissociation. Tiselius [2] pointed out that the effective mobility is the sum of all products of the degree of dissociation and the ionic mobilities: meff.=
7 aimi
(3.17)
where meff.is the effective mobility, ai is the degree of dissociation and mi is the ionic mobility.
32
CONCEPT OF MOBILITY
To summarize, we can state that the effective mobility of an ionic species depends on several factors such as the ionic radius, solvation, dielectric constant and viscosity of the solvent, shape and charge of the ion, pH, degree of dissociation and temperature. It is very difficult to give a precise mathematical expression for the effective mobility. When speaking about effective mobilities, we shall use the expression
meff.= Ci cui rimi
(3.18)
where cti is the degree of dissociation, yi is a correction factor for the influence of relaxation and retardation effects and mi is the absolute ionic mobility. The correction factors c+ and yi will be described in more detail. 3.4.1. Partial dissociation
If an ion does not exist in the free form, but is in an equilibrium with the undissociated form, its effective mobility is smaller than its ionic mobility. For example, acetate, in water, is always in equilibrium with acetic acid according to the equation HAc +Hz 0
* H3O++Ac-
(3.19)
and the equilibrium constant is (3.20)
As the degree of dissociation is defined as cu=
[Ac-] [HAc] + [Ac-]
(3.2 1)
then, during time t, the ionic species exists in the form of acetate during time cut. Therefore, the migration distance in time f is
s = v a t = cumEt
(3.22)
Normally, the migration distance of an ion is s = v t=m Et
(3.23)
From eqns. 3.22 and 3.23, it can be concluded that the effective mobility can be calculated as
meR.= a m (a <1) Tiselius [2] pointed out that a substance consisting of several forms with different mobilities in equilibrium with each other will generally migrate as a uniform substance with an effective mobility of meff.=
F
aimi
(see eqn. 3.17) provided that the time of existance of each ionic species is small in
EFFECTIVE IONIC MOBILITY
33
comparison with the duration of the experiment. As the equilibrium adjustments are very slow, the ionic species seems to consist of two components (an example is the esterification of oxalic acid in methanol, see section 16.2, Fig.16.1) and sometimes disturbances can be expected (see Chapter 9). For the equilibrium states, we shall distinguish two types of interactions, viz., protolysis and complex formation. 3.4.1.1. Protolysis
Here a proton takes part in the dissociation reaction, as shown in the dissociation of acetic acid (see eqn. 3.19). The degree of dissociation depends on the pH and the equilibrium constant. The relationship between pH and pKa and the degree of dissociation is given by the Henderson-Hasselbalch equation: (3.24) (positive for anionic species and negative for cationic species). Also, for ionic species with more than one pK value, thls equation can be used if the differences between the pK values are not too small. In Fig.3.3, a nomogram is given by which the degree of dissociation can be obtained for given pH and pK values. The relationship between the degree of dissociation and the pH for some anionic species is shown in Fig.3.4, from which it can be concluded that changes in pH are important between k 2 pH units from the pK value. Between these values, the degree of dissociation changes from about 1%to 99%, and hence the effective mobility changes from 1% t o 99%of the absolute ionic mobility, neglecting other influences on the absolute ionic mobility. In Fig.3.5, some relationships between effective mobility and pH are shown for anionic species, cationic species and amphiprotic substances. Of course, the mobilities depend on the absolute ionic mobility chosen. Fig.3.5 shows clearly that differences in pH have a great effect on the effective mobility near the pK values. 3.4.1.2. Complex formation
Now a particle different from a proton takes part in the dissociation reaction, e.g. Pb(CH3C00)2
=+ Pb(CHjCOO)++
CH3COO-
(3.25)
The degree of complex formation depends mainly on the partial concentrations and the complex constant. Corrections can be made for this effect in a manner similar to that described above. Often, both types affect the effective mobility, e.g., for Al*: Al(H20)F* Al(OH)(H,O)T+ H+ AI(CH3COO)3
=+
Al(CH3COO)T + CH3COO-
Further dissociations are possible.
(3.26) (3.27)
CONCEPT OF MOBILITY
34 14
13
12
--
11
10
9
8
7
6 C A
T I 0 N
5
4
3
2
1
PH
0 pKa
Fig.3.3. Nomogram giving the relationship between pH, pKa and the rate of dissociation (a).
35
EFFECTIVE IONIC MOBILITY
Fig.3.4. Relationship between
CY
and pH for some anionic species.
Fig.3.5. Relationship between the effective mobility, meff., and pH. (a) Cationic species with an absolute ionic mobility m , = 40 and pK = 3; (b) cationic species with m a= 20 and pK = 3; (c) cationic species with ma=40and pK = 5 ; (d) anionic species with ma= 40 and pK = 10. ( e ) amphiprotic compound with tn; = 30 and mi = 30 and p K = 3 and 11.
If the dielectric constant decreases, the interionic forces increase. This effect, especially for cationic species with h g h charges, results in stronger complex formation. The pK values of the dissociation also depend on the dielectric constant of the solvent.
36
CONCEPT OF MOBILITY
3.4.2. Relaxation and electrophoretic retardation According to Hiickel, Debye and Onsager (see ref. I), the conductance can be written as (3.28) A = ' 0 - Arel. - 4 e t . where A,,. and he,are corrections for the decreasing effects on the conductivity due to the relaxation and retardation effects, respectively. (3.29) (3.30)
(3.31)
lz+l iz- I s = ___ IZ+l+ lz-
I
A: 1.2-
I A:
+ A;
(3.32)
+ 12' I A,
Substitution of eqns. 3.29, 3.30, 3.31 and 3.32 into eqn. 3.28 gives for the molar conductivity (3.33)
A = A ~ - ~ & with
(3.34)
In a similar way [ 11, for the equivalent conductance we can derive
A* = A*0 -a* ,/ (k+I+ 12- I)c*
(3.3 5)
with (3.36)
(3.37)
In order to show the importance of the influences for different solvents and for different charges of the ions, we calculated the effective mobilities according t o these expressions for monovalent and divalent cations in water and methanol for a hypothetical value of the absolute mobility of 50 lo-' cm*/V s at a concentration of 0.01 N . The results are shown in Table 3.1.
-
-
DETERMINATION OF IONIC MOBILITIES
37
TABLE 3.1 TIIEORETICAL EFFECTIVE MOBILITIIiS OF MONO- AND DIVALENT CATIONS IN WATER AND METHANOL (9570, w/w) In both instances the counter ions are monovalent. Methanol
Water 105
Univalent cations and anions Divalent cations and univalent anions
50 50
meff.-1O5 m,.105
ineff; lo5
46 43
25
50 50
31.5
For water as solvent at 25°C: (3.38) For methanol as solvent at 25°C: (Y
* = 1.1 5
2s ___
1 +&
- (z' z- 1 A8 + 55.3’ZI(
I + 1z-I)
(3.39)
The effects discussed above are even stronger for solvents with lower dielectric constants and for cations with higher charges.
3.5. DETERMINATION OF IONIC MOBILITIES As already mentioned in preceding sections, ionic mobilities can be calculated from equivalent conductivities and corrections can be made for the influence of concentration, relaxation and retardation effects. As the exact data for many ionic species are unknown, many workers have sought correlations between ionic mobilities and parame t e n such as the radius of the molecule, ionic volume and the entropy of the ions. Some of these approaches are considered here and may be useful in estimating unknown mobilities. 3.5.1. Relationship between volume and ionic mobility
In general, it is said that for a 'steady flow' of molecules, Stokes' law can bc applied in order to calculate the resistance force (assuming a spherical particle in an infinite fluid [3]). If the ionic radius is not too small, the following equations can be deduced [4-61 : v * = (qE+F,,, +Fre,.)/fc (see eqn. 3.5) so that at infinite dilution
v d =4Elfc
(3.40)
m i = v d/E=q/fc =z'e/6nqr
(3.41)
For smaller particles (3-5 A) [7, 81, a modified expression can be used, viz. :
mi= z'el [5nvrCf/fo)]
(3.42)
38
CONCEPT OF MOBILITY
where flfo is a correction factor for non-spherical particles. For water (21 C), this means that
m f =1.14.10-3~f/[TCflf~)]
(3.43)
From this equation, it can be concluded that the ionic mobility is a function of the shape, charge and radius of the ion and the viscosity of the solvent. Edward [7] and Bondi [9] calculated the contribution of different groups in a molecule to the volume of the molecule (and hence to the radius) from the covalent radius according to Pauling and the Van der Wads’ radii and angles [ 101 . Perrin [ 111 derived equations for friction factors from the ratio of the axes of prolate and oblate ellipsoids. Edward and Waldron-Edward [12] showed the possibility of calculating friction factors from diffusion constants. In the papers mentioned, reasonable results were obtained for the calculated values in comparison with the experimental values, deviations being found for small ions and strongly polar groups. Values for non-spherical and nonellipsoid ions, such as the “knobby shape” ions, can also be calculated. Very irregular ions cannot be treated
Fig.3.6. Relationship between entropy (S)and ionic mobility (m)for some cations (a) and anions (b). The values correspond to those given in Table 3.2.
39
DETERMINATION OF IONIC MOBILITIES TABLE 3.2 IONIC MOBILITY AND ENTROPY OF IONIC SPECIES
-
~
Ionic species
m lo 5
S
NH: cs+ Li+ K+ Tl+ Na+ Rb+
74 78 38.7 73.5 62 76 50.5 76.5
27 31.8 3.4 24.5 17.7 30.4 14.4 29.1
HCO; 10; HC, 0; HSO; HSO; CHOOBrO; Cl0; Cl0; NO;
44.5 41 40.2 50 50 54.6 56 65 68 71.5
22.7 27.7 36.7 31.6 30.3 21.9 40.9 39 43.5 35
Ag+
~~~~~
Ionic species
m lo'
S
Ba2+
63.8 54 59.3 51 50.5 54.5
3 -14.8 -13.2 -37.1 -38.2 -23.6 -27.1 -25.5 5.1 -28.2 -9.4 -20
CdZ+ Ca'+ co2+ Ni"
cuz+ Fez+ Znz+ Pb"
54
Mn'+
54 70-73 53 60 52
Brc1FICN-
78.4 76.5 54.7 77 78
Mgl+
sr2+
19.2 13.2 -2.3 26.1 28.2
because their friction factors are unknown and, in general, they have lower mobilities than spherical ions of the same volume. 3.5.2. Relationship between entropy and ionic mobility
Zolotarev [13] tried to relate entropy to ionic mobility in aqueous solutions. Combination of the equations derived by Kapustinskii [141 :
s=(A/r)+B
(3.44)
and
m f = z'e/6n qr (see eqn. 3.41) gives S = ( K 1 mf)+Kz
(3.45)
This equation is valid for a series of equally charged substances. In Table 3.2, the entropies and absolute ionic mobilities of some ionic species are given. The relationship between entropy and mobility is shown graphically in Fig.3.6. In Fig.3.6a, the relationship for mono- and divalent cations can be seen to be linear, according to eqn. 3.45. A similar relationship for anionic species, however, is less evident (see Fig.3.6b).
CONCEPT OF MOBILITY
40
3.5.3. Discussion In this section, some approaches for the estimation of ionic mobilities have been considered. A different approach was used by Lindemann [ 1 51, based on the kinetic theory of gases, in which the ions are supposed to suffer repeated collisions with solvent molecules, at each of which it retains a certain fraction of its velocity depending on the relative mass. Between collisions, it moves freely under the influence of the electric field. A relationship is thus established between the mobility of the ion and its mean free path between collisions. Although some effects that affect the effective mobility can be described mathematically and although the ionic mobilities can be treated theoretically from data such as entropy and Stokes' law, the estimation of mobilities in practice is difficult. The mathematical models cannot be applied to all ionic species and specific interactions give differences between experimental and theoretical values, especially when non-aqueous solvents are used. Experimental measurements often have to be carried out for the determination of the ionic mobilities.
REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
H. Falkenhagen, Elektrolyte, Verlag von S . Hirzel, Leipzig, 1932. A. Tisellus, Nova Acta Regiae soc. Sci. Upsal., Ser. 4 , 4 (1930) 7. J.T. Edward, Advan. Chrornutogr., 2 (1 966) 64. P.V. Chengand H.K. Schachrnan, J. Polym. Sci., 16 (1955) 19. W. Weidel and E. Kellenberger, Biochim Biophys. Acru, 17 (1955) 1. J.T.Edward, J. Polym. Sci., 25 (1957) 483. J.T. Edward, Chcm Ind (London), (1956) 714. J.T.Edward, Sci. Proc. Rqv. Dublin Soc., 9 (1956) 273. A. Bondi,J. Phys. Chem, 68 (1964) 441. L. Pauling, Nature sf'thc Chtmical Bond, Cornell Univ. Press, Ithaca, N.Y., 2nd. ed., 1948. F. Perrin, J. Phys. Radium,7 (1936) 1 ; 5 (1934) 497. J.T. Edward and D. Waldran-Edward, J. Chromarogr., 24 (1966) 125. E.K. Zolotarev, Russ. J. Phys. Chcnz., 39 (1965) 573. A.F. Kapustinskii, A c f u Physicochim. URSS, 14 (1941) 508. F.A. Lindemann, 2. Phys. Chem (Leipzig], 11 0 (1924) 394.
Chapter 4
Mathematical model for isotachophoresis SUMMARY In isotachophoresis, as already described in Chapter 2, the sample, whch is a mixture of anionic and cationic species, is introduced between a leading electrolyte and a terminating electrolyte. For the separation of anionic species, the leading anionic species, A,, is chosen such that its effective mobility is higher than those of all other anionic species, whereas the terminating anionic species, A,, is chosen with a mobility lower than those of all other anionic species. As an electric current is passed through such a system (see Fig.4.1), in the first instance all ionic species will migrate with a velocity determined by, e.g., the actual pH, ionic strength, the absolute mobility and the potential gradient. In fact, this first stace in the electrophoretic separation procedure is a movingboundary separation. After this stage, in which the anionic species of the sample are to be separated according to differences in effective mobilities, a ‘steady state’ will be reached i n which all zones migrate with a velocity equal to that of the leading anionic species. Each zone will contain only one anionic species. Only in this case can we speak of isotachophoresis proper*. The first sample zone contains the sample anionic species with the highest mobility, and the last zone that with the lowest mobility. In section 4.2, the general equations for electrophoretic separations are derived and applied to a model of moving-boundary electrophoresis. In section 4.3, these equations are applied to a model of isotachophoresis, with which all quantities, such as concentrations, conductivities of the zones and pH values of the zones, can be calculated. The model is subsequently verified (section 4.4).
4.1. INTRODUCTION Experiments based on the principle of electrophoresis have been carried out for many years and theoretical models have already been described by several workers [l-171. In 1897, Kohlrausch [ 121 gave a mathematical model for electrophoretic processes. Using the divergence theorem, the continuity equations can be derived and, using the principle of electroneutrality and assumptions such as constant relative mobilities, he formulated the so-called ‘beharrliche funktion’:
4e= C.
constant
*Although ideal mixed zones can always be present, they do not influence the other zones. 41
42
MATHEMATICALMODEL FOR ISOTACHOPHORESIS
0
Fig.4.1. The original situation for the separation of anionic species. A mixture of anionic and cationic species has been introduced between a leading electrolyte and a terminating electrolyte. AL, leading anionic species; A, . .Ir sample anionic species; AT, terminating anionic species; BL, buffering counter ionic species of the leading electrolyte; B, . . counter ionic species of the sample; BT, counter ionic species of the terminating electrolyte.
,.,
This regulating function prescribed that at any point the sum of concentrations divided by the mobilities must be constant for all ionic species. In practice, all theoretical models, which have been described in several papers, are essentially based on this principle, although the situation is complicated by the use of different names and approaches. Also, often no clear distinction has been made between the different performances of the electrophoretic separations. In this chapter, a theoretical model is described for isotachophoretic separations and a number of experiments are described with which the model was verifie'd. A clear distinction is made between the first stage of the separation by isotachophoresis, which can be compared with moving-boundary electrophoresis, and isotachophoresis proper, i.e., at the steady state if all ionic species of the sample are separated. For a model as general as possible, all substances will be regarded as amphiprotic polyvalent molecules, so that the molecules can contain different chemical groups with different chemical equilibrium constants. For such a molecule, the following equilibria can be set up:
(In this model, only proton interactions are taken into account. Equilibria referring to other dissociations, complex formation etc. are neglected.) The symbol A represents an anionic species and the subscript r characterizes that anionic species. The superscript zA, indicates the anionic form of the anionic species A,, i.e., it refers to the charge of that ion. The
GENERAL EQUATIONS
43
anionic species A, has n A, pK values, ordered according to increasing pK values. The particle A?*r, i.e., the ionic form with the highest charge Z A ~is taken as the reference in all calculations. Although the difference between anionic and cationic species disappears when this notation is used, we still use the notation A and B for anionic and cationic species for the sake of clarity and in order to reduce the number of indices used. Whether a particle is an anion or a cation depends on its pK values and the pH in the zones. The electrolyte system has to be chosen such that one of the ionic species acts as the leading ionic species (anionic for the separation of anions) and another acts as a buffering counter ion (cationic for the separation of anions) at the chosen pH. The way in which an appropriate choice can be made will become clear in Chapter 5. In section 4.2, the equations that describe the first stage in the separation, in fact a kind of moving-boundary electrophoresis, are derived.
4.2. GENERAL EQUATIONS For the derivation of the general equations in electrophoretic processes, we shall consider the formation and movement of zone boundaries when an electric field is applied over an existing zone boundary between two electrolyte solutions (see Fig.4.2). On one side of the boundary, a mixture of several anionic and cationic species is present, and on the other side a 'single electrolyte'. The anode is placed in the single electrolyte. Only the migration of the anionic species is considered, and the effective mobility of the anionic species of the single electrolyte is assumed to be higher than that of any of the anionic species in the mixture. After some time, all of the anionic species wd1 have the same counter ion B, because the cationic species B1 . .. r are moving in the opposite direction. The anionic species migrate in the direction of the anode, which results in a partial separation (moving-boundary electrophoresis). A number of boundaries will be formed and a situation as shown in Fig.4.3 will be the result. The anionic species A l , with the highest effective mobility in the mixture, has the highest migration velocity and will be partially separated from the other anionic species. It creates its own zone, Al, which becomes elongated in time. In the next zone, the anionic species Az is separated from A3. . . in a similar way and, together with A1, it forms the zone Al + A z . Each subsequent zone will contain one anionic species more -B
-
1 . . .r
0
BL
' I . . .r-
m A
~
. .r .
<
m AL
Fig.4.2. A zone boundary between a mixture of several anionic and cationic species and a single electrolyte.
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
44
0 B t
Concentration boundary
r-I
t t t t t t !
t
separation
Boundary
l‘. e. -A
boundaries
< r n
< AP-l
.......... ernA 2
i
rn
< Al
I
rn A1
Fig.4.3. Zone boundaries formed when an electric current is passed across a zone boundary as shown in Fig.4.2.
from the mixture, viz., that anionic species with the highest effective mobility of the anionic species that remain. The last boundary created is the boundary A , . .. J A l . . . (r- I ) . The last zone boundary is the original boundary A l . . .,-/Al .. . r , where an adaptation in concentrations according to Ohm’s law takes place. This concentration boundary can be considered as stationary [ 6 ] .Two types of boundaries have to be distinguished, viz., the concentration and the separation boundaries. For the concentration boundary, the number of anionic species is identical on both sides of the boundary, whereas for the separation boundaries one particular ionic species is present on one side of the boundary only. In general, r t 1 boundaries will be present if an electric field is passed across the original boundary as shown in Fig.4.2, considering the separation of anionic species, viz., one concentration boundary (the original boundary), r-1 separation boundaries and the boundary between the single electrolyte and the zone containing the anionic species with the highest effective mobility in the anionic mixture (see Fig.4.3). The velocity of the boundary A,/A, is equal to the velocity of the anionic species A, and 4,. The velocities of the separation boundaries are equal to the velocities of the ionic species with the lowest effective mobilities in those zones (see section 4.2.3). These anionic species are not present in the preceding zones. For the derivation of the general equations, the following assumptions are made: the electric current is constant; the cross-section of the tube is constant; the influence of diffusion, hydrostatic flow and electroendosmosis is neglected. The activity coefficients and the influence of the radial temperature differences can be neglected. Further, only those boundaries that are formed between the original zone boundary and the anode are considered. The general equations describing electrophoretic processes are: the equilibrium equations; the electroneutrality equation; the mass balances for all ionic species; and the modified Ohm’s law. These equations are considered in more detail in sections 4.2.1-4.2.5.
45
GENERAL EQUATIONS
4.2.1. Equilibrium equations The thermodynamic equilibrium constant for an equilibrium d
A-B+C
can be defined as
K , =-aBaC
(4.3)
aA
where a A ,a B and ac denote the activities of substances A, Band C, respectively. Often the concentration equilibrium constant is used, defined as
The concentration equilibrium constant can be calculated from K , by correcting for the activity coefficients, which are dependent on the ionic strength. For the sake of clarity we shall use K , in all derivations. Considering reaction 4.1, the general expressions for the equilibrium constants will be (4.5a)
(4.5b)
(4.5c)
The indices A,,, U and i indicate that the equilibrium constant refers to the ith ionization equation of the anionic species A, and is valid for the Uth zone. An indication of the zone is needed, because all zones have, for example, different temperatures and concentrations so that each substance will have different equilibrium constants in each of the zones. With eqn. 4.5, the concentrations of each ionic form can be expressed as the concentration of the ionic form with a higher charge. In this way, we can write for the relationship between the concentrations of the ionic forms with charges of 2%-i andz+: (4.6a) and, in a similar way:
46
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
(4.6b)
(4.6~) Replacing the ionic concentration on the right-hand side with the concentration of the higher charged ionic forms, we find the relationship with the concentration of the highest charged ionic form. Eqn. 4 . 6 ~gives
or i
(4.7)
In this way, all concentrations of the ionic forms can be expressed as the concentration of the ionic form with the highest charge by means of the equilibrium constants and the concentration of the hydrogen ions. These equations will be used later to derive the expressions for pH-dependent quantities such as the effective mobilities. The total Concentration of an ionic species is &,U = “A,., V,zAr ‘“A,,, U,zA,l
Substitution of eqn. 4.7 gives
or
+C
A,., V,~
~
+.-. . 2
GENERAL EQUATIONS
41 i
Similar equations can be derived for all ionic species in all zones. Combining eqns. 4.7 and 4.9, the ionic concentration cAr, u, zAr-i, can be expressed as the total concentration of A,.:
(4.10)
(4.1 1)
c ~ R V,zA , R
This equation w ill be used in the following sections 4.2.2. Electroneutrality equations
In accordance with the principle of electroneutrality, the arithmetic sum of all products of the concentrations of all forms for all ionic species and the corresponding valences, present in each zone, must be zero. While the first zone contains one ionic species of the sample, each following zone always contains one ionic species more, viz., that ionic species with the highest effective mobifity of the ionic species that remain. The Uih zone will consequently contain Uionic species of the sample. For one ionic species, the sum of all products of the concentrations and the corresponding valences for the different ionic forms is
(4.12) This is the total amount of charge present per volume for this ionic species. If the ionic species are numbered in order of decreasing effective mobilities, for the Uth zone we can write as ‘electroneutrality equation’: U
CH,rJ-COH, U +
2 r=
[2
1
[(‘Ar-’)
‘Ar,U,zAr-i])
+ ~ ~ ( ‘ B - ‘ ) ‘B,U, z g - i ] =
(4.13)
48
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
Substitution of eqns. 4.7 and 4.9 into 4.13 for both the sample ionic species and counter ions gives
-+ r= 1
(4.14)
4.2.3. Mass balances for all ionic species In the stationary state (N.B.,the ‘steady state’ is not meant here), if all zone boundaries are formed and migrate, some ionic species will migrate more rapidly and others more slowly than a particular zone boundary, and ionic species will therefore pass continuously those zone boundaries that have a lower velocity. For the ionic species that pass zone boundaries, mass balances can be formulated. In order to decide which ionic species will pass zone boundaries and their amounts, we shall consider the velocities of the zone boundaries. The velocity of the concentration boundary can be neglected, so that for constant effective mobilities the ratios of the concentrations on the two sides of the concentration boundary are identical for all ionic species (see eqn. 4.18). The velocity of a separation boundary, S, is equal to the migration velocity of the ionic species with the lowest effective mobility in that zone (see Fig.4.4). The velocity of the zone boundary (U--l)/(U-2) is equal to the migration velocity of the (U-1)th anionic species, which is not present in the preceding zone U-2. Similarly, the velocity of the zone boundary U/(U-1) is equal t o the velocity of the anionic species A,. If the electric field strengths in the zones are E,, Eup1 and E,-,, respectively, the migration velocities of those boundaries are E,-l mA and E , MAu, U- 1 respectively. In these terms, the quantities indicated with a bar (m) do not apply t o ions, but t o the equilibrium mixtures of all forms of the constituent; consequently, FI represents the effective mobilities of the ionic species. As the boundary velocity is determined by the llth ionic species, the subscript r in M is replaced with U. For the A, effective mobility, Tiselius 1161 pointed out that a substance which consists of several forms with different mobilities in equilibrium with each other will generally migrate as a
49
GENERAL EQUATIONS
Uthzone
(U-llthzone (U-Zjthzone
Fig.4.4. The Uth zone contains Uanionic species of the sample (A,, . u).The voltage gradient in the Uth zone is Eu: The (U-1)th and (U-2)th zones contain one and two anionic species less of the sample, respectmly. The migration velocity of the zone boundary U / ( U - 1 ) is determined by the migration velocity of the anionic species A y which is not present in the (U-1)th zone.
uniform substance with an effective mobility given by
ii
aimi =
= i= 0
$ /cimi/ct>
(4.1 5 )
i =O
provided that the time of existence of each ionic species is small in comparison with the duration of the experiment. In this effective mobility, factors such as the relaxation effect, the electrophoretic effect and the influence of temperature are neglected. Substituting eqns. 4.7 and 4.9 into eqn. 4.1 5, we can write for the effective mobility the expression
(4.16)
For the separation boundary U/(V-l), this means that the ionicspecies A1 to AUp1 can continuously pass this boundary, as their migration velocity is higher than > r71A u ). For the anionic species A,-,, for EufiA (fiA,> fiA2> . . . . > f i A u-1 exampye, we have the following situation (see Fig.4.5). An ion at point P (at time t = 0) can just reach the separation boundary S within one unit of time (at time t= 1). In this time, the separation boundary has moved from S o to S 1 . An ion at point So (at time t=O) can just reach point M (at time r= 1). This means that all ions of the anionic species AU-l present between points P and So (at time t = O ) will be found again between
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
50
Fig.4.5. Migration paths for the different ionic species over a separation boundary S. For furthe1 explanation, see text.
the points S1 and M (at time t = 1). The distance SoSl is equal to EUriiAp u. The ion present at point P (at time t = 0) migrates in the zone U, so the distance PS1 is equal to EUfiAu-l, U and the ion present at point So (at time t = 0) migrates in the (U- 1)th zone, so the distance SoM is equal to E U - l ~ A u - l , The amount of ions between P and So (at time t = O ) is
o c ~ u - l ,U (psI-sO
sl)
=
ocAu-l,
U(EUriiAu-l,
U - E U r i i A , U)
is the total where 0 is the cross-sectional area of the narrow-bore tube and c i U-l’U concentration of the anionic species A,, in the Uth zone. The amount of the anionic species A,, between the points S1 and M (at time t= 1) will be
between P and So (at time r = 0) reaches the The amount of the anionic species separation boundary within one unit of time and the amount between S1 and M passes the separation boundary within one unit of time. These amounts must be identical for : a stationary state, so we can write for the mass balance of the anionic species A,, ‘kU-,,U
(EUmAu-,,TEUfiAu,U)=
c~~-,,U(EU-l i fiAu-l,U-l-EUfiAu,U)
(4.18)
The general expression for the mass balance of an anionic species is
‘A,.
U
WEUfiAu,
U) =
A,.,U-1 ( E U - l
fiA,., U-l-EUmAu,
U)
(4.19)
In a similar manner, the following expression for the counter ions can be derived: ‘B,t U- 1 (EU-l
‘B
,U-1 -k EU fiAu, U) =
‘i,U (EUfiB, U -k EUriiAu, U )
(4.20)
51
GENERAL EQUATIONS
4.2.4. Modified Ohm’s law Working at a constant current density:
i/C = constant = E
h,
(4.21)
(The Faraday constant is included in G). The overall electrical conductivity of a zone is the sum of t h e values cinz,lzj\, and consequently
I/G=EU
i
u
coH,u’ptoH,u+cH,umH,u +
nAY
C 2
(~zA;ilcA,.,u,
r=O i = O
zALi
mAr,u,zA
-i)
+
(4.22) J
Substitution of eqns. 4.7 and 4.9 into eqn. 4.22 gives for the modified Ohm’s law: 1
(4.23)
4.2.5. Parameters and equations
The general equations given above describe the moving-boundary model. If the compositions of the leading electrolyte and of the sample are known, all parameters can be calculated. In Table 4.1, all parameters, known parameters and equations are listed for all zones. For each ionic species, both n 1 ionic concentrations and n equilibrium equations are present. Using eqns. 4.7 and 4.9, all ionic concentrations can be expressed as the total concentration for each type of ion. In this way, both the number
+
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
52
TABLE 4.1 NUMBER OF PARAMETERS, KNOWN PARAMETERS AND EQUATIONS FOR THE DIFFERENT ZONES IN MOVINGBOUNDARY ELECTROPHORESIS Zone
Parameters and equations
Leading
Parameters: EL, pHL, pOHL, n g concentrations of eA
+ 1 ionic concentrations of c%, nAL + 1 ionic
L
Known parameters and equations: c&, ckL, pK,, Ohm's law, electroneutrality equation, nBL + nAL equilibrium equations
First
Parameters: E , , pH,, pOH, ,n + 1 ionic concentrations of cB, ,nA, + 1 ionic Bl concentrations of c A, Known parameters and equations: pK,, Ohm's law, electroneutrality equation, buffer mass balance, mass balance of A,, nB, + nAl equilibrium equations, isotachophoretic condition
Second
Parameters: E , , pH,, pOH, , n g , + 1 ionic concentrations of c B,, nA, + 1 ionic concentrations of cA, ,nA, + 1 ionic concentrations of c A2
Known parameters and equations: pK,, Ohm's law, electroneutrality equation, mass balance of the buffer, mass balances of A, and A,, ng, + "A, + nA,equifibnum equations
Uth
+ 1 ionic concentrations of the buffer, and + 1, nA, + 1, nA, + 1, . . .,:f + 1 ionic concentrations of the anionic species
Parameters; E y pHU, pOHv n
nA,
Known parameters and equations: %ass balance of the buffer, U mass balances of the anionic species, Ohm's law, electroneutmlity equation, pK,, "B + nA, + . . . + nAu equilibrium equations
Terminating
Parameters: ET, pHT, pOHT, n g + 1 ionic concentrations of the buffer, and nA, nA, + 1, nA, + 1, ., n + 1 ionic concentrations of the anionic species
..
+ 1,
AU
Known parameters and equations: Ohm's law, electroneutrality equation, pK,, c i T , t t t CA,,CA,. . .,C A ~ng+ , nAl + . . .+ "Au equilibrium equations
.
of parameters is reduced by n and the number of equations is reduced by n. Further, the pOH value can be expressed as pH by using the pK, value. In Table 4.2, the reduced number of parameters and equations is given. It can be seen that the first zone has a surplus of one equation, whereas the terminating zone has a shortage of one equation. Note the unusual part of the terminating zone, in this zone being taken as unknown. It might be thought that c i could be determined by the choice of the pH in the terminating zone, the type of buffer ionic species and its concentration, but this is not so. Of course, the pH and the concentration of the counter ion can be fixed, but if the stationary state is reached and if all original counter ions have migrated to the cathode, the counter ions will be replaced with those of the leading electrolyte,
ci
53
GENERAL EQUATIONS TABLE 4.2
REDUCED NUMBER OF PARAMETERS, KNOWN PARAMETERS AND EQUATlONS FOR THE DIFFERENT ZONES IN MOVINGBOUNDARY ELECTROPHORESIS Zone
Parameters and equations
Lea ding
Parameters: ifL,P H ~c,k , cx,
Known parameters and equations: ck, c i , Ohm’s law, electroneutrality equation Number of known parameters and equations is equal t o the number of parameters First
Parameters: E , , pH,, c i , c$, Known parameters and equations: Mass balances of B and A,, electroneutrality equation, Ohm’s law, isotachophoretic condition Surplus of one equation
Second
Parameters: E,, pH,, c fj, c a , cL2 I
Known parameters and equations: Mass balances of B, A, and A,, Ohm’s law, electroneutrality equation Number of known parameters and equations is equal to the number of parameters In a l l other zones, the number of anionic species is increasing. Consequently, the number of unknown parameters increases, but the number of mass balances also increases, and the number of unknown parameters and equations and number of parameters become equal again Uth
Parameters: E u pHU, cfj, c a
t
...
Known paramefers and equations.’ Mass balances of B, A , , A,, . . .,AU, Ohm’s law, electtoneutrality equation Number of known parameters and equations is equal to the number of parameters Terminating
Parameters: ET pH.,., ck, c i , . . ., c i u 1
Known parameters and e9Uan’onS: c i r , equation Shortage of one equation
. . ., ci,
Ohm’s law, electroneutrality
and the pH and the concentration of the counter ions in the terminating zone are determined by the buffer mass balance of the leading electrolyte zone (the surplus of one equation). This indicates the problem or calculations with the moving-boundary model. A surplus of one equation in the first zone determines the pH in the last zone, whereas the pH in the last zone determines the effective mobilities of the anionic species in that zone and hence the mass balances of those anionic species which determine the situation in the first zone. Thus the pH, requires a calculation from the first zone in accordance with the buffer mass balances, whereas the composition of the first zone is determined by calculations from the last zone in accordance with the mass balances of the anionic species. For nearly all calculations in moving-boundary electrophoresis, simplifications have to be made in order to avoid this difficulty. A m d e l suitable for calculations on strong electrolytes (for which the mobilities are independent of the pH), neglecting the
Fig.4.6. Simplified model for the formation of the zonesin an isotdchophoretic separation of a five-component sample (A, -As). The sample is introduced already sandwiched between the leading and terminating electrolytes. At various times, mixed zones disappear, as a function of the effective mobilities of the ionic species and their actual concentrations. Such a figure can only be realized in practice if a fast scanning device is available. At the time r=8 (x), the steady state has been reached and the sample zones will not broaden further, assuming that the electrolyte is of constant composition and the crosssection of the separation chambe1 is constant. The zone lengths are also not influenced by variations in the electric current, assuming that the pK values of the ionic species present are not influenced by the temperature. In this sample, the ‘dilution’ effect of isotachophoresisis shown. If one compares this figure with Fig.2.7, it should be noted that the situationgiven in the present figure can be obtained only if a counter flow of electrolyte is present, because for a complete adaptation of all concentratidns the terminator ion must have passed the position where the sample is introduced, although we recommend to start the counter flow of electrolyte as soon as the terminating zone has passed the injection point.
MATHEMATICAL MODEL FOR THE STEADY STATE
55
presence of hydroxyl and hydrogen ions, was given by Brouwer and Postema 161. This model describes the first stage in the Isotachophoretic separation, which is a movingboundary system. In Appendix A, a simplified model for moving-boundary electrophoresis is described, for measuring the effective mobilities of strong electrolytes.
4.3. MATHEMATICAL MODEL FOR THE STEADY STATE IN ISOTACHOPHORESIS 4.3.1. Concept of isotachophoretic separation In the previous section, the first stage of isotachophoretic separations was discussed. The formation and migration of zones were described for the case when a stabilize< electric current is passed across a zone boundary (see Fig.4.2) between a mixture of anionic and cationic species on one side and a single electrolyte on the other side. In general, r+ 1 zone boundaries will be obtained for the separation of anionic species (see Fig.4.3). No complete separation of the anionic species can be obtained in this way, however. In the model discussed only those zone boundaries which are formed between the original boundary and the anode were considered. Essentially, this means that the amount of the mixture in the cathode compartment is taken to be unlimited (exhausting phenomena being neglected), and no attention is paid to the influence of the counter ions. For an isotachophoretic separation, however, a limited amount of sample ions is introduced between a leading and a terminating electrolyte. The terminating ionic species can never pass the sample ionic species as its effective mobility is chosen so as to be lower than those of the sample ions, and hence all sample ionic species will migrate between the terminating and leading anionic species. In front of the original sample zone, a series of zones will be formed, as described in the previous section, but behind the original sample zone a series of zones will now also be formed, because sample anionic species also remain behind according to their lower effective mobilities. The last zone formed will contain one anionic species of the sample, viz., that with the lowest effective mobility of the sample. The last zone but one will contain two anionic species of the sample with the lowest effective mobilities and each subsequent zone contains one anionic species more of the sample, in accordance with their increasing effective mobilities. Analogous to the formation of a series of mixed zones in front of the original sample, a series of mixed zones will also be formed behind the original sample, divided into two series of mixed zones. If an adaptation in concentration according to Ohm’s law has taken place, the whole system migrates through the capillary tube, during which the separation of the anionic species continues until a steady state is reached, i.e., all anionic species of the sample are separated and all sample zones contain only one anionic species of the sample. Only in this instance can we speak of an isotachophoretic separation. In Fig.4.6, a very simplified model for the formation of the zones for an isotachophoretic separation of a five-component sample is shown. At zero times, a mixture of Al . . . is introduced between A, and A,. After a certain time, two series of mixed
56
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
zones are obtained. The original sample zone length has been shortened. The whole system migrates between A, and A,, whereas the mixed zones elongate with time until the anionic species of the sample are separated. The developed zones are shown that are present in the narrow-bore tube at different times. As the amount of the sample is limited, the sample anionic species Al and, for example, As will be separated completely at a given moment. The two anionic species A, and A5 are separated completely if the last ion of the ionic species with the highest effective mobility (Al) has overtaken the first ion of the slowest ionic species (A5). The length of the original sample zone is taken as Al and the length of the capillary tube needed for a separation is I (the distance after which Al and AS are separated) (see Fig.4.7). This means that the time needed for the separation of Al and A5 is obtained as follows. Distance covered by Al :
Eml t = li-Ai Distance covered by A5 : Em5 t = l
Thus: A1 = Et ( m l - m 5 ) or
Al t =EAm
(4.24)
After this time 1, the anionic species A, and A5 are not present together in one mixed zone. The time of separation depends on several factors (see eqn. 4.24) such as differences in effective mobilities, the concentrations and the amount of the sample. At a certain moment, each ion of the anionic species Al will have migrated from all other zones and can be found only in its own zone Al . From this moment, this zone does not elongate further with time. This procedure occurs for all ionic species and in Fig.4.6, for example, all ionic species are separated except one mixed zone of A3 +Az at time t = 7 .
Fig.4.7. The last ion of the anionic species A, will have overtaken the fust ion of anionic species A, in the original sample zone at point P. The separation time will be t = Al/E Am.
51
MATHEMATICAL MODEL FOR THE STEADY STATE
If all anionic species are separated, the zones are constant in length and number and all zones, containing only one ionic species of the sample, migrate through the capillary tube with a velocity identical with that of the leading zone. We can then speak of a ‘steady state’ and this situation is called an ‘isotachophoretically separated system’. Before discussing the equations that describe this steady state, we shall consider the number of parameters and equations. Only the mass balance of the buffer will be used, as the anionic species of the sample are not present in other zones and wd1 never pass zone boundaries. However, each zone must conform to the isotachophoretic condition. In Table 4.3, all of the relevant parameters and equations are given. In Table 4.4, a reduced number of parameters and equations are given, obtained by expressing all ionic concentrations of one type as the total concentration of that ionic species using the equilibrium equations. Further, the pOH value can be expressed as pH by using the pK, value. In Table 4.4, it can be seen that for the leading zone two unknown parameters and two equations remain, by means of which all parameters can be calculated. For all other TABLE 4.3 NUMBER OF PARAMETERS, KNOWN PARAMETERS AND EQUATIONS FOR THE DIFFERENT ZONES IN ISOTACHOPHORESIS Zone
Parameters and equations
Leading Parameters: EL, pOHL, pHL, n + 1 ionic concentrations of the buffer, nAl + 1 ionic concentrations o f A L Equations: n g + n equilibrium equations, pK, electroneutrality equation, Ohm’s law AL Known parameters: c k and c t AL ~
First
Parameters: E l , pOH, , pH,, n B + 1 ionic concentrations of the buffer, n A , + 1 ionic concentrations of A, Equations: n + n A equilibrium equations, pK,, buffer equation, Ohm’s law, electroneutrality equation, isotachophoresis condition As all other zones (including the terminating 73ne) have only one anionic species and the same buffer ionic species, all other zones have an equal number of parameters and equations
TABLE4.4 REDUCED NUMBER OF PARAMETERS, KNOWN PARAMETERS AND EQUATIONS FOR THE DIFFERENT ZONES IN ISOTACHOPHORESIS Zone
Parameters and equations
Leading Parameters: EL. pHL, c k , caL
Known parameters: ct and c t 3 AL Equations: Ohm’s law, electroneutrality equation Other
Parameters: El , pH,, c:,
C:
Equations: Electroneutrality equation, Ohm’s law, buffer equation, isotachophoretic condition
MATHEMATICALMODEL FOR ISOTACHOPHORESIS
58
zones, four unknown parameters and four equations are obtained, and these parameters can also be calculated. AU zones are correlated with the leading zone by means of the buffer balances, in which all zones are determined by the conditions of the leading zone and do not affect each other. Each zone can be calculated in relation to the leading zone directly. The equations needed for the calculations are described in section 4.3.2. 4.3.2. Mathematical model of isotachophoresis By analogy with the general equations and with the same assumptions, we give here the equilibrium equations, the mass balance of the buffer, the electroneutrality equation and the modified Ohm's law, whch, in combination with the isotachophoretic condition, describe the isotachophoretic separation. The equations are valid for separations of anionic species, while analogous equations can be derived for separations of cations. The computer program discussed in section 4.3.3 can be used for both anionic and cationic species. 4,3.2.1. Equilibrium equations
In a similar manner to that described in section 4.2, we can derive for the equilibrium constant, ionic concentrations and total concentration of an ionic species the following equations* cAv.zAv-icH, KAv,i=
V
(4.25) c~ v,
zA v-(i.- 1)
(4.26)
(4.27) These equations are valid for molecules with equilibria according to eqn. 4.1. 4.3.2.2. The isotachophoretic condition In the steady state, all zones move with a velocity identical with that of the leading zone and therefore *In eqn. 4Sa, the concentration has been characterisedby the subscripts A, (indicating the anionic species), II (indicating the zone) and z the ionic form), because all anionic species 4- 1V(indicating can be present in all zones. Here, in a zone , only one anionic species can be present, called A v The second subscript, V, indicating the zone, is superfluous. An exception must be made for the hydroxyl and hydrogen ions, present in all zones: for these ions, the zone must be indicated.
59
MATHEMATICAL MODEL FOR THE STEADY STATE
EL rEAL = EvfiAv
(4.28)
where f i and fiA are the effective mobilities of the leading ion in the leading zone and AL . 1.I the sample ions A, in the Vth zone, respectively.
(4.29)*
For all other ionic species, a similar expression for the effective mobilities can be derived. The isotachophoretic condition is the essential difference between isotachophoresis and other electrophoretic methods. 4.3- 2.3. Mass balance of the buffer
The movements of the zone boundaries LV and VW per unit of time are equal (AX; see Fig.4.8):
A X = E L f i A L = EV f iA y = EW f iA W
(4.30)
A buffer ion P i n the Vth zone (at t=O) can just reach the zone boundary VW at t=1 if the distance over which it moves during one unit of time is
(4.3 1 )
B2X = Ev%v and a buffer ion Q (at t=O) can just reach the zone boundary LV if B1X =
ELMB.
(4.32)
This means that the amounts of the buffer that pass the zone boundaries LV and VW are the amounts of the buffer present in the volumes A, and A2 at time t = O . The amounts of the buffer entering and leaving a zone must be equal in the steady state, and therefore OAIC&= O A ~ V C ~ or O(AX+BlX) cr = O(AX+B2X) BL
4V (4.33)
*Compare with eqn. 4.16.
60
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
I I
I
I I
I
t. = 1
!
I
;zone zone t WI
2.e.
+p I
I
I
I
vw
1
1
I
I
LV
Rg.4.8. Migration paths of the ionic species and movement of the zone boundaries in an isotachophoretic system.
Combining eqns. 4.30 and 4.33, we obtain
ci, (1 + fiJj,/fi*,) = c& (1 + f i B V / f i A V )
(4.34)
This equation is the mass balance of the buffer, valid for all zones. All zones are directly related to the leading zone by the mass balance.
4.3.2.4. Bnciple of electroneutrality In accordance with section 4.2.2, we can write for the electroneutrality the equation
. ipl
".[
2
i KAv,i]
('Av-'>
+ZAV
('H,
i= 1
%, V*OH,
V
-k
I + C If n A ~
V)'
KAv,j
i=1
i=l
( c H , ~ ) ~
MATHEMATICAL MODEL FOR THE STEADY STATE
61
1
r-
(4.3 5)
4.3.2.5. Modified Ohm s’ law Working at a constant current density: IIG = constant = ELhL = E , X,
(4.36)
The overall electrical conductivity of a zone is the sum of the values ci mi bil and consequently
(4.37) Substitution of eqns. 4.26 and 4.27 in eqn. 4.37 gives COH,L %H,L
r
+ C H , L ~ H , L+cAL
1
(4.38)
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
62
A similar expression can be obtained for the sample zone. Calling the right-hand side of eqn. 4.38, QL and Q , for the leading and Vth zones, respectively, the function RFQ defined as (4.39)
must be zero according to eqn. 4.36. 4.3.3. Computer program for calculation of the steady state
4.3.3.I . Compu ration procedure If all mobilities and pK values are known, and suitable values for the total composition and pH of the leading electrolyte are chosen, the effective mobilities and the products of the equilibrium equations (which are constant at a given pH) of both the leading ions and the buffer ions in the leading zone can be calculated. From an equation similar to eqn. 4.27 ‘AL, zAL can be calculated from the total concentration, and with eqn. 4.26 all 9
partial ionic concentrations of the ionic species A, can be found. With eqn. 4.35, the total buffer concentration in the leading zone can be obtained and with equations similar to eqns. 4.26 and 4.27 the partial ionic concentrations of the buffer ions can be found. Further, QL and the term on the left-hand side of the buffer eqn. 4.34 can be obtained. All parameters of the leading zone are now known. Assuming a certain pH for the following zones, in a similar manner to that indicated for the leading zone, we can obtain the effective mobilities and products of the equilibrium equations. With eqn. 4.34, the total concentration of the buffer in the following zones can be found and with eqns. 4.26 and 4.27 all other partial concentrations. With eqn. 4.35, the total concentration of the sample anionic species in the zones can be obtained. With eqn. 4.38, QV can be obtained and eqn. 4.39 gives the value of the function RFQ for the assumed pH. This value must be zero for the correct pH,- In fact, several zero points will be possible, and the method of finding the correct pH, zero points is dealt with in the next section.
4.3.3.2. Iteration procedure As mentioned in section 4.3.2.5, the function RFQ must be zero for the correct pH, value. For several cases this function is calculated as a function of the pH. In Fig.4.9, the function is plotted for the separation of univalent cations and anions, the buffering counter ions also being univalent. In Fig.4.10,the function is plotted for polyvalent sample ionic species and buffer ions and in Fig.4.11 the function is shown for a system in which, in the leading zone, the leading ion acts as a buffer instead of the counter ions. Only in the sample zones do the counter ions act as a buffer and in general this means that there is a large difference in pH between pHL and pH,. This effect is used in disc electrophoresis according to Ornstein [18] and Davis [7]. In Figs.4.9,4.10 and 4.1 1 , anionic and cationic separations are indicated by the symbols 8 and @, respectively. The functions are indicated by numbers
63
MATHEMATICAL MODEL FOR THE STEADY STATE
t@
te
pH = 3
L
16 7
pHL= 1 1
B
A
~
5
10
-
5
PH"
I
-1
-
10
PH"
1
3
2 9 1
I
1 0
2
1
-1
Fig.4.9.
-1
(Continued on p . 64)
64
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
e 12
3
3
2
pHL=6
2
1
1
0
i!
2 t
t
-1
-1
pHL= 10 0
13
G 2
1
I
1
i t
5
-1
Fig.4.9 (continued).
10
-PS
t -1
pHL = 4
MATHEMATICAL MODEL FOR THE STEADY STATE
65
pHL=1 1
le
I
pHL=3
i
3
2
1
: I
1-
i
@
pH = 1 2
e
L
I
pHL=2
2 I
3
I
L
1
Fig.4.9. Relationship between the function RFQ and pH in the zones for several isotachophoretic systems. For A-L, see Table 4.5.
66
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
co 1
! I i'i
.I
-1
I
I
2
I 1
/ /
I
1
E
z1
t
-1
-1
;n
-1
w
-2
pH = 6 L
8
pHL=6
3
2
\
I
1 0
2 t
-1
Fig.4.10. Relationship between the function RFQ and pH in the zones for several isotachophoretic systems. For A-D, see Table 4.5.
MATHEMATICAL MODEL FOR THE STEADY STATE
61
PHL’ 4 . 7 5
-2
Fig.4.11. Relationship between the function RFQ and pH in the zones for a disc electrophoretic system.
representing the pK values of the sample ionic species. All assumed pK values and ionic mobilities for the leading electrolyte and sample ionic species are given in Table 4.5. For all of these electrolyte systems, different functions were obtained, some of which show no real zero points, two zero points and with some discontinuities occur. All of these effects depend on quantities such as pK values and mobilities. Although not all possible functions have been calculated, we can conclude that all systems have one common property, viz., in a cationic separation the correct zero point is always the transition between a negative and positive value of the function RFQ in the direction of higher pH values and for an anionic separation it is a transition between a positive and a negative value of RFQ (for the false zero points, negative concentrations were obtained). The method of finding the correct zero point is therefore as follows. In the computer program, a pH, is first searched for with a positive (or negative) value of RFQ and then a pH, with a negative (or positive) value of RFQ for an anionic (or cationic) separation. The correct pH, at w h c h the function RFQ is zero, within certain limits, is obtained by iterating these two values. If n o pair of positive-negative or negative-positive pH, values can be obtained in a range of six pH units from the pH, value, then 'NO REAL ZERO POINTS will be printed out by the computer. The iteration procedure is shown in Fig.4.12.
68
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
TABLE 4.5 pK VALUES AND IONIC MOBILITIES OF THE IONIC SPECIES USED FOR THE CALCULATIONS OF THE RELATIONSHIP BETWEEN THE FUNCTIONRFQ AND THE pH VALUES IN THE ZONES ~~
~
Fig.
~~
Leading zone
Buffer ionic species
4.9A 4.9B 4.9c 4.9D 4.9E 4.9F 4.9G 4.9H 4.91 4.9J 4.9K 4.9L 4.10A 4.10B 4.10C 4.10D 4.1 1
Leading ionic species
rn. 105 (cm2/V. s)
PK
n
z
Concn. (molell)
m-105 pK (cm’/V. s)
n
z
pHL
0.50 19,O
3 11 4 10 6 6 10 4 11 3 12 2 2,4,8 4.75 6 6
1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1
0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
75,O 0,76.5 75,O 0,76.5 75,O 0,76.5 75,O 0,76.5 15,o 0,76.5 75,O 0,76.5 75,O 75,o 0,763 0,76.5 0,40
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0
3 11 4 10 6 6 10 4 11 3 12 2 5 5 6 6 4.75
030 30,O
0,50 19,O 0,50 30,O 0,50
30,O 0,50 30,O 50,0,50,70 0,40
19,O 19,O 19,O
8
14 -2 14 -2 14 -2 14 -2 14 -2 14 -2 14 14 -2 -2 4.15
~
Fig.
Sample ionic species m.105 (cm2/V.s)
4.10A
50,O 50,O
4.10B 4.10C
4.10D 4.11
50,O 70,30,0,30 70,30,0,30 70,50,0 50,O 0,50
0,50,70 50,0,30,60 50,0,30,60 50,0,50 70,70,0,50,70 30,0,30
PK
n
Z
1 1 1 3 3 2 1 1 2 3 3 2 4 2
1 1 1 2 2 2 1 0 0 0 1 1 2 1
Fig *
PK
4.9A 4.9B 4.9c 4.9D 4.9E 4.9F 4.9G 4.9H 4.91 4.95 4.9K 4.9L
3,s , 6 J 9,10,11,12 3,4,5,6,8,10,12 1-6,9,12 3,5,7,9,13 1,6,10,11,12 4,8,10,13 1,4,5,10 2,4,8,10,11 4,598 2,4,8,12 1,4,5,8
*Because in this instance the assumed mobilities for the monovalent cations and anions were 50,O and 0,50, respectively, only the pK values of the sample ionic species are given.
VALIDITY OF THE ISOTACHOPHORETIC MODEL
69
pH
rp = [H+L)/2
= pH
d
c-
PHV = Q
-
SxO.2
pHV = pHV + 0 . 2
if( I H - L ~ < ~ o - ~ I system = 4
c-
y
COMPUTATION
j
pHy=pllv+0.2
ocI
m
I I
PQ
: P 30
L -DH..
svsltem=2
t PRINT
RESULTS
Fig.4.12. Flow chart of the iteration procedure of the computer program (Fig.4.13).
4.3.3.3. Discussion Sometimes, the function RFQ shows no real zero point, i e . , the function i s always positive (e.g., Figs.4.9a, 4.9b and 4.9~).This effect is mainly observed at low pH values for cationic and at high pH values for anionic separations. The exact pH values at which tlus phenomenon occurs depend on the pK values and mobilities of all ionic species and a general treatment to determine them cannot be given. The importance of this effect is that theoretically the mathematical model is not valid at these pH values. In practice, it means that at these pH values the influences of the hydrogen and hydroxyl ions are such that real isotachophoresis does not occur. The isotachophoretic condition is lost, i.e., the isotachophoresis changes into a moving-boundary process. With the equations derived in section 4.3.2and in the manner shown in section 4.3.3,a computer program has been developed, as given in Fig.4.13. An example of the input and output is also shown. The results of experiments and calculations have been compared in order to check this mathematical model (see section 4.5). 4.4. VALIDITY OF THE ISOTACHOPHORETIC MODEL 4.4.1. Introduction
In section 4.3,a mathematical model of isotachophoresis was given and, based on this model, a computer program was developed for the computation of quantities such as
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
LIST 0010 0100 01 10 0120 0125 0130 0150 0170 0172 0173 0180 0190
0195 0200 0201 0210 0220 0230 023 1 02 40 0250 0%60 0270 0275 0280 0290 0300 0305
0310 0320 0330
'REG IN' 9 M~HL~I~~HL,M~~LS~HPLJQHL,TITU!~J 'REQL' PHLJCSTLI~MI~LI KTLI ,KMI-I K I LI K I ML I 9 K T t n - J K M L 3 K Iu3 ,KIMLQJH, BH J CULI ,WUL I, MLI 1 ,c ULH, c s m , NF.ULU, w i i 1 ,QC IM,KIIL, S,(JHI QL, K ULT Hb-il; ' 1VTE:GER' 4, NL I > I I J, il, NLR ,ZI 3 ZY Lt V t Mi 'HEAL' ' AiXR4Y 'PKLI> MLI J P K D ,P I,KL I,KLB, MH,MBH, M l l I ,MBR CO :10 1, CSTn JCST I JCOI,CBU, NEU9 ,NEU I,PH, C~HIHPI MI 1 3 M3 1 J KTB. J
J
J
J
KI~~KIR~KP~~"RJKI~I~KII~KMIJKTICO:~OI~KI~KR~
PKIJKIJPK:3rTUHEO:1 0 ~ 0 1 :01; ' INTEGER' 'AR%4Y' NItWi,ZIN,ZFjNCO: 10 I;
s :=READ ;
PHL: =IIEAD;A:=HEAD;CSTLI:=FIEAD;NLI:=READ;MdLI:=HEAD; ZI:=READ; 'F0H'I:=l'STEP9 I'UNTIL'NLI'DB' 'RF:GIiV' PKI-IC I 1: =READ ;MLI C I 1:=READ; ' EN!O' ; MCIHL: =READ;MHL: =READ;NLF3: =!?EAD;MOLS: =READ; Z9 :=READ; 'FOii'I:=l'STEP'l'UNTIL'NLF3'DB' 'REG IN'PKLB C I 1:=REAL,; Mi-V C I 1:=READ; 'EN>' ; 'FLlil'I:=l'STEP'I'UNTIL'A'DB' 'BEGIN' NI C I 1:=READ;MHC I 1:=READ;M0HC I 1: =IIEAD;MBI C I 1: =REAP;
ZINC 11: =ilEAD; ' FOR ' J: =1 'STEP ' 1 'UNT IL'NI C I 1'Dl3' 'REGIN'PKI C 1, J 1: =READ; MI C I, J 1:=READ; 'END'5 NF3 C I 1:=READ;M09 C I 1 :=ilEAD; ZRN C I 1:=READ; 'FBR * J: =1 'STEP' 1 'UYTIL'N5 C I 1 ' DO ' ' BEGIN'PKl3 L: I J 3 :=REAL); M3 C 1, J 1:=READ; 'END' J ' END ;
,
0400'CBMPENT' q a l c u l a t i o n f i r s t z o n e : 0410 HPL: = l oT ( -PHL)j UHL: =1 O t ( -1 4+PHL); KLI t 01:= 1 ;KTLI :=KMLX :=KILI :=K II%I :=O; OM0 0430 'FkJR'I:=l'STEP'l'UNTIL'NLI'DB' 'REGIN'KLI CI I: =KLI[I-1 1*10t( -PKLICI l)A-IPL;QR:=ZI-I; 0440 KTLI :=KTLI+KLIC I 3; KILI :=KILI+KLI C I l*QH; 0450 Fig.4.13.
I1
VALIDITY OF THE ISOTACHOPHORETICMODEL 0460 0470 0480 0490
0500 0510 0520 0530 0535 0540 0550
0560 0570
0580 0590 0600 0610 0620 0630 0640
0650 0660
0670 0680 0690
0700 07LO 0720 0730
KMLI:=KMLI+KLICI WMLICI 3*SIGN
’ Iv);FIXT(6,3,PHL); PHINTTEXT(’(’PHL= ’ 1 ’ 1 ;FIXT( 6~4, MLI 1 ;NLCR; PRINTTEXT(’ ( ’ MOBLI= KLB CO 1 := 1 3 KTLB :=KMlE:=KILR:=KIF1LB:=O; ’FC32’I:=O’STEP’1’UNTILVNLI’DB’ ’BEGIN’FIXT(5rOrZI-I ;FL[?T(5r2rKLIC 1IMXLI);NLCR; ’END’; CSTLI=’ ’)’);FL(3T(5,2rCSTLI);NLCR;NLCH; I ’ R INTTEXT ( ’ ( ’ ’FQR’I:=l’STEP’l ’UNTIL’NLB’DQ’ ’BEGIN’KLQ C I 1 :=KLJ3C I - 1 1*10t ( -PKLHC 1 1) /HPL;QR: =ZB -1; KTLR: =KTLB+KLgC I I; K I M :=KILB+KLBC I I*QR; KMR: =KMLB+KLBCI I*MLR C I l*S IGNCQR); KIMLR: =KIMW+KLBCI l*ABS (QR 1*MLB C I 1; ’ENr)’;
R :=1 +KTLFI;NEULB :=( ZR+KILR /H; CSTL~:=-(NEULI+HPL-I2IHL)/NEULn;COtR:=CSTLR/R; MLB 1 :=(MIILR*SIGN( ZB>+KMLH)/R; BCBR:=(l+ARS(MLBl )/ABS(MLIl ))*CSTLB; T: k0LI* CARS( ZI ) *MBLI+K IMLI 3 TUW: =C0LB*(AW( ZR) *MQLR+KIMU31 ; KBL: =HPL*MHL+VIHL*M")HL+T+~~~~; PR INTTEXTC ’ ( ’ M0F3LE = ’ ) ’ 1;F IXT(614 r MLB 1 1i NLCR; ’ FBR ’ I :=O * STEP’ 1 ’ UNTIL* NLR ’ DO ’ ’BEGIN’FIXT~SrOrZR-I~~F’L0T~5r2rKlECII*CBLR~~NLCK~’END’~
PRINTTEXT(’<’ CSTLB= ’ ) ’ ) ;FLUT<5 ~2JCSTLB1 5 NLCRSNXR; 0740 PRINTTEXT(’(’ IAM3DA= ’)’);FLBT(Sr2rKUL); 0750 NLCR;NLCR;NLCR; O~OO’CBMMENT’ c a l c u l a t i o n next z o n e s : 0810 ’FUR’L:=l’STEP’l’UNTIL’A’D@’ 0820 ’BEGIN’ ’ SWITCH’SYSTEM:=L1rUrL3rL4rL5rL6,L7rL8; 0821 V :=L;M: =2; K :=1; 0830 PHCV 1 :=PHL; 0840 L1: HPCV 1 :=lot < -PHCV1) ;OHCV 1 :=lot ( - 14+PHCV 1) ; 0850 KItVrOI: =1 ;KTICVI:=KMI CV 1: =KIICVI: =KIM1CV 3: =O; 0860 ’FdR’I:=l’STEP’l’UNTIL’NICVl’DB’ 0870 ’BEGIN’ QR:=ZINCVI-I; 0880 KICVrI l:=KICVrI-I I*~O~(-PKICVJ I l)/HPCVI; 0890 KTICVl:=KTICVl+KICVrI I; 0900 KMICVI:=KMICVI+KICVJ I I*MICVr I l*SIGN(QR); 0910 KI I CV 1 :=KII CV l+K I CVr I l*QK; 0920 KIMICVl:=KIMICVl+KICVrII*ABS(QR)*MICVrI I; 0930 ’END’; MI1 CVI:=(M0I C V l * S I G N ~ Z I N C V l ) + K M I C V l ~1/+KTI ~ CVI); 0940 KR CVJ0 1 := 1 3 KTR CV I := K W CV 1 :=KIR CV 1 :=KIM3 CV 1 2 =o; 0950 0960 ’FGIR’I:=l ’STEP’l’UNTIL’M3CVl’DB’ ’BEG IN’ OR :=ZBNCV 1- I5 0970 0980 KBCVJIl:=KRCVrI-l I*lOt<-PKBCV,Il)/HPCVl; KTO CV 1 :=KTD CV l+KI3 [Vr I I; 0990 Fig.4.13 (continued).
(Continued on p. 72)
72
1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
KPBEV l:=KM3CVl+KBCVr I l*M3CVr I I*SIGNCQR); K IB C V 1 :=KIB C V 1+KBC V r I I*QR 5 KI("BCVI:=KItvACVl+KBCV~I l*ADSCQH)*IVBCVrI I; ’END’; M31 CV 1: = C M B CV ]*SIGN( ZBNCV I > + K WCV I)/( 1 +KTBCVI); CSTB CV 1 :=BCOR/C 1 +ABSC P B1 CV 1 )/ARSC MI 1 CV 1) 1 ; CBM C V l :=CSTR EV 1/C 1 +KTR C V 11 ; NEUR C-V 1 :=
;NLCII;NLCR; 1170 ’GWTU’SYSTEMC8 I; 1200 L2 : ’ IF ’ -S*FIFO>=O’ THEN’ ’BEGIN’QL: =PP CV 1; K: =3;PHCV 1 :=PHCV 1+0-2; 1210 K:=l;’GGlTO’SYSEMCl ];’END’ ’ELSE’ ’REG IN ’FH CV I :=PHCVl-S*O .2;K: =K+ 1 ;’ IF’KC30’ THEN’ 1220 ’GBTB’SYSTEMC 1 ]’ELSE’ ’G(ZITO’SYSTEMC71; ’END’ ; 1222 1230 L3: ’ IF’-S~~FQ~~O’THEN’’BEGIN’Qt~:~PHCV1~~~:~4~PHCVl~~CG\H+QL~/2~ 1240 K: =1; ’GUTB’SYSTEMC 1 1; ’END’ ’ELSE’ ’BEGIN’PHCVI: =PHCV 1+0*2;K:=K+l$ ’ IF’K<30’THEN’ 1250 1252 ’G0T0’SYSTEMC 1 I’ELSE’ ’GBTB’SYSTENC7 13 ’END’ 3 1260 L4: ’ IF’-S*RFQ>=O’THEN’ ’REGIN’QL:=PHCVl; ’GBTB’SYSTEMC51; 'EIUD' ’ELSE’ ’REtiIN’OH: =PHCVI; ’GUTB’SYSTEMCS I; ’END’; 1270 1280 L5: * IF’AP,SCQH-CL)/2;’G(ZIT0’SYSTEMCIl;’END’ ’ ELSE ’ ’REG IN’ PH CV 1 :=CQL+QH /2; ’GGTB’SYSTEKC 1 1; ’ END ’ ; 1300 1400 L6: PRINTTEXT( ’ C ’ rJex t o n e ’ 1 ’ ;FIXT(5rOrL) ;NLCR; 1410 PRINTTEXT<’C’PH\/= ’)’);FIXT(6r3rPHCVl)j 1420 PRINTTEXT C ’ C ’ IyoBI= ’>’);FIXTC6r4rE"Il CV1);NLCR; 1430 ’FBH’I:=O’STEP’l’UNTIL’NI[VI’G0’ ’BEG IN’ F IXTC5r O r ZINCV 1-1 1 5 FLUTt5r2J KI C V r I ]%@I CV 1 i 1440 1450 NLCHJ’END’; 1460 PRINTTEXT(’(’ CSTI= '>');FLffiT<5r2rCSTICVl);NU=R; 1470 NLCR;PRINTTEXTC ’ ( ’ M B B= ’)’);FIXT(~~~DI~B~CVI); 1480 NLCR ; ’ F0R ’ I :=O ’ STEF ’ 1 ’ IJNTIL' NB C V 1 ’Dfl ’ 1490 ’REGIN’FIXTC5rOrZBNCVl-I );FL0Tt5r2rKBC’Jr I IKBEICVI)3 1500 1510 N G R ; ’END’ ; 1520 PRINTTEXTC’C’ CSTB= ’ 1 ’ 1 ;FLQT(5>2rCSTBCV I) 5 1530 NLCHJNLCR; 1540 PRINTTEXT(’<’ LAYBDA * )’);FLOTISr2rKBLT); 1550 PKINTTEXTC’C’ RFO= ’ 1 ’ 1 i FLOT(Sr2rRFQ ) ;NLCR; 1555 l-8: K:=l; 1560 NLCR; ’END’ ; 1700 ’END’; 1800 ’END’; Fig.4.13 (continued).
73
VALIDITY OF THE ISOTACHOPHORETIC MODEL
HUN WAIT
?enera1 inqornation
-1 ~4.8>3>0.02>
1
lrO>0>4.7S>41>200~350~ 1 > 19>1,8>0>
.~.ea~
lr350>200r0>0>7~30> J! rH>O> 1~19rl
*Second z o n e
1>19>1>8>0>
, Y
i.
)
2 ~ 3 5 0 ~ 2 0 0 ~ 0 ~ 0 ~ 7 ~ 2 0 ~T 8 h~i 3r d0 ~z o n e
anionic cationic anionic
\ cationic A
1 >2.2>0>9 2>350>200>30> 1 > 19>1>8>0>
an i o n i c cationic
anionic cationic
Leadinp zone
PHL=
+4-800 0 +.94250’- 2 -1 +.10575’- 1
CSTLI=
+-2OOOO'-
-21-6788
MIlDLI = 1
+18 9880 +1 +.10559’- 1 0 +.66624’- 5 CSTU3= +. 10566’- 1
M0BLf3=
LAPBDA=
+ 63975’ + 0
+1 +6.880 MmI= 0 +.10276’- 1 -1 +.77890’- 2 CSTI= +.1806S’- 1
?!ext z o n e PHV=
-12.9352
+17 6613 M0BU= +1 +.77889’- 2 0 +.59041’- 3 csm= +.83794’- 2
IArSDA
+.38172’+ 0
Yext zone
HFO
-.13039’- 6
+2
PHV=
+6.734 MWI= 0 +.91648’- 2 -1 +.49642’- 2 -2 +*26889’-3 CSTI= +.14398’- 1
-7.4560
MUBRR = + 1 8.0237 +1 +.55019’- 2 0 +.29802’- 3 csm= +.57999’- 2 Fig.4.13 (continued).
(Conrinued on p . 7 4 )
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
74
LAlvBDA
+.22003'+ 0
"Text z o n e +3 PHV = +8 7 0 7 +1 +.50943'- El 0 +.16384'- 1 -1 +.13924'- 2 CSTI= +.17776'-
HFQ=
-.57742'-
7
-2.3498
MPBI=
1
MOBB = +3.1162 +1 +.13975'- 2 0 +.71232'- 2 CSTl3= +.85206'- 2 LAM3DA
END
OF
+.69343'-
1
RFQ=
+.35763'-
6
JDB
GO AHEAD
Fig.4.13 Computer program for the calculation of concentrations, conductivities, pH values and effective mobilities, useful for the steady state in isotachophoretic separations. For computations, the following input is required: -I or I (anionic or cationic separations, respectively), pH the L' all pK values and ionic mobilities of the ionic species number of zones, c i L , nAL, mA
4, moH,L,
myL, nBL, mgLJ zones we require nAv, mY v, nBy,
L' AL' zAL' zBL and all pK values and ionic mobilities of BL. For the following
3'
v,mA V'
Ay' zAVi
all pK values and ionic mobilities of A v ,
% v $ z ,~zBV ~ and all pK values and ionic mobilities of.,B,
the concentrations of sample and buffer ionic species, electrical conductivities of the zones, the pH values of the zones and effective mobilities of the ionic species in the zones during the steady state. For the calculations, the composition of the leading electrolyte zone and the ionic mobilities and pK values of all ionic forms must be known. In this model, the activity coefficients, influence of temperature (different in each zone), relaxation and electrophoretic effects, diffusion, hydrostatic flow and electroendosmosis were neglected*. In this section, some of these factors are discussed. For some of them, corrections are made in the calculations and the results of these cgculations are compared with the results of some experiments in order to check the validity of the model. Factors that affect the effective mobility have already been discussed in Chapter 3. 4.4.2. Influence of diffusion on the zone boundaries
In the model of isotachophoresis, the influence of diffusion was neglected, although it affects the sharpness of the boundary, giving a finite width to the zone boundary. This *For some of these effects, corrected values can be introduced in the computer program by repeated calculation.
VALIDITY OF THE ISOTACHOPHORETIC MODEL
15
effect can be neglected only if the zone boundary width that results from it is very small in comparison with the zone length. Several workers [ 10, 13, 15, 201 have given an approximation for this effect and showed that the width of the zone boundary due to diffusion is less than 0.1 mm; for long zone lengths, this can be neglected. 4.4.3. Influence of axial and radial temperature differences
During electrophoretic experiments, radial differences in temperature exist in the zones and axial differences in temperature between the different zones. Several quantities, such as mobilities and pK values, depend on temperature and the concentrations and pH values of the zones are also affected by temperature. HjertCn 1211 and Routs [I51 studied the influence of temperature in the radial direction and found that a parabolic shape of the zone boundary can be expected. Another important point is the difference in pK values of the ionic species due to the different temperatures of the zones. In Fig.4.14, the pK values of some ionic species are shown as a function of temperature. From Fig.4.14, it can be concluded that particularly the positively charged ionic species such as imidazole, tris and histidine, which are used as buffering counter ions for
1
T
80
60
40
20
PK Fig.4.14. Relationship between temperature ( r ) and pK values of some ionic species. 1 = pK, of glutamic acid; 2 = pK, of glycine; 3 = pK of formic acid; 4 = pK, of glutamic acid; 5 = pK, of oxalic acid; 6 = pK of acetic acid; 7 = pK, of histidine; 8 = pK of imidazole; 9 = pK, of citric acid; 10 = pK of tris (hydroxymethy1)aminomethane; 11 = pK of 2-amino-2-methyl-l,3-propanediol; 12 = pic of orthoboric acid.
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
76
the separation of anionic species, show a strong temperature dependence. Therefore, it is to be expected that for the separations of anions of very low effective mobility this influence cannot be neglected. In the computer program, different mobilities and pK values can be entered for the different zones and corrections for this effect can be made. 4.4.4. Influence of activity coefficients
#en
an equilibrium
is considered, the pH and pK values are defined as pH = -log aH and pK=-log K = pH +log
(uAH/uA)
and the activities are defined as -
A ‘
- ‘A TA
where a,is the activity, cAis the molar concentration and yAis the activity coefficient of component A. These activity coefficients can be calculated from the Debye-Huckel limiting law as log yA=Kz’fl where K is a constant, z is the valence and Z is the ionic strength of the solution. Although it is possible to compute all activity coefficients and to develop a computer program that includes these coefficients, they are neglected in our isotachophoretic model. This means that the following definitions are used: pH = - log [H+] and P K = PH + log ([A] / [AH1 ) Interpreting all pH values as -log [ W ] and all pK values as p&, correct computations can be carried out, The p& values can be calculated from the p& values by correction for the activity coefficients and repeated calculations give the exact values.
4.5. CHECK OF THE ISOTACHOPHORETIC MODEL When working with a stabilized electric current, the conductivity of a zone determines the characteristic potential gradient over the zone. The heat produced per unit volume corresponds to ZE and determines the temperature of the zone in the steady state. For a check of the theory, the difference between the temperature inside the capillary tube and the temperature of the air (air cooling) should be known. The difference in temperature measured with a thermocouple (dT,,) is different from the
CHECK OF THE ISOTACHOPHORETIC MODEL
77
true value, but there is a linear relationship between dTth and the real difference in temperature [22] (see Chapter 6). As a linear relationship between the conductivity of a zone and the temperature inside the capillary tube can be expected over a limited traject, a linear relationship can also be expected between the conductivity of the zones and the temperature detected by means of a thermocouple. This relationship is used t o check the theory. In this section, some calculations of the parameters of the different zones are made and the results are compared with those obtained in some experiments. Calculations were made both for anions and cations, correcting for the influence of activity coefficients, relaxation and electrophoretic effects and different temperatures in the zones. The temperatures in the zones were estimated from the thermocouple signals and the temperatures in the capillary tube [22] . Calculations were made for the cations BaZ+,Caz+,Mg2+,Fez+,k?, A g and Na+. These cations were chosen because the slope of the function A. = KJc* agrees reasonably well with the expected slope according to the Onsager relationship. If other influences such as complex formation occur, the decreasing effect on the mobility should be greater and the calculations would not be valid as the computer program does not deal with effects such as complex formation. For the anionic calculations, acids were chosen for which data such as ionic mobilities and pK values were readily available [ 13, 19,23,24] . The concentrations, pH values, step heights and zone resistances are given in Table 4.6 for cations in the system WKAC (see Table 11.3) and in the Tables 4.7 and 4.8 for anions in the systems histidine hydrochloride and imidazole hydrochloride (see Tables 12.1 and 12.2) respectively. Firstly, calculations were made with no corrections. The relationship between the experimentally measured step heights and the uncorrected calculated conductivities of the zones are given in Figs.4.l5a, 4.16a and 4.17a. Although one continuous relationship would be expected, two distinguishable curves are obtained for these relationships. This can be understood easily, as follows. If the zone resistances are computed without applying corrections for the Onsager relationship, there will be deviations from the real electrical resistances actually present. The zone resistances calculated will be smaller than the actual resistances because relaxation and electrophoretic effects, which decrease TABLE 4.6
SOME EXPERIMENTAL AND CALCULATED VALUES FOR CATIONS IN THE OPERATIONAL SYSTEM AT pH 5.4 (SEE TABLE 11.3) A
values are given in C’cm-I.
Cation
l / h . los without corrections
i / h 10' with corrections
K+
0.874 1.029 1.272 1.013 1.077 1.210 1.188
0.8930 1.0440 1.2825 1.1152 1.1818 1.3215 1.2969
&+
Na+ BaZ+ Ca ’+ Mg" Fe 2+
-
Calculated concentration of the ionized part (mole/ 1)
PH
Step height (mm)
0.0100 0.0094 0.0086 0.0048 0.0046 0.0044 0.0045
5.39 5.36 5.32 5.36 5.35 5.33 5.33
220 260 302 264 284 3 14 3 12
78
MATHEMATICAL MODEL FOR ISOTACHOPHORZSIS
TABLE4.7 SOME EXPERIMENTAL AND CALCULATED VALUES FOR ANIONS IN THE OPERATIONAL SYSTEM AT pH 6 (SEE TABLE 12.1) Ionic species
l/h. lo3 without corrections
l/h. lo3 with corrections
Calculated concentration of the ionized part (molell)
PH
Step height (mm)
Acetic acid Benzoic acid rn-Nitrobenzoic acid pNitrobenzoic acid Capric acid Caprylic acid Chloric acid Crotonic acid Formic acid Glycolic acid Hydrofluoric acid Iodic acid Lactic acid Nicotinic acid Nitric acid Nitrous acid Methacrylic acid Pelargonic acid Picric acid 0-Chloropropionic acid Salicylic acid Sulphamic acid Sulphanilic acid Isovaleric acid
2.036 2.504 2.561 2.560 3.075 3.064 1.230 2.414 1.474 1.996 1.468 1.977 2.268 2.526 1.120 1.115 2.295 3.100 2.648 2.283 2.334 1.623 2.483 2.660
2.195 2.689 2.749 2.764 3.246 3.235 1.349 2.591 1.608 2.160 1.600 2.142 2.450 2.697 1.225 1.219 2.469 3.286 2.832 2.461 2.512 1.766 2.672 2.831
0.0082* 0.0078 0.0078 0.0078 0.0070 0.0070 0.0097 0.0078 0.0092 0.0084 0.0092 0.0085 0.0081 0.0076 0.0099 0.0099 0.0080 0.0070 0.0077 0.0081 0.0080 0.0090 0.0078 0.0075
6.12 6.13 6.13 6.13 6.19 6.19 6.04 6.14 6.06 6.10 6.06 6.09 6.11 6.16 6.03 6.03 6.12 6.20 6.14 6.12 6.13 6.07 6.13 6.16
366 430 440 44 2 51 1 510 243 416 276 360 277 358 39 1 436 220 21 7 404 494 446 399 408 304 420 460
Adipic acid Maleic acid dl-Malic acid Malonic acid Oxalic acid Pimelic acid Succinic acid Sulphuric acid Tartaric acid Tartronic acid
1.543 1.689 1.402 1.257 1.098 1.626 1.511 0.996 1.257 1.203
1.869 1.900 1.655 1.520 1.331 1.972 1.759 1.204 1.521 1.458
0.0045** 0.0030 0.0027* 0.0042 0.0047 0.0049 0.0044 0.0013 0.0038* 0.0050 0.0047 0.0048
6.06 6.1 1 6.07 6.04 6.03 6.07 6.09 6.02 6.04 6.04
334 312 286 280 236 345 304 224 280 256
*Concentration of the monovalent anions. **Concentration of the divalent anions.
-
79
CHECK OF THE ISOTACHOPHORETIC MODEL TABLE 4.8 SOME EXPERIMENTAL AND CALCULATED VALUES FOR ANIONS IN THE OPERATIONAL SYSTEM AT pH 7 (SEE TABLE 12.2) Ionic species
l/h- lo3 without corrections
l / h - lo3 with corrections
Calculated concentration of the ionized part (mole/l)
PH
Step height (mm)
Acetic acid Benzoic acid rn-Nitrobenzoic acid p-Nitrobenzoic acid Capric acid Caprylic acid Chloric acid Crotonic acid Formic acid Glycolic acid Hydrofluoric acid Iodic acid Lactic acid Nicotinic acid Nitric acid Nitrous acid Methacrylic acid Pelargonic acid Picric acid p-Chloropropionic acid Salicylic acid Sulphamic acid Sulphanilic acid Isovaleric acid
1.5049 1.9019 1.9610 1.9608 2.2575 2.2567 0.9482 1.7952 1.1259 1.5239 1.1236 1.5171 1.7388 1.8520 0.8594 0.8536 1.7407 2.2594 1.7893 1.7398 1.7894 1.2454 1.8972 1.9680
1.5821 1.9711 2.0351 2.0299 2.3104 2.3016 1.0156 1.8668 1.2013 1.6009 1.1985 1.5920 1.8144 1.9182 0.9232 0.9137 1.8715 2.3100 1.8493 1.8140 1.8632 1.3194 1.9654 2.0322
0.0075* 0.0065 0.0064 0.0064 0,0059 0,0059 0.0093 0.0068 0.0087 0.0074 0.0087 0.0074 0.0069 0.0066 0.0097 0.0098 0.0068 0.0059 0.0068 0.0069 0.0068 0.0082 0.0066 0.0064
7.1 3 7.18 7.19 7.19 7.23 7.23 7.03 7.17 7.06 7.13 7.06 7.13 7.16 7.18 7.01 7.01 7.16 7.23 7.17 7.16 7.17 7.08 7.18 7.19
281 340 340 345 4 00 400 190 326 216 286 218 290 314 342 174 170 312 393 350 316 323 244 344 360
Adipic acid Maleic acid dl-Malic acid Malonic acid Oxalic acid Pimelic acid Succinic acid Sulphuric acid Tartaric acid Tartronic acid
1.1783 1.0679 1.0014 0.8422 1.2458 1.0411 0.7681 0.9611 0.91 82
1.3499 1.2207 1.1510 1.0831 0.9634 1.4228 1.1946 0.8931 1.1083 1.0642
0.0042** 0.0042 0.0045 0.0046 0.0049 0.0041 0.0044 0,0051 0.0046 0.0047
7.07 7.06 7.04 7.18 7.01 7.08 7.05 6.99 7.03 7.02
252 216 222 204 180 264 224 169 216 195
*Concentration of the monovalent anions. ** Concentration of the divalent anions.
80
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS
Fig.4.15. Relationship between the measured step heights, as found in the linear trace of the thermometric signal, and the calculated zone resistance for some cations in the operational system at pH 5.4 (see Table 11.3), without corrections (left) and with corrections (right).
h
I
40(
3M
Fig.4.16. Relationship between the measured step heights, as found in the linear trace of the thermometric signal, and the calculated zone resistance for some anions in the operational system at pH 6 (see Table 12.1), without corrections (left) and with corrections (right).
REFERENCES
81
Fig.4.17. Relationship between the measured step heights, as found in the linear trace of the thermometric signal, and the calculated zone resistance for some anions in the operational system at pH 7 (see Table 12.2), without corrections (left) and with corrections (right).
the mobility, have been neglected. Consequently, the resistances of the zones increase. As these effects are stronger for divalent ionic species, two different curves can be expected, as illustrated. The influence of the different temperatures on the pK values and ionic mobilities and the influence of the activity coefficients do not differ very much for mono- and divalent ionic species. After corrections have been made for the effects of temperature, activity coefficients and the Onsager relationship, only one curve is obtained for both mono- and divalent ionic species (Figs.4.15b, 4.16b and 4.17b, in accordance with the theory. In all instances the calculated pH values of the zones before and after applying the corrections do not differ appreciably (not more than 0.01 pH unit for most ionic species). Therefore, no pH measurements were used as a check on the theory. Reasonable values were obtained, however, by Everaerts and Routs [ 111 .
REFERENCES 1 R. A. Alberty, J. Amer. Chem. Soc. 72, 2361, 1950. 2 J.L. Beckers, Thesis, University of Technology, Eindhoven, 1973. 3 J.L. Beckers and F.M. Everaerts, J. Chromatogr., 51 (1970) 339. 4 J.L. Beckers and F.M. Everaerts, J. Chromatog., 68 (1972) 207.
5 M. Bier, Electrophoresis, Vols. I and 11, Academic Press, New York, 1959 and 1967. 6 G. Brouwer and G.A. Postema, J. Electrochem. SOC., 117 (1970) 7 and 874.
82 7 8 9 10 11 12 13 14 15 16 17 18 19
20 21 22 23
24
MATHEMATICAL MODEL FOR ISOTACHOPHORESIS B.J. Davis, Ann. A! Y. Acad. Sci, 121 (1964) 404. E.B. Disrnukes and R.A. Alberty,J. Amer. Chem. SOC.,76 (1954) 191. V.P. Dole,J. Amer. Chem Soc., 67 (1945) 119. F.M. Everaerts, Thesis, University of Technology, Eindhoven, 1968. F.M. Everaerts and R.J.,Routs,J. Chromatog., 58 (1971) 811. F. Kohlrausch, Ann. Phys. [Leipzig),62 (1897) 208. L.G. Longsworthand D.A. McInnes, Chem. Rev., 11 (1932) 171. J.C. Nichol, F.B. Disrnukes and A.A. Alberty,J. Amer. Chem. SOC.,80 (1958) 2610. R.J.Routs, Thesis, University of Technology, Eindhoven, 1971. A. Tiselius, Nova Acta Regiae SOC.Sci. Upsal.. Ser. 4,4 (1930) 7. D. Tondeur and J.A. Dodds,J. Chim. Phys., 3 (1972) 441. L. Omstein, Ann. N Y. Acad Sci., 121 (1964) 321. J. Bartels, P. ten Bruggencate, H. Hausen, K.H. Hellwege, KI. Schafer and E. Schmidt (Editors), Landolt-Bornstein-Zahlen werte und Funktionen aus Physik, Chemie, Astronomie, Geophysik und Technik, Band 11, Teil 7, Springer, Berlin, Gottingen, Heidelberg, 6. Aufl., 1960 B.P. Konstantinov and O.V. Oshurkova, Sov. Phys.-Tech. Phys., 11 (1966) 693. S. Hjerth, Thesis, University of Uppsala, Uppsala, 1967. J.L. Beckers, Graduation Rep., University of Technology, Eindhoven, 1970. W.W. Edward, J.W. Clarence, F.R. Bichowsky, N.E. Dorsey and A. Klemenc, International Critical Tables of Numerical Data, Physics, Chemistry and Technology, McGraw-Hill, New York, London, 1933. G. Kortiirn, W. Vogel and K. Andrussow, Dissoziations-konstantenOrganischer Sauren in Wussriger Losiing, Butterworths, London, 1961.
Chapter 5
Choice of electrolyte systems SUMMARY This chapter describes the method of choosing the most appropriate analysis for separations according to pK values or mobilities and according to differences in solvents. Several examples of problems are discussed and the solution of these problems by the use of isotachopherograms and practical data is illustrated.
5.1. INTRODUCTION
In this chapter, we shall consider the choice of electrolyte systems for isotachophoretic separations. In isotachophoresis, ionic species can be separated if their effective mobilities differ sufficiently. The effective mobility is defined as
meK,= Z aiyimi i
The degree of dissociation, ai,depends mainly on the pK values, temperature and pH in the zones. The value of yi, a correction factor for the decreasing effects on the mobility of the relaxation and electrophoretic effects as described by Onsager, depends mainly on the ionic concentrations. The value of midepends on several factors such as solvation, the radius and charge of the ions and the dielectric constant and viscosity of the solvents. All of these parameters influence the effective mobility and a well considered choice of the electrolyte system makes a good separation possible. The use of different solvents (influence of the dielectric constant and solvation) or different buffers (change in pH and the influence of complex formation) allows numerous possibilities. The separation of ionic species can be carried out in different ways, as follows. (1) The differences in absolute ionic mobilities can be used for the separation of the ionic species. A particular pH of the buffered system is chosen such that all ionic species are almost completely dissociated. We shall call these separations ‘separations according to mobilities’. (2) The differences in the pK values of the ionic species can be used for the separation. A particular pH is chosen such that most ionic species are not completely dissociated, especially when many ionic species have about the same ionic mobility. A pH is chosen in such a way that maximal differences in effective mobilities are obtained. These separations will be called ‘separations according to pK values’. (3) Other solvents can be applied in order t o obtain a complete separation. This technique can be used if the ionic species have about the same ionic mobilities and pK values, and/or are not or only slightly soluble in a certain solvent.
83
84
CHOICE OF ELECTROLYTE SYSTEMS
(4) Further, other factors such as complex formation, precipitation [ 1] and other specific interactions can be used. We shall not look into these possibilities too deeply, although they automatically affect the effective mobility. In the Section Applications, where practical information is given, this subject is discussed in more detail.
A general method of findmg a suitable electrolyte system cannot be given, but in this chapter we shall discuss several important factors that play a role in the choice of electrolyte systems (operational systems) and must therefore be taken into account. At the end of the chapter, we present examples of some problems and separations that have been solved in order to illustrate the principles of choosing electrolyte systems. 5.1.1. General remarks
In choosing a suitable electrolyte system, several factors play an important role. In general, the most important requirement is that the system must be chosen in such a way that the ionic species to be separated have maximal differences in effective mobilities, in order to achieve a rapid and complete separation. Sometimes, however, it is not possible to follow this general rule as particular conditions may be necessary for the sample and there may be limitations to the apparatus available. The choice of a suitable electrolyte system will often be a matter of experience by which, sometimes intuitively, the advantages and disadvantages of the different possibilities must be weighed against each other. In some instances, a suitable electrolyte system can only be determined experimentally (Section Applications). In this chapter a number of factors that can play a role in choosing the electrolyte system are discussed, and some practical examples are given of electrolyte systems for which data and separations are considered elsewhere in this book. The most important factors in choosing electrolyte systems that are discussed are: the choice of the solvent; the choice of the buffering counter ionic species; the choice of the pH of the leading electrolyte; the choice of the leading ionic species; the choice of the terminating ionic species; additions such as spacers (and carriers), stabilizers, surfaceactive compounds and reference compounds for identification and concentration calibration (internal standards).
5.2. CHOICE OF THE SOLVENT
The first problem in choosing an electrolyte system is to decide which solvent can be used. In most instances, water is used as a solvent in electrophoresis, not only because of its price, availability, etc. but particularly because of its superior solubility properties and its ionization power. However, other solvents can be used that are more suitable for particular applications, such as for the separations of substances that are insoluble or only slightly soluble in water (fatty acids, amino acids, proteins and complexes). When a non-aqueous solvent has to be used, the choice depends mainly on the properties of the sample.
CHOICE OF THE SOLVENT
85
In general, a solvent suitable for isotachophoresis in capillary tubes must meet the following requirements: (1) It must have as small a self-conductance as possible, as a large conductivity results in undesirable elution phenomena. (2) The sample must dissolve in the solvent chosen. With regard to the process of dissolution, two aspects of solvent behaviour are important. The first aspect is the tendency of the solvent molecules to interact with or to solvate the sample molecules. For example, water molecules can be considered as dipoles that can arrange themselves around either positive or negative ions. For this reason, the dipole moment of the solvent has to be taken into account. The second important role of the solvent is to decrease the electrostatic interactions between the oppositely charged particles of the ionic substances as a result of its dielectric constant, according to Coulomb’s law:
The dielectric constant alone is not an adequate measure of the suitability of a solvent and plays only a minor role in the solubility of ionic substances. Of particular importance is the specific solvation of anionic and cationic species. (3) The sample must form charged particles in the solvent. The sample substances can form charged particles by accepting or losing a proton and by dissociation, whereby the ions formed will be solvated. In a strongly acidic solvent, the dissolved substance will accept a proton. For example, an amino acid in 98%formic acid will give
RNH2
+ HCOOH
RNg,
+ HCOO-
(5.2)
In a basic solvent, e.g., liquid ammonia, the dissolved amino acid will lose a proton: RCOOH + NH3
RCOO-
f
NP4
(5.3)
The dissociation of salts can be expressed by an equilibrium:
M+X-zW+X-
( 5 -4)
In solvents with high dielectric constants and in very dilute solutions, only free ions are present, while at lower dielectric constants, the equilibrium lies towards the left-hand side. According to Brdnsted’s theory (see ref. 2 ) , solvents can be divided into eight classes, with respect to three properties of water, viz., the basicity, the acidity and the dielectric constant. The dielectric constant is assigned as positive for a value higher than 30 and as negative for a value lower than 30. The acidity and basicity can also be expressed numerically. Analogous to the expression of Peters (see ref. 2 ) for a redox system:
E,,
= E&
+-RT In F
ox red
-
*The terms ‘ox’ and ‘red’ indicate the activities of the oxidant and reductant.
(5.5)
CHOICE OF ELECTROLYTE SYSTEMS
86
Schwarzenbach [3] expressed the acidity as the so-called normal acidity potential, which is the potential on a platinum electrode, saturated with hydrogen gas at 1 atm, when dipped into a conjugated acid-base system.
This gives
where 'acid' and 'base' represent the activities of these substances. If E: for water is taken as zero, the values listed in Table 5.1 are obtained. TABLE 5.1 NORMAL ACIDITY POTENTIALS ACCORDING TO SCHWARZENBACH 131 Solvent
E; -EQ
NH, N,H, H2O CH,CN HCOOH
-1.00 -0.92 0.00 0.24 0.72
H,O
The eight classes of solvents according to Brbnsted are given in Table 5.2. For the equivalent conductance, Onsager gave the following expression (see ref. 4): (5.7)
where A = equivalent conductance, A, = equivalent conductance at infinite dilution, D = dielectric constant, T = absolute temperature, z = valency, c = concentration and 1) = dynamic viscosity. Assuming that for the dissociation constant we can write
it will be clear that the effective mobility decreases rapidly as the dielectric constant decreases, so that solvents with low dielectric constants are not suitable for isotachophoresis in general as too high potentials would be required and the heat production would be too high and could cause boiling of the solvent*. After the division of the solvents into eight classes and considering the above remarks, it is clear that solvents suitable for isotachophoresis should be chosen from the classes with high dielectric constants. For polar substances, amphprotic solvents are useful, whereas for the analyses of very weak acids and bases, basic and acidic solvents, respectively, are.suitable. When considering these last classes, it must be borne in mind that not all types of apparatus can be used because of the aggressive properties of some solvents (e.g., formic acid on acrylic ware). A reason*It is possible to I;se very thin narrow-bore tubes, and moreover, very effective cooling systems are now available. This procedure obviates the problems mentioned.
87
CHOICE OF THE SOLVENT TABLE 5.2 THE CLASSES OF SOLVENTS ACCORDING TO BRONSTED’S THEORY For further explanation, see text. Class
Members
Examples
D
Acidity
Basicity
I I1
Amphiprotic media Acidic media
+ +
+ +
+
I11
Basic media
+
-
+
IV
Aprotic media with high D Amphiprotic media with low D Acidic media Basic media
Water, methanol Hydrocyanic, formic, hydrofluoric and Sulphuric acids Formamide, ethanolamide N-methy lpropionamide Dimethyl sulphoxide, dimethylformamide ace tonitrile Ethanol, cyclohexanol
+
-
-
+
V
VI VII
VIII
Aprotic media with low D
Acetic and propionic acids Pyridine, diosan, diethyl ether ethylenediamine Acetone, benzene, carbon tetrachloride, cyclohexene
-
t
-
+
able solvent for most types of substances is methanol. The apparatus developed in our laboratory meet all of the demands made by the use of methanol as a solvent, and it is discussed in more detail in the Section lnstrumentation. 5.2.1. Methanol as a solvent
5.2.1.1. Comparative behaviour with water
Methanol, like water, belongs to the group of amphiprotic solvents with relatively high dielectric constants. Its dielectric constant (31) is lower than that of water (81), however, and hence the interionic forces in methanol are larger than those in water, according to Coulomb’s law. In order to compare the acid-base behaviour of water and methanol, we can study the following reactions: (a) NW4 +HzO =NH3
+ H3@
(b) NV4 + ROH=NH3
+ ROP2
+ H2 0 =CH3COOH + O H CH3 COOH + OR(d) CH3 COO- + ROH
(c) CH3 COO-
In these reactions, the number of ions is the same on each side of the equations, so that the influence of differences in dielectric constants is mainly eliminated. Measurements on those equations showed that the acid-base characters of water and methanol do not differ much. If the number of ions is not the same on each side of the equation, the differences in the dielectric constants can cause differences in the acid and base constants. For
CHOICE OF ELECTROLYTE SYSTEMS
88
example, for the reaction of an acid HA with the solvent S, we can have the following reaction :
+
HA S=A-
+ SH'
During the reaction, the number of ions increases. If the interionic forces between Aand SH+ are small (high dielectric constants), the equilibrium lies on the right-hand side. With lower dielectric constants, the equilibrium lies towards the left-hand side. On a purely electrostatic basis, it can be derived that [2]
where K = equilibrium constant; zA = zB + 1;zA and zB are the charges of the acid-base pair; e = standard electrical unit of charge; r = radius of the ions; k = Boltzmann constant; T = absolute temperature. This equation gives the relationship between the acid and base constants in the different solvents, and some examples are discussed below.
The acid constant of NH: in water and methanol Reaction: NP4 + S=SW
+ NH3
In this instance, zA =1 andzB = 0. Substituting the constants in eqn. 5.8 for water and methanol we obtain log
( k= ) - 1.24 (22,-
1 ) = - 1.24
KCH,OH
Thus the acid constant of NH; in methanol is about 17 greater than that in water.
The acid constant of acetic acid in water and methanol Reaction: CH3COOH + S E C H 3COO-
+ SH+
Here zA = 0 and zB = -1. Substitution in eqn. 5.8 shows that the acid constant for acetic acid in methanol is about 17 smaller than that in water. It can be seen that the change in the acid constants depends on the type of reaction. In practice, the differences are much larger because, for example, the dimensions of the molecules are not known exactly and the electrostatic model is not valid as the influence of the acid-base behaviour of the solvents is neglected. Another point in comparison with water is the self-dissociation of methanol: 2 CH3OH
CH30-+ CH3OK2
The dissociation constant of methanol is about (for water it is about 10-14). As with water, we can define a pH and a pOCH3 value for methanolic solutions. Especially when choosing the pH of the electrolyte systems and when choosing the counter ions, the pK values of the substances must be known for the solvent chosen. The way in which
89
CHOICE OF THE SOLVENT
pH and pKvalues can be determined in methanolic solutions is dealt with in the next section.
5.2.1.2. Determination of pK values in methanolic solutions* Determination of p f f in methanolic solutions The operational definition of the pH determined electrometrically in water is based on E measurements of cells of the type
?t:ti: 1
Aqueous solution of standard; pH,
I
KC1, reference electrode
Aqueous solution
[
KCI, reference electrode
In general, the indicator electrodes are glass electrodes and the reference electrodes are calomel electrodes. Es and Ex can be expressed as (25°C)
E s = E ref -Eomd - 0 . 0 5 9 1 6 l 0 g a ~ , ~ + l $ ~
Ex = Emf- Eqmd- 0.05916 log^^,^ +E;:,
(5.9)
(5.10)
Combination of eqns. 5.9 and 5.10 gives - log aH,x= - log aH,s
Ex-Es - E ) , x - E j , s +0.0591 ____ 6 0.05916
(5.1 1)
The operational definition of the pH is
-4
pHx = pHs + ___ 0.0591 6 EX
(5.12)
Comparison of eqns. 5.11 and 5.12 shows that
PH, = -logaH,x if pH, = -log
(5.13)
I Z ~ and, ~
Ej,x = Ej,s
(5.14)
In general, this is not exactly true. Bates [5] of the National Bureau of Standards determined the pH, values of some standard buffer solutions for which PHs = -log aH,s If the solution x has about the same ionic strength in the solvent used for the standxd solution, Ej,Scan be considered to be equal to Ej,x and then pH, can be interpreted as -log aH,x' For pH measurements in methanolic solvents, the same procedure can be followed. Because of the different liquid junction potentials for aqueous buffer solutions and *For other solvents or combinations of soIvents, a simiIar procedure can be followed.,.
90
CHOICE OF ELECTROLYTE SYSTEMS
unknown methanolic solutcons, one must look for standard buffer solutions in the same kind of methanolic solution as that used for the unknown solution. Using this standard solution, the two liquid junction potentials will cancel each other again and the measured pH can be interpreted in terms of hydrogen ion activity. De Ligny et ul. [6,7] determined the pH (- log c,yk) for some standard solutions in methanolic solvents according to the method of the National Bureau of Standards for aqueous solutions. In the determination of the pH* of standard solutions ( the asterisk here and on other symbols indicates that the quantities refer to the solutions considered and not to aqueous solutions) for methanolic solvents, corrections have to be made for the slight association of ions to give ion pairs. Fuoss and Onsager [8,9] developed a method for the calculation of the closest approach b and the dissociation constant K of an incompletely dissociated electrolyte in water, but because for methanolic solvents no accurate values of the conductivity of electrolytes were available, De Ligny et al. did not correct for the ion pair association. For the estimation of log y*, De Lgny et el. used the Gronwdl-LaMer-Sandved equation:
(5.15) The pH* values for some buffers as determined by De Ligny et al. are given in Table 5.3. In the experiments, the reference electrode (calomel) was placed in a potassium chloride solution of the solvent that was used to prepare the buffers. Using the values mentioned, TABLE 5.3 pH* VALUES FOR THE OXALATE AND SUCCINATE BUFFER IN METHANOLIC SOLUTIONS AS DETERMINED BY DE LIGNY [ 11 ] Reproduced by permission of Dr. C.L. de Ligny. 0.01 MH,Ox Methanol
+ 0.01 MNH,HOx PH*
0
Methanol
PH*
(%I
(%I 10 20 30 40 50 60 70 80 90 100
0.01 MH, Succ + 0.01 MLiHSucc
2.15 2.19 2.25 2.30 2.38 2.47 2.58 2.76 3.13 3.73 5.19
0 10 20 30 40 50 60 70 80 90 100
4.12 4.30 4.48 4.67 4.87 5.07 5.30 5.57 6.01 6.73 8.75
91
CHOICE OF THE SOLVENT TABLE 5.4 LIQUID JUNCTION POTENTIALS BETWEEN STANDARD SOLUTIONS IN AQUEOUS MIXTURES 1 1 ] Methanol and a saturated solution of potassium chloride in water for oxalate and succinate buffers. Reproduced by permission of Dr. C.L. de Ligny. Oxalate buffer
Succinate buffer
Methanol
Methanol (%)
E;
0 43.31 64.2 84.1 84.2 94.19 100
0.0041 0.0083 0.0132 -0.0091 -0.0086 -0.0485 -0.1329
(%I 0 39.13 70 84.2 84.21 94.2 100 100
0.0046 0.0091 0.01 14 -0.009 -0.0082 -0.0435 -0.1338 -0.1347
De Ligny et al. determined the liquid junction potential between the buffer solutions in methanol and a saturated solution of potassium chloride in water. The liquid junction potentials between standard solutions in methanol-water mixtures and a saturated solution of potassium chloride in water are given in Table 5.4. When the pH of a solution of methanol-water mixtures is measured by means of a pH meter, standardised by a solution of potassium chloride in water, the error due to the liquid junction potential can be calculated by means of the equation
E:* (methanol-water)
-
E:,...-&-
(5.16)
For higher percentages of methanol, this dpH* value can be very high. In order to calibrate the pH meter for measurements in methanolic solutions, a standard buffer solution in water can also be used [lo, 111 and then the correct pH* can be calculated from the observed pH by subtracting a correction factor (6) [12]. The 6 values are given in Table 5.5. The liquid junction potentials at the standard solution (alcohol-water mixtures)/ saturated aqueous potassium chloride boundaries are independent of the nature of the buffering solution. TABLE 5.5 6
CORRECTION TERMS FOR SOME METHAhOL-WATER MIXTURES
Methanol
6 (pH* units)
(%I 0 43.3 64 94.29
0.11 0.22 -0.86
92
CHOICE OF ELECTROLYTE SYSTEMS
In the pH* measurements carried out in the work described in this chapter, the same procedure was used as described by De Ligny et al. Standard buffer solutions and pH* values used were as determined De Ligny et al.
Determination of pK values in methanolic solutions The determinations of pK values [13] can be carried out in several ways, the most important of which are the conductivity, electrometric, spectrometric and colorimetric methods. In this section, the electrometric method is discussed, Rorabacher et al. [14] gave some definitions relating to the pK. The activity equilibrium constant is defined as (5.17) The equilibrium constant based on concentrations is K,* = [HI [A1 /[HA1
(5.18)
and the mixed-mode equilibrium constant is defined as K$ = a$ [A] /[HA] or K z = K:rfi
(5.19)
Hence
(5.20) In the electrometric method, the concept of the half neutralization point (HNP) is used. The HNF’ is the point in the acid-base titration at which half of the amount of acid (or base) present has been neutralized. According to eqn. 5.1 1,this means that the pK; is determined. The thermodynamic equilibrium constant can be calculated from the mixed-mode constant by correcting for the activity coefficients (eqn. 5.20).
Expenmen tal values In order to choose an optimum electrolyte system in isotachophoresis, the pK values of the buffers and the pK values of the sample ionic species must be known. Some pKk values for anionic species and bases have been determined in 95% methanol by the electrometric method and the results are given in Table 5.6.
5.3. CHOICE OF THE BUFFERING COUNTER IONIC SPECIES
With regard to the choice of the buffering counter ionic species, three important points can be distinguished. Firstly, the buffering counter ions act as a counter ion by which the principle of electroneutrality is obeyed. At the same time, the counter ionic species can be used to form complexes with the sample ionic species in order to affect the effective mobility of these ionic species in a favourable manner, particularly if the ionic species to be separated have similar mobilities. Even buffering counter ionic species with which particular sample ionic species do not migrate or are precipitated can be chosen; by this they do not disturb the separation procedure. Deman [ 11 used this
93
CHOICE OF THE pH OF THE LEADING ELECTROLYTE TABLE 5.6 EXPERIMENTALLY DETERMINED pK& VALUES FOR SOME ANIONIC SPECIES IN 95% METHANOL Ionic species
PKh
Ionic species
Acetic acid Adipic acid Azelaic acid Benzoic acid Bu tyric acid Caproic acid Caprylic acid Die thanolamine Formic acid Glutaric acid Hippuric acid Histidine Irnidazole Lauric acid Linoleic acid
7.9 7.55-9.1 7.65-9.0 7.5 8.0 8.0 8.0 9.6 6.45 7.5-9.2 6.95 6.0- 10.15 6.55 7.9 7.9
Maleic acid Malonic acid Monoethanolamine Myristic acid Orotic acid Oxalic acid Palmitic acid F’imelic acid Pyruvic acid Salicylic acid Suberic acid Succinic acid Triethanolamine Tris Isovaleric acid
PKL
4.6-? 5.9-9.7 9.6 8.1 8.8 4.5-8.3 8.0 7.6-8.95 5.9 6.2 7.6-8.95 7.25-9.4 7.9 9.05 8.05
principle for his ‘precipitation electrophoresis’. In isotachophoresis in capillary tubes, precipitation is undesirable as it may produce stoppages in the capillary tube. Asecond point to be considered is the use of buffering counter ions with a W absorption power, if a W detector is used. The concenqations of the counter ions and the pH are different in the various zones and, if we use a buffer with a molar extinction coefficient that is influenced by the pN (i.e., if only a particular ionic form of the buffer shows a UV absorbance), the different zones can be detected by the differences in the UV absorption of the buffer ions in these zones. This method of detection can be applied particularly if the sample ions show no or only a slight UV absorption. The third point and the most important function of the buffering counter ionic species is its buffering capacity for the stabilization and regulation of the pH in the different zones, by which effective mobilities of the ionic species are fixed and by which a ‘steady state’ can be maintained. The selection of a suitable pH, in combination with the type of buffer, is considered in the next section.
5.4. CHOICE OF THE pH OF THE LEADING ELECTROLYTE In this section, we shall consider separations according to pK valves because these separations are closely related to the choice of the pH of the leading electrolyte. For separations according to mobilities, the pH is of less importance. Two points are very important here: firstly, the choice of the pH itself, and secondly, the choice of the type of buffering counter ionic species, which defines the pH at which the analysis is t o be performed. In general, the pH is chosen in such a way that maximal differences in effective mobilities can be obtained according to eqn. 3.18, but a limitation is that if the pH in a zone differs more than 2 pH units from the pK values of the ionic species in that
CHOICE OF ELECTROLYTE SYSTEMS
94
zone, such low effective mobilities are obtained that the potentials required rise above the maximal potential of the stabilized d.c. power supply (this factor is of minor importance for the buffer.) Another limitation is due t o the buffering capacity of the counter ions. A maximd - 1. Hence the buffer will have a buffering capacity is obtained if pK 1 pK low buffering capacity if its pK value differs more than about 2 pH units from the pH in a zone. The pH lies between the pK values of buffer and sample ionic species, so that we cannot use a buffer when its pK value differs more than about 3 p K units from that of the sample ionic species (this is valid when the pK is lower than the pK values of the sample ions). In order to demonstrate this important effect, the relationship between the pK values of ionic species in the sample and the pH values of their zones is shown in Fig.5.1 for a pKB of 6 and a pH of the leading electrolyte, pH, of 5.75. Fig.5.1 shows clearly that the buffer has a low buffering capacity if its pKB differs more than about 3 pH units from the pK of the ionic species. In general, a buffer should be chosen with a pKB less than 3 pH units lower than the pK value of the anionic species to be separated. After considering the limitations concerning demands for the buffering ions at a chosen pH, the next problem is to choose the pH, value, and two approaches are possible. If no data such as pK values and mobilities are available, the experimental method must be used. All step heights of the substances concerned have to be measured at different pH, values and for several electrolyte systems, after which a pH, value can be chosen for the optimal separation (maximal differences in step heights). A combination of systems can be applied. If all data are known, theoretically all effective mobilities can be calculated and from the results obtained the pH, that shows maximal differences in effective mobilities can be decided. In order to demonstrate those two approaches to separations according to pK values, eleven anionic species that cannot be separated according to mobilities in the system histidine/histidine hydrochloride at a pH, of 6.02 (see Table 12.1) were selected. The effective mobilities were computed with a computer program for five electrolyte systems at different pH, values and all step heights were measured for the systems. In Table 5.7, the conditions are given for the five electrolyte systems and Table 5.8 gives the calculated effective mobilities (theoretical method) and measured step heights (experimental method). In Fig.5.2 the step heights are plotted for the different systems. The results indicate that the differences in effective mobilities (and step heights) are much greater at lower pH values of the leading electrolyte, which permits better separations to be achieved. Some separations have been carried out. Fig.5.3A shows the electropherogram for the separation of a mixture of trichloroacetate, P-chloropropionate, benzoate, crotonate, paminobenzoate and trimethyl acetate at a pH, of 6.02. The terminator was glutamate, and the leading ion was chloride. No complete separation could be achieved. In Fig.5.3B, the separation is shown for the same mixture in system E (see Table 5.7) at a pH, of4. Trimethyl acetate was used as the terminator and a complete separation could be easily achieved. A thermometric detector (copper-constantan thermocouple) was used.
+
CHOICE OF THE pH OF THE LEADING ELECTROLYTE
95
9
/
/
I /
8
/ /
I / 7
/ 6
0
za
t, 0
-
6
10
P K i o n - apeciea
Fig.5.1. Relafonship between the pH of the zone and the pK value of an anionic species for pHL = 5.75 and pK (counter ion) = 6 .
96
CHOICE OF ELECTROLYTE SYSTEMS
TABLE 5.7 ELECTROLYTE SYSTEMS FOR SEPARATIONS ACCORDING TO pK VALUES System
Leading electrolyte
PHL
A B C D E
0.01 N H C l + pyridine 0.01 N H Q + pyridine 0.01 NHCl + aniline 0.01 NHQ +aniline 0.01 NHQ +aniline
5.5
I0 70 70 70 70
5.0 5.0 4.5 4.0
TABLE 5.8 EXPERIMENTAL AND CALCULATED VALUES FOR ANIONS IN SYSTEMS A-E (SEE TABLE 5.7) The mobilities (meK) are given in 10 NO.*
1 2 3 4 5 6 7 8 9 10 11
cm2/V.sec.
System A
System B
System C
System D
System E
meff
H(mm)
meff
meff
H(mm)
meff
H(mm)
meff
H(mm)
26.33 28.13 29.59 31.20 32.21 34.58 31.16 31.97 30.24 34.26 36.60
428 424 403 380 317 338 377 372 380 361 344
22.39 24.36 25.94 27.81 30.45 33.26 30.80 31.16 30.24 34.10 36.60
21.42 23.41 25.08 27.08 30.24 33.15 30.19 31.12 30.24 34.09 36.60
590 533 518 478 428 394 429 398 418 379 370
16.76 18.62 20.20 22.19 26.78 30.25 29.80 29.15 30.24 33.60 36.60
73.2 629 618 547 477 435 426 404 408 382 372
13.81 15.44 16.85 18.65 23.31 26.86 27.99 26.41 30.24 32.49 36.60
810 722 688 624 522 449 433 409 408 392 370
H(mm) -
455 432 41 3 382 363 377 360 313 347 343
*1= Trimethylacetic acid; 2 = p-aminobenzoic acid; 3 = butyric acid; 4 = crotonic acid; 5 = benzoic acid; 6 = 0-chloropropionic acid; 7 = p-nitrobenzoic acid; 8 = sulphanilic acid; 9 = picric acid; 10 = salicylic acid; 11 = trichloroacetic acid.
5.5. CHOICE OF THE TERMINATING AND LEADING IONIC SPECIES As already described earlier (section 2.4), the sample is introduced into the apparatus between a leading and a terminating electrolyte. The choice of the buffering counter ions for these electrolytes depends on the choice of the pH. The terminating and leading ions are generally chosen such that the leading ion has a higher and the terminating ion a lower effective mobility than those of all sample ionic species. Another requirement is that all substances must be very pure. Small amounts of impurities in the terminating solution, having higher mobilities than that of the terminating ions, will be pushed forwards by the large potential gradient on the spot, will migrate through all preceding sample zones and will create zones of impurities at the separation boundaries according to their effective mobilities. These impurity zones become elongated with time, depending on the effective
CHOICE OF THE TERMINATING AND LEADING IONIC SPECIES
97
SOD-
100-
System
E
D
C
8
A
-
300
Fig.5.2. Graphical representation of the step heights (mm) as measured from the linear signal of a thermometric detector. The step heights were obtained in five electrolyte systems: see Table 5.7 for the definition of the electrolyte systems A-E and Table 5.8 for the key to the numbers 1-11.
CHOICE OF ELECTROLYTE SYSTEMS
98
c
t
Fig.5.3. Difference in the separation according to mobilities and the separation according to pK values. The electropherograms were obtained with a thermometric detector. The electric current was stabilized at 70 PA. T = Increasing temperature and t = time. Operational system: A, pH = 6 (Table 12.1); B, system E (Tabie 5.8). 1 = Chloride; 2 = trichloroacetate; 3 = p-chioropropionate; 4 = benzoate; 5 = crotonate; 6 = p-aminobenzoate; 7 = trimethylacetate; 8 = glutamate.
mobilities and concentrations of the impurities and the time required for the analyses. In a similar way, impurities in the leading electrolyte will remain behind if their effective mobilities are lower than that of the leading ions. Impurities in the terminating electrolyte with mobilities lower than that of the terminating ion and impurities in the leading electrolyte with mobilities higher than that of the leading ion do not affect the separation procedure. In experiments with thermocouples as the detector, electrolyte solutions were used that were later found to be too impure when using detectors with a higher resolving power such as W and conductivity detectors. Especially in these instances and if very dilute samples are analyzed, the purity of the electrolyte solutions is very important. The purity of the electrolyte solutions chosen can be checked by running a blank experiment without a sample. If a counter flow of leading electrolyte is used in order to extend the time of analysis, small amounts of impurities can be detected. It is not remarkable that chemical substances that are chromatographically pure often appear to be very impure in isotachophoretic analyses. Sometimes, the rule m L >n~,,,,,~,>m, need not be followed. If one is interested
ADDITIONS TO THE ELECTROLYTE SOLUTIONS
99
only in a particular component of the sample solution, a leading andlor terminating ion can be chosen with a mobility such that only some particular sample ionic species will have a mobility between those of the leading and terminating ions. Only these components of the sample will form consecutive zones between the terminating and leading zones. Sample ionic species with higher or lower mobilities run in front of the leading zone or remain behnd the terminating zone, respectively*. Such a choice of the electrolyte system can facilitate i;ie interpretation of complicated isotachopherograms. It is particularly useful when ionic species at very large concentrations are present in the sample, e.g., Na', K’and Cl- ions in biological fluids. These ionic species can be removed from the sample by using a leading ion with a lower effective mobility. Long analysis times, however, can still be expected.
5.6. ADDITIONS TO THE ELECTROLYTE SOLUTIONS 5.6.1. Stabilizers
In several chromatographic and electrophoretic techniques, stabilizing media are used. Stabilization can be effected by choosing suitable supporting media (e.g ,paper, cellulose acetate, glass walls) or by additions to the solvents used (e.g. ,starch gels, Sephadex, sucrose gradients). In many instances, these systems can be used only once, because of adsorption phenomena. For isotachophoresis in capillary tubes, no stabilizing media are needed for the separations of particles with an average molecule weight of less than about 3000. As the methods of stabilization are treated in detail in the literature, only those stabilization media used in our own experiments are considered. 5.6.2. Surface-active chemicals
Sometimes, additions are needed in isotachophoretic experiments in which highresolution detection systems are used. In Chapter 6, additions when W and conductometric detectors are used are described. In the Section Applications (Chapters 8-17), additions are given for the electrolyte systems used. These components are added in order to suppress the undesirable electroendosmotic flow. 5.6.3. Reference materials for identification and calibration of concentrations
Reference materials for the identification and calibration of concentrations can sometimes be used. These additions are described in the Section Applications. 5.6.4. Spacers and carriers
Spacers can sometimes be used in electrophoretic separation methods. In isotachophoresis, the use of spacers can never improve separations according to differences in effective mobilities, for the following reasons. A spacer is generally an ionic species with an effective mobility between those of the ionic species to be separated. Hence, if the *These ions do not influence the separation process.
CHOICE OF ELECTROLYTE SYSTEMS
1.00
differences between the effective mobilities of the ionic species to be separated are too small for them to be separated, the addition of a spacer will further reduce the differences in mobilities so that a separation cannot be achieved. Sometimes, however, it can be advantageous to use a spacer, for instance if ionic species can be separated easily, but if their zones are small and close together so that there is a risk that the detector cannot distinguish the separated zones. In such a case we can use, for example, a non-UVabsorbing spacer (if a UV absorption detector is being used) that separates these zones so that they can be detected separately. Similarly, we can utilize a UV-absorbing spacer in order to make the detection of consecutive zones of non-UV-absorbing ionic species possible. Another application (see Chapter 13) of spacers is in the separation of molecules with a high molecular weight, e.g., proteins. For the separation and detection, a series of compounds can be used with a large range of effective mobilities in the operational system chosen and, almost always related to this, a large pH gradient. Of course, these additives are a combination of spacers and carriers (see Chapter 13), but proteins normally require stabilization with electrolytes. If a protein is introduced in such a gradient, it will migrate together with the carrier, by which it is diluted, at such a position that its effective mobility corresponds to the related pH. This subject is dealt with in greater detail in the Section Applications, where practical information on protein separations is presented.
5.7. DISCUSSION
Prescriptions for the selection of electrolyte systems that are always valid cannot be given, because the choice of an electrolyte system depends to a great extent on the sample being analyzed. In order to demonstrate the method of choosing a suitable electrolyte system, some examples of electrolyte systems are considered in the remainder of this chapter. Further information and experimental data are given in the Section Applications. A scheme that can be of help in choosing an electrolyte system is shown in Fig.5.4.
5.8. EXAMPLES
Example A. Suppose we wish to separate two anionic species A and B with ionic mobilities* of 30 and 50 and with pK values of 1 and 3, respectively. We must decide the preferred type of separation (according to pK values or according to mobilities), the pH, and the limits for the effective mobilities of the leading and terminating ionic species. The effective mobility of the leading ionic species must be greater than 50 and that of the terminating ionic species must be less than 30. (One must consider the possibility that at certain pH values the effective mobilities of the sample ionic species can be much lower than 30 or 50). In this instance we would prefer a separation according to mobilities. Here the differences between the ionic species are sufficiently large and the pH, should be about 2 (because the pK values are 1 and 3) for a separation to be carried out according to pK values. At this pH, the concentration of the hydrogen ions is so high that the current carried by the counter ions and hydrogen ions is the largest part of the *.10-5 -
cm*/V sec.
101
EXAMPLES Choice of solvent. Can water be used?
--
NO
-
YES
I
NO
in chosen solvent
Look for another solvent **
--
Choose several electrolyte systems that could be possible*
c YES
t
with computer program an optimal electrolyte system can be calculated
I
-
Follow experimental method in order to find an optimal system
+
Separations can be carried out? If no separations can be carried out because the differences in effective mobilities are too small, look for another solvent
t Electrolyte system can be chosen *This step is very important. Here one must take into account all possibilities dependent on the sample given. Keep in your mind factors such BS complex formation, precipitations, pH, the choice of leading and terminating ionic species, concentrations etc. **Consider the choice of basic and acidic media. Consider also the possibility that the substances must take a charge.
Fig.5.4. Scheme for the choice of an electrolyte system.
total current. Hence the effective current carried by the anions i s very small, so that long analysis times can be expected (small step heights may be the result). We can choose a pH, of about 5 or above, at which level both anionic species are nearly completely ionized. If the pK values are 5 and 7 and the mobilities remain 30 and 50, for instance, we could apply a combination of separations according to pK values and mobilities. At a pH of about 6 , the effective mobility of anion A would be nearly 50, but that of anion B would be about 3 because its degree of dissociation is about 0.1. In that event, a terminating anionic species with an effective mobility of less than 3 should be used.
CHOICE OF ELECTROLYTE SYSTEMS
102
Example B. Let us consider the type of buffer solution that would be preferred for the separation of Al*, Ba2+and Na': (a) hydrochloric acid; (b) potassium acetate-acetic acid; or (c) potassium hydrogen sulphate. The best system to choose is system (b), for the following reasons. Alw is a so-called cationic acid; it undergoes partial protolysis according to the reactions
Al(0H) (HZ0)y + H’
Al(H20):
Al(0Wz (HzO); + W Al(0H) (HzO)? etc. As a result of this property, a solution of aluminium chloride has a rather low pH, which means that A13+loses H’according to the above reactions. During the analysis, the H’migrate away from the Al zone because its effective mobility is much greater than that of N3'; hence the equilibrium in the zone is disturbed and the reaction tends towards the right-hand side. By this procedure, we shall not have an isotachophoretic system but a moving-boundary system if we do not use a buffering counter ionic species. For this reason, system (a) is not suitable, and system (c) is not suitable because barium sulphate is not soluble and it also does not have a buffering effect. ExampZe C The determination of the alkali metals is one of the more difficult problems in analysis. Complicated treatments are necessary in order to determine them, and a mixture of a l l of them is particularly difficult to analyse. Let us consider the type of electrolyte system that could be used for the isotachophoretic separation of mixtures of alkali metals. In the first instance, we could choose water as the solvent. The ionic mobilities of the alkali metals in water are known (see Table 5.9). The pK values of these metals are not important because all ionic species are completely ionized. On considering the mobilities, it will be clear that in water Cs+, Rb' and probably K’ cannot be separated as the differences in their effective mobilities are too small. The use of different counter ions and different pH, values will also not be successful as the alkali metals show a similar behaviour. For this reason, the next step is to look for another TABLE 5.9 MOBILITIES AND STEP HEIGHTS OF SOME CATIONS MEASURED AS THE LINEAR SIGNAL OF A THERMOMETRIC DETECTOR The step heights are measured on top of the leading ion H+,in the system MHC1.
Ion
H+
a+ Rb+ K+ Na+
Li+
a"
m . l o 5 (cm'/V*sec)
Water
Methanol
362.2 81.3
149.7 62.5 58.4 54.4 46.8 40.4 -
80.3 76.7 52.8 40.2 -
H(mm)
17 25 31 46
61 125
EXAMPLES
103
solvent, hoping that a different solvation will affect the ionic mobilities in a favourable way. As the ions concerned do not show any proton interaction, we must seek a suitable solvent in the class of amphiprotic solvents, preferably with a high dielectric constant. In that case, we can try methanol. The ionic mobilities of the alkali metals in methanol are given in Table 5.4.It can be seen that the differences in the ionic mobilities are much more favourable in methanol, so that we can use methanol for the separation of the alkali metals. The second problem is the use of a leadtng ion. In nearly a l l solvents, the alkali metals have higher ionic mobilities than other positive ions except H’.Therefore, we should choose H’as the leading ion (in methanol there are some positive ions with a higher effective mobility than CS', e.g., the tetramethylammonium ion). As the terminating ionic species many positive ions can be used; in this example we tried Cu2+ions. In general, it is preferable to use a buffering counter ion, but for the separation af the alkali metals the pH is not important and, because no disturbances can be expected, we chose a non-buffering ion (chloride) as the counter ionic species. We carried out some experiments in order to check this system, The step heights measured with a thermocouple are given in Table 5.9. As the leading electrolyte we used a solution of 0.OlNhydrochloride in methanol (95%) (MHCl) and as the terminator a solution of 0.1N coppel(I1) chloride in methanol. Firstly, all step heights of the alkali metals were measured and then a separation of a mixture of the alkali metals was carried out. The isotachopherogram for this separation is shown in Fig.5.5. A rapid and complete separation was easily obtained. In Chapter 16, more data about cationic separations with both water and methanol as solvents are given.
Example D. In Chapter 14 the separation of some nucleotides is considered; in this example, we shall discuss how to choose a suitable electrolyte system for the separation of nucleotide diphosphates. As the solvent we use water as it dissolves all ionic species easily. As not all pK values and mobilities of the diphosphates are known, we have to use the experimental method in order to find a suitable electrolyte system. We have chosen some electrolyte systems with pH, values of 3.4,3.7,4.2,4.6, 6.0 and 7.0 (these values were chosen because several nucleotides have pK values between 2 and 5). As the diphosphates will be separated as negative ions at the chosen pH values, we use chloride as the leading ion and positively charged ionic species as the buffering counter ionic species. It can be seen that the pH, values of the systems do not differ much from the pK values. The conditions for the chosen electrolyte systems are given in Table 5.10 and the measured step heights are given in Table 5.1 1 and are shown graphically in Fig.5.6. It can be seen from Fig.5.6 that maximal differences in effective mobilities are obtained at lower pH values. For the separation of a mixture of diphosphates, we chose a pH, of 3.7. The isotachopherogram of this separation is shown in Fig.5.7. The detection was performed with a thermometric detector (copper-constantan thermocouple). Example E. Fatty acids, especially the higher fatty acids, are slightly soluble in water, so that water cannot be used as the solvent for their separation. Methanol is a better
CHOICE OF ELECTROLYTE SYSTEMS
104
7>
I:
Fig.5.5. Isotachopherogram for the separation of alkali metals in methanol (for operational system, see Table 16.4). The detection was performed with a thermometric detector. T = increasing temperature; t = time: The electric current was stabilized at 70 PA. 1 = H+; 2 = Cs+;3 = Rb'; 4 = K+; 5 = Na+; 6 = LT; 7 = Cu2+.
TABLE 5.10 DIFFERENT ELECTROLYTE SYSTEMS FOR THE SEPARATION OF NUCLEOTIDES For operational systems, see section 14.2
No.
System
pH
Leading electrolyte
Electric current
Terminator
o( A)
I I1 111 IV
v
VI
WAdQ WaNCl WAnCI(1) WAnCl(I1) WHiScl WImCl
3.4 3.7 4.2
4.6 6.0 7.0
0.01 NHCl + adenosine 0.01 NHCl + a-naphthylamine 0.01 N HCl + aniline 0.01 NHCl +aniline 0.01 NHCl + histidine 0.01 NHCl+ imidazole
70 70 70 70 70 70
Caproic acid Caproic acid Pivalic acid F'ivalic acid Cacodylic acid Benzyl-dl-asparigine
105
EXAMPLES TABLE 5.11 STEP HEIGHTS OF THE DIPHOSPHATES OF NUCLEOTIDES MEASURED AS THE LINEAR SIGNAL OF A THERMOMETRIC DETECTOR The step heights are given in millimetres from the level of the leading electrolyte zone, System
Ionic species
ADP GDP CDP UDP
1
I1
111
IV
V
VI
318 230 356 172
268 21 0 312 164
224 176 276 168
170 152 192 136
186 192 184 178
108 112 100 100
solvent for the higher fatty acids and in this example we shall consider the separation of some fatty acids in methanol. The mobilities of the fatty acids and their pK values in methanol are not known exactly, and we therefore have to use the experimental method in order to find a suitable
4 ""*\ 300
200
100
0
-
I . . . , v. , I1
I
111
IV
VI
S
Fig.5.6. Graphical representation of step heights of nucleotide diphosphates, (iz mm) measured as the linear trace of a thermometric detector. The step heights were measured in different operational systems (s), as given in Table 5.10.
CHOICE OF ELECTROLYTE SYSTEMS
106
67
/
6
i-
Fig.5.7. Isotachopherogram for the separation of a mixture of ADP, GDP, CDP and UDP in the operational system at pH = 3.7 (Table 14.2). The detection was performed with a thermometric detector. T = increasing temperature; t = time. The time in this experiment was short (15 min) because there is a great difference in the effective mobilities. The electric current was stabilized at 7 0 p k 1 = Chloride; 2 = UDP; 3 = GDP; 4 = ADP; 5 = CDP; 6 = caproate.
electrolyte system for their separation. In Table 5.6, some pK values of fatty acids in methanol are given; most of them are about 8, and we therefore have to choose a pH, of 8-9 in order to separate them according to pK values. As a buffering counter ionic species, Tris or Triethanolamine can then be used. We chose as the counter ionic species Tris in combination with chloride as the leading ion. The step heights of some fatty acids were measured for some concentration ratios of hydrochloric acid and Tris, and the results are given in Table 5.12. With the chosen electrolyte, the fatty acids could easily be separated and in Fig.5.8 the isotachopherogram for the separation of some fatty acids is given for system A. The detection was performed with a thermometric detector (copper-constantan thermocouple).
Example E If sample ionic species do not show any W absorbance, a UV detector can still be applied by using a W-absorbing counter ionic species. The sample zones can
107
EXAMPLES TABLE 5.12 STEP HEIGHTS OF SOME FATTY ACIDS IN METHANOL MEASURED AS THE LINEAR SIGNAL OF A THERMOMETRICDETECTOR The step heights are given in millimetres from the level of the leading electrolyte zone. Ionic species
Leading electrolyte 0.02 N Tris0.01 N HCI (system A)
0.0085 N Tris0.01 N HC1 (system B)
0.01 N Tris0.018 N HCl (system C)
Formic acid Acetic. acid Butyric acid Isovaleric acid Caproic acid Caprylic acid Pelargonic acid Capric acid Lauric acid Myristic acid Palmitic acid Stearic acid
3’ 88 128 137 148 168 180 190 204 220 240 252
21 64 91 104 114 124 126 136 146 156 166
18 78 110 122 132 144 148 156 172 184 204 222
Terminator solutions Litocholic acid Cacodvlic acid
400
216
256 -
be detected, because the counter ions have different concentrations and have different pH values in those zones, and hence show differences in UV absorbance (see section 5.3). In order to demonstrate this effect, we carried out separations with the sample ionic species chlorate, formate, acetate and glutamate, which do not show UV absorbance. Firstly, a separation was carried out with a non-UV-absorbingcounter ionic species and then with a UV-absorbing counter ionic species, for which the molar extinction coefficient is a function of the pH. For the first separation we chose as the leading electrolyte a solution of 0.01 N hydrochloric acid and e-aminocaproic acid at a pH of 4.5. The terminator was a solution of 0.0 1Nmorpholinoethanesulphonic acid (MES). In the second separation, the leading electrolyte was a solution of 0.01 N hydrochloric acid and creatinine at a pH of 4.5 and the terminator was a solution of 0.01 N MES. As detectors we used a conductivity detector (a.c. method; see Chapter 6 and Fig.6.18) and a U V detector (256 nm; see Chapter.6). The isotachopherograms are shown in Figs.5.9a and 5.9b. It can be seen that the influence of the buffering counter ions is sufficiently large for the sample zones to be detected with a UV detector. The presence of several impurities that form zones between the sample zones has already been mentioned in section 5.5. The conductimetrically measured signals are nearly identical in both figures although differences in step heights occur owing to the differences in the effective mobilities of the counter ions.
108
CHOICE OF ELECTROLYTE SYSTEMS
fT
Fig.5.8. Isotachopherogram for the separation of some fatty acids in a methanolic system (for operational system see Table 16.1). The detection was performed with a thermometric detector. T = Increasing temperature; t = time. The electric current was stabilized at 70 PA. 1 = Chloride; 2 = formate (C, 1; 3 = acetate (C2); 4 = butyrate (C4); 5 = n-caproate ( C 6 ) ;6 = ncaprylate (C,); 7 = n-caprate (&); 8 = n-laurate (C12);9 = n-myristate (C14);10 = n-palmitate (C16);11 = n-stearate (CIB);12 = cacodylate.
Example G. Sometimes, different sample ionic species have identical effective mobilities at a certain pH, so that they form stable mixed zones. By using different electrolyte systems with different pH, values, they can generally be separated according to their pK values. However, if we do not know the composition of the ionic species present in the sample, difficulties can arise. The use of both a conductivity and a UV detector can then be advantageous. In Fig.5.10, the isotachopherograms are shown for phosphate, salicylate and a mixture of them. The conductimetric signals are identical and the mixed zone cannot be recognized. In this experiment, the leading electrolyte was a solution of 0.01 N hydrochloric acid and 0-alanine at a pH of 4 and the terminator was 0.01 N glutamic acid. Because the pK values of orthophosphoric acid are 2.12,7.21 and 12.67 and the pK value of salicylic acid
109
Fig.5.9. Isotachopherograms of the separation of 1pl of a mixture of chlorate (0.01 M), formate (0.0 1M), acetate (0.01 M) and glutamate (0.01 M). In both instances morpholinoethanesulphonic acid was used as the terminator, which is the reason why the electric current was stabilized at 30 fiA. Detection was performed with a linear conductivity detector (a.c. method) and a UV absorption detector (256 nm), both of which are described in Chapter 6.R = Increasing resistance; t = time; A =increasing UV absorbance. The time of analysis was 15 min. For a comparison with the isotachopherograms obtained with a thermometric detector (e.g. Fig.5.8), it should be noted that the speed of the recorder paper was five times higher in the isotachopherograms shown here. In the experiment shown on the right, the buffering counter ion E-aminocaproic acid, which shows no UV absorption, was used as the buffer, added to 0.01 N hydrochloric acid (pro analysigrade) to a pH of 4.5. On the left, an isotachopherogram is shown for the operational system consisting of creatine (as the buffering counter ion), which has a molar extinction coefficient that is influenced by the pH. The creatine was also added to 0.01 N hydrochloric acid to a pH of 4.5. Special attention should be paid to the impurities, revealed by both the detectors, and of course the shift in the pH, as normally obtained in an isotachophoretic separation but now shown in the linear W trace in the left-hand isotachopherogram [examine the pH of the zone of glutamate ( S ) ] . The difference in step height, as obtained in the linear trace of the conductivity detector, must be ascribed mainly to the difference in the counter ion taken, rneff. and pK. 1 = Chloride; 2 = chlorate; 3 = formate; 4 = acetate; 5 = glutamate; 6 = morpholinoethanesulphonate.
110
1
CHOICE OF ELECTROLYTE SYSTEMS
*
A
1
Fig.5.10. Isotachopherogramsfor the separation of phospate and salicylate. The leading electrolyte was 0.01 N hydrochloric acid (pro analysi grade), adjusted to a pH 4 by the addition of recrystallized p-alanine; the terminating electrolyte was glutamic acid (0.01 N ) , adjusted at pH 4 by the addition of Tris. The electric current was stabilized at 70 PA. The detection was performed with a linear conductivity detector (a.c. method) and a UV absorption detector (256 nm), both of which are described in Chapter 6. In the left-hand experiment 10 nmole of phosphate, in the centre experiment 10 nmole of phosphate plus 10 nmole of salicylate and in the right-hand experiment 10 nmole of salicylate was introduced. Attention should be paid to the difference in step heights, as obtained in the linear traces of the W absorption detector. t = Time; R = increasing resistance;A = increasing UV absorption. I = Chloride; 2 = salicylate; 3 = glutamate; 4 = phosphate.
is 3.1, we can separate them according to their pK values. In Fig.5.11 this separation is shown for three different pH values. The left-hand isotachopherogram shows the separation with a leading electrolyte consisting of 0.01 N hydrochloric acid plus 0-alanine at a pH of 3.2 and glutamate as terminator. In the centre as shown the mixed zone as in Fig.5.10 and on the right is shown a separation at a pH of 7 with a leading electrolyte consisting of 0.01 N hydrochloric acid plus imidazole and glutamate as terminator. It can be seen in Fig.5.11 that the problem is not whether the ionic species can be separated, but how to recognize a mixed zone. The UV detector can provide the solution. The UV signals for zones with only one ionic species of the sample show sharp step heights and each sample zone has its own characteristic step height in a particular electrolyte system. However, when mixed zones are present, a typical form is often shown as can be seen in Fig.5.10 (centre), while its average step height lies between those of the pure sample zones, depending on the concentrations of the sample ionic species present in the mixed zones.
Example H Suppose we wish to separate anionic species with ionic mobilities of about 30, but with pK values of 2, 3, 5,7 and 8. In this instance, of course, we have to choose a separation according to pK values. Thus we have to choose a leading electrolyte with a pH lying between the pK values of
EXAMPLES
4
111
3
II Fig.5.11. Isotachopherograms for the separation of phosphate and salicylate in various operational systems, to show the difference in separation according t o pK values and according t o mobilities. The centre isotachopherogram is as described in Fig.5.10 (centre). AU other conditions are as in Fig.5.10, except for the operational systems. Left-hand isotachopherogram: leading electrolyte, 0.01 N hydrochloric acid (pro analysi grade) adjusted to pH 3.2 by the addition of p-alanine. Right-hand isotachopherogram: leading electrolyte, 0.01 N hydrochloric acid (pro analysi grade) adjusted to pH 7 by the addition of imidazole. In both instances, a complete separation could be achieved. t = Time; R = increasing resistance; A = increasing W absorption. 1 = Chloride; 2 = phosphate; 3 = salicylate; 4 = glutamate.
the ionic species to be separated. We could use a leading electrolyte with a pH, of about 5, but there is then a problem. When the pH in the zones is about 5, the ionic species with pK values of 2 and 3 have nearly identical effective mobilities and they cannot be separated. For the ionic species with pK values of 7 and 8, the effective mobility is rather low and it is then preferable to carry out the separation in two runs. In the first run, we use a leading electrolyte with a pH of, e.g. ,3.5,so that we can easily separate the anionic species with pK values of 2 , 3 and 5 . Further, a terminating ionic species is chosen such that its effective mobility is higher than those of the ionic species with pK values of 7 and 8. In the second run, we take a leading electrolyte with a pH of about 6.5 and we can easily separate the anionic species with pK values of 5,7 and 8 (other ionic species will generally form a mixed zone). With the two runs, we can thud separate the whole mixture. In such a separation, we can speak of a ‘combination of systems’. As with differences in pK values, we also can combine electrolyte systems with the aim of using different properties such as complex formation for the separation of metal ions and amino acids (see section 13.1.4).
CHOICE OF ELECTROLYTE SYSTEMS
112
/ /
/
I I
00-
Pb
Y.
t,
mo K
WHCl
WKAC
MHCl
f
MKAC
Fig.S.12. Step-height differences (differences in effective mobility) of some cations for different operational systems. For more information, see Chapters 11 and 16.
REFERENCES
113
Example I. As example C shows, pronounced differences in effective mobilities can be expected if instead of water methanol is used as solvent. Example G shows some differences in effective mobilities, due to the change in pH. The differences in the effective mobilities, as found in the various systems, always must be interpreted carefully. The influence of the counter ion, the solvent and the pH always results in changes in the effective mobilities of the various ionic species considered. Therefore another example of these various effects can be given. Fig.5.12 shows clearly the influence of the various systems on the effective mobilities (step heights) of the cations. The systems WHCl, W A C ,MHCl and MKAc are listed in Tables 11.1, 11.3, 16.4 and 16.5, respectively. The behaviour of the cations K, Na and Li is similar, while highly charged cations such as Ce, Al and Pb show shifts due to effects of pH and complex formation. A large shift is shown for the tetraethylammonium ion in the aqueous and methanolic systems due to the effect of solvation and change of dielectric constant of the solvent. Much more information about this subject can be found in the literature considering “structure breaking” and “structure making” properties of ionic species. Moreover, in methanolic systems the influence of a change in pH on the divalent cations is remarkable.
REFERENCES 1 2 3 4 5 6
J. Deman, Anal. Chem, 43 (1970)321. R.P. Bell, Acids and Bases, Methuen, London, 2nd ed., 1969. G.Schwarzenbach,Helv. Chim Acta, 13 (1930)870. J. Dingemans, Electrochemie, Waltman, Delft, 5th ed., 1964. R.G. Bates, Electrometric p H Determinations, Wiley, New York, 1964. C.L. de Ligny, P.F.M. Luykx, M. Rehbach and A.A. Wieneke, Rec. Trav. Chim. Pays-Bas, 79
(1960)699. 7 C.L. de Ligny, P.F.M. Luykx, M. Rehbach and A.A. Wieneke, Rec. Trav. Chim Pays-Bas, 79 (1960)713. 8 R.M. Fuoss,J. Amer. Chem. SOC.,79 (1957)3301. 9 R.M. Fuoss and L. Onsager, J. Phys. Chem., 61 (1957)668. 10 W.J. Gelsema, Thesis, University of Utrecht, Utrecht, 1964. 1 1 C.L. de Ligny, Thesis, University of Utrecht, Utrecht, 1959. 12 C.L. de Ligny and M. Rehbach, Rec. Trav. Chim Pays-Bas, I9 (1960)727. 13 J. Kucharsk; and L. Safarik, nitrations in Non-Aqueous Solutions, Elsevier, Amsterdam, 1965. 14 D.B. Rorabacher, W.J.MacKellar, F.R. Shu and M. Bonavita, Anal. Chem. 43 (1971)561.
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INSTRUMENTATION
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Chapter 6
Detection systems SUMMARY In the previous chapters, various theoretical and practical aspects were considered, and it was shown that the choice of the electrolytic system in which an analysis is to be performed determines whether an electrophoretic experiment will be carried out according t o isotachophoretic principles. This chapter is devoted to detection systems that can be used with electrophoretic equipment specially developed for isotachophoretic analyses, including the thermometric detector, the conductivity detector (a.c. method), the potential gradient detector (d.c. method) and the UV absorption meter. Some recent developments such as the highfrequency detector with micro-sensing electrodes in indirect contact with the electrolyte inside the narrow-bore tube and the polarimetric detector are mentioned only briefly, as these types of detector need to be developed more thoroughly. Some effects caused by the additives that must be added to the electrolytes in order to suppress electroendosmosis or electrode reactions, and the coating of the microsensing electrodes of the conductivity meter or potential gradient detector are briefly discussed. It is shown that these effects which may occur if high-resolution detectors are applied, are obtained only if the necessary precautions are not taken. Attention is paid to these effects so that once they occur they can quickly be recognized and appropriate measures can be taken.
6.1. INTRODUCTION Because the principle of isotachophoresis can be applied to separations on both analytical and preparative scales, the detection systems that can be used are numerous and of different construction for the two types of instrumentation involved. In this book, most attention is paid to analytical applications, although the operational systems considered may be applied in both types of application. Even in analytical isotachophoresis, various types of instrumentation may be chosen. With these instruments, a choice can be made as to whether or not stabilizing agents should be used. Again, we shall focus attention on the equipment in which narrow-bore tubes are used. In such equipment, no stabilizing agent needs to be used and also volatile and aggressive solvents can be used in addition to water. Because the volume of the separating chamber and the concentrations of the electrolytes in it are small, this type of equipment is particularly applicable t o analyses of samples that consist of different components present in low concentrations or of samples of which only small amounts are available. Basically, the isotachophoretic equipment consists of a narrow-bore tube [l-31 made of an insulating material (glass or PTFE) with an inside diameter of cu. 0.4-0.6 mrn and an outside diameter of cu. 0.7-1.0 mm. The inside diameter must not vary by more than 117
118
DETECTION SYSTEMS
ca. 2%. The choice of the material of which the equipment is constructed influences the
electroendosmosis considerably. The length of tube needed for a complete separation depends on the difference in the effective mobilities of the ions in the sample that are most difficult to separate, the concentrations of the constituents of the sample and the availability of a counterflow of electrolyte (see Chapter 7). Because the choice of detection system determines the type of construction of the equipment, the detection systems that are currently available for analytical isotachophoresis are summarized first. Some equipment is considered in detail in Chapter 7. The detectors that are available can be divided into three main classes: universal detectors, specific detectors and combinations of both, and these types are considered in the following sections.
6.1.1. Universal detectors When a universal detector is used, the information obtained is directly proportional to the effective mobilities of the ionic constituents [4], and the information derived therefore has a continuous stepwise character. From the height of a step, qualitative information can be deduced, while the length of a step provides quantitative information. Universal detectors may be divided into two classes: (1) Detectors of which the sensing element is not in direct contact with the electrolytes inside the narrow-bore tube [ S ] . This class can be divided into two sub-classes: (la) Detectors with a low resolving power, e.g., temperature-recording detectors [l]. (lb) Detectors with a high resolving power, e.g., high-frequency conductivity detectors. (2) Detectors in which the sensing element is in direct contact with the electrolytes inside the narrow-bore tube [ 6 ] .This class can also be divided into two sub-classes: (2a) Detectors that involve a.c. recording of the conductivity between two micro-sensing electrodes mounted equiplanar or axially [7]. (2b) Detectors that record the potential gradient directly, making use of the direct driving current between two axially mounted micro-sensing electrodes [8] .
6.1.2. Specific detectors When a specific detector is used, the information obtained is not directly proportional to the effective mobilities of the ionic constituents. A series of components, separated isotachophoretically, may have different, non-continuous, responses on the detector, so that the absolute value of the measuring signal may be different from zone to zone. One can use the principle of absorption of light measured during the analysis, or polarimetric detection can be used [9]. The succesful use of radiochemistry has so far been applied only in analyses on strips [ 101.
THERMOMETRIC RECORDING
119
6.1.3. Combinations of universal and specific detectors
There are two main possibilities for combining universal and specific detectors: (1) Specific detectors and universal detectors both mounted in a similar piece of equipment. This will be discussed in Chapter 7, where the construction of the equipment is dealt with. (2a) A universal detector may serve simultaneously as a specific detector. Particularly if micro-sensing electrodes, which are in direct contact with the electrolyte inside the narrow-bore tube, are coated with a suitable polymer [7], these electrodes give specific infor mation. (2b) A specific detector may serve simultaneously as a universal detector. If, for instance, a W-absorbing component, for which the electrophoretic migration in the operational system applied is almost zero and the U V absorption is a function of the pH, is added to the leading electrolyte, the W detector gains ‘universal characteristics’ if non-UV-absorbing species are present. This effect is due to the different pH values characteristic of each zone [ l 11 . Before the detectors are discussed in detad in the following sections, a survey is given of the phenomena that occur during isotachophoretic analyses (Table 6.1). A survey of the detectors used in analytical isotachophoresis is presented in Table 6.2.
6.2. THERMOMETRIC RECORDING 6.2.1. Introduction
The electric field strength (V/cm) varies from one zone to another and is inversely proportional to the effective mobilities of the ionic species, giving all zones the same speed. If a stabilized electric current is applied, the heat production increases from the front side towards the rear in a well defined way. Consequently, the zone boundaries are characterized by sharp changes in temperature [l, 121. This effect can serve to indicate the positions of the zone boundaries or to characterize the zones themselves if the actual temperature is measured simultaneously. While the zone length provides quantitative informtion, the actual temperature characterizes the ionic species in a particular zone. Hence thermometric recording in an isotachophoretic analysis provides all the qualitative and quantitative information required. 6.2.2. Construction
The temperature of the individual zones can be measured with micro-thermocouples [13, 141 or micro-beat thermistors [15]. Both types of detectors can be mounted around the narrow-bore tube with a suitable adhesive (elastic type). This adhesive, in addition to fixing the detector, also improves the thermal contact of the detector with the narrow-bore tube.
DETECTION SYSTEMS
120 TABLE 6.1
SURVEY OF SPECIFIC PROPERTIES THAT CAN BE RECOGNIZED IN ISOTACHOPHORETIC ANALYS: Type of electrolyte
Initial conditions
Steady state
Conductivity
Conductivity
Leading electrolyte (L.E.)
Determined by the choice of the operational system in which the analysis is carried out.
Determined by the initial choice of the operational system.
Sample zone(s)
Unknown, but generally adjusted to the conditions of the L.E. with respect to pH and the concentration of the ionic species (roughly).
AU zones adjusted to the concen-
Chosen to be of approximately the same order of magnitude as the leading anion (anion separation) or cation (cation separation), to minimize the effect of fast-moving impurities. (pH is adjusted approximately to the pH of the leading electrolyte to prevent sample ions being 'missed'.)
T h e concentration is adjusted to the
Terminating electrolyte (T.E.)
tration of the leading anion (anion separation) or cation (cation separation).
concentration of the leading anion (anion separation) or cation (cation separation).
The conductivity decreases from the L.E. towards the T.E. (except for 'enforced' isotachophoretic systems).
An easy method of making these thin thermocouples is as follows. Copper (30 pm) and constantan (25 pm) wires are twisted symmetrically together, after the ends of each have been fixed in a small piece of shellac placed on a rod [ 1] . The difference in the diameters of the wires is necessary because otherwise, owing to their very different flexibilities, the twisting of the two wires of identical diameter results in an asymmetrically wound thermocouple, the copper wire being wound around the constantan wire. The procedure for mounting a thermocouple that is not symmetrically wound around the narrow-bore tube is very difficult and the thermocouple easily breaks on the copper side, especially if both diameters are 30 pm. Copper wires of 25 pm diameter easily breaks during the twisting procedure, especially if the wires are corroded. The tightly twisted part is cut so that a length of about 1 mm remains twisted. This twisted end is silver soldered by inserting it into molten silver solder, protected with a small amount of flux. This silver solder is kept molten by utilizing the heat capacity of a thick-walled Pyrex glass tube (Fig. 6.1). Other methods of making thin thermocouples are given in ref. 1.
121
THERMOMETRIC RECORDING
Potential gradient
Temperature
PH
Determined by the direct driving current chosen and the conductivity of the L.E.
Determined by the direct driving Determined by the ratio of the concentration of the ionic current and the conductivity species of the leading electroof the L.E. lyte and their pKa values.
Determined by the direct driving current chosen and the concentration of the anion of the L.E. (anion separation) or the cation of the L.E. (cation separation) and the effective mobility of the ionic constituent present.
Determined by the direct driving Determined by the ratio of the current and the concentration concentration of the ionic of the anion of the L.E. (anion species present in each zone separation) or cation of the and their pKa values. L.E. (cation separation).
Determined by the direct driving current chosen and the concentration of the L.E. initially chosen and the effective mobility of the terminating ion.
Determined by the direct driving current and the concentration of the L.E. initially chosen.
Determined by the ratio of the concentration of the ionic species present in this zone and their pKa values.
The potential gradient is a constant for each zone and increases from the L.E. towards the T.E. (except for ‘enforced’ isotachophoretic systems).
The temperature is constant for each zone and increases from the L.E. towards the T.E. (except for ‘enforced’ isotachophoretic systems).
The pH tends to increase in anion separation and to decrease in cation separation from the L.E. towards the T.E.
If this thermocouple is mounted around the narrow-bore tube, a linear stepwise recording of the isotachophoretic zones is obtained as soon as they have passed this fixed thermocouple. In order to make the zone boundaries more pronounced electronically, the differential of this signal can be obtained. An example of a possible circuit is given in Fig.6.2. Another possibility is to make a differential thermocouple with two copper-constantan junctions, about 2 mm apart. This thermocouple can be mounted around the narrow-bore tube in a similar way by means of a suitable elastic adhesive. The two twisted (and silver soldered) ends must be bent until they are approximately at right-angles to the surface of the narrow-bore tube. While the values from the passage of a zone boundary recorded by a normal thermocouple can be expected to be of the order of millivolts, a differential thermocouple indicates the passage of a zone boundary with a signal of the order of microvolts, and amplification is therefore necessary. The differential thermocouple has to be balanced. Normally, there is a difference in temperature between the two junctions of the differential thermocouple, because both
-
TABLE 6.2
N
SURVEY OF THE DETECTORS USED IN ANALYTICAL ISOTACHOPHORESIS Lmin. = minimum detectable zone length; Qmin, = minimum detectable amount of ionic component in gramequivalents; t,, = average time for analysis; I = direct driving current; Scan = possrbdity of scanning. Type
Performance
‘min.(mm)
Qmin.
t,,(min)
Scan
Dependence on 1
General information
Thermal
Thermocouple, 25 fim (Cu-constantan) thermistor (Philips micro-beat)
5
0.5*109
30
No
I=
Qualitative Quantitative General detector
Conductivity (high frequency)
Micro-sensing electrodes not in contact with electrolyte
2
2.100
20
Yes(?)
No
Qualitative Quantitative General detector
Conductivity
Micro-sensingelectrodes in contact with electrolyte
0.05
0.5
*
lo-”
10
No
No
Qualitative Quantitative General detector*
Potential gradient
Micro-sensing electrodes in contact with electrolyte
0.05
0.5
*
lo-’
10
No
I
Qualitative Quantitative General detector
uv
Micro-cell wavelengths: 205,256,280 and 340 nrn
0.05
0.5
lo-”
10
Yes
No
Quantitative Specific detector**
*A coating on the sensing electrodes gives the detector ‘specific’ characteristics.
**The use of strong Wabsorbing counter ions of which the W absorption is a function of the pH changes the specific characteristics of this detector into ‘general’ characteristics.
8i3
2: cn
THERMOMETRIC RECORDING
123
/2
Fig.6.1. Preparation of micro-thermocouplesby silver soldering twisted copper and constantan wires by means of a thick-walled Pyrex glass tube. 1 = Silver solder; 2 = flux.
the contact with the wall of the narrow-bore tube and the heat loss at each junction are different. This difference in temperature will not remain constant, but will be greater or smaller after the passage of a zone boundary. The differential thermocouple can be
Fig.6.2. Electronic circuit for differentiating the stepwise linear signal derived from the thermocouple during the passage of the zone boundaries. All resistances are given in aTunless stated otherwise.
124
'DETECTION SYSTEMS
balanced by cutting a piece from one of the junctions, by setting one of the junctions at a different angle to the wall or by putting extra adhesive on one of the junctions (or alternatively by removing some of the adhesive from the other junction with a suitable solvent). In order to check if the differential thermocouple is well balanced, the electric current is switched on and off, when the signal derived from the differential thermocouple should not vary. However, an effect can still be obtained, even if the differential thermocouple is well balanced, if difference in heat capacity between the two junctions is large. The switching on and off of the electric current may then result in a peak or a dip, the height of which and the time required to reach the balanced position (zero) again may be such that they cannot be considered to be negligible. This may disturb the electrophoretic pattern recorded by the differential thermocouple, especially if large temperature differences need to be recorded. The impression can be given that a zone is preceded by a small zone of lower temperature (enforced isotachophoretic system) or that an extra component (impurity) is present. If the electronic differential is taken, of course, no balancing procedure needs to be carried out. The great advantage of a differential thermocouple, however, is that the direction of movement of the temperature step is recorded. Mistakes can always be made in the interpretation if a zone of high conductivity (e.g.,H'ions that originate from the pH jump at the membrane [16] moving through the narrow-bore tube) migrate in a direction opposite to that of the sample ions. This zone causes a lower temperature, which migrates and is therefore detected by the differential thermocouple as a hot zone coming from the opposite direction. Because the differential thermocouple never has a position on the narrow-bore tube similar to that of the linear thermocouple, which has only a single junction on the wall, the time of recording clearly shows this effect. This effect, however, may cause severe problems, especially because in practice a lower temperature zone may migrate in front of zone of higher temperature in exceptional cases (e.g., enforced isotachophoretic systems). If electronic circuits are used in order to differentiate the signal derived from the linear thermocouple, this problem can be solved if at least two thermocouples are mounted axially on the wall of the narrow-bore tube. The simultaneous recording of these thermocouples indicates both the rate of separation (are mixed zones still present?) and the direction of movement of various zones. Although a thermometric detector is very cheap, its resolving power is, compared with that of other detectors, not very high, although for many applications it is sufficient. This will be shown in later chapters, where some applications are discussed. The fronts, as finally detected by the thermometric detector, lack sharpness with respect to the concentration profiles inside the narrow-bore tube, because the heat generated inside has to pass through the wall*. The longitudinal conduction of heat, both in the liquid and the insulator, spreads the temperature change along the tube. Also, considerable time is required to heat the part immediately behind the front in order to obtain dynamic equilibrium of the temperature step. The wall must not be too thin, however, because the thermocouple and the instrumentation connected to it must be insulated from the high potential inside the narrowbore tube. Even if another precaution is taken, e.g., by using an insulated amplifier, and the thermocouple is mounted closer to the centre of the narrow-bore tube, the final recording is not improved very much (Fig.6.3), because the time required for dynamic equilibrium *See also Appendix B.
THERMOMETRIC RECORDING
T
125
tl
Fig.6.3. Temperature profiles of zone boundaries in isotachophoretic analyses, as derived from micro-thermocouples.In the direction X,the micro-thermocoupleis mounted closer to the centre of the narrow-bore tube. In the initial phase, the transient response of the thermocouple, mounted closer to the centre, is more rapid, but the resolution is not improved much. T = Increasing temperature; t = time.
of the temperature step to be attained is not changed very much; the total mass is not changed or is changed in the wrong direction. Calculations show that the sharpness of the temperature step approaches that of the concentration step if the narrow-bore tube is made of ‘infinite’ thickness [ 171. Alist of data for thermometric detection is given in Tables 11.6 and 12.3. The resolution and stability of thermistors are comparable with those of thermocouples, but thermistors are not discussed further here because more complicated electronic circuits are necessary. Optical means of detection have not been tested so far, because the temperature differences are relatively small and the optics are very expensive, compared with the thermocouples and thermistors [18] . The information derived from liquid crystals [19] painted on the wall of the narrow-bore tube is poor and needs expensive instruments for automatic recording.
6.2.3. Experimental Thermometric detectors lack high resolution because the heat generated by the electric current has to diffuse through the wall of the narrow-bore tube. The various heat transition coefficients influence the final recording of successively migrating narrow zones. As a general rule, the zone length needed for a full qualitative and quantitative recording must be about 5 mm, making use of a PTFE (or Pyrex glass) narrow-bore tube with an outside diameter of 0.7 mm and an inside diameter of 0.45 mm. This value can vary, depending on the heat production of the adjacent zones, the electric current applied, the type of solvent used and some other minor factors (e.g., the addition of surfactants to the electrolytes in order to depress the electroendosmotic flow). In Fig.6.4, some graphs are shown of actual temperature measurements carried out with a thin thermocouple mounted on the outside of a narrow-bore tube.
DETECTION SYSTEMS
126
4'0
30
T
Fig.6.4. Relationship between the temperature inside a narrow-bore tube and the output signal of a thermocouple mounted on the outside of the tube. 1 = Theoretical relationship; 2 = practical relationship, found when water at a known temperature flows through the narrow-bore tube; 2% of the surfactant Mowiol (polyvinyl alcohol) was added to the water; 3 = as 2, with no surfactant; 4 = as 2, with methanol instead of water. The experiments with methanol were difficult to perform because a suction pump was used, and the methanol began to boil.
These temperatures were compared with the actual temperatures inside the narrowbore tube as follows. Water was pumped through the narrow-bore tube until the signal derived from the thermocouple reached a constant value. Simultaneously, the water temperature before entering the narrow-bore tube was measured. The results indicated that in the region of the temperature of the terminating electrolyte (35-45"C), mistakes can be expected in the qualitative recording, especially if surfactants are present. 6.2.4. Resolution
If the concentration of an ionic species in the narrow-bore tube is about 0.01 g-equiv./l and the cross-section is about 1.6 cm2, the minimum amount of that ionic species which can be detected is about g-equiv. If the volume of the sample injected is 3 pl, the minimum concentration in the sample that can be detected is thus 2.7 g-equiv./l [20]. To illustrate the effect of the introduction of samples of different sizes, some isotachophoretic separations are shown in Fig.6.5 of the anions oxalate, formate, acetate, and P-chloropropionate in the operational system at pH 6*. The conditions for this system are listed in Table 12.1. The concentrations of the various anions were: oxalate, 0.005N ; formate, 0.01 N, acetate, 0.01 N, and P-chloropropionate, 0.015 N . The volumes injected were (a) 1 pl, (b) 2 1.11 and (c) 3 p1. The ameunts that can be detected are therefore 5 * 1O+, 1O* , 1O-' and 1.5 10-8 moles for the anions in the order listed for the case when 1 pl was injected. It can be stated that the isotachopherogram in Fig.6.5 for the separation of 1 p1 of sample represents a complete separation of the anions in the mixture.
-
-
*For a more extensive description, see Chapter 10.
THERMOMETRIC RECORDING
127
7 It--
a
I
b
C
Fig.6.5. Isotachopherogram showing the separation of some anionic species in the operational system at pH 6. The signals were derived from thermometric recording of the passage of zone boundaries. T = Increasing temperature; t = time. The injected volumes were (a) 1 pl, (b) 2 p1 and (c) 3 pl. 1 = Chloride (leading ion); 2 = oxalate; 3 = formate; 4 = acetate; 5 = p-chloropropionate; 6 = glutamate (terminating ion).
The steady state during isotachophoretic separation is attained earlier if a smaller amount of ionic material is injected. Thus, although this isotachopherogram simulates an incomplete separation, the steady state has been reached*. From this isotachopherogram, however, only quantitative information can be deduced, so the actual sequence must be known. It should be remembered that for quantitative analyses, only the transition of *This is in contradiction to similar looking records in chromatography.
DETECTION SYSTEMS
128
the zone boundaries is required. The other two isotachopherograms contain both the qualitative and the quantitative information. In Table 6.3 the results of the separation are given. The time interval between two peaks, measured with a stop-watch. is given in seconds. The use of electronic equipment for measuring the time intervals more accurately decreases the detection limit. The detection limit can be decreased further by using a leading electrolyte with a lower concentration, because all other zones will adjust their concentrations in the zones according to the concentration of the leading electrolyte. It must be emphasized, however, that a decrease in the concentration of the leading electrolyte automatically implies that the pH limits between which experiments according to the isotachophoretic principle can be carried out safely are narrower. While at a concentration of the leading electrolyte of lo-* N a pH of about 3.5 is the lower limit and a pH of about 10 is the upper limit, at TABLE 6.3 QUANTITATIVE INFORMATION THAT CAN BE DERIVED FROM A THERMOMETRIC DETECTOR The figures given are zone lengths, expressed in seconds. The quantitative information that can be derived from conductivity and W detectors is discussed in Chapter 10,where the quantitative aspects of the thermometric detector are also discussed in more detail. Compound
Amount injected (nmoles)
Oxalate
Average Formate
Average Acetate
Average 0-Chloropropionate
5
10
15
20
30
20 21 21
43 43 43 43
21
43
64 64 63 64 64 64
20 20 19
39 41 41 40
20
40
62 61 61 61 63 61.5
22 22 21
47 47 47 47
22
47
45
72 72 71 71 72 71.5
37 37 39
71 74 73 73
38
73
111 108 107 108 110
Average
109
THERMOMETRIC RECORDING
129
a concentration of the leading electrolyte of 10-3N these pH limits are narrowed t o 4 and 9, respectively. The upper limit is determined mainly by the interference in the analyses by carbon dioxide from the air. The detection limit can also be decreased by the injection of a larger sample in a suitably constructed sample tap. Some possibilities for this approach are considered in Chapter 7. The sample tap may have a volume of 30 pl, which decreases the minimum detectable concentration by a factor of 10 compared with sample introduction via a microsyringe. An important aspect of the use of a sample tap is that the sample is already separated from the leading and terminating electrolytes and the separation takes place in the tap. On injection with a syringe, the sample is always mixed with the highly mobile chloride or with the terminating electrolyte, which may decreaFe the pH of the sample generally in anion separations and increase it in cation separations. If the average concentration of the ionic species in the sample is low, a sample tap is always recommended, if no sample pre-treatment can be applied. The detection limit can also be decreased by using a regulated counter flow of electrolyte, again because larger sample volumes can be used., in spite of the short length of the narrow-bore tube available for separation. The time of analysis, of course, will increase considerably. Because detectors are available with a higher resolving power than that of a thermometric detector, the detection limit in an isotachophoretic analysis must not be established by using a thermometric detector, and therefore the use of a sample tap and a counter flow of electrolyte in combination with a thermometric detector will not be discussed, It is important, however, to establish the limit of concentration that can be detected with a thermometric detector. For this purpose, analyses with a leading ion concentration of g-equiv./l were carried out. Again the operational system at pH 6 was chosen. The basic information is listed in Table 12.1. The concentration of the hydrochloric acid was decreased to 0.001 N. Because excessive heat production may render the analysis useless and also the driving potential available is limited, the direct driving current was decreased to 7 pA. Fig.6.6 shows the isotachopherogram of the separation of nitrate, chlorate, formate, citrate and adipate. Acetic acid (0.001 N) was used as the terminating electrolyte. A complete separation could easily be obtained, but the disadvantage is shown very clearly. Because at these low concentrations only small temperature differences can be expected, the signals derived from the thermocouples need to be amplified too much. 6.2.5. Conclusion
Thermometric recording acts contrary to the requirement that for a complete reproducible analysis by electrophoretic techniques, optimal thermostating is necessary. If thermometric detection is used, all of the equipment can be optimally thermostated, but at the position where the detector is mounted good thermostating will destroy the temperature differences necessary for measurement. Another disadvantage is that in thermometric detection the direct driving current plays such an important role (I2)and the detection is only proportional to the concentration adjustment (R). This disadvantage is partly overcome by the construction of a good current-stabilized power supply, which can now be obtained commercially.
130
DETECTION SYSTEMS
Fig.6.6. Isotachopherogramof a mixture of anions using the operational system at pH 6. The concentration of the leading anion (acetate) was decreased to 0.001 N,and the direct driving current co:sequently was stabilized at a lower value of 7 PA. A thermometric detector was applied. T = Increasingtemperature; t = time. 1 = Chloride; 2 = nitrate; 3 = chlorate; 4 = formate; 5 = citrate; 6 = adipate; 7 = acetate.
The influence of the direct driving current on both the leading and terminating electrolytes is shown in Fig.6.7. A current of 250 yA increases the temperature inside the narrow-bore tube to 62OC for the leading electrolyte, while the terminating electrolyte attains this temperature if a driving current of 150 yA is applied. Fig.6.7 shows that a current of 100 pA gives a temperature of 26°C for the leading electrolyte and 42OC for the terminating electrolyte. These values are obtained if the narrow-bore tube of PTFE (I.D.0.45 mm, O.D.0.7 mm) is hanging free in air; a cooling device will decrease these values, of course.
6.3. HIGH-FREQUENCY CONDUCTIVITY DETECTION 6.3.1. Introduction In order to give all zones an identical speed, the field strength per zone increases from the leading electrolyte side towards the terminator side. The current density is the same for all zones. Hence the electric resistance increases from the front side towards the rear. This resistance can be measured with a high-frequency detector in which the measuring electrodes are not in direct contact with the electrolyte inside the narrow-bore tube. Polarization of the measuring electrodes, caused by the driving current, is impossible [7]. By this means, undesirable oxidation (or reduction) reactions, which occur on the microsensing electrodes and which may influence both the separation and the detection are prevented.
131
HIGH-FREQUENCY CONDUCTIVITY DETECTION
h
i100
50-
0-
I ,
,
20
1
40
1
I
60
80
T OC
Fig.6.7. Temperature differences expected when isotachophoretic experiments are carried out in narrow-bore tubes hanging free in air. The temperatures were measured in the operational system at pH 6 (Table 12.l),with chloride (0.01 N) as the leading ion (B)and glutamate as the terminating ion (A). The values on the arrows indicate the direct driving current (B for the leading electrolyte and A for the terminating electrolyte). T = Increasing temperature; h(mm) = step height as found in the linear trace of the thermometric detector. The direct driving currents are given in @A.
The high-frequency conductivity detector needs good shielding [21] and zone lengths of 2 mm can be detected. The reproducibility, however, is poor. The development of this type of detector is in the initial phase, so that it would be premature to state that it is possibly the detector of the future for isotachophoresis. 6.3.2. Construction
The conductivity changes that occur during an analysis inside the narrow-bore tube of the isotachophoretic equipment can be measured with the circuitry shown schematically in Fig.6.8. The signal produced by the generator is led via the symmetry transformer TI (coil ratio 1:10) to the emitting electrodes El and E2.Two trimmers, the capacitors C3 and C4, permit exact symmetry of the high-frequency signal on the emitting electrodes to earth.
132
DETECTION SYSTEMS
Fig.6.8. Schematic diagram of the high-frequency conductivity detector. The four electrodes (E, ,E,, E, and E4), which are not in direct contact with the electrolytes inside the narrow-bore tube, are mounted equiplanar. By using screening, the resolution is improved, although a much higher amplification is necessary, which decreases the signal to noise ratio. A = Amplifier; G = generator (cu. 1 MHz).
The emitting electrodes El and E2 are in contact with the receiving electrodes E3 and E4 via the capacity of the narrow-bore tube. The electrodes El,E2,E3 and E4 are mounted equiplanar. In order to prevent a fan-shaped high-frequency signal between the emitting and receiving electrodes, which of course would decrease the resolution, shielding is necessary, as shown in Fig.6.8. The signals picked up by the electrodes E3 and E4 are fed to the second symmetry transformer (coil ratio 1:1) and, after arnplification and rectification, are recorded with a potentiometric recorder. The signals derived from the probe are directly proportional to the effective mobilities of the ionic material at the position of the electrodes E l , E2,E3, E4 and between the shielding. For optimal operation of the conductivity probe, a good symmetry of the emitting electrodes El and E2 to earth is necessary. If this symmetry is not correct, boundary passages of various shapes are recorded, which, of course, do not exist in reality. It was even found that some boundary passages were not recorded at all. Poor symmetry to earth of the receiving electrodes E3 and E4 influences only the final amplification, and does not influence the shape of the recorded transition. In some isotachophoretic analyses using the high-frequency detector, the reproducibility was found to be poor. Particularly when a series of zones needed to be detected, the resolution was far lower than that with a conductivity detector with the micro-sensing
CONDUCTIVITY DETECTION
133
Fig.6.9. Boundary passage of an isotachophoretically moving zone (cNoride/glutamate) recorded with a high-frequency conductivity detector (solid line) and compared with the a.c. method of conductivity determination (broken line), discussed in section 6.4. A small amount of impurity (sulphate) was detected by the a.c. conductivity detector, which was 'missed' by the high-frequency conductivity detector. The analysis was performed in the operational system at pH 6 (Table 12.1). The direct driving current was stabilized at 40 pA. The speed of the recorder paper was 6 cmlmin. R = Increasing electric resistance: t = time.
electrodes in direct contact with the electrolyte. The high-frequency detector, if it is possible to make an operational type, still has advantages, however, especially if aggressive solvents are chosen for electrophoretic analysis. A further small advantage is that the means of detection does not interfere with the electrophoretic separation procedure. There is the possibility of making a scanning detector, although in practice deviations in the resistance of the wall will be greater than the variations in electric conductivity. Although the detector is not yet operational, Fig.6.9 shows the boundary passage of the zone chloride/glutamate, carried out in the operational system listed in Table 12.1. If more ions were introduced, the resolution was found to be greater than that with the thermometric detector, and the reproducibility was found to be smaller.
6.4.CONDUCTIVITY DETECTION 6.4.1. Introduction
In isotachophoretic analyses, the sample ions separate according to their effective
134
DETECTION SYSTEMS
mobilities and form discrete zones with concentrations that are constant with time, homogeneous throughout each zone and directly related to the concentration of the leading ion. If the current is stabilized, all of the velocities of the various zones, in the steady state, are identical and constant with time. The boundary between two successively moving zones is sharpened by the electric field, which increases stepwise, following each zone in which it is a constant, to compensate for the less mobile ions. This stepwise increase in the electric field causes a stepwise increase in the electric resistance according to Ohm’s law. In addition, this stepwise increment is automatically directly proportional to the effective mobilities of the ionic species actually present in each zone. If the operational systems, and hence electrolyte systems in which the isotachophoretic analyses can be carried out properly, are chosen well, the electric resistance of each zone will characterize the ionic species in the zones. These conductivities are not defined by the electric current, supplied by the current-stabilized power supply, if the contribution of the temperature is left out of consideration. This is in contrast to thermometric detection, where the zone characteristics are determined by p . As already discussed in section 6.2, this is a disadvantage of thermometric detection. Special attention should be paid to the fact that even if only a stabilized voltage power supply is available and this source is used in isotachophoretic analyses (the electric current is thus constantly decreasing), the conductivities of the various zones are still identical with those in experiments with a stabilized-current power supply. All of the concentrations of the various zones are determined by the concentration of the leading electrolyte. If a voltage-stabilized power supply is used, the velocities of the various zones, which characterize the amounts present, decrease but all remain identical with each other. Hence the simple relationship between zone length and the amount of an ionic species injected is lost. The conductivity of the various zones can be determined in different ways: (A) with the micro-sensing electrodes not in direct contact with the electrolytes inside the narrowbore tube (see section 6.3), and (B) with the micro-sensing electrodes in direct contact with the electrolytes inside the narrow-bore tube. No further attention will be paid t o the type of detector in class A, because they are classified not as conductivity detectors but as detectors in which the sensing element is not in direct contact with the electrolyte (universal type). The method of detection mentioned under B needs further specification. This class can be subdivided into sub-classes indicating the way in which the detector is constructed: (1) with the micro-sensing electrodes mounted axially, and (2) with the micro-sensing electrodes mounted equiplanar. For the micro-sensing electrodes, of course, various noble metals can be used (Pt- 10-30% Ir was found to be the best). The electrodes can be coated with a suitable polymer or plated with platinum black. The frequency of the measuring current can also be varied, but this does not give a new class of detector. Only two of many possibilities in subclass B will be considered. In one case the driving current itself and in the other case an external current source for the measuring current is applied. These two cases are considered briefly below, and are then considered in more detail in sections 6.4.2-6.4.4.
CONDUCTIVITY DETECTION
135
The d.c. method of resistance determination or the potential gradient detector. This type of measurement of the resistance of the various zones makes use of the potential gradient that characterizes each zone. While in thermometric detection there is a quadratic relationship with the driving current, in this method of detection there is a linear relationship. While in thermometric detection low driving currents could not be applied, because the heat has to pass through the wall of the narrow-bore tube and too small a signal remains for detection, the d.c. method allows low driving currents to be used. The A; if this value increases to A, electrode current for measuring is about reactions (see Fig.6.43) will result. The a.c. method of resistance determination. This type of measurement of the resiss is applied tance makes use of an external measuring current (1-lOpA). T h ~ method especially in sub-class 2 (see above), where the micro-sensing electrodes are mounted equiplanar. Special care must be taken in insulating the low-potential circuit from the high-potential circuit, in order to minimize the leak current. This leak current (as h g h as 10+ A) may disturb the detection because this method of detection is particularly sensitive to all types of coatings formed by the electrode reactions. The d.c. and a.c. methods of resistance determination are discussed in detail in the following sections. Special attention is paid to the various types of electrode reactions and their influence on the recording of the isotachopherograms finally obtained. The construction of the various measuring cells is shown, and the coatings required and the necessary additives to the electrolytes are discussed. These additives need to be added both in order to prevent electrode reactions, which in many instances create unwanted coatings on the micro-sensing electrodes, and in order to reduce the electroendosmotic flow by increasing the viscosity in the vicinity of the wall of the narrow-bore tube. 6.4.2. The d.c. method of resistance determination
The construction of a conductivity cell for use in combination with the narrow-bore PTFE tube is shown schematically in Fig.6.10 [22]. Pieces 1 and 2 are made of brass in order to prevent an unnecessary increase in the temperature of the electrolyte in the detector. These pieces clamp the interrupted narrow-bore PTFE tube liquid tight without the use of adhesive (even if 6 atm pressure is applied) in the central hole drilled through them, the diameter of which is identical with the outside diameter of the narrowbore tube. The narrow-bore tube is first drawn over a certain length and then pulled through the hole until it fits tightly. The narrow-bore tube is cut off after about half an hour in order to compensate for shrinkage of the PTFE material of which it is made. The ends of pieces 1 and 2 are supplied with a piece of Perspex (acrylic) for three reasons: ( 1 ) Perspex is an extremely good material for clamping the PTFE narrow-bore tube; a brass fitting without this piece of Perspex did not clamp the tube satisfactorily. Other plastic materials were less effective. (2) Electric leak currents towards this piece of brass must be avoided. (3) The thin electrodes are finally mounted between these pieces. If n o plastic material
DETECTION SYSTEMS
136 5
4
2
1
3
6
e
-a 0.
I
Pt
....
1
Pt
Fig.6.10. Conductivity probe for use in combination with a narrow-bore tube. 1 , 2 = Pieces for clamping the narrow-bore tube; 3 = brass housing, inside which is a cylinder of Kel-F for insulating pieces 1 and 2; 4 = screw-cap; 5 , 6 = electric connections, A = Pt measuring electrodes, sputtered on a disc of insulating material; B = Pt (or Pt-Ir) foil measuring electrodes, separated by a disc of insulating material.
is present, damage to the micro-sensing electrodes can be expected during clamping. Two types of measuring electrodes were tested, as shown scaled up in A and B in Fig.6.10. A disc of insulating material (0.05 mm) with R sputtered on both sides, and a configuration in which two discs of Pt-Ir, separated by a similar disc of insulating material (0.05 mm), were used. The electric contacts were provided by a small copper pin and a spring mounted in the brass pieces 1 and 2. The pieces 1 and 2 and the measuring electrodes were all aligned by precise boring in the insulating material (Amite) inside the brass housing 3. The brass clamping piece 2, of course, must not make electrical contact with the brass housing, as the clamping piece 1 does, which is why an insulating disc is fixed at the bottom. The whole unit is clamped by the screw-cap 4. The final contact to the transformer, to give a good galvanic separation of the micro-sensing electrodes from the measuring electronics, is made by cables fixed in the rings 5 and 6. In this construction, the inner profile of the narrow-bore tube is n,ot perturbed locally. Conductivity determinations in the various zones during isotachophoretic analysis by the d.c. method can be performed in several different ways: with an insulated d.c. volt meter; with a floating high-voltage power supply (HSP) source; and with an insulated d.c. amplifier. The 272 J amplifier of Analog Devices (Norwood, Mass., U.S.A.) is such an amplifier, although the measuring current is rather high. A possible electronic circuit for measuring the resistance by the d.c. method is shown in Fig.6.11. Because the driving current is used for the determination of the conductivity between
137
CONDUCTIVITY DETECTION
1kR
15~F
Diff 330pF
Hi
4.7 k n
V
Fig.6.11. Electronic circuit for the determination of the conductivity of various zones by the d.c. method (potential gradient measurement). A much better device is shown in Fig.6.14.
the two discs, the resulting potential between them is a direct measure of the resistance, and a correction must be made for variations in the electric driving current. The input impedance of the 272 J amplifier was found to be high enough to prevent the formation of disturbing gas bubbles, but other electrode reactions were not completely suppressed. Because the maximum voltage on the input of the 272 J amplifier is limited, an attenuator (20 and 5 Ma)has to be applied. If a 272 J operational amplifier is used, only those HSP stabilized power supplies which are equipped with a polarity switch for the case when both anions and cations need to be separated can be chosen. One can only select the high voltage side to be as far away from the measuring cell as possible. This decreases the chance of destruction of the operational amplifier, which has a limited voltage (maximal value) of 5 kV. In addition to this advantage, the electrioleak currents via the micro-sensing electrodes will be as small as possible because the electrodes are always at relatively low potentials. As already mentioned, these leak currents may cause a build-up of a layer on the electrodes that may obscure the detection, especially in the a.c. method of resistance determination, which is often applied simultaneously with the d.c. method. In order to measure the small difference in d.c. voltage that will be obtained after a zone boundary on the micro-sensing electrodes, on the output of the 272 J amplifier, a certain voltage has to be subtracted for zero adjustment. Experimentally, we found that the
138
DETECTION SYSTEMS
addition of an external source, in spite of its high stability, gave poor results with respect to the drift. There appears to be no other explanation that no compensation can be made on the input of the 272 J amplifier. The drift obtained if an external source is used for zero adjustment originates mainly from the variations in the current of the currentstabilized power supply. Experimentally, we found that for simple compensation, the driving current itself could be taken, as shown in Fig.6.11. The value of the compensation is chosen such that the resistance halfway between the resistances of the leading and terminating electrolytes is optimally compensated. This method of compensation works better if the relative change in conductivity of the various zones is smaller or if the distance between the micro-sensing electrodes is reduced as much as possible. The signals finally obtained were of such a value that an attenuator had to be applied for recording on a 100-mV recorder. Because the driving current is used for compensation, changes in the electric current have less influence on the detection, as mentioned before. Because the measuring current must be low, if the d.c. method is chosen for resistance determination, the micro-sensing electrodes may be made extremely thin. In order to demonstrate this, experiments were carried out in which electrodes were made by sputtering Pt on both sides of a foil of an insulator (0.05 mm thick). An isotachopherogram is shown later in Fig.6.50. If these thin electrodes are mounted in the conductivity cell, no simultaneous a.c. measurements can be made because this destroys the electrode surface. The disadvantage (a.c. method) of the axial construction of the sensing electrodes is that the measuring current will flow mainly directly along the wall between the sensing electrodes. Wall effects, e.g., electroendosmosis, will influence the detection more than when the measuring current can flow through the centre of the narrow-bore tube. The addition of surface-active substances, which directly influence these wall effects, improved the detection by the a.c. method more than that by the d.c. method, in which much less current has to pass the electrode-electrolyte interface. Nevertheless, surface-active substances need to be added in order to achieve high resolution (as was found to be necessary, too, if W detection was applied). In order to make a comparison of a detector with the sensing electrodes in direct contact with the electrolytes inside the narrow-bore tube with a thermometric detector possible, a thermocouple was mounted around the same narrow-bore tube. The microsensing electrodes and the thermocouple were mounted as close to each other as possible. The result is shown in Fig.6.12. The measured isotachopherogram was compared with a theoretical curve calculated from a rough model of the current distribution. Fig.6.13(2) shows how, in this model, the current used for the detection is distributed over the electrolytes in the neighbourhood of the micro-sensing electrodes. Two cross-sections of the narrow-bore tube are shown; one is perpendicular to the axis (Q), located between the two electrodes, and the other coincides with the axis (P). When the narrow-bore tube is homogeneously filled, the detection current is perpendicular to the cross-section Q. The simplified current pattern is represented by parallel currents through different resistances a and b in Fig.6.13(2). These two resistances are assumed to be proportional to the length of the lines a and b and to the resistivity of the electrolyte. In this model, the passage of a zone boundary can be dealt with by dividing each
CONDUCTIVITY DETECTION
139
Fig.6.12. Comparison of proffles obtained from thermometric recording and detection with a conductivity probe. The dotted curve is the profile of the boundary choride/glutamate determined with the conductivity probe, and the solid curve is the thermometxjc profile. The current was stabilized at 70 MA.The speed of the recorder paper was 6 cm/min in both instances. The analysis was performed in the operational system at pH 6, and the recording was made simultaneously in a PTFE narrow-bore tube (I.D. 0.45 mm, O.D. 0.75 mm). R = Increasing electric resistance; T = increasing temperature; t = time.
resistance in sections with different values of resistance per unit length. On passage of a boundary, this approximation procedure leads to a resistance versus time curve as shown in Fig.6.13(1), curve A. The correspondence with the measured curve B is acceptable, apart from the deviations at the top of the curves. These deviations probably have three causes: (a) the model is highly simplified; (b) in the region directly behind a boundary, both the composition and the temperature of a zone may not be completely homogeneous; and (c) parts of the measuring equipment introduced a certain time delay. The detectox discussed in this section h a s also been applied in experiments where coatings and additives were studied, which are described later in this chapter. The influence of a coating on the micro-sensingelectrodes can be illustrated by comparing results from both the d.c. and a.c. methods of resistance determination during isotachophoretic analyses. A small coating on the micro-sensing electrodes only slightly influences the signal derived from the detector if the d.c. method is applied.
DETECTION SYSTEMS
140
I-,B
;a-
z
-
E
--
--
0
E
Fig.6.13. (1) Comparison of a theoretical model (A) with a practical curve (B) for conductivity determination with the micro-sensing electrodes. (2) Current distribution in the electrolyte near the micro-sensingelectrodes, from which the theoretical model is calculated. R = Zone boundary; re, rb and rc satisfy the equations r i = r:l4 and r;l = ri14.
6.4.3. The d.c.-a.c. converter
Fig.6.14 shows an electronic circuit (d.c.-a.c. converter) that can be used in combination with the conductimeter discussed later (Fig.6.18). The conductimeter was developed for resistance determinations between 50 kS2 and
141
CONDUCTIVITY DETECTION 100 k R
Fig.6.14. The d.c.-a.c. converter.
10 Ma, although between 10 and 50 kR a fairly linear response can be obtained. With the converter, as shown in Fig.6.14, a maximal potential difference of 10 V can be measured between two points, which has a maximal common mode potential of 6 kV with respect to earth. The impedance between the two points, at the input of the circuit shown in Fig.6.14, is greater than 10l2!d and the common mode impedance is greater than 10’’ R. The junction-field effect transistor (FET) is used as a source follower. This junctionFET is supplied by a battery, which eventually can be replaced with an electronic circuit, although it is used here in order to minimize both the leak current towards earth (discussed in section 6.6.4) and the parasitic capacitance towards earth. An advantage is that the supply current of the circuit given is very small (<3 PA). The diode protects the electronic circuit against any incorrect connection of the battery and against a possible high positive input voltage (e.g.,if a gas bubble is present at the micro-sensing electrodes). If V , increases or decreases, the LC circuit in the conductivity measuring circuit is more or less damped. The output signal of V , can be determined via the output signal of the conductivity measuring circuit. With an adjusting potentiometer (100 ka), the circuit shown in Fig.6.14 can be calibrated. The ntc thermistor is fitted in the neighbourhood of the pnp transistor in order to reduce the temperature drift. The calibration can be carried out as follows. First the calibration of the conductimeter must be performed, as described on p.151, where the importance of the controls ‘Zero’ and ‘Range’ are also discussed. Connect the output ‘En’ of the circuit shown in Fig.6.18 with a voltmeter with a range of 100 mV and an accuracy of better than 0.1%. Switch the ‘Range’ control to the 1 M a position and the control ‘Int’ to 2. Reduce the input voltage, Vh, of the d.c.-a.c. converter (Fig.6.14) to zero and adjust the output voltage of ‘En’ with aid of the ‘Zero’ control. Adjust Vh of the d.c.-a.c. converter to 7 V (+0.1%) and adjust the output voltage of ‘En’ to 70 mV with aid of the adjusting potentiometer shown in Fig.6.14. Repeat the last two actions until no further correctionsare required. Eventually on the d.c.-a.c. converter, the position of the control ‘Zero’ can be noted behind the word ‘Offset’. To record the voltage on V,, a recordei with an input impedance of 100 mV can be connected on the output of ‘En’. If we make allowance for the value of the ‘Offset’, noted on the d.c.-a.c. converter, V , is given by
V. A=-.V 2 +Zero-Offset 5 1OV 0.1 V Int
DETECTION SYSTEMS
142
where Yis the voltage on the potential recorder, and Int and Zero are the positions of the controls ‘Int’ and ‘Zero’, respectively. The pA meter indicates 50 pA if V, = 0 V and 100 pA if Vh = 10 V. The accuracy in measuring Vin is better than 50 mV. If the ambient temperature changes from 10 to 35 C, the difference in the measured value of Yb, which of course does not change during this procedure, is less than 20 mV. In Fig.6.15, an isotachopherogram of a test mixture of anions in the operational system at pH 6 (Table 12.1) is given. In the conclusion of this chapter, more attention is paid to this method of detection. It can be seen that Fig.6.15 is comparable with the linearized isotachopherogram obtained with the a.c. conductimetric circuit, shown in Fig.6.18; in fact, we did not find any characteristic differences.
a.c.
d.C.
rO
10
i I
10
6
-
7T/J1 10
8
1
-
Fig.6.15. Isotachopherogram of a test mixture of anions in the operational system at pH 6 (Table 12.1), as derived from the d.c.-a.c. converter in combination with the circuit shown in Fig.6.18. For comparison, an isotachopherogram obtained with the circuit shown in Fig.6.18 is also given. This test mixture was applied in almost all isotachopherograms, for pattern recognition, in order to show the various effects that may occur if insufficient precautions are taken. The leading electrolyte consists of 0.01 N hydrochloric acid (pro analysi grade) and histidine, adjusted to pH 6; 0.05% (w/w) of Mowiol (polyvinylalcohol) was added to the electrolyte. Glutamic acid (0.005 N) was used as the terminating electrolyte, adjusted to pH cn. 6 by addition of Tris. 1 = Chloride; 2 = sulphate; 3 = chlorate; 4 = chromate; 5 = malonate; 6 = pyrazole-3,5-dicarboxylate; 7 = adipate; 8 = acetate; 9 = P-chloropropionate; 10 = glutamate. R = Increasing electric resistance; V = increasing potential gradient; t = time.
CONDUCTIVITY DETECTION
143
6.4.4. The a.c. method of resistance determination In order to measure the conductivity (resistance) of an electrolyte, in which a potential of about 6 kV towards earth is present, good galvanic insulation between the sensing electrodes and the electronic circuit (i.e., the conductimeter) at low potential is necessary. This can be realized by measuring the conductivity with an a.c. current that passes through a transformer with two separated coils, the construction of which will be described in detail. All types of electric leak currents must be prevented; even a leak current via the sensing electrodes of 10-9 A will have a considerable influence on the measurement of the conductivity. This is shown particularly in this chapter, where the coating of electrodes is dealt with. We found that the conductivity of isotachophoretic zones could be determined optimally with a probe in which the micro-sensing electrodes were constructed to be equiplanar. In order to prevent an electric current flowing from one sensing electrode towards the other, if the electrodes are mounted badly so that a potential difference exists between the electrodes by the driving current via the transformer, a capacitor is arranged in series with the transformer. It can be repeated (see section 6.4.1) that in isotachophoretic analyses the sample ions separate according t o their effective mobilities and form discrete zones with concentrations that are constant with time, homogeneous throughout each zone and directly related to the concentration of the leading electrolyte. If the electric current is stabilized, all of the velocities of the zones, in the steady state, are identical and constant with time. The boundary between two successively moving zones is sharpened by the electric field, which increases stepwise, following each zone in w h c h it is a constant, to compensate for the less mobile ions. This stepwise increase in the electric field causes a stepwise increase in the electric resistance according to Ohm’s law. In addition, this stepwise increment is automatically directly proportional to the effective mobilities of the ionic species actually present in each zone. If the operational system is chosen well (e.g., Table 12.1), the electric resistance of each zone is determined by the electric resistance of the leading electrolyte zone. These conductivities are not defined by the electric driving current, assumed temperatures can be neglected. Because the conductivities of the zones are determined, the length of the zones provides the quantitative information.
6.4.5.Conductivity probe with equiplanar-mounted sensing electrodes The construction of the measuring cell is shown in Fig.6.16, which shows also the principle of its construction. In a round piece of transparent insulating material, e.g., Perspex (acrylic), a hole of diameter 0.4 mm is drilled along part of its length (a). A metallic foil (e.g., Pt- 10-30% Ir of thickness 0.01 mm) is glued to this piece of transparent insulating material at the opposite end to that where the 0.4-mm hole has been drilled. Cyanolite@proved to be a good adhesive when Perspex was used as the insulating material. If different transparent material (e.g., TPX) is used, a different procedure has to be followed. A small core of TPX is prepared, which is surrounded with a cylinder of acrylic that fits exactly. The remainder of the procedure can then be followed as for Perspex. With aid of a template (shown in Fig.6.16a), the centre is located with aid of a 0.2-mm drill. Special care has to be taken to ensure that this 0.2-mm hole does not
144
DETECTION SYSTEMS
C
d
Fig.6.16. Conductivity probe with the measuring electrodes mounted equiplanar. All dimensions are given in millimetres. For explanation, see text.
CONDUCTIVITY DETECTION
145
contact the 0.4-mm hole opposite to it, because Cyanolite is applied again in a subsequent step and if it penetrates into the 0.4-mm hole, this hole will be rough. With alancet under a microscope, excess of the Pt- 10-30% Ir foil is cut away such that the profile shown in Fig.6.16b remains. A new piece of insulating material is now glued to the first one with Cyanolite, applying a high pressure for at least 5 min. The pieces are glued well if the entire piece is completely clear again, which can easily be checked by immersing the acrylic in kerosene; if TPX is used, immersion in glycerol is necessary because TPX dissolves in kerosene. If the two pieces are glued satisfactonly (Fig.6.16c), they are placed in alathe and, after turning the piece, the 0.4-mm hole can now be drilled through the entire piece. On both sides, collars are made for mounting the brass pieces with a screw-thread (Fig.6.16d). These pieces are also glued to the Perspex with aid of Cyanolite. Finally, the brass pieces are futed stably with a lock pin, which penetrates the brass cylinder that covers the whole piece (Fig.6.16e). The cables that provide the electrical contact are supplied with extra insulation; generally the PTFE narrowbore tube can be used so as to minimize the chance of contact of the brass housing with the cables. The cables are fixed to the micro-sensing electrodes with a suitable metal paint, which is covered with a small amount of Cyanolite for optimal solidity. The connection with the interrupted narrow-bore tube is made in a simple manner. A piece of Perspex is provided with a hole with an inside diameter equal to the outside diameter of the PTFE narrowbore tube. The narrow-bore tube is first drawn out over a certain distance and is then pulled through the piece of Perspex. After a few minutes, the narrow-bore tube is cut off straight with a lancet. These clamping pieces are pressed in the detector with a clamping screw. To prevent any leakage, on the top of the clamping piece of perspex, where the narrowbore tube is cut, a small O-ring of soft rubber is applied. A film of electrolyte between the clamping piece of Perspex and the Perspex of the detector may cause a leak current to pass through towards the brass detector housing, which may render the analysis useless*. The basic principle of the electronic circuit is shown in Fig.6.17. This conductimeter is the result of the latest research and gives a linear response as a function of the resistance to be measured. Some of the isotachopherograms, however, were obtained with conductimetric equipment in which this linear relationship did not hold. This will be discussed separately because the isotachopherograms obtained by the older electronic measuring circuits differ. Later, the linearities of various conductimeters are compared. If the electric resistance of both coils of the transformer can be neglected and the coupling of both coils is assumed to be unity, the transformer can be considered to be an ideal transformer with a resistance R , and a coil L in parallel (Fig.6.17). The losses in iron and copper are responsible for this resistance R,. If the material of the core is not saturated, then R , can be considered to be a constant. The capacitance C and the coil L together form a resonance circuit with a resonance frequency given by
*According to this principle, also a probe for potential gradient measurements (d.c. method) has been made with the electrodes mounted axially.
DETECTION SYSTEMS
146
Fig.6.17. Electronic circuit suitable for the determination of the conductivity of the various zones by the a.c. method.
or=-
1
m
If the ratio of the number of turns is unity, the impedance of the circuit between the inverting input and output of the operational amplifier of those signals which have a frequency or can be written as
R"R Impedance = R, + R The resistance R is the unknown resistance, for example between the micro-sensing electrodes of the conductivity cell. If vc = V, cos art(v = a.c. voltage, V = d.c. voltage) and we assume that the amplification of the operational amplifier is infinity and d l input currents are zero, we can write v1 = v 2
and
If
RZ =R1 R3 then
R,
(6.4)
CONDUCTIVITY DETECTION
147
We can now write
and (6-9)
or (6.10)
Then (6.1 1)
Thus
(6.12)
R2 R1 We can conclude that vc is a constant if - = - and the amplitude of v u is proportional R3 Rv to R . After rectification and smoothing of vu, the resulting potential is also proportional to R. In order to keep the frequency of vc equal to the resonance frequency a,., a comparator is used, which generates vc. This comparator is controlled by vu, a squarewave voltage; in all of the above equations we have considered only the first harmonic of this square-wave voltage. The higher harmonics are suppressed by the circuitry applied, assuming that R is not too small. These higher harmonics can be neglected in this case. The circuit as finally applied is shown in Fig.6.18. IC2 is the operational amplifier as already discussed in Fig.6.17. lC3 rectifies the voltage v u in a single-phase d.c. mode. The pA meter measures the average value of this rectified signal. By means of IC5,a pre-adjusted voltage can be added to this signal, w h c h is then smoothed and amplified by IC4. The smoothmg capacitcr is chosen such that the maximal time constant involved in the amplification of IC4 is 0.1 sec. The potential recorder used in our laboratory in combination with the conductimeter also has a time constant of ca. 0.1 sec. Both the d.c. voltage and the amplification can be adjusted by two potentiometers (P3 and P4), which are supplied with a set of Multi-dials (Spectro Electronics, Plainview,
120kR
Lin
out Lin
fc,-IC5:
$7
+15V
@4
-15v
1C2-IC5: Dq-Dg:
p A 709 pA741 iN 4148
p1 # P2 :
udjusting potentiometer, 1 0 0 k f i (10 tui’ns)
1q:
P3 : P4 : P5 :
U
m 4 rn
rnetul film I * / . AH resistances :
i/e w
TR:
2 x 1000 turns,
Potcore :
P 36122, 387 or 3H1 ,pe=2030
6 0.1mrn
potentiometer, 100 k n (10 turns) adjusting potentiometer, 10 kSL potentiometer, 50 k h
Fig.6.18. Circuit suitable for the recording of isotachophoretic zones present in consecutive zones inside the narrow-bore tube.
a
CONDUCTIVITY DETECTION
149
N.Y., U.S.A.). The lowest position of both of these dials corresponds with an output voltage of ICs and amplification of IC4 of zero. The circuit with IC1 represents the comparator. The 1-pF capacitor and the 1000-kQ resistor are included so as to ensure that the oscillation of the oscillator formed by ICI , IC2 and IC3 is always guaranteed. The 47-kS2 resistor in series with the 47-pF capacitor prevents undesirable oscillation of ICI during triggering. Th~scircuit for resistance determination was developed for use with micro-sensing electrodes. The volume of the conductivity cell is approximately 16 nl. The output voltage IC1 is attenuated 11 or 110 times, depending on the ‘Range’ switch, if the ‘Range’ switch is in the open position, resistances can be measured between SO kS2 and 1 MQ, while if it is closed, resistances can be measured between 1 and 10 MQ, less accurately than in the open position. The proportions and construction of the transformer are mainly determined by the measuring range chosen. If the inductance of the primary coil is too high, the quality factor of the resonance circuit is too small, which is particularly inconvenient if small resistances have to be measured. The measurement of these resistances are no longer accurate because the square-wave voltage from IC, is fdtered badly. If the inductance of the primary coil is too low, the transformer is already saturated if the resistance between the micro-sensing electrodes is high. Consequently, the voltage over the primary coil is low, if the resistance between the micro-sensing electrodes is low. A high capacitance of the capacitor results in rapid saturation of the primary coil, but a low capacitance makes the influence of parasitic capacitances too great. Of many possibilities, a capacitor of 2.2 nF, a self-induction of the primary coil of about 800 m L and a ratio of number of turns of unity were chosen. The resonance frequency is then CQ. 4000 Hz and the quality factor is about 1, if the resistance to be measured is of the order of 20 kQ. Thls value is acceptable for a sufficiently accurate measurement of the resistance. The quality factor is, moreover, dependent on the quality of the capacitor applied, and a mica capacitor is therefore recommended as the dielectric losses are small. It should be noted that the circuit does not work efficiently with resistances below 1 kQ, as the coupling of the coils can no longer be assumed to be unity. If one measures a resistance that is, for example, a factor A smaller, the number of turns of the secondary the number of turns of the primary coil remains coil must decrease with a factor of unchanged. The core material is P 36/22. 3B7 or 3H1, p, (permeability) = 2030. This potcore is provided with a gap by applying a foil of insulating material between the two parts in order to limit the temperature drift of the inductance. A potcore P 33/22, pe = 220, can also be used; this is already provided with an air gap. The micro-sensing electrodes can have a maximum potential of approximately 6 kV towards earth, otherwise the leak current towards earth is intolerable. In order to attain this value, the secondary coil must be well insulated, eg.,by constructing both the primary and secondary coils in a PTFE housing. A possible construction is shown in Fig.6.19. The extra PTFE ring is mounted around the secondary coil. The wires leaving the PTFE via a small hole made in the PTFE are insulated with an extra PTFE narrow-bore tube. This transformer must be mounted as near as possible to the micro-sensing electrodes so as to diminish losses of electricity towards earth.
t/x;
150
DETECTION SYSTEMS
/
primary coil
30
Fig.6.19. Construction of the transformer for a good galvanic separation of the high potential at the micro-sensing electrodes from the low potential of the conductivity measuring circuit. A good insulation is necessary because a leak current towards earth often causes the formation of a coating that may obscure the recording. All dimensions are given in millimetres.
In our equipment, this transformer, which separates galvanically the sensing electrodes from the circuitry at low potential was mounted on the electrophoretic equipment itself about 3 cm away from the conductivity probe. Even if a well insulated cable is used, a length of about 1 m is enough to influence the recording by the parasitic capacitance resulting from it. This,as already mentioned, results in the formation of a coating deposited on the micro-sensing electrodes, built up by the electrolytes present inside the narrow-bore tube during the analysis. This effect is particularly large if pyridine is used as a buffering counter-ion, but even with moderate buffers such as histidine the effect is far from negligible in the long term. More attention is paid to these undesirable effects in this chapter, where the coating of electrodes is dealt with. Uncontrolled coating of the microsensing electrodes decreases the resolution of the detection of the isotachophoretically moving zones and, in particular, the passage of a zone boundary is recorded more slowly. The detector must be cleaned either with aqua regia while it remains mounted in the electrophoretic equipment or with a suitable metal polish while it is dismounted. For optimal detection, the electrodes, made of Pt or Pt-Ir, must be passivated, which can be
CONDUCTIVITY DETECTION
151
achieved by passing a 5-PA current for 5 min. After the passivation, a new equilibrium must be attained, which takes about 1.5 h. Passivated electrodes were found to be less sensitive for all types of electrode reactions under the conditions used in our electrophoretic equipment. It should be particularly noted that the difference in resistance determined for an arbitrarily chosen electrolyte, after a procedure during which hydrogen or oxygen is evolved on the micro-sensing electrodes, may be as great as the difference in resistance between the leading and terminating electrolytes. If nonpassivated electrodes are applied, automatic passivation can occur during the analysis by the driving current, especially if reactive ions are present, e.g., chromate. It is clear that the qualitative information will be obscure if the micro-sensing electrodes are partially passivated during the recording of an isotachophoretic experiment*. Several noble metals and their alloys were tested, and some electropherograms obtained with these electrode materials can be found in Section 6.6. Experimentally, we found that hard electrode materials were especially suitable for our purpose. The circuitry for the determination of the conductivity by the a.c. method (Fig.6.18) can be tested as follows. Make the offset voltage of IC3, IC4 and lC5 minimal. Connect the output ‘Lin’ with a voltmeter with a measuring range of 100 mV and an accuracy better than 0.1%. Short-circuit the diode D4.Turn the dial ‘Zero’ to its minimum position, the dial ‘Int’ to position 1 and the switch ‘Range’ in the l-Ma position. The adjusting potentiometer ‘Lin’ is arranged in a position such that on the output a value of approximately 90 mV is obtained if the conductivity probe, with no liquid in it, is connected to the secondary coil. The resistance is now defined as ‘infinity’. The capacity of the conductivity probe, which is part of the measuring circuit, is compensated in this way. The short-circuit of the diode D4 must now be removed and a 1-Maresistor connected in parallel with the conductivity probe. The output voltage is adjusted to 100 mV by means of the adjusting potentiometer ‘Gain’. The correct shunt resistance for the pA meter to give it a full-scale deflection is then sought. The potentiometer ‘Zero’ is turned to its maximum position and the output voltage is corrected for zero by means of the adjusting potentiometer ‘Zero adjust’. The circuit is now ready for use in the determination of resistances up to 1 M a . If higher resistances need t o be measured, e.g., if the concentration of the leading electrolyte is decreased to or even N , the following procedure should be followed. Turn the potentiometer ‘Zero’ to its minimum value. Select the range 10 M a and mount a 9-Ma resistor in parallel with the conductivity probe. Adjust the output voltage to 90 mV by means of the adjusting potentiometer ‘Lin’. Replace the 9-MQ resistor with a 1 - M a resistor. Set the ‘Range’ switch in the’ 1-MS2 position and adjust the output voltage t o 100 mV by means of the adjusting potentiometer ‘Gain’. Repeat these last procedures until no further corrections need to be made. For continuous recording of the resistance, the output ‘En’ is connected with a potential recorder with a sensitivity of 100 mV. If the ‘Range’ switch is in the 1-MSZ position, the resistances to be measured can be determined from the equation
--R 1 MC!
-
V -.100mV
0.1 Int
+-Zero 1
*This was found especially when the electrodes were made of Pt instead of Pt-Ir.
(6.13)
152
DETECTION SYSTEMS
where R is the resistance to be measured, Pis the output voltage of ‘En’, and Int and Zero indicate the ratio between the real and the maximum values of the multi-dial unit connected to the potentiometers ‘Int’ and ‘Zero’, respectively. For the determination of resistances higher than the 1 Ma,the ‘Range’ switch is set in the second position. In a similar way, the resistance can be determined from the equation
Fig.6.20. Results from the circyit shown in Fig.6.18 with two measuring ranges: 50 kR-1 M n and 1-10 MR. Between these limits, a linear response as a function of the resistance is obtained. The linearity (a) is compared with that of an electronic measuring circuit (b), which was used amongst others during the study of the effect of additives and coatings on the microsensing electrodes discussed in this chapter. R = Increasing resistance.
U V ABSORPTION METER
R -_-.10MR
V l00mV
0.1 Int
153
+-Zero 1
(6.14)
The potentiometers ‘Zero’ and ‘En’ must be arranged in a position such that during the analysis the output voltage on ‘Lin’ always remains between 0 and 100 mV. An example of the linearity of the circuit shown in Fig.6.18 is given in Fig.6.20, in comparison with that of the older circuits. Most of the isotachopherograms considered in this chapter were obtained with non-linear circuitry, but the data collected for the various operational systems that are given in Chapters 11-17 were obtained with linear circuitry. At a resistance of 1 MR, the accuracy of the resistance determination with linear circuitry is better than 2 kf2, whde at 10 MR the accuracy is better than 30 kR. If the ambient temperature increases by 10°C, the difference in resistance determination at a level of 1 Mi2 is less than 1 k R and at 10 Mi2 it is less than 20 kR. The stepwise trace obtained during an isotachophoretic analysis when the zones pass the conductimeter can easily be interpreted for qualitative and quantitative information, because the steps are sufficiently sharp. This is in contrast with thermometric recording. Two main reasons can be given why a differentiator was constructed. (1) If small zones are present, stacked between the others, these zones can be detected much easier and better with an electronic differentiator. (2) If electronic devices are available and applied for measuring the time interval between two successive peaks, a pulse is needed for the printer. A possible circuit for such a differentiator is given in Fig.6.21. The circuit with IC6 is actually the differentiator. Its amplification can be chosen by the potentiometer ‘Diff. The time constant is 24 msec, which is small enough to differentiate the signal on the output ‘En’. The circuit IC7 and lCs is a double-phase rectifier. A potential recorder with a sensitivity of 100 mV can be applied in combination with t h s differentiator. IC9 forms, together with the two resistors on the non-inverting input, a Schmitt trigger with a very small hysteresis. The 10-pF capacitor ensures that the input signal is equal to the first differential of the output signal of the rectifier. If this value is zero, the Schmitt trigger is triggered. This procedure is shown schematically in Fig.6.22. The printed values of the time intervals between the fast moving (about 1 m/h) zone boundaries increase the accuracy of time recording and hence the quantitative data handling and, moreover, simplifies the latter. The accuracy in time recording is better g-equiv./l, assuming an electric than 10 msec, which represents an accuracy of 5 driving current of 70 /.LAand a concentration of the leading electrolyte of lo-* g-equiv./l.
-
6.5. UV ABSORPTION METER 6.5.1. Introduction Because in the steady state of an isotachophoretic separation all components move in individual zones with identical speeds and only the counter ion is mixed with these components, specific detectors such as the W absorption meter can offer much additional
154
Fig.6.21. Differentiator for the a.c. conductivity detector and the circuit that produces signals suitable for the printing of the various zone transitions needed for the quantitative measurements. T h i s circuit can be used in combination with the circuit given in Fig.6.18.
DETECTION SYSTEMS
UV ABSORPTION METER
155
Fig.6.22. Control of the printer by signals derived from the a x . conductivity detector.
information about the ions of interest. The main disadvantage of these types of detectors is the small cell volume for which specific information can be obtained, because narrowbore tubes are used. The enlargement of this cell volume by measuring the absorption in an axial direction, as is commonly done in equipment for liquid chromatography, is impossible because one expects small zone lengths in isotachophoresis. For this reason, a new type of detector that is not yet commercially available has been developed. Another disadvantage is that some of the non-UV-absorbing ions, especially cations, which are present in the sample can easily be ‘missed’ if they form zones that combine with each other. However, some possibilities will be mentioned for removing this last disadvantage in some specific instances. 6.5.2. Construction of the UV source Microwave mercury electrodeless lamps can be used successfully for the UV absorption meter, because nowadays stable transistors are available that operate at a frequency of 100 MHz with a power of at least 5 W. The lamps can consist of thin-walled quartz tubes with a diameter of about 1 cm. The lamps that we tested had a volume of about 8 ml and were filled with about 5 mg of mercury [23] . A clean gold-plated carrier is used to facilitate the weighing and transportation of the mercury during the preparation of the lamp. The preparation is carried out as follows (Fig.6.23). Some quartz tubes are melted on to a central tube, and the system is then evacuated to a pressure of about torr. Under this vaccum, these tubes are baked at about 1000°C for several hours, while in the side-tube the mercury on its goldplated carrier is kept at the temperature of liquid nitrogen. In order to permit the escape of water and other gases collected during the baking procedure, the liquid nitrogen must be removed temporarily, but the temperature must not be allowed to rise too much. After this procedure, the entire system is filled with dry argon to a pressure of 3 torr. A discharge is then run in the quartz tubes for a few minutes. This discharge is not run
156
DETECTION SYSTEMS
Fig.6.23. Schematic diagram of device for the preparation of the mercury electrodeless microwavepowered lamps. The mercury is easily handled by using a gold-plated carrier.
in the side-tube, where the mercury is kept on its gold-plated carrier, because the temperature will rise too much and the mercury will be released. Also, this tube will not be used as a lamp and substantial losses of the mercury must be prevented. The argon is then pumped off and the liquid nitrogen is removed from the side-tube. Now the entire system, Le., the quartz tubes and the side-tube, is separated from the pump by means of a valve in order to prevent too much of the mercury from being lost during the next step. The mercury is distilled in the quartz tubes, all of which are cooled in turn by gently heating the side-tube. After the distillation has been completed, the liquid nitrogen is placed around the side-tube again. The valve is opened and dry argon is admitted to a pressure of about 2 torr. Again a discharge is run while the argon is pumped off very quickly. If t h s procedure is repeated about three times, all lamps light up brightly. Because each time the pumping time is very short, only a small amount of mercury is lost. Before the lamps are sealed off at the constrictions A, the mercury condensed at the constrictions A and B is redistilled into the lamps with the aid of a burner, while the lamps remain cool at the bottom. The brightness of each lamp is slightly different, however even if stringent precautions are taken during the preparation to make all lamps as reproducible as possible. A circuit suitable for exciting the mercury electrodeless lamp is shown in Fig.6.24. The microwave-powered mercury electrodeless lamp is placed between the plates of the capacitor, clearly shown in Fig.6.25. The lamp itself is fixed in the housing, that surrounds the electronic circuit. For optimal stability, this surrounding must be made of metal. It must not be made too small in order to prevent the jump-over of the highfrequency signal applied. The housing must be earthed. If modulation is not necessary, the resistance R 1 must be increased to 56 Q, and points B and C must be short-circuited. By t h s means, the capacitor C7 and the radio-frequency choke are disconnected. The circuit shown can be modulated 100%via the modulation input 'Mod'. If the voltage on this input is approximately - 15 V, the W source produces the maximum amount of W light. When the electric current through R1 is zero, the UV source is switched off. Because the mercury lamp must ignite each time when the source has been switched
W ABSORPTION METER
157
r
+15V
-15V
2N3553 Ti : D~- D :~ i~ 4 1 4 a 33n,1/4w R1:
u2:
10kh,1/aW
C1,C2’: c3 : C4- G e : c7- c 9 : Lsm : L:
Mod 4.7pF 120 pF 4.7 n F ca. 5 n ~ radio -frequency choke 3
+ 12.5 windings, @ 2mm
Fig.6.24. Electronic circuit suitable for continuous excitation of the mercury electrodeless lamps. L is a coil made of copper wire (2 mm diameter) of 3 12.5 turns; the outside diameter is 15 mm.
+
off, the modulation frequency must not be lower than 100 Hz (safe limit). Sometimes, if no modulation is required, low-pressure lamps are difficult to ignite. This can often be remedied simply by rubbing with a wool cloth. The modulation input ‘Mod’ is connected with the point ‘to Mod’ shown in Fig.6.29. The supply current has an average value of 80 mA, whether or not modulation is chosen. This means that in both instances the average amounts of W light are comparable (Table 6.4). It is very important not to decrease the frequency at which the lamp is excited too much. Tests on mercury lamps operating at a variety of frequencies showed that these lamps become discernibly darkened in a few days when operated at a frequency below 50 MHz. Lamps operated continuously at 80 MHz for a t least 1000 h showed only slight discoloration, which could easily be corrected with the circuitry used. The transistor oscillator circuit needs careful construction. The coil must be fixed stably to the printed circuit plate because vibration may alter the capacitance between the various parts and influence the coupling of the coil and the lamp. The light produced by the lamp would change in intensity and noise would result. The solder points must be made as short as possible and the wires that have to be used must be made as flat as possible, because both solder points and wires may influence substantially the coupling and hence the brightness of the lamp. In order to make a UV source that operates well, it
158
DETECTION SYSTEMS
Mod +15V -15V
Fig.6.25. Mechanical construction of the UV source. The printed circuit plate is surroundedby a metal box to give optimal stabilization of the source and to decrease the influence of the source itself on the final recording by the W detector. For optimal results, all sources must be made as similar as possible. All dimensions are given in millimetres.
is essential t o build the circuit shown in Fig.6.25 so as to conform as precisely as possible to the values given. In order to prevent the electromagnetic field causing a disturbance, for instance by radiation, the circuit is surrounded with a metal box. Even the cables for the power supply and the connection of the modulation input ‘Mod’ towards the modulation output ‘Mod out’ are screened. If lamps are used under different laboratory conditions, the coil
W ABSORPTION METER
159
TABLE 6.4 PROPERTIES OF THE TWO TYPES OF UV SOURCES Type of UV source
Noise voltage (mV)
Microphonic Sensitivity noise (V/N
Modulated Non-modulated
<0.5 <0.1
Yes No
Drift (10-50 C) (mV)
3.10~ o 9 ~ 1 0 ~ <0.5
Influence of external light source No Yes
and the capacitor plates should be gold plated, although in our laboratory we have worked for several years with no gold plating without any problems. It was found that the UV light eventually corrodes the soft solder on the coil and the plates of the capacitor, but this can be prevented by gold plating the metal parts that are directly exposed to UV light. If the temperature of the laboratory is not constant (even the sun shming on the lamp is sufficient) special precautions need to be taken in thermostating the UV lamp. An increase in temperature of 10°C may change the brightness of the lamp by 40%. A piece of metal mounted at the end of the UV lamp serves as a cooling fin and can be thermostated for optimal operation of the UV lamp. When the lamp is in the bright mode, the argon lines are not visible and do not interfere. To summarize, the stability of the W lamp of the microwave-powered electrodeless type is influenced by the temperature of the lamp, the stability of the oscillator and the mechanical stability of the circuit. With a combination of interference filters and coloured glass filters (end fdters), the U V lamp can be used at various wavelengths.
6.5.3.W detector in combination with a non-modulated W source Various detectors have been tested for use in combination with the W source of the type described above. Experimentally, it was found that a Type R330 photodiode (Hamamatsu, Hamamatsu City, Japan) is the most suitable. The circuit of the detector is given in Fig.6.26. The anode current of the R 330 photodiode is proportional t o the amount of light that penetrates into the photodiode if the potential at the anode is sufficiently high (5 V). T2 is an n-channel metal oxide semiconductor (M0S)-FET. One can choose from several types, provided that 70
R,, the value of resistor R,, is selected so that v,< 1 V when the light flux in the photodiode is at a maximum. R,, however, may reach a maximum of 100 G 52. R, and C, can be short-circuited if R , < 10 G52. If the ambient temperature changes from 10 to 50°C, the drift in v u is less than 0.5 mV. The top-top value of the noise is less than 0.1 mV if R , < 100 GQ and is less than 0.04 mV if R , Q 10 GS1. Because of the very high input
160
>
In
c
m
+-@
-+
Fig.6.26. The UV detector to be used in combination With the non-modulated UV source. B is the Type R 330 UV-sensitive photodiode (Hamamatsu).
DETECTION SYSTEMS
161
W ABSORPTION METER
230
240
2%
m z m 280 EC
GO
30
m
330
wovelength (nm)
Fig.6.27. Optical filters used for the UV absorption measurements on the various zones. A combination of an interference filter and an end filter (coloured glass filter) was always used. From this figure, an estimation of the band width can be made for the experiments included in this book.
impedance, the circuit must be surrounded with a metal frame in order to prevent disturbances. Special care must be taken in selecting the 104-Maresistor, which is basically responsible for a bad signal-to-noise ratio and drift. In the PTFE narrow-bore tube (I.D. 0.45 mm, O.D. 0.75 mm), in combination with a slit width of 0.3 mm*, the difference in signal (uv) between dark and light is approximately 100 mV, which is the normal value if a non-absorbing component is inside the narrow-bore tube with water as the solvent and the combination of interference filter and coloured glass filter (end filter) is chosen, as shown in Fig.6.27. This value of 100 mV is chosen arbitrarily and depends mainly on the sensitivity of the potential recorders available. 6.5.4. UV detector in combination with a modulated UV source
In the UV detector, the alternating current, due to the alternating influx of W quanta, in the phototube is changed to an alternating voltage, which is then detected synchronously. *Later experiments learn that with a slit of 0.1 mm and a narrow-bore tube (I.D. 0.2 mm, O.D. 0.4 mm), sharper boundaries could be detected between the various zones.
DETECTION SYSTEMS
162
The modulation frequency must always be chosen to be greater than 100 Hz. A preferable modulation frequency in our laboratory was found to be 125 Hz,at which value the influence of possible electric currents in the phototube with a frequency of 50 Hz (mains frequency) or higher harmonics of t h s frequency is minimal. These electric currents may originate in the 100-Hz modulation in the electric lighting and in disturbances in the mains. The circuit is shown in Fig.6.28. The circuit with IClo is comparable with the part shown in Fig.6.26. The resistor , R may not have a value greater than 1 G!2 because otherwise the band width of the circuit is adversely affected. If this value is not exceeded, a source follower on the input of IClo can be applied. This source follower can be a normal junction-FET, which is less noisy than an MOS-FET. By means of ICll , the alternating voltage on the output of IClo is amplified by a factor of 100. The circuit is operated such that the noise voltage on the output of the synchronous detector is minimal. If the sensitivity is too great, the value of ,R and/or the amplification of ICll can be decreased. The output voltage of IClo should not exceed 1OV.In order to minimize the influence of the UVsource on the W detector, the circuitry is surrounded with a metal frame and all connection cables between them are screened. The output of ICI is connected with the input ‘Dem in’, as shown in Fig.6.29. A synchronous detector is shown, combined with the oscillator that controls both the detector and the W source. The oscillator is a symmetrical emitter coupled with a multivibrator, which controls the transistor T4 such that it is periodically saturated and blocked, The UV source, of which the modulation input ‘Mod’is connected with the collector of T4,is thus periodically switched off. With the l-kn potentiometer, the modulation frequency can be adjusted to 125 Hz.
*
All resistances : l/8 W PA 741 2 N 5245
IClo, IC1, : Tg :
Fig.6.28. UV detector that can be used in combination with the modulated W source. This circuit is applied in combination with the synchronous detector shown in Fig.6.29.
100 mV
to Mod (Fig 6.24)
oscillator AH resistances : 1/8w
U IC12 : IC13 :
metal film 1 % 7796 p A 741
I I
synchronous detector
Tq : T5 :
40361 2 N4124
Tg-Tg:
2N4126
Dg,D10:
1N4148
Fig.6.29. Synchronous detector that handles the signals derived from the electronics of Fig.6.28. The electronic circuit converts the current variations in the R 330 phototube (Hamamatsu) into voltage variations. c
m W
164
DETECTION SYSTEMS
IClz is a double-balanced modulator/demodulator. The input 'Dem in' is connected with the output of the circuit shown in Fig.6.28. The potential difference between the connection points 7 and 8 of the ICll is a square wave that is in phase with the modulation of the W source. Synchronous detection is achieved by multiplying the voltage on the input by this square-wave voltage. If UV light from the UV source penetrates the W-sensitive R 330 phototube on the input, a squarewave voltage also results. On the output of the differential amplifier I&, a d.c. voltage is the result, which is proportional to the amplitude of the square-wave current in the phototube. Alternating voltages on the input with frequencies that are not identical with the modulation frequency or the odd harmonics cause alternating voltages on the output. These voltages are suppressed by the 6.8- and 68-pF capacitors. The time constants that result from these capacitors in the amplification of the differential amplifier are of the x 3,’i same magnitude as that of the potential recorder. The output voltage 1 ~ ~ lo9 where Pis the peak-to-peak value of the square-wave current in the phototube; vu can never exceed 100 mV. The peak-to-peak value of the noise voltage on the output is less than 0.5 mV.
6.5.5.UV cell A schematic diagram of the UV detector cell is given in Fig.6.30. The PTFE narrow-bore tube (1) is not interrupted and is pulled through a slit (3), shown scaled up in order to demonstrate its construction. The slit is made of brass with an axial hole of 0.7 mm so as to enable the narrow-bore tube to pass through. Perpen-
Fig.6.30. Schematic diagram of the W detector. A = direction towards the injection system (terminator compartment). B = direction towards the counter electrode compartment. 1 = PTFE narrow-bore tube; 2 =position free for mounting the conductivity detector; 3 = W slit; 4 = quartz rod (optical quality); 5 = holder for the quartz rod; 6 = microwave-powered mercury electrodeless lamp; 7 = photodiode (R 330, Hamamatsu); 8 = UV detector; 9 = holder for end fiter and interference filter; 10 = construction for assembling 11 and 9; 11 = holder for the quartz rod; 12 = construction for fixing 1, 3, 5 and 11; 13 = construction for mounting 5,14 and a slide; 14 = UV source.
UV ABSORPTION METER
165
dicular to this hole, a hole is drilled of diameter 0.3 mm with a conical shape at the outside on both ends, so that the quartz rod (4) can approach the central hole as close as possible. The diameter of the quartz rods (optical quality) is 3 mm. The distance between the quartz rods and the narrowbore tube must be made as small as possible, otherwise some of the UV light is lost by absorption by oxygen. The quartz rods are fixed by brass holders (5,ll). Before mounting, the outside of the optical quartz rods and the inside of the brass holders must be cleaned carefully with cyclohexane in order to remove all UV-absorbing material. After t h s procedure, the quartz rods must be handled with a pair of clean tweezers in order to prevent dirt from sticking on the surface. An adhesive must not be used to fix the quartz rods in the holders. Any resin on the surface of the rods absorbs large amounts of W light; when the rods were fixed in the holders with Cyanolite, the signal was reduced to 1% of its original value. The two brass holders, with the quartz rods fixed simply with an O-ring, clamp the slit holder (12) by means of a set of O-rings. The flanges fit the central housing (not shown in Fig.6.30) and fixes the slit holder at a pre-determined position. The edges on the ends of the holders of the quartz rods act as an important lock for daylight, together with components 10 and 12. This lock is not as important at the side of the W source because the combined interference filter and end fdter is mounted at the side of the UV detector (8). If this lock is not positioned in front of the photodiode (R 330) at least a noisy signal may be expected and too much daylight may even destroy the phototube. The holder 9 contains the combined interference filter and end filter. In the W source (14), the UV light is generated by the microwave-powered low-pressure mercury electrodeless lamp (6). A slide (13) makes it possible for the narrowbore tube not to be exposed constantly to the UV light, which may damage the PTFE. After a long exposure time, the quality of PTFE coloured by UV light is poor. For optimal stability of the UV lamp, it is preferable to have the lamp constantly in the bright mode. After switching on, it requires at least 1.5 h to attain full optimal stability. The slit holder (12) contains an extra hole that permits the conductivity detector to be mounted near the W detector cell. It has proved to be unimportant if the sequence of either the UV detector and the conductivity detector is altered. Of course, exceptional cases can occur.
6.5.6.Experimental It does not need a long explanation about the way in which the UV detector will produce supplementary information about the isotachophoretic separation, because many ions lack W absorbance and so many successively moving zones that contain ions without any UV absorbance will not be detected. In some instances, minor UV-absorbing components (see Fig.6.15) are present in the electrolytes (the leading electrolyte, the sample and the terminating electrolyte). These impurities can ‘mark’ a zone boundary, because these components are also concentrated in zones, sandwiched between the sample zones. If a mixture of mainly non-UV-absorbing components is available, one can add to the sample an extra amount of UV-absorbing markers in such a concentration that, if these markers cannot be separated from the sample ions and form stable mixed zones, they
166
DETECTION SYSTEMS
do not really contribute to the increase in zone length (quantitative information). These markers must not interfere with the sample ions or electrolytes of the operational system, and they must be present in such concentrations that they can be detected (the zone length is not important) by the W detector, if separated isotachophoretically. In many instances, one can use another approach*, as follows. A concentration always changes at a zone boundary, of the order of 2-20% for the ions to be separated. A change in the concentration of the counter ion is also likely, although this component is selected on the basis of its pK value and determines the pH at which the analysis is performed. If all conditions are fulfilled satisfactorily, the counter ion always remains in its region of dissociation. For this reason, the concentration step for the counter ion is only a few per cent; it may be positive, negative or zero, because it is related to the change in dissociation and pH across the zone boundary. As we are working in the buffer region of the counter ion and therefore the acidic and basic forms of the ion can be compared, we can select this counter ion on the basis of its pK value and its large difference in absorptivity between the acidic and basic forms, especially in the W region of the detector [ 111 . The pH difference across a zone boundary will give rise to an absorbance difference that is sufficiently large to be detectable. This procedure is shown in the isotachopherogram in Fig.6.31.P-Alanine (of the highest commercial grade) and re-crystallized from water-ethanol (1 : 1) was used as the counter ion in (b). Detection was carried out with both a conductivity and a W detector. In (a), creatinine (also of the highest commercial grade) was chosen as the counter ion. Both the leading electrolytes had chloride as the mobile ion (0.01 N) and the pH in both instances was chosen as 4.1. Creatinine is well known for the large difference in the molar absorptivities of the acidic and basic forms. For this reason, the absorption must vary visibly if the pH of a zone varies, even if a non-W-absorbing ion is present, and a ‘stepwise’ function of the W signal is generated. The final signal is not proportional to the effective mobilities, especially if other UVabsorbing ions are present and somewhat obscure. It should be noted that the pH does not always increase from one zone to another in the direction of the terminating zone in anion analyses and does not always decrease in cation analyses. As indicated in the Section Theory, the pH of a zone is a function of various parameters. This method of indirect W detection can, of course, also be applied in operational systems that are suitable for the separation of cations, many of which lack W absorbance. The following are some of the counter ions that have been tested so far that can be used in operational systems: sulphanilic acid, 4.23 > pH > 3 , 2 5 6 nm; fumaric acid, 4.94 > pH >3,256 nm; and ascorbic acid, 4.6> pH>3.6,280 nm. The principle of indirect W detection can also be applied in operational systems in which methanol is used as the solvent. Attention has so far been paid to the separation of cations in methanol because the mobilities of cations in water do not differ so much and separation according t o pK values is difficult because many of the cations have similar pK values in water. This subject is discussed more extensively in the Section Applications and the data can be found in Chapters 11-17. Sulphanilic acid was found to work well in methanolic systems at 256 nm. Sulphanilic *The ‘indirect UV method’.
167
Fig.6.31. Isotachopherograms for the separation of some anions that lack W absorbance. (a) Creatinine, for which the molaf absorptivity of creatinine is function of the pH. Leading electrolyte = HCl(O.01 M , pro analysi grade) t creatinine (purified); pH = 4.5. Terminating electrolyte = morpholinoethanesulphonic acid (MES) (re-crystallized three times). (b) Counter ion for which the change in pH of a zone does not influence the molar absorptivity (p-alanine). Leading electrolyte = HCl (0.01 M,pro analysi grade) t e-aminocaproic acid (purified); pH = 4.5. Terminating electrolyte = MES (re-crystallized three times). Non-W-absorbing ions can thus be detected by the ‘indirect UV method‘. A = Increasing UV absorption; R = increasing electric resistance; t = time. The current was stabilised in both instances at 30pA. The chart paper speed was 2 cm/min. An injection was made of 1 pl of the sample 0.01 Mchlorate t 0.01 Macetate + 0.01 M formate + 0.01 M glutamate. Peaks: 1 = chloride; 2 = chlorate; 3 = formate; 4 = acetate; 5 = glutamate; 6 = MES. In (a) the lower pH of the glutamate zone with respect to the zone preceding it and following it is clearly visible. From this isotachopherogram, the pH can easily be checked as it can be calculated with the computer program discussed in Chapter 4. The difference in the step height as found in the linear conductivity trace, due t o the difference in the counter ion, should be noted. The conductimeter used is discussed elsewhere (Fig.6.18); the measuring electrodes were mounted equiplanar. Various impurities commonly present in the chemicals can be observed in the traces from both the U V and conductivity detectors.
DETECTION SYSTEMS
168
acid has a low electrophoretic mobility in methanol, although it dissolved sufficiently in it. A solution of methanol saturated with sulphanilic acid can be used to indicate the pH differences in the succesive zones in cation separations if acetate is used simultaneously as the electrically conducting counter ion with buffering capacity. As already mentioned, the contribution of sulphanilic acid to the buffering capacity and conductivity is negligible. The W detector can also be used for the determination of trace amounts of Wabsorbing material. An arbitrarily chosen component, salicylic acid, is used because it shows moderate UV absorption. For the determination of trace amounts of, e.g., ATP or ADP, the following method works more satisfactorily because of the higher molar absorptivity of these ions. Suppose the concentration of the salicylic acid is so small that even with the concentration effect of isotachophoresis the zones are too small for complete qualitative and quantitative determinations t o be effected by the W detector o r any detector with equal resolution. One can decrease the concentration of the leading ion, because the subsequent zones will be more dilute than the leading ion and longer zone lengths can be expected. The contribution to the conductivity from the solvent itself will be greater the more dilute are the solutions, because the mobility of, e.g., H’and O H , is great if water is used as the solvent. While at a concentration of the leading ion of 0.01 N a pH of 3 is a critical value, at a concentration of the leading ion of 0.001 N a pH of 4 is critical. The use of a
Y
7
7 3
2
d
I
f
Fig.6.32. Isotachophoretic separation of phosphate, salicylic acid and a mixture of them in an operational system at pH 4.2. HCI (0.01 M pro analysi grade) was taken and p-alanine (re-crystallized) added until the pH reached 4.2; 0.05% of Mowiol was added to this electrolyte. The terminating ion was glutamate. Separations: (a) phosphate; (b) 1:l mixture of phosphate and salicylic acid; (c) salicylic acid. The shift in the step height of the UV traces should be noted. An enrichment of salicylic acid was revealed by the W detector in (b), but not by the conductivity detector. 1 = Chloride; 2 = salicylate; 3 = glutamate; 4 = phosphate. R = Increasing electric resistance;A = increasing UV absorption; t = time.
UV ABSORPTION METER
169
50
Fig.6.33. Plot of step heights (h mm) in the UV traces for the mixed zone (Fig.6.32b) against the concentration ratio of phosphate to salicylate (r). BY this ‘dilution’ technique, the W detector sensitivity is improved for the UV-absorbing ion. For salicylic acid, the sensitivity is improved at least 50-fold.
counter flow of electrolyte is feasible, but longer times of analysis are involved and very pure electrolytes and even more complicated equipment are necessary. Alternatively to these two procedures, a decrease in the concentration of the leading electrolyte and counter flow of electrolyte may be applied for both W-absorbiag and non-UV-absorbing ions. Because salicylic acid shows UV absorption, another approach is possible. An operational system is chosen such that a stable mixed zone can be made of salicylic acid and a non-UV-absorbing acid. At pH 4, phosphate has been found to be satisfactory. In Fig.6.32, the isotachophoretic separation of phosphate, salicylic acid and a mixture of phosphate and salicylic acid is shown. The leading electrolyte was 0.01 N hydrochloric acid (pro analysi grade) plus 0-alanine, re-crystallized from water+thanol (1 :l), adjusted
170
DETECTION SYSTEMS
to pH 4.2. The electric current was stabilised at 70 PA and W detection was carried out at a wavelength of 256 nm. The drop in the height of the UV trace is clearly visible. The trace from the linear conductivity detector does not resolve these two acids in the mixture. The step height in the UV trace for salicylic acid can be plotted against the concentration ratio of phosphate to salicylic acid, as shown in Fig.6.33’. A 50-fold dilution of salicylic acid could easily be determined, which means that the resolution improves by a factor of 50. The step height in the W trace may be influenced by the following factors: the pH of the ‘mixed zone’ may vary as a function of the composition, which may influence the step height if there is a large difference between the acidic and basic forms of the molar absorptivity; and the molar extinction coefficient of the W-absorbing component. It does not need to be explained that a larger improvement in the resolution may be expected if the molar absorptivity increases. Moreover, the use of a En-Log converter will further improve this method. Anticipating on analyses discussed later, Fig.6.34 demonstrates that salicylic acid and phosphate can be separated at another pH, the so-called separation according to pK values. T h e e isotachopherograms are shown, demonstrating the separation of phosphate and salicylic acid (1 :1) at pH values of 3.2,4.0 and 7.0. It can clearly be seen that these two acids can be separated at pH values both below and above 4.0. At a high pH, the influence of carbonate can be seen, because no precautions were taken.
-7
w4
3
2
7L i
l
1
a
I ~
-
2+3
L;@
R
, - 1
-L
I-
Fig.6.34. Isotachopherograms of the separation of phosphate and salicylic acid, demonstrating that the separation is possible at both a ‘high‘ pH (7) and a lower pH (3). Because no precautions were taken during the preparation of the operational system at pH 7, the influence of carbonate can be seen. This aspect is considered further in Chapter 12. (a) Separation at pH 3; (b) separation at pH 4.2: (c) separation at pH 7. Glutamate was used as terminator. 1= Chloride; 2 = phosphate; 3 = salicylate; 4 = glutamate. A = Increasing UV absorption; R = increasing electric resistance; t = time. *The signal-to-noise ratio of the W detector is such that an amplification of at least 1000-fold is possible.
ADDITIVES TO THE ELECTROLYTES
171
6.6. ADDITIVES TO THE ELECTROLYTES 6.6.1. Introduction
As soon as the high-resolution UV detector became avdlable and the results could be compared with those of the conductivity detector, with comparable resolution, the initially non-reproducible results of both the conductivity detector and the UV detector could be studied more intensively. The UV detector mainly does not disturb the isotachophoretic pattern by its presence, except for compounds that may be destroyed by the UV light applied or if the material of whch the narrow-bore tube is constructed is eventually affected by the UV light. The conductivity detector, however, may disturb the electrophoretic pattern as a result of the polarization initiated by the driving current or due to a leak current, or due to excessive heat produced by the measuring current. Because in our systems the last mentioned current is small compared with the driving current, the heat produced by the driving current can be neglected. The aim of making additions to the electrolytes may vary. The addition of surfactants, for instance, not only sharpens the zone boundaries by depressing electroendosmosis, especially visible if the combination of a UV and a conductivity detector can be applied, but also influences the overpotential against electrode reactions on the micro-sensing electrodes of the conductivity detector. Additives can be classified into three categories: additives that affect the electroendosmotic flow; additives that influence various electrode reactions; and additives that show both of these effects. A study was undertaken in order to elucidate these phenomena. Another purpose of the study was to show the difficulties that might arise if the electrophoretic equipment is not well constructed. Many of the problems that were initially present during the development of the conductivity detector have been overcdme, but more useful information can be gained from considering these problems than from presenting the final solution only. 6.6.2. Effect of additives on the electroendosmotic flow
Electroendosmosis is the movement of a liquid with respect to a solid wall as the result of an applied potential gradient. Although it is generally assumed that the electroendosmotic flow can be neglected in a single narrow-bore tube, with high-resolution detectors this is not so. In the beginning of isotachophoresis (displacement electrophoresis), the viscosity of the electrolytes was increased in order to suppress the electroendosmotic flow, to prevent hydrodynamic flow (semipermeable membranes were not used) and to suppress convection. The viscosity was increased by the addition of hydroxyethylcellulose, linear polyacrylamide, arrowroot, agar agar or methylcellulose. These viscous liquids were purified by shaking them with a mixed-bed ion exchanger. One of the disadvantages was that between analyses considerable time was needed for rinsing the narrow-bore tube. In the early days, a precise classification could not be made. Most electrokinetic phenomena have to be explained in terms of the interaction between a flow of liquid in the double layer, but the exact structure of the double layer may generally be left out
172
DETECTION SYSTEMS
of consideration, especially if one is interested only in the suppression of the electroendosmotic flow. In isotachophoretic analyses, the electroendosmotic flow is not constant in all zones, but increases in the direction of the terminating zone. Ths effect increases the turbulence of the liquid in each zone, but it is beyond the scope of this book to go into great detail. Because hydrodynamic flow in the narrow-bore tube is blocked at one side by the semipermeable membrane, a profile as shown in Fig.6.35 may be postulated for both the electroendosmosis and the temperature differences in the various zones. There are still some differences of opinion concerning the boundary conditions for the movement of liquids, especially if this is compared with the movement of the zone boundaries. As in all types of calculation, the potential at the wall is taken determinative for the electroendosmosis. This potential is often called the { (zeta) potential. When an
A
B
Fig.6.35. Profile of a zone boundary in a narrow-bore tube that is blocked at one side by asemipermeable membrane. The arrows indicate the movement of the zone boundary; Xindicates the direction in which the sampk zones move. In both (A) and (B), the parabolic profile due to the difference in temperature between the centre and the wall of the narrow-bore tube is in the same direction as the movement of the zone boundary (-.-.-). A correction must be made for the difference in temperature on both sides of the parabolic profile. In (A), the electroendosmotic flow is chosen to be in the same direction as the movement of the zone boundary, while in (B) this flow is in the opposite direction. The dotted line indicates this electroendosmotic proffle. A correction must also be made for the difference in electroendosmotic flow on both sides of the boundary, because the potential gradients in the two zones are not equal. The final profiie (hypothetical) is indicated in both (A) and (B) by a full line.
173
ADDITIVES TO THE ELECTROLYTES
electric field E is applied, a stationary state is reached after a short period of time. We can divide the forces that are responsible for the electroendosmosis into two main classes: the force exerted by the external fieldE on ihe ions in the double layer, the force being transferred by these ions by liquid friction to the layer as a whole; and the force exerted by the friction on the layer considered by the neighbouring layers, moving with a different velocity. The force due to the difference in electroendosmosis in the consecutive zones is not taken into consideration. In order to gain an impression of the electroendosmotic velocity, vE, the following equation can be given: (6.16) where E is the dielectric constant, { is the potential at the wall, E is the electric field applied and q is the viscosity. The volume of liquid moving by electroendosmosis can be measured for each zone, but the net result is zero, because one side is blocked. If this side was not blocked, this volume transport would be
Q=vEO,
(6.17)
where 0 is the cross-section of the narrow-bore tube. We can eliminate 0 by means of Ohm’s law:
I
OE=-
x
(6.18)
where I is the current through the narrowbore tube and h is the specific conductivity of the liquid. For a rough estimation, the volume transport in a system in which no semipermeable membrane is applied is (6.19) We have not considered the contribution of the surface conductance, because in the systems applied by us they can be neglected. Under normal operating conditions, e.g., if analyses are performed at pH 6 (Table 12.1), an estimation can be made of the values of Q in the leading and terminating zones, the values being about 40 and 80 pl/h, respectively. The final profde of a zone boundary is, of course, influenced by these values. By adding a suitable surfactant, the viscosity in the vicinity of the wall can be increased at least 100-fold, which suppresses the electroendosmotic flow sufficiently. Finally, it should be noted that the time of analysis is not influenced by the electroendosmosis, again because one side is blocked by a semipcrrneable membrane.
114
DETECTION SYSTEMS
6.6.3. Effect of additives on the micro-sensirrg electrodes The physical chemist usually distinguishes between two extreme types of ideal electrodes [27, 281. The first type is the reversible electrode, on which ions from the solution are actually charged and discharged, so that a steady current is possible. The d.c. potential of the electrodes has a well defined value, which depends on the current and the composition of the solution. The second type is the polarized electrode, in which no transformation of ions take place, n o steady current can pass and any current that does pass represents the charging and discharging of a double layer made up of the electrode and the ions very close to its surface. As is well known, the double layer is a structure that acts as a capacitance, the value of which is dependent on the potential across it. This second type of electrode has no well defined d.c. potential. It may vary greatly under apparently identical circumstances and is greatly influenced by trace amounts of substances or impurities, as will be shown. Metallic electrodes are, in fact, always combinations of both types and their impedance as a function of frequency shows the extent to which one or other mechanism dominates their behaviour. For instance, a bright platinum electrode in a fluid that is rich in adsorbable compounds has an impedance that is very nearly proportional to W' , over the frequency range from 1 to 20 kHz, and it is therefore nearly an ideal polarized electrode. For the same electrode in a saline solution, a more complicated behaviour is observed. By the addition of, e.g., Triton X-100 to this saline solution the relationship mentioned above is again obtained. Without the addition of an inhibitor for electrode reactions (redox reactions), the electrode reaction is rapid and the current is limited by diffusion of the reacting ions and the products between the surface of the electrode and the bulk of the solution. The impedance will decrease proportional to w-f. If the electrochemical reaction itself is slow, the impedance will be lower for small w and higher for large w than in the case when diffusion predominates. In practical cases, inhomogeneities in the electrode material will spread out the band of frequencies for which the impedance decreases only slowly with frequency, as the rate of the reaction is strongly dependent on the d.c. potential of the electrode, which varies over the surface. In instances in which insoluble reaction products cover the electrode surface, the multiplicity of diffusion paths may have a similar effect. This is the case with a silversilver chloride electrode in either a saline solution or a saline plus gelatin solution. It has an impedance that decreases approximately proportional to w-t over a wide range of frequencies. The d.c. potential of the electrode can make a considerable difference in the impedance function by changing the rate or even the nature of the reaction carrying current. Therefore, the balance between this potential and diffusion is responsible for the impedance. The real and imaginary components of the impedance of a particular electrode decrease as approximately the same function of w. A fluid-filled micro-electrode can be compared with a low-pass filter that is d.c.-stable. They must be used when signals are large and for which d.c. and low potentials are of interest. The metallic electrode is a high-pass filter, which is d.c. unstable. Its optimum use is when rapidly varying signals are of interest and the amplitude of the signals may be close to the noise level. It should be remembered that the micro-sensing electrodes described in this book are
ADDITIVES TO THE ELECTROLYTES
175
also a combination of both types. Of course, those micro-sensing electrodes are meant which have a direct contact with the electrolyte inside the narrow-bore tube. Owing to the driving current, polarization of the micro-sensing electrodes occurs, Le., these electrodes may act as charge-transfer electrodes. This depends on the potential gradient across the electrodes caused by the driving current and the composition of the electrolyte. In those cases when the driving current itself was used for measuring the conductivity (the so-called d.c. method), difficulties similar to those found by several workers who used metallic electrodes were observed. Partial polarization of the metallic electrode made the recording of the boundaries obscure. In order to study the interaction of the electrolyte. the driving current and the micro-sensing electrodes, electrodes were constructed such that the electrolyte inside the narrow-bore tube remained surrounded by an uninterrupted cylindrical wall (Fig.6.10). In t h s measuring probe, the distribution of the measuring current is much more linear than in other constructions considered, although the measuring current flows mainly along the wall of the narrow-bore tube. This is especially so if the results of current distribution are compared with those for the probe in w h c h the micro-sensing electrodes are mounted equiplanar (Fig.6.16). The capacitance of the measuring cell used was about 3 pF. In the experiments described, the value of R,, varies from approximately 15 kf2 at the beginning to 50 kS2 at the end*. While the driving current is kept constant, the potential varies during the experiment from 4 to 12 kV between the anode and the cathode of the electrophoretic equipment. The polarization of the micro-sensing electrode, which is in direct contact with the electrolyte, due to the driving current is shown schematically in Fig.6.36. Although the platinum has the same potential over all of its surface, it acts as a bipolar electrode with the cathode directed towards the anode compartment of the electrophoretic equipment and the anode towards the opposite side. Depending on the potential gradient and the composition of the electrolyte, the micro-sensing electrodes can be ‘ideally’ polarized or act as a charge-transfer electrode, as discussed above. Normally the electrodes, under the conditions used, fall between the two extremes. The moment at which oxidation and/or reduction starts depends on various factors: the roughness of the electrode surface, the composition of the electrolyte and the configuration and material of the electrodes. Minor effects are the temperature, the pretreatment of the electrode surface, the pressure and the current density. All of these values are determined in our equipment. Data from the literature show that under the conditions used in our equipment, an overpotential of about 70 mV is adequate for thz evolution of hydrogen, while the evolution of oxygen requires at least 700 mV (bright platinum electrodes). In many instances the chloride ion (0.01 N ) is chosen as the mobile ion, but for the evolution of chlorine a higher overpotential is required. For hard electrode material, hgher values for the overpotential can be expected. Of course, difficulties can sometimes be expected if the micro-sensing electrodes are directly in contact with the electrolytes. If, for instance, ions are present that can be oxidized more easily than the proton, e.g., the equilibrium Fe3+=+Fe2+,particularly *If the distance between the measuring electrodes (axially mounted) is decreased, or the microsensing electrodes are very thin, these values increase.
DETECTION SYSTEMS
176
V
f
C
t
I
t
I
I
Fig.6.36. Polarization of the micro-sensing electrode. The potential gradient inside the narrow-bore tube at the position where the microsensing electrode is mounted decreases if these measuring electrodes change from an 'ideal' polarized electrode to a charge-transfer electrode, owing to the neghgible resistance of the platinum electrode. As a result of this effect, the concentration of the electrolyte, again inside the narrow-bore tube at the position where the measuring electrodes are mounted (l),will decrease if the electrode changes its character in order to fulfil the isotachophoretic conditions (2). L = position in the narrow-bore tube; V = increasing potential gradient; c = increasing ionic concentration; Z = centre of the electrode.
obscure results are obtained. Although under normal conditions some hydrogen may be produced at the beginning of the experiment, the evolution stops because the difference in potential between the anodic side of the bipolar sensing electrode and the electrolyte, which is surrounded by this electrode, is insufficiently great to start the evolution of oxygen (provided that no anion is present that can be oxidized more easily than the hydroxyl ion). If a sensing electrode changes, for any reason, into a charge-transfer electrode, the zone length, as actually measured, of the ionic species present in that zone is longer than can normally be expected according to the concentration in the sample. If the micro-sensing electrodes are made of Pt-Ir, Pt, Pd or Au considerable amounts of hydrogen and/or oxygen can be bound in the first two metallic layers of the electrodes. If hydrogen is bound, the impedance of the electrolyte increases, but with oxygen the contact of the electrolyte and the metallic electrode improves, which causes an apparently lower impedance of the same electrolyte. If the overpotential against the formation of oxygen is exceeded, the bipolar electrode always starts to produce both hydrogen and
ADDITIVES TO THE ELECTROLYTES
177
oxygen. The zone boundary, which causes the electrodes to start the production of gas, is mainly recorded with an overshoot (Fig.6.37). Fig.6.37 shows a series of boundary passages. The leading electrolyte consisted of hydrochloric acid (0.01 M), an unbuffered system. The cations themselves were used each time as the terminating ions. The electric current was stabilized at 50 PA. For any ion that is slower than Li' under these conditions, including also the construction of the probe: the evolution of gas is such that it is produced continuously and cuts off the electric current. This happens if, for example, Fe3+ is used as the terminating ion. At the moment the electrodes start to conduct electricity, i.e., when the electrodes change from polarized electrodes to charge-transfer electrodes, the potential gradient over the electrolyte, surrounded by the charge-transfer electrode, decreases immediately. Owing to the electroneutrality principle, the ions in this zone must follow the equally charged ion of the same species in front of it. The only possible way in which the condition can be fulfiled is for the concentration to decrease. The electrodes are slowly coated with a layer of gas, and less of the driving current then passes through the sensing electrodes. The potential gradient adjusts again and so does the concentration. If the potential over the zone considered is not too great, the sensing electrodes change again into polarized electrodes at the moment when the electrode surface is entirely covered with gas. The evolution of gas in this case stops automatically, and the micro-sensing electrodes become protected against the electrode reaction characteristic for this zone. This can be seen in the lithium zone in Fig.6.37. A second effect may result from the micro-sensing electrodes being first covered with more hydrogen. As soon as enough oxygen has been produced, this influence on the electrodes predominates. Electrodes on which oxygen is bound always records the conductivity as a lower value than do electrodes on which hydrogen is bound. Another possible explanation of the overshoot is the following. The more the zone is situated towards the terminating zone, i.e., the smaller the net mobility is, the higher is the temperature and consequently the Joule heat produced by the sum of the direct driving current and the measuring current. The conductivity increases with temperature and so an overshoot may be expected if a boundary passage is measured with a fairly high difference in conductivity with respect to the leading zone, because time is required for warming up the detector. Later experiments showed, however, that this effect is negligible. Later experiments, in the period the conductivity detector has reached its final construction, showed, however, that sometimes an overshoot can still be obtained. Such overshoots were also seen with the W absorption detector if a buffering counter ion was taken, for which the extinction coefficient was a function of pH. The overshoot appeared in those instances when the buffering capacity of the counter ion was not sufficient. Experiments in which no buffer was used showed the effect more clearly. Some overshoots may therefore be ascribed also to the fact that two consecutive moving zones may have a mutual effect on the pH of the zones involved. A lower pH of the first moving zone may decrease the conductivity of the zone following at the front side if the buffer capacity is not sufficient. If n o buffer is used, even the higher pH of the zone moving in the second position may cause a small region of higher conductivity in the zone of lower pH moving ahead of it. Of course all of these effects may (partially) play a role. The change of a polarized electrode to a charge-transfer electrode may also be due to a *The measuring electrode used was rather thick (0.1 mm).
HCI :0.01 M
Li
CS
Mg I
Ca Sr
Ba
K+NH4 Rb
0
Fig.6.37. Step responses of several zones after the leading electrolyte HCl(O.01 M). The electric current was stabilized at 50 p A because rather thick measuring electrodes (0.1 mm) were used. Clearly visible is the decrease in the concentration if a slow terminating ion (Li+)is applied, possibly owing to the change in character of the measuring electrode. The potential gradient over the Li zone was not so great that the analysis was disturbed by the production of too much gas. The overshoot may be also explained by a pH jump, because a non-buffered system is applied (see Chapter 9). If, instead of Li’, Few was chosen, the electric current was cut off.
ADDITIVES TO THE ELECTROLYTES
179
different cause. The potential on the electrodes may be so high that a leak of current to earth results. This leak to earth often causes the micro-sensing electrodes to be coated with a polymer derived from the components of the electrolytes, and this coating is sometimes not easy to remove. Cationic buffers, which mainly bear reactive nitrogen-containing groups, are especially liable to produce these coatings. These coatings are easily recognized by the decay in resolution of the conductivity detector. This effect will be discussed later in section 6.7. If the surface of the bright platinum electrodes is covered with platinum black, the contact with the electrolyte improves but the overpotential against oxidation and reduction is decreased considerably. Hence low current densities must be applied for separation. The adsorption of ions m d uncharged substances can be distinguished in the treatment of isotherms. Accurate measurements need to be carried out, and it appears that, at present, the dependence of capacity-potential curves on the bulk activity of the adsorbate provides the best criterion. The dependence of the standard free energy of adsorption on the electrode potential (or charge) is different for charged and uncharged species. While ionic adsorption (specific) leads to a linear relationship, uncharged particles give a quadratic dependence. The addition of, e.g., Triton X-100 affects the d.c. measurement of the conductivity, of course, more than the a.c. measurement, especially with respect to the electrode reactions that may occur. In order to demonstrate this effect, two isotachopherograms of the separation of oxalic, citric and acetic acids are shown in Fig.6.38. The traces represent the conductivities of successive zones as measured by the a.c. method (curve b) and by the d.c. method (curve a). A mixture of histidine (0.01 M) and lustidine hydrochloride (0.01 M) was used as the leading electrolyte. The terminating electrolyte was glutamic acid (0.01M). The current was stabilized at 40 PA. Because thicker electrodes are used than under normal conditions*, a greater direct driving current would cause the prcduction of gas at the beginning of the experiment. In general, the mobilities of the anions are low in comparison with those (absolute values) of the cations. It can be seen in Fig.6.38 that the potential gradient from the oxalate zone is sufficiently great to start an electrode reaction. Gas may be produced by this electrode reaction and a layer of a ‘histidine polymer’ coating may be deposited on the electrode surface by a combination of both a leak current to earth and the affect of the bipolar electrode. A close look at the two traces shows that the resistance, as measured by the d.c. method, increases in each zone and the conductivity of each zone no longer seems to be constant. The increment is greater in zones that are situated nearer the terminating zone, which can be explained by the higher potentials that exist in these zones. The impedance as measured by the a.c. method is initially not or only slightly influenced. In a long run (30-50 experiments), the resolution of the a s . method of conductivity determination is smaller and effects characteristic of coatings are obtained (see section 6.7). Later experiments showed that a large proportion of the ‘histidine’ coating is rinsed off by simply refilling the narrow-bore tube, contrary to the effect using other buffers such as aniline and pyridine. *In this experiment a thickness of 0.1 mm was used, while the thickness of the electrode material used in other experiments was only 0.01 mm.
DETECTION SYSTEMS
180
R
t
1
t
Fig.6.38. Detection of zone boundaries in isotachophoretic analyses performed by the a.c. method (b) and the d.c. method (a) simultaneously. At the point marked with an asterisk, the micro-sensing electrodes change their behaviour from polarized to charge-transfer electrodes. In this particular instance, gas was produoed. ?he coating of the electrode is more visible in the stepcurves of the d.c. method. The difference in inclination in the trace of the d.c. method in each zone should be noted. 1 = Chloride; 2 = oxalate; 3 = citrate; 4 = acetate; 5 = glutamate.
If stable coatings are obtained for any reason, the electrodes must be cleaned by rinsing with aqua regia for about 10 sec. The effect of the increment in the d.c. trace in Fig.6.38 must be ascribed largely to the evolution of gas. The small layer of gas influences the d.c. method much more than the a.c. method of conductivity determination. 6.6.4. Additives
Components that inhbit electrode reactions are characterized by strong adsorption on the electrode surface. The electrode reactions may be inhibited in two ways: (a) the transport of ions involved in the electrode reactions towards the electrode decreases as a result of an increase in viscosity in the vicinity of these electrodes; (b) the inhibitor, as it is adsorbed, inhibits the reaction by its presence. In general, adsorption on the electrode surface is caused by the interaction of free-electron pairs (e.g., in oxygen, nitrogen and sulphur compounds) or by n-electrons (e.g., in aromatic compounds). Again, two groups can be distinguished; (1) surface-active compounds, including detergents; (2) organic nitrogen or sulphur compounds, commonly used as corrosion inhibitors.
181
ADDITIVES TO THE ELECTROLYTES TABLE 6.5 SURFACE-ACTIVE COMPOUNDS USED IN ISOTACHOPHORETIC ANALYSES Compound Commercial source Structure Triton X-100
(C, H, 0)9- monoisooctylphenol
Ethomene T/20
(C, H, O), -talc amine
Priminox 32 Serdox ZCA-10
(C, H, 01, -tertiary amine (chain length unknown) (C, H, O),,, -C,,-,, amine
Serdox NJADZO Nonic 21 8 Mowi018-88
(C,H, 01, -C,,-,, amine (C, H,O),-,,-tert-dodecylmercaptan (-CH, -CH-), (polyvinyl alcohol)
I
Rohm & Haas, Philadelphia, Pa., U.S.A. Armour Industrial Chem. Co., Chicago, Ill., U.S.A. Rohm & Haas Servo, Delden, The Netherlands Servo Pennsalt Chem. Corp., Philadelphia, Pa., U.S.A. Hoechst, Frankfurt, G.F.R.
OH
u-
\ (polyvinylpyrrolidone)
PVP
-CHPEG 200
CH,
Fluka, Buchs, Switzerland
-
(-CH, -CH, -O-),, (polyethylene oxide, molecular weight 200)
E. Merck, Darmstadt, G.F.R.
Because the additives are to be used in electrophoretic analyses, compounds must be selected that do not take part in the electrophoretic transport (non-ionogenic compounds). Exceptions are those compounds which both inhibit the electrode reaction and can be applied as the buffering counter ions, e.g. pyridine and related compounds. The surfaceactive components studied were not only detergents, but also some soluble polymers. Detergents consist of a polar and an apolar part. The non-ionic part consisted mainly of 8-20 units of ethylene oxide, condensed with units of 8-20 carbon atoms, with or without functional groups. The polar part can be formed by alkylphenols, alkyl alcohols, alkylamines, alkylmercaptans or alkanes. Some possibilities are shown in Table 6.5. Of these additives, Triton X-100 and Mowiol 8-88 are especially useful. All of these compounds were purified on a mixed-bed ion exchanger. The nitrogen and sulphur compounds were expected to be particularly useful, because they tend to show surfaceactive activity* and are used commercially as corrosion inhibitors. However, these compounds adversely affect the analysis, possibly because they take part in the electrophoretic transport. These additives could not inhibit the interaction between the microsensing electrodes and active components present in the electrolytes such as chromate or malonate. In order to give an impression of the effect of the addition of the different additives on the recording and/or separation of the various ions, a test mixture was prepared as *It should be borne in mind that not only the electrode reactions need to be suppressed, but also the electroendosmosis.
182
DETECTION SYSTEMS
described in the legend to Fig.6.15 and all of the separations were carried out in the operational system at pH 6 (operational system prepared with histidine, see Table 12.1). The amount of additive differs enormously from compound t o compound, and the optimal amounts were therefore established in separate series of experiments. The electric direct driving current was stabilized at 80 PA. In Fig.6.39 and later in this chapter, unless otherwise stated, the isotachopherograms were unfortunately obtained from an a.c. measuring circuit that was not as good as those now available; the linearity is shown in Fig.6.20. The a.c. measuring circuit was poor not only with respect to linearity, but also with respect to the insulation towards earth and the RC time. The measuring probe was constructed of 0.05-mm platinum foil (nowadays Pt-Ir of 0.01 mm thickness is used). Later experiments showed that the typical reaction during the passage of chromate and malonate, components of the test mixture, could be suppressed by addition of 0.05% of Mowiol8-88 (polyvinyl alcohol). In order to check separately the influence of additives on electrode processes, currentvoltage characteristics were obtained. The equipment used is shown in Fig.6.40. An improvement in the detection was found when either an a.c. or d.c. method was used for the determination of the conductivity, although clearly a difference in behaviour between these two modes was observed. In order to accentuate this difference, gold was used as the electrode material, because it is known that it can easily be passivated and the influence of possible electrode reactions is greater. Unusual effects were obtained when gold was used. In order to give an impression of the recording of isotachopherograms with a conductivity detector with the sensing electrodes made of gold, the test mixture of anions (Fig.6.1 5), in the operational system with histidine hydrochloride as the leading electrolyte at pH 6 (Table 12.1), was again examined (Fig.6.41). The isotachopherogams in Figs.6.39 and 6.41 show that additives need to be used. In the experiments shown in Fig.6.41, the direct driving current was stabilized at 80 PA: It should be noted that in the trace shown in Fig.6.41 (l), where the impression is given that the conductivity of the zones decreases towards the terminator zone, this isotachopherogram was obtained by using the ax. method of conductivity determination. The simultaneous detection of the conductivity with aid of the d.c. method, as in Fig.6.41(2), shows the normal isotachophoretic tendency, viz., a stepwise increase in the resistance. This difference must be ascribed to the dominating influence on the capacity of a passivated oxide layer of the gold surface of the micro-sensing electrodes. These effects are discussed in more detail in section 6.7. Many other coatings were also tested with these gold electrodes because they easily adhered to gold. Sometimes the coatings were formed automatically by the driving current during the electrophoretic process. Some other unusual effects occurred when surface-active compounds were added. For instance, the amount of a surface-active agent added does not influence the analyses substantially; The concentration of many of them can be varied from 2 t o 0.5% without any recognizable difference in the recording of the zone boundaries. Of course, the material added to the electrolytes must not contain ionic impurities. Another phenomenon that occurs is the ‘memory’ effect. When an analysis was carried out with Nonic 2 18 and the narrow-bore tube was then rinsed carefully, subsequent experiments without the addition of Nonic 218 gave a low resolution. However, when experiments with Mowiol
ADDITIVES TO THE ELECTROLYTES
183
Fig.6.39. Influence of additives on the final recording of the isotachophoretic separation of a test mixture of anions (see Fig.6.15), carried out in the operational system at pH 6 (Table 12.1). 1 = 0.05% Ethomene T/20; 2 = 0.05% Serdox ZCA-10; 3 = 0.05% Serdox NJAD-20; 4 = 0.05% Priminox 32; 5 = 0.05% Triton X-100; 6 = 0.1% polyvinylpyrrolidone; 7 = 0.05% Nonic 218; 8 = 0.1% Mowiol (polyvinyi alcohol). The isotachopherogam shown in the centre represents the analysis of the test mixture of anions after the narrow-bore tube and the detector had been rinsed well with doubledistilled water after a series of experiments carried out with Mowiol, to show the ‘memory effect’ with this surfactant. The resolution disappears again when about ten experiments have been carried out.
were performed, many subsequent analyses could be made without the addition of Mowiol, as Mowiol is difficult to remove. It can therefore be concluded that the adsorption of surface-active components is really important. Other workers have also reported
184
DETECTION SYSTEMS
Fig.6.40. Equipment used to characterize the influence of additives and coatings on the micro-sensing electrode via current-voltage curves. It includes a platinum double electrode, a calomel electrode (S.C.E.) together with a Luggia capillary filled with agar agar (3%)and potassium chloride (30%) and a counter electrode in a separate compartment filled with 0.1 Mpotassium chloride solution, provided with a ceramic filter. AU experiments were carried out in 0.1 Mpotassium chloride solution.
that polyvinyl alcohol (Mowiol) shows little desorption if adsorbed. From our experiments so far, Mowiol proved to be superior to the other additives, even Triton X-100,especially if the effect is studied in long runs. Triton X-100 shows a type of saturation effect after some time, which results in a poor resolution. Some corrosion inhibitors were also tested in two groups of experiments: (1) small amounts were added to the leading electrolyte, e.g., thiourea and benzothiazole; (2) compounds were used as the buffering counter ions, e.g., pyridine and 0-picoline. These compounds also sharpened the pattern, but were not better than Mowiol. When gold electrodes were used, coatings were formed during the analysis that were recognizable in the electrophoretic recording because coated electrodes become sensitive to doubly charged ions (Fig.6.47). As usual, the d.c. method, applied as before, gave a slightly different behaviour. When gold was used as the electrode material, a layer was formed more easily, possibly containing the sulphur component, as it is known that thiourea can easily form such layers. In the experiments in which pyridine and /3-picoline were used as the buffering counter
ADDITIVES TO THE ELECTROLYTES
185
Fig.6.41. Isotachopherograms of the test mixture of anions (Fig.6.15) obtained in the operational system at pH 6 (Table 12.1). The isotachopherograms were derived from a conductimeter (a.c. method) with the micro-sensing electrodes made of gold. 1 = k c . recording with passivated electrodes; 2 = simultaneous detection by the d.c. method; 3 = a.c. recording when no addition of surfactants was made to the leading electrolyte; 4 = a.c. recording with the addition of 0.05% of Nonic 218; 5 = resolution of the a.c. recording increases if experiments lasting several hours were carried out with the addition of 0.05%of Nonic 218; 6 = a s . recording with the addition of 0.1% of Mowiol (polyvinyl alcohol).
186
DETECTION SYSTEMS
ions, the pH of the leading electrolyte was about 6, containing 0.01Nhydrochloric acid (pro analysi grade). The pKa values for pyridine and P-picoline are 5.25 and 5.69, respectively. Analyses of the test mixture of anions (Fig.6.15) were carried out and sharp zones were observed. Unfortunately, W detection cannot be used, because the W absorption of these counter ions is strong between 250 and 300 nm. It must be remembered that the effective mobilities of pyridine and 0-picoline are greater than that of hstidine. This results in the need for longer narrow-bore tubes for the separation of similar mixtures, because mixed zones are formed much more easily as components with a higher effective mobility transport a higher proportion of the electricity. Nevertheless, here also the disturbance in the detection of the chromate zone (electrode reaction) was found to be a function of the driving current, which illustrates further that an electrode reaction indeed occurs, as shown in Fig.6.42 (1-3). The electrode reaction is shown to be a part of the profile finally recorded if chromate is used as the terminating ion. The reaction time for the electrode is therefore of the order of seconds. All analyses, carried out with the 0.05-mm platinum electrodes and the coil, for galvanic separation of the high potential of the micro-sensing electrodes and the low potential of the conductivity-measuring electronics, which are not well insulated, show this typical reaction, but at low pH (e.g., 4) it is less pronounced. If the chromate zone has passed the measuring electrodes, these electrodes are (partially) passivated. All other zones following the chromate zone are measured correctly if the chromate zone instead of the leading electrolyte is taken as a reference. Thus a shift is obtained: all zones before chromate (of the test mixture of anions) are of correct height and all zones after chromate are of correct height. An extra impedance, reversible and stable, arises during the analysis, but if the narrow-bore tube is rinsed after the experiment has been completed, this impedance ‘disappears’ again. If malonic acid is injected as a sample or is used as the terminating ion, while n o chromate zone is created before the malonate, a similar behaviour to that found with the chromate is found, as shown in Fig.6.42 (4 and 5). If both chromate and malonate are present, and the chromate zone may be very small, the typical behaviour of the electrodes can be recognized only during the passage of the chromate zone, as shown in Fig.6.42(6). If we look more closely at the isotachopherograms in Fig.6.42, in which chromate and malonate are used as terminating ions, a typical shape can be seen in both traces. Even sulphate, when used as a terminating ion, shows this behaviour if the recording of the sulphate step is scaled up. The shape has three different and clearly distinguishable parts: an overshoot, a slow decrease and an increase towards a constant value. The following explanation can be put forward. The anionic constituent present in a zone, at the concentration and pH determined by the operating conditions chosen, may be the cause of a change in behaviour from a polarized micro-sensing electrode partially to a charge-transfer electrode, (during the passivation of the electrode by the chromate ion). This always causes an overshoot, because the concentration must decrease if a current is applied to give an electrode reaction in addition to the electrophoretic transport, in order to fulfil the isotachophoretic condition and the mass balance of the buffer. Especially if oxygen is generated, for instance as a result of the electrode reaction (which means passivation of the electrode), the gas diffuses into the metallic structure. We found that passivated electrodes record the conductivity of a particular electrolyte with an apparently
187
ADDITIVES TO THE ELECTROLYTES
R
L 1
2
3
4
5
6
Fig.6.42. The a.c. recording of isotachophoretic zones of chromate and malonate. In spite of the addition of Mowiol (O.l%), electrode reactions of these types could not be prevented. In later experiments, in which the thickness of the micro-sensing electrodes was reduced, and in which Pt-Ir has been used, these electrode reactions disappeared. In traces 1-3, the electrode reaction caused by the chromate ion is shown. The final step height of the glutamate (terminator) is not constant, but depends on the amount of chromate injected into the system. In trace 3, chromate itself was taken as the terminating ion. Similar behaviour was found with malonate (4 and 5 ) . When both chromate and malonate were present ( 6 ) , the typical effect was only found during the passage of the chromate ion. R = Increasing electric resistance; t = time.
lower impedance than non-passivated or even activated electrodes. The full explanation of the trace can be given as follows. Owing to the change in behaviour of the electrode, the isotachophoretic zone is recorded with an overshoot; owing t o passivation, the conductivity of the zone is recorded with an apparently higher value (simultaneously the electrode reaction stops, which means that the real conductivity of the zone between the micro-sensing electrodes increases); the oxygen is adsorbed more strongly to the electrode surface and a new equilibrium is established, which is why the trace shows a different inclination. This inclination is not observed if hydrogen can be produced as a result of an electrode reaction (activation of the measuring electrodes). During an isotachophoretic separation and recording by means of the a.c. method, these effects are often difficult to observe, because the zone length is often too small. In
DETECTION SYSTEMS
188
order to prove that electrode reactions of all types influence the recording of the conductivity, a leak current (lo4 A) was created artificially. The leak current is small compared with the direct driving current (lo4 A). The result is shown in Fig.6.43. Again the test mixture of anions (Fig.6.15) was separated in the operational system at pH 6 (Table 12. I). This isotachopherogram shows the separation as recorded if a leak current towards earth is permitted. The isotachopherogram was obtained with the linearized a.c. conductimeter as described in this chapter. The W detector was mounted after the conductimeter in this instance in order to check if the concentrations of the zones had really changed or not. Fig.6.43 shows that good construction and insulation of the conductimeter probe are necessary. That the material of which the equipment is made plays an important role in the resolution of the detector proves the following. When experiments were carried out in
I"
Fig.6.43. Isotachopherograms of the test mixture of anions (Fig.6.15) in the operational system at pH 6 (Table 12.1). This figure shows the disturbance of conductimetric detection (a.c. method) if leak currents towards earth are not prevented. The UV trace is given for comparison of the resolution. In the experiment shown,a leak current towards earth of 10- A was created artificially. The isotachopherogram is difficult to interpret, although from later experiments we know that, owing to the leak current towards earth, a coating is deposited on the micro-sensing electrodes (the electrodes are sensitive to the presence of doubly charged ions). R = Increasing electric resistance; A = increasing UV absorbance; t = time.
ADDITIVES TO THE ELECTROLYTES
189
narrow-bore tubes made of PTFE in combination with a conductivity detector made of Perspex, sharp isotachopherograms were obtained only when a surfactant was added (Fig.6.44). When the UV detector was used it was also found that an additive is necessary, as can be seen in Fig.6.44. When the conductivity detector was made of TPX, the additives showed much less influence on the detection with the conductivity detector. Now, the wetting capacity of
Fig.6.44. Resolution in the absence (below) and presence (above) of surfactants. When no surfactants were added to the electrolytes, the conductimetric detection had poor resolution. This fgure also shows that additives need to be added when a UV detector is used. This proves that the electroendosmotic profite is reduced by the addition of a surfactant, which increases the viscosity in the vicinity of the wall. Sample: test mixture (Fig.6.15).
190
DETECTION SYSTEMS
TPX was found to be very poor, even if surfactants in high concentrations were applied. Experiments in which the TPX was 'coated' with a small layer of silicone oil showed improved resolution, which means that the TPX itself makes a large contribution to the electroendosmotic flow, which is difficult to suppress. TPX also show a poorer performance in methanol compared with Perspex, although TPX must be used because Perspex is affected in a long run. No additives have so far been found that can be added to methanolic electrolytes to give improved resolution. The inhibition by the surfactants of electrode reactions, if the thickness of the electrodes is too great or the insulation towards earth is not sufficiently suppressed, is poor. Therefore, additives still need to be added for this purpose, or the electrode reactions must be prevented in another way: low current densities and thin electrodes of hard material (Pt-Ir). A disadvantage of most of the additives that are suitable for this purpose is that most of them show U V absorption, which can be neglected if they need to be added only in trace amounts, but they cannot be used as counter ions. No observable difference in the current-voltage curve could be found if trace amounts of surfactants were applied (even high concentrations gave a smaller effect than expected, as shown in Fig.6.45. This aspect, however, will be discussed in more detail in section 6.7.
Fig.6.45. Current-voltage curve measured with the equipment shown in Fig.6.40. (a) Bright platinum electrodes with the addition of 2%of Mowiol (polyvinyl alcohol). (b) Bright platinum electrodes with no addition of surfactant. The curves were measured in a 0.1 Mpotassium chloride solution. They show that the surfactant must reduce the electroendosmotic profile (compare the results shown in Fig.6.44); the effect on the electrode reactions is small.
COATING OF THE MICRO-SENSING ELECTRODES
191
6.7. COATING OF THE MICRO-SENSING ELECTRODES 6.7.1. Introduction
The second means of preventing electrode processes is to apply a polymer coating to the micro-sensing electrodes. The main problem is to find a method of coating that gives a uniform layer. Two different methods were tested: (1) the electrophoretic coating process and (2) the electrolytic coating process. In the electrophoretic process for preparing coatings of polystyrene, acrylic and epoxy resins, both water and methanol were used as solvents. The platinum metal is probably not suitable for these coatings, and it is known that the metal plays a very important role in the coating process. In the electrolytic process, the electrode metal is less important, and therefore only electrolytic coatings are considered below.
6.7.2. Experimental The anodic polymerization of aromatic amines was particularly successful. The more aromatic rings present in the compound, provided that a sufficient amount could be dissolved, the more stable the coatings were found to be. 1-Aminonaphthalene dissolved in ethanol (saturated solution at room temperature) was employed in several experiments. A few drops of this solution were added to 10 ml of 1M potassium chloride solution and water was then added to give a total volume of 100 ml. The solution was filtered in order to remove undissolved 1-aminonaphthalene. The filtrate was approximately 0.01 M i n the aromatic amine. During anodic oxidation at 700 mV, a violet-coloured layer was formed. The electric current was maintained at 0.1 mA for 5 min and an increase in the electrode potential up to 2000 mV was obtained; the cell constant increased from 0.68 to 2.5 cm-' . The layer formed was cathodically very stable; even after drying and heating (lOO°C), the quality of the electrode improved. While the results with the coating of 1-aminonaphthalene were satisfactory, the results with 1-aminoanthracene were even better. The colour of the coating layer was yellow, and the cell constant increased from 0.68 to 3.5 cm-'. For these electrodes, current-voltage curves were obtained in order to characterize this quality. However, as it is difficult to estimate the thickness of the layers, experiments in the isotachophoretic equipment were still carried out. A conductivity measuring probe was used in which the micro-sensing electrodes were mounted axially as shown in Fig.6.12. In order to discriminate between electrodes, only a selection of thin and thick coatings was examined, depending mainly on the electric current applied during the coating procedure. The isotachopherograms obtained with the a.c. method of conductivity determination were unusual for the separation of both anions and cations. In order to demonstrate the difference between the a.c. and d.c. methods, the influence of different coatings and the influence of changing the frequency of the measuring current and the
192
DETECTION SYSTEMS
Fig.6.46. Effect of a coating deposited on the micro-sensing electrodes on the final recording of the isotachophoretic separation of the test mixture of anions (Fig.6.15) in the operational system at pH 6 (Table 12.1). 1 = A.c. method (4 kHz) with a phenol coating; 2 = a.c. method (4 kHz) with a coating formed by ‘Kolbe electrolysis’ 3 = a.c. method (4 kHz) with a thin coating of 1-aminoanthracene; 4 = a.c. method (1 kHz) with a thick coating of 1-aminoanthracene; 5 = a.c. method (4 kHz) with a thick coating of 1-aminoanthracene. In the analysis shown in 5 , the same coating as in 4 was used but the frequency of the measuring current was altered. Traces 6 and 7 are simultaneously recorded isotachopherograms obtained by the d.c. method, corresponding to traces 5 and 1, respectively. No surfactants were added to the electrolytes.
DETECTION LIMITS
193
electric driving current, a series of experiments was performed with the test mixture of anions as described in Fig.6.15. Also in this series of experiments, a non-linear a.c. conductimeter was used. The operational system at pH 6 (Table 12.1) was chosen and the direct driving current was stabilized at 80 PA, unless mentioned otherwise in the figure captions. In Fig.6.46, a series of isotachopherograms are shown, which indicate that the a x . method gives unusual results for the test mixture of anions before the coating. The sensitivity (selectivity) of the combination of the a.c. method with coated electrodes for the doubly charged sulphate ion was such that the following zone of chlorate was measured with a negative step, which suggests that this zone has a higher conductivity than the preceding zone. This is in contradiction to the isotachophoretic principle, if these ions are involved. When the thickness of the coating layer was increased, this effect also increased, as shown in Fig.6.46 (3 and 4). An increase in frequency of the measuring current also demonstrates this effect. Even the acetate-adipate transition shown in Fig.6.46 (5) is recorded with a negative step. In Fig.6.46 (3 and 4), the acetate-adipate transition was recorded with a smaller difference than under normal conditions (without a coating). The difference between the simultaneous detection by the a.c. and d.c. methods of determination of the conductivity, as already found in some instances when passivated gold electrodes were applied, must be ascribed to the change in capacity of the conductivity cell. In all experiments, the simultaneously performed d.c. method of conductivity detection showed a normal isotachophoretic pattern, as does UV detection. Similar behaviour was found if cations were separated, as can be seen in Fig.6.47. Hence the coating layer is only selective for the difference between singly and doubly charged ions. If, during an isotachophoretic run, a coating is deposited on the micro-sensing electrodes by an electrode reaction due t o a leak current or a change in the nature of the sensing electrode from polarized to charge transfer due to the driving potential, similar effects can be expected. The effect occurs especially when this coating layer is formed very slowly after a series of experiments, even if the most stringent precautions are taken. Cleaning must therefore be carried out from time to time. That a coating is formed more quickly if a high current density of the driving current is applied is shown in Fig.6.48. Owing to the higher potential gradient, the electrode reactions typical of the chromate zone are a function of the driving current. Also, the ratio of step heights is changed more quickly than under normal conditions, for which a change in the ratio of step heights could not be observed.
6.8. DETECTION LIMITS 6.8.1. Introduction
Although i t is somewhat premature at the present stage of isotachophoretic development, brief information will be given on detection limits in isotachophoretic experiments. More research aimed at optimizing detectors, equipment and Operational systems will
194
DETECTION SYSTEMS
Fig.6.47. Influence of a coating deposited on the micro-sensing electrodes on the final recording of the isotachophoretic separation of the cations. Ba2+,Ca'+, Na', Cd'+ and ( C , H, l4 N+ in the operational system at pH 5.39. K+ (0.01 N) was used as the leading ion, acetate was the counter ion and Tris' was the terminating ion. The electric current was stabilized at 80 PA. 1 = No coating; 2 = with a thin coating of 1-arninoanthracene (4 kHz); 3 = with a thick coating of 1-aminoanthracene (4 kHz).
certainly improve the detection limits in the future. Particularly when micro-scale preparative equipment becomes available it will be possible to combine various specific detection techniques with isotachophoretic equipment. Because isotachophoresis is still in the development phase, it is impossible to determine the ultimate detection limit of this technique.
DETECTION LIMITS
195
Fig.6.48. Influence of the current density of the driving current on the final recording of the test mixture of anions (Fig.6.15) isotachophoretically separated in the operational system at pH 6 (Table 12.1). An addition of 0.05%of Nonic 218 was made to the leading electrolyte. The recording was made by the a.c. method (4 kHz): 1 = 40 PA; 2 = 80 PA; 3 = 150 MA.
The following advances will give improvements in detection limits: if it will be possible to reduce the diameter of the narrow-bore tube and the electroendosmotic flow can be suppressed efficiently, the transitions of the zones will become smaller, which will improve the sensitivity of the method (see Appendix B); and if the sensitivity (or selectivity) of the detectors can be increased, smaller zones of ionic material at lower concentrations can be recorded. Of course, some of these aspects overlap.
196
DETECTION SYSTEMS
Apart from the above areas of development of the method, we should consider the following. (1) Are the chemicals available pure enough? (2) Is the operational system well chosen, Le., such that the proportion of the electric current carried by the buffering counter ion is small and the buffering capacity large enough, and is the solvent well chosen? (3) Is the detector sensitive enough? An example of t h s is the isotachopherogram in Fig.6.32, where an enrichment of salicylic acid is shown by the W detector, whereas the conductivity detector gives an ‘ideal’ mixed zone. (4) Is the time of analysis well chosen? If, for instance, the difference in the effective mobilities of a given pair of ions is small, a longer narrow-bore tube must be applied. If the difference in effective mobility is critical, the counter flow of electrolyte will not give relief (this aspect is discussed in Chapter 7). (5) Has the equipment for a special application been constructed well? Convincing evidence that demonstrates the variations in detection limits that can be obtained is provided by the difference in resolution attained by thermometric, conductivity and W detectors. A low-resolution detector gives no information about the real detection limits of the isotachophoretic separation process. The use of electrolytes at low concentration limits the choice of pH and hence the operational systems to be used, because of the increasing influence of O H and H ions on the electrophoretic separation procedure. An increasing eluting effect will be the result and zone electrophoretic effects can be expected. This means also that theoretically isotachophoresis is impossible. However, other solvents may be explored, which alter these limits. In the following discussion, some information is given on detection limits in isotachophoretic separations carried out on the equipment developed in our laboratory with commercially available chemicals, although purification was necessary, especially in analyses at low concentrations. This aspect is dealt with in more detail in Chapter 10. The detection limits in thermometric detection are discussed in section 6.2; they provide no information on the detection limits of the isotachophoretic process. Special attention is paid to UV and conductivity detectors with the electrodes mounted equiplanar (0.01 mm, Pt-Ir) in direct contact with the electrolyte inside the narrow-bore tube in combination with the linearized electronic measuring circuit as considered in this chapter. For the W detector, a round slit of 0.3 mm diameter was used. 6.8.2. Experimental
In order to find the lower detection limit, a series of experiments was carried out with ADP, because its ion can be detected by both W and conductivity detectors. Moreover, it was found to be very pure and dissolved easily compared with other strongly Wabsorbing compounds available in our laboratory. The effect of the direct driving current, temperature and the concentration of the leading electrolyte were studied. The experiments were carried out at pH 4 (see the operational system at pH 4.5, Table 12.5), and some results are given in Table 6.6. All of the data given are average values from three separate experiments. The analyses were carried out for each concentration range of two batches of electrolytes. The minimal amount needed for detection by the W detector was found to be about the same as that in the a s . method of conductivity determination, although if two
197
DETECTION LIMITS TABLE 6.6 SURVEY OF THE MINIMAL AMOUNTS THAT CAN BE DETECTED BY HIGH-RESOLUTION UV AND CONDUCTIVITY DETECTORS
CLE= Concentration of the leading anion (M); Quv = minimal amount of ADP that can be detected by the UV detector (pmoles); Qa.,. = minimal amount of ADP that can be detected by the a.c. detector (pmoles); QKv = minimal amount of ADP necessary for qualitative and quantitative detection by a UV detector (pmoles); and Qf,. = minimal amount of ADP necessary for qualitative and quantitative detection by an a.c. detector (pmoles). The injected volume was 1 pl. By using the dilution method (Fig.6.33), the UV detection limit can be further decreased. CLE
0.01 0.005 0.001 0.0005
25 20 15 5
25 20 15 10
150 130 100
so
150 130 120 100
W-absorbing species were present the resolution was lower (Fig.6.49). This effect may be due to the fact that a longer zone boundary is detected due to the parabolic profile of the zones and the fact that the fan-shaped field lines of the a.c. detector are less than 0.3 mm (the diameter of the slit). Table 6.6 shows that the minimal amount that can be detected by diluting the concentration of the leading electrolyte is far less than expected. Dilution by a factor of 10 decreases the limit by a factor of only about 2. The reason must be ascribed t o the poor development of the profile in the low concentration of electrolytes, because the electroendosmotic flow cannot be suppressed sufficiently, and to the increase in the electrophoretic transport by the more mobile ions (impurities, H?,O H ) . Changes in the temperature of the thermostated narrow-bore tube have only a slight effect, although a drastic change (from 20 to 4°C) occasionally decreases the separating capacity by about 50%. This is to be expected because ionic mobilities increase by 2-3% per 1°C change in temperature. T h s means that the differences between two ions that are difficult to separate change in a similar way, although the effective separation length increases. The separating capacity was measured by comparing the times of analysis of the standard mixture of anions (Fig.6.15), as follows. At 25"C,an amount of the standard mixture was injected just such that no mixed zones were obtained. The mixed zones are found especially in the beginning of the isotachopherogram, for zones at the rear always have a longer time of separation compared with the zones at the front because the detector is mounted at a fixed position. If the temperature is decreased, mixed zones soon appear. The extra time required for complete separation, if a counter flow of electrolyte is used, is taken as a measure of the separating capacity. Of course, one has to take account of the fact that the counter flow of electrolyte always disturbs the profiles and that the difference in effective mobility between the various ions is affected in a negative way by the counter flow. This was checked by observing the profiles of dyes moving in the narrow-bore tube with and without a counter flow of electrolyte. The influence of temperature on the pK values of the counter ion and the sample ions was not taken into account. The influence of the diffusion constant is negligible because the diffusion constant is directly proportional to the absolute temperature.
DETECTION SYSTEMS
198
t
I
t.
Fig.6.49. Isotachopherogram in the operational system at pH 4, with HCI (0.01 N) and e-aminocaproic acid as the counter ion. The terminating ion was glutamate. While the UV detector (below) indicates only one of the two UV-absorbing components injected, the conductimeter (above) shows the separation of the two components. In the trace derived from the conductimeter, a further component is determined, which is an impurity from the electrolytic system. The current was stabilized at 80 PA. R = Increasing electric resistance;A = increasing UV absorption.
The influence of variations in the direct driving current were small in the range studied. In order to prevent the already discussed electrode reactions, this driving current has to be limited to 150 PA. However, experiments at 300 pA showed that the standard mixture of anions was separated in a few minutes, although the resolution decreased, The main reason for this effect must be that high current densities increase the radialnon-uniformity of the temperature profile inside the narrow-bore tube. This causes an increased parabolic profile, especially for the zones that are situated towards the rear side. Also, the electroendosmotic profile increases. The use of the dilution method of concentration determination improves the resolution of the UV detector (Fig.6.33) about 50-fold. This factor depends on the molar extinction coefficients of the ionic species involved. The disadvantage of this method of detection, as can be seen in the determination of salicylic acid in Fig.6.32, is that a small change in the pH of the leading electrolyte may change the effective mobilities between the two ions forming the mixed zone in such a way that an enrichment of one of the components is soon detectable in the UV trace*. This sometimes makes an accurate determination of the step height in the UV trace (quantitative determination) less accurate. If a W-absorbing ion can be sandwiched between two non-W-absorbing ions, minimal amounts of the UV-absorbing ion can be measured quantitatively because one can make use of the parabolic profile of the consecutive zones. The W-absorbing ion can be determined, in spite of its small zone length (e.g., less than 0.01 mm), because the *A similar effect can be expected if the pK, values of the components involved differ much.
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CONCLUSION
average length of a parabolic profile is commonly about 0.4 mm. This is shown later in Fig. 17.3, in which the profiles are visible because coloured ions are used. Special calibration graphs must be prepared for each ionic species. When using equipment in which high-resolution detectors are mounted, for compounds present in the range from micromoles t o nanomoles (average molecular weight loo), full qualitative and quantitative results can be obtained; at the picomole level or even lower, in special cases quantitative results can be obtained, as is discussed above.
6.9. CONCLUSION The choice of the method of detection, especially in analytical isotachophoresis, must be carefully considered. All of the types of detectors discussed in this chapter are not always needed, and for many purposes only one type of detector (specific or universal, with low or high resolution) is sufficient. Especially if one is interested only in the amount and/or quality of a single component, a detector of very simple performance can be chosen*. The choice of the method(s) of detection determines to a great extent the final construction of the equipment, but also makes demands on the purity of the chemicals used in the various operational systems. To compare the various method of detection, Figs.6.50 and 6.51 can be considered. In Fig.6.50, three isotachopherograms of the test mixture of anions (Fig.6.15), in the
T
R
-
a
b
'
c
Fig.6.50. Isotachophoretic separation of the test mixture of anions (Fig.6.15) in the operational system histidine/histidine hydrochloride at pH 6 (Table 12.1). Detector used: (a) d.c.; (b) non-linear a.c.; (c) thermometric. Speed of the recorder chart paper: (a) and (b) 2 cmlmin; (c) 5 mm/min. Average time of analysis: (a) and (b) 15 min; (c) 45 min. The linear traces should be noted. R = Increasing electric reisstance; T = increasing temperature; f = time. *Moreover, the use of thin-wall narrow-bore tubes with a small I.D. (e.g., 0.2 mm) improves the resolution (Appendix B).
200
DETECTION SYSTEMS
f.
11L
1 ’
1’
Fig.6.51. Isotachophoretic separation of the test mixture of anions (Fig.6.15) in the operational system histidinelhistidine hydrochloride at pH 6 (Table 12.1). Conductimetric detection was carried out with a linear conductimeter. The UV trace was derived from a UV absorption detector (not chopped) at 256 nm. The speed of the recorder chart paper was 6 cm/min and the time of analysis was 12 min. The electric current was stabilized at 70 PA. R = increasing electric resistance; A = increasing UV absorption; t = time. 1 = Chloride; 2 = sulphate; 3 = chlorate 4 = chromate; 5 = malonate; 6 = pyrazole-3,5-dicarboxylate; 7 = adipate; 8 = acetate; 9: p-chloropropionate; 10 = glutamate; X = impurity, possibly propionate (a degradation product of p-chloropropionic acid).
operational system at pH 6 (Table 12.1), are shown. The traces of the linear signals have been equalized photographically in order that a valid comparison of the results can be made. The recording of the final sharpness of the zone boundaries and the difference in the time of analysis with a high-resolution and a low-resolution detector can clearly be
REFERENCES
201
seen. Again i t is clear that in order to observe a sample zone with a thermometric detector the zone length must be greater (Table 6.2) than if a high-resolution detector is applied (UV, conductimeter). Hence more sample has been introduced into the system and consequently a longer time of analysis is needed. In Fig.6.51, an analysis under conditions identical with those in Fig.6.50 is shown, recording being effected with a linearized conductimeter (Fig.6.18) and a W-absorption detector (256 nm) (Fig.6.26). It should be pointed out that the various isotachopherograms shown in this chapter are given mainly for pattern recognition, in order to show different effects such as sharpness of the profiles, electrode reactions and impurities. It is difficult to compare one isotachopherogram with another, although a single test mixture of anions was used. In preparing the manuscript, the various isotachopherograms were treated photographically in order to make comparisons simpler. In the Section Applications (Chapters 8-17) the time axis is also given on the relevant isotachopherograms, so that the qualitative and quantitative information can be deduced more easily. Although electrode reactions may sometimes still occur during detection with a conductimeter with the electrodes in direct contact with the electrolyte, its resolution is lugh compared with that of other types of universal detectors. Moreover, possible coating of the electrode can easily be observed by using a combination of an a.c. and d.c. detector (see also Fig.8.1.). We recommend that the entire system should be cleaned from time to time with a non-ionic surfactant, which can be purified by running it through a mixedbed ion exchanger, because all types of material may be adsorbed on walls made of Perspex, TPX, Pt or even PTFE. When adsorbed, these impurities change the {-potential and hence the electroendosmosis, and thus the resolution of both conductivity and UV absorption detectors is decreased. For effective rinsing of the electrophoretic equipment, we recommend the surfactant Extran (Merck, Darmstadt, G.F.R).
REFERENCES 1 F.M. Everaerts, Thesis, University of Technology, Eindhoven, 1968. 2 F.M. Everaerts and Th.P.E.M. Verheggen,J. Chromatogr., 53 (1970) 315. 3 F.M. Everaerts and Th.P.E.M. Verheggen, in P.G. Righetti (Editor), Progress in Isoelectric Focusing and Zsotachophoresis, North-Holland, Amsterdam, and Elsevier, New York, 1975, p. 309. 4 F.M. Everaerts, J.L. Beckers and Th.P.E.M. Verheggen, Ann. N Y . Acad. Sci., 209 (1973) 419. 5 F.M. Everaerts, Graduation Rep., University of Technology, Eindhoven, 1964. 6 F.M. Everaerts and Th.P.E.M. Verheggen, J. Chromatog., 91 (1974) 837. 7 F.M. Everaerts and P.J. Rommers,J. Chromatogr., 91 (1974) 809. 8 F.M. Everaerts and Th.P.E.M. Verheggen,J. Chromatogr., 73 (1972) 193. 9 F.M. Everaerts, internal report, University of Technology, Eindhoven, 972. 10 A. Vestermark and B. Sjodin, J. Chromatogr., 71 (1972) 588. 11 L. Arlinger and H. Lundin, Protides Biol. Fluids, Proc. Colloq., 21 (1973) 667. 12 A.J.P. Martin and F.M. Everaerts, Anal. Chim.A c ~ Q38 , (1967) 233. 1 3 A.J.P. Martin and F.M. Everaerts, Proc. Roy. SOC.,Ser. A , 316 (1970) 493. 14 B.P. Konstantinov and O.V. Oshurkova, Sov. Phys.-Tech. Phys., 37 (1967) 1745. 15 I. Vacik, J. Zuska, F.M. Everaerts and Th.P.E.M. Verheggen, Chem. Listy, 66 (1972) 545. 16 F.M. Everaerts, J . Vacik, Th.P.E.M. Verheggen and J. Zuska, J. Chromatogr., 49 (1970) 262. 17 M. Coxon and M.J. Binder,J. Chromatogr., 101 (1974) 1.
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Publication No. 556f424,AGA, Infrared Instruments Department, Lidingo, Sweden, 1974. J.L. Fergason, Sci. Amer., 231 (1974) 76. J.L. Beckers, Thesis, University of Technology, Eindhoven, 1973. M. Demjanenko, J. Vacik and .I. Zuska, Chem Listy, in press. Th.P.E.M. Verheggen, E.C. van Ballegooijen, C.H.Massen and F.M. Everaerts, J. Chromatogr., 64 (1972) 185. 23 D.I. Shernoff, Rev. Sci. Instrum, 40 (1969) 1418.
18 19 20 21 22
Chapter 7
Instrumentation SUMMARY This chapter is devoted to the electrophoretic equipment developed for isotachophoretic analyses. Many classifications can be considered but, of the series of equipment resulting from the development of the instrumentation, only three clearly distinguishable types have been selected. Because the various instruments generally are combinations of injection systems, counter electrode compartments and detectors, these components are considered insofar as they were not discussed in Chapter 6. Special attention is paid to the counter flow of electrolyte during isotachophoretic analyses. In particular, the optimal regulation of this counter flow of electrolyte and simple and accurate means by which it can be achieved are considered.
7.1. INTRODUCTION The design of isotachophoretic instruments, for analytical purposes is determined mainly by the detection systems used. The stabilizing effect of narrow-bore tubes makes the use of stabilizing agents, e.g., polyacrylamide, agar agar, arrowroot and dextran, unnecessary. The shape of the narrow-bore tube, cylindrical or flat, has some influence (Appendix B). So far, only narrow-bore tubes made of Pyrex glass, quartz glass, Perspex (acrylic) and PTFE have been tested. In this chapter, most attention is paid to the injection system, the counter flow compartment next to the compartment with the semi-permeable membrane, and the means by which a counter flow of electrolyte can be achieved. Some instruments as constructed by Verheggen and Everaerts and used in our laboratory are discussed.
7.2. INJECTION SYSTEMS 7.2.1. Introduction The method of introducing a sample into equipment for isotachophoretic analyses may have a great influence on the time of analysis and even the separation of the ionic species involved. The sample can be introduced sandwiched between the leading and terminating electrolytes with aid of a sample tap, in which case the ionic species are separated from the mobile leading ion and the less mobile terminating ion. The influence of both the leading and terminating ions is minimal and also the pH of both electrolytes has virtually no influence in the initial phase. The amount of sample, however, can be changed only by
203
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INSTRUMENTATION
varying the concentration of the sample or by inserting a small piece of insulating material in the bore of the tap. The latter procedure is very complicated. Introduction of the sample with aid of a syringe seems to be the most commonly used technique, because the sample size can be vaned quickly and usually a smaller amount of sample is required. However, if the sample is introduced in the leading electrolyte, mixed zones can be expected between the leading ion and the fastest moving ion of the sample. If the sample is injected in the terminating electrolyte, ionic species with a low pK value (cationic separation) or a high pK value (anionic separation) can be retarded so much that considerable amounts of these ionic species can be missed or even lost. Reproducible quantitative results can hardly be expected. Particularly if experiments are carried out at low concentrations (0.001 N ) , special care must be taken in selecting the concentration and the pH of the terminating electrolyte. If the sample is mixed with a terminating electrolyte that has too high a concentration or an incorrect pH, both the qualitative and quantitative results will be poor. In addition, the influence of impurities in the electrolyte may play an important role, but this is not influenced by the method of sample introduction. More attention is devoted to this aspect in the Section Applications. Of course, if a syringe is used for sample introduction, some of the sample will always be mixed with the leading and terminating electrolytes if the sample is introduced at the boundary between these electrolytes, as this boundary is never well defined. 7.2.2. Four-way tap The principle of the four-way tap is shown in Fig.7.1. The mechanism is shown in four alternative positions. In position 1 the narrowbore tube is rinsed and can be filed with the leading electrolyte, in position 2 the terminating electrolyte can be introduced into the reservoir for the terminating electrolyte, in position 3 the sample tap can be rinsed and filled with the sample and in position 4 the sample is sandwiched between the leading electrolyte and the terminating electrolyte. The analysis can be performed with the tap in position 4, in which case the connections must fit exactly, because no dead volumes can be allowed (gas bubbles may stick to these connections and if the dead volume is located between the narrow bore and the sample tap the time of analysis is adversely influenced). The other connections are not important in this respect, because they are used only for rinsing and filling the various compartments of the electrophoretic equipment . The tap initially applied by us was made of Pyrex glass, although any other insulating material can be used. A combination of Kel-F and Arnite can be particularly recommended. The average volume of the tap applied by us was 20-100 pl. The volume of the tap was sometimes changed by inserting a piece of insulating material, but this procedure proved to be very complicated if good qualitative and quantitative results were to be obtained.
205
INJECTION SYSTEMS
II!
n I Fig.7.1. Principle of the four-way tap for rinsing and re-filling the electrophoretic equipment and for sample introduction. Position 1: the narrow-bore tube can be rinsed and re-fiied. Position 2: the reservoir with terminating electrolyte can be rinsed and re-fiied. Position 3 : the sample can be introduced. Position 4: the analysis can be performed.
7.2.3. Six-way valve Fig.7.2 shows the way a six-way valve is used, while Fig.7.3 shows an exploded view of this valve in order to demonstrate its construction. The conical plunger is made of Amite, while the plunger housing is made of Kel-F. This plunger housing is surrounded by a brass hexagon for mechanical stability. Moreover, this hexagon prevents any shift of the plunger and the plunger housing due to the weakness of the Kel-F and the forces on the plunger so that a liquid-tight connection is obtained. Holes are drilled in the brass hexagon for connection of the various components via the holes drilled in the plunger housing and the plunger. In each of these holes in the hexagon, a threaded base is soldered, so that with screw-caps and collars liquid-tight connections can be made, as shown in Fig.7.4. It does not need further explanation that the liquid inside the various bores may not have any electrical contact with the brass hexagon. By means of the special construction shown in Fig.7.3 (parts 5 and 6), the six-way valve can be turned only through 60°, so that the three canals inside the plunger are always connected with the bores inside the plunger housing. The connections with the narrow-bore tube and the piece of insulating material that provides the connection with the injection block or directly with the reservoir filled with the terminating electrolyte must fit exactly, otherwise a dead volume will occur that will decrease the effective length for separation enormously.
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INSTRUMENTATION
4 A
6
Fig.7.2. Principle of the six-way valve used for rinsing and re-filling the isotachophoretic equipment and sample introduction (J. Vacik, Prague, private communication). In position A, the narrow-bore tube is rinsed via an open Hamilton valve (1MM1)at the side of the counter electrode compartment; (3) is the connection towards drain. The sample is introduced via the syringe ( S ) , while (2) again is connected with the drain. The reservoir of the terminating electrolyte can be rinsed via (6); (1) is the reservoir for the terminating electrolyte. In position B, the valve is shown in the ‘running’ position.
By varying the central bore inside the plunger, the volume to be injected can be varied. The tap constructed in our laboratory had a volume of 5 pl. The narrow-bore tube is connected with the six-way valve without the use of any adhesive, using a piece of insulating material that has an outside diameter such that it fits exactly in a chamber made for it in the plunger housing. The length of tlus piece of insulating material is about 2 cm. In order to make a liquid-tight connection with the piece of insulating material, it must be smooth and flat on top. Moreover, an extra small O-ring made of rubber is mounted on top of this cylinder of insulating material. In the cylinder, a hole is drilled with a diameter equal to the outside diameter of the narrowbore tube in which the analyses are performed. The narrow-bore tube that is to be mounted is first stretched over a length of about 4 cm t o enable it t o penetrate the cylinder of insulating material via the central bore. The narrowbore tube is then pulled through this central bore until it fits exactly. After allowing for shrinking (this piece of insulating material with the narrow-bore tube is inserted in hot water), the narrow-bore tube is cut with a lancet. The cylinder of insulating material with the narrow-bore tube can be connected to the plunger housing by fitting a screw-cap over the threaded base. A water pressure of at least 7 atm can be applied without any visible leakage at this clamping piece. However, a pressure n o higher than 6 atm could be applied, because at this pressure the narrow-bore tube shows its porosity and droplets appear all over it. The pressures applied for rinsing and re-filling are, of course, much lower. The connection of the six-way valve with the injection block (or directly with the reservoir filled with terminating electrolyte) is achieved with a cylinder of insulating material with
INJECTION SYSTEMS
207
Fig.7.3. Exploded view of the six-way valve. 1 = Brass hexagon with screw-caps for connection of the various parts liquid-tight to the plunger housing (2), made of Kel-F; 3 = pins for locking the plunger housing in the brass hexagon (1);4 = Arnite plunger with three pardel canals; 5 = stainless-steel screw-cap provided with a ridge for the exact determination of the position of the plunger in the plunger housing, in combination with component (6); the plunger can be switched through 60"; 7 = handle; 8 = narrow-bore tube. The clamping device of the nanowbore tube, provided with a small O-ring (see section 7.2.3.), should be noted.
a bore of 1 mm. This cylinder of insulating material has two collars, and on both ends it is flat and provided with two small rubber O-rings. Again, liquid-tight connections can be made with screw-caps. In practice, the tap is very reproducible in sampling, especially when various people use the instrument. For the use of syringes, more ability is needed. It need not be explained that a shorter length of narrow-bore tube is needed for separation, because the sample is not mixed with the leading and terminating electrolytes. This six-way valve was very useful particularly when experiments were carried out in which the position of the sample is important, e.g., zone electrophoresis in narrow-bore
INSTRUMENTATION
208
/
\
2
6
\
A
Fig.7.4. Cross-section of the six-way valve in the ‘running’ position. 1 = Connection towards the reservoir of the terminating electrolyte; 2 = connection towards drain; 3 = connection towards drain; 4 = narrow-bore tube in which the separation is performed; 5 = position where the syringe filed with sample can be mounted; 6 = position where the syringe fiied with terminating electrolyte can be mounted. Materials: a = brass; b = Amite; c = Kel-F; d = Kel-F.
tubes or movingboundary experiments. It can also be recommended for automation purposes. 7.2.4. Injection block
A method for sample introduction with a micro-syringe is demonstrated in Fig.7.5, and a photograph of the injection block is shown in Fig.7.6. . The leading electrolyte can be introduced via an open tap at the side of the counterelectrode compartment, not shown in the figure (see Fig.7.9). The tap between the injection block and the connection towards drain (4) is opened during this procedure, while tap (2) is closed. The tap at the side of the counter flow compartment is then closed and tap (2) is opened. The terminating electrolyte can now flow towards drain. In general, no suction need be applied. Next, tap (4) is closed and a ‘well’ defined boundary is obtained between the leading and terminating electrolytes. A sample can now be introduced via the septum (3) with a normal micro-syringe. The sample introduction can be effected in the leading electrolyte, in the terminating electrolyte or at the boundary of the two electrolytes, as desired.
INJECTION SYSTEMS
209
Fig.7.5. Injection block suitable for isotachophoretic analysis. 1 = Reservoir for the terminating electrolyte; 2 = PTFE-lined Hamilton valve (1MM1);3 = silicone rubber septum; 4 = tap provided with a conical tip, which gives the connection towards drain; 5 = narrow-bore tube, provided with a Perspex clamping piece (see section 7.2.3). This clamping piece is provided with a small O-ring for a liquid-tight connection with the injection block.
Of course, as sharp a plug profile can never be obtained as when the sampling is performed with a sample tap. The connection with the narrow bore tube is made by the construction discussed in
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INSTRUMENTATION
Fig.7.6. Photograph showing the injection block in Fig.7.5 and the six-way valve in Figs.7.2-7.4.
COUNTER ELECTRODE COMPARTMENTS
21 1
section 7.2.3. The injection block was made of Perspex and PTX. The conical tip of tap (4) was made of silicone rubber (shape 90"). This tap is not available commercially as a single piece. The other taps used were commercially available PTFE-lined Hamilton (1MM1) taps (Hamilton, Bonaduz, Switzerland). 7.2.5. Simplified injection block Because the construction of the injection block described in section 7.2.4 is rather complicated, an injection block of much simpler construction (T-way) is shown in Fig.7.7. Such injection blocks have been made of Perspex, TPX, Kel-F, PTFE and polypropylene. The connection with the narrow-bore tube is similar to that described in section 7.2.3. A Hamilton (1MM 1) PTFE-lined valve is mounted between the injection block and the reservoir containing the terminating electrolyte. Another tap, also a PTFE-lined Hamilton (IMM1) valve, is mounted between the injection block and the drain. The equipment can be rinsed and re-filled with leading electrolyte via a tap at the side of the counter electrode compartment (not shown in Fig.7.7, but shown in Fig.7.16). Tap B is opened during this procedure, while tap A is closed. The tap at the side of the counter electrode compartment is then closed and tap A is opened, while tap B remains open. The terminating electrolyte now flows towards drain. No suction or pump need be applied. After this procedure, tap B is closed and the sample can be introduced via the septum with a standard micro-syringe. In this method of sample introduction, the injection can be made only in the leading electrolyte. A large amount of mobile ions of the leading electrolyte are behind the sample introduced and these ions must overtake the sample ions during the isotachophoretic separation procedure. This may be a complication, especially if the concentration of the sample ions is hgh. Because some of the leading electrolyte is mixed with the terminating electrolyte before the analysis, as a result of the introduction of the needle of the micro-syringe, then after the injection of the sample has been made, tap B must be opened in order to remove the leading electrolyte that is mixed with the terminating electrolyte in the horizontal canal. Because of its simple construction, this type of injection block can be recommended in many instances, especially when some precautions can easily be taken with respect to the leading and terminating electrolytes. The concentration of all of the sample ions must not be too high.
7.3. COUNTER ELECTRODE COMPARTMENTS
7.3.1. Introduction Because in narrow-bore tubing a stabilizing effect is obtained, in most experiments no stabilizing agents (e.g., agar agar, polyacrylamide, arrowroot, dextran, agarose) are added to the electrolytes. The counter flow compartment must therefore consist of a semipermeable membrane in order to prevent any hydrodynamic flow of electrolyte between the two electrode compartments owing to the difference in levels in these compartments.
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Fig.7.7. Simpler injection block for electrophoretic equipment suitable for isotachophoretic analyses. Two Hamilton (1MM1) PTFE-lined valves are applied: between the reservoir of the terminating electrolyte and the I-mm narrow-bore tube (A), and between the 1-mm narrow-bore tube and the drain (B). The sample can be introduced into the narrow-bore tube filled with leading electrolyte, so that it is always mixed with the leading electrolyte. A considerable amount of the leading ion must be behind the sample if no intern standard is applied.
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Even if the narrow-bore tube is arranged in a horizontal position, this membrane is needed. Moreover, gas will generally be produced at the electrodes as a result of the electric current necessary for electrophoretic separations. These gas bubbles may also introduce a hydrodynamic flow of electrolyte if the electrodes are not separated by a semipermeable membrane from the narrow-bore tube in which the separation is performed. It is of minor importance that the electroendosmotic profile is somewhat suppressed by the semipermeable membrane, as discussed in Chapter 6 . Moreover, mainly those conditions such that electroendosmotic flow can be prevented must be sought. Although semipermeable membranes need to be applied, one must bear in mind that their use always causes a shift in pH on both sides of the membrane, due to the potential gradient across the membrane and the difference in the ionic mobilities of the various ions through the membrane. This shift in pH may disturb or minimally influence the analysis in a long run, especially if a counter flow of electrolyte is applied.
7.3.2. Cylindrical counter electrode compartment Fig.7.8 shows schematically a cylindrical counter electrode compartment. The main parts of this electrode compartment should be made of material resistant to various solvents; so far, Perspex, Kel-F, Arnite and Pyrex glass have been used. The membrane, made of cellulose polyacetate, fits around the two cylinders that are provided with a central bore. The membrane is fixed with Araldite, which in fact does not really stick the membrane to the two central cylinders, but still prohibits any leakage from the side on which the electrode is mounted towards the narrow-bore tube, or vice versa. The cylindrical membrane is made by wrapping a sheet of cellulose polyacetate (0.1 mm) around a rod with an external diameter equal to the external diameter of the cylinders on which the membrane will finally be mounted. During the wrapping of the cellulose polyacetate, acetone, in which the membrane is soluble, is applied. In order to remove this acetone, the rod, with the wrapped sheet on it, is immersed in a stream of water. A white, small-pore cylindrical membrane is the result, which is easy to remove from the rod with aid of a sheet of abrasive paper. The mechanical stability of the membrane is very high, the thickness being approximately 0.3 mm. The main advantage of a cylindrical membrane is that during rinsing and re-filing of the instrument with leading electrolyte, possible gas bubbles can easily be removed and do not stick to the wall. Also, the washing of the entire system is very easily effected. If experiments with a counter flow of electrolyte are performed, this procedure is normally carried out via the tap, a common PTFE-lined Hamilton (1MM1) valve. The disadvantage is that the fresh electrolyte has t o pass the membrane, by which the existing pH jump is transported by the counter flow quickly into the narrow-bore tube. Of course, the separation is influenced by this effect. This has been partially overcome by the construction of a special connection for the counter flow of electrolyte between the counter flow compartment and the narrow-bore tube in which the separation is carried out. (In section 7.3.3, another counter flow compartment is described that is much more suitable for experiments with a counter flow of electrolyte.) The connection with the narrow-bore tube in which the separation is carried out is similar to that described in section 7.2.3. At the side on which the electrode is mounted, the counter electrode compartment is
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Fig.7.8. Cylindrical counter electrode compartment, provided with a semipermeable membrane. 1 = Piece of Perspex on one side of which the semipermeable membrane is mounted, provided with an Wing; 2 = brass screw to clamp component (1)liquid-tight to the electrophoretic equipment; 3 = brass support for component (1); 4 = cap for the electrode compartment, provided with an O-ring; 5 = electrode (Pt); 6 = cylindrical semipermeable membrane made of cellulose polyacetate; 7 = wall of the electrode compartment; 8 = bottom of the electrode compartment with a PTFE-lined Hamilton (1MM1) valve, a connection for the currentstabilized power supply.
COUNTER ELECTRODE COMPARTMENTS
21 5
generally filled with double-distilled water in order to decrease any interference from impurities formed by electrode reactions. Moreover, a rapid change from one operational system to another is possible because the membrane is not ‘soaked’ with different types of electrolytes. If another operational system is chosen, less attention needs to be paid to the membrane compartment, as explained briefly below. Suppose one is interested in anion separations and for a complete separation three different operational systems are needed. In general, in all systems chloride will be chosen as the most mobile ion, because it is pure, stable and cheap. Even if another anion is chosen as the leading ion, this will not affect the analysis because it migrates through the membrane in the direction of the anode. Of course, the buffering counter ions move in the opposite direction and in a different operational system another counter ion must be taken. If double-distilled water is placed in the reservoir surrounding the anode, no buffering counter ion coming from this reservoir will be present. Therefore, the membrane is not saturated with the buffering counter ions. In most instances, simple rinsing of the system is sufficient for cleaning the membrane. The disadvantage when double-distilled water is used in the electrode compartment with the semipermeable membrane is that a large potential drop is caused. Especially if a conductivity detector is applied, this potential drop may cause an electric leak towards earth because the detector electrodes may finally reach too high a voltage for which the insulation is not adequate. The disadvantage of the cylindrical construction of the counter electrode compartment is that sometimes small leakages may arise because the Araldite employed to fix the membrane does not really fix it. Also, if experiments with methanol are performed, the Araldite becomes brittle and electrolyte may flow from the reservoir of the terminating electrolyte towards the counter electrode compartment. If these leakages are small, they are hardly noticeable, but ultimately there may be a decrease in resolution. Because a decrease in resolution may have many origins [e.g., electroendosmosis by adsorbed material on the wall and electrode reactions (if the a.c. method is used for conductivity determinations), due both to the driving current (polarization) and to electric leakages to earth], the hydrodynamic flow cannot be directly localized in the initial phase often.
7.3.3. Counter electrode compartment with flat membrane A more advanced counter electrode compartment is shown schematically in Fig.7.9 and a photograph is shown in Fig.7.10. The electrode vessel is separated from the narrow-bore tube in which the analysis is performed by a flat membrane made, for instance, of cellulose polyacetate (0.2 mm thickness). This membrane is clamped by two screws and an O-ring. The tap used is a common FTFElined Hamilton (IMMI) valve that provides the connection with the reservoir of the leading electrolyte. This reservoir is generally an ordinary polypropylene syringe with a volume of 20 ml. If the entire bystem has to be rinsed or re-filled with fresh leading electrolyte, the liquid applied flows as well along the membrane as along the septum constructed for the experiments with a counter flow of electrolyte. Because the bore is relatively large compared with the inside diameter of the narrow-bore tube ( 2 mm), the potential drop in the canals is small. Therefore, a normal metal syringe can be inserted for the experiments with a counter flow of electrolyte without the risk that gas will be produced owing to polarization (Fig.6.36). In addition to
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2
8
L
8. 12
u
l7
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the large bore, a more direct connection between the narrow-bore tube and the electrode compartments exist, so that the potential gradient in the canal where the syringe will be inserted is negligibly small. Of course if any gas were produced, it would destroy the analysis. So far, n o other electrode reactions have been observed. The connection with the narrow-bore tube is as described in section 7.2.3, The great advantage of this counter electrode compartment is that a counter flow of electrolyte is permitted that does not pass the membrane. A considerable time is needed for the pH jump at the membrane to enter the narrow-bore tube, where the analysis is carried out, by the direct electric current, because again the bore, which forms a direct connection between the PTFE narrow-bore tube and the membrane, is relatively large, so that a small potential gradient exists in this bore. In addition, the surface area and thickness of the membrane are small tie., the disturbance is relatively small) and, moreover, the buffer capacity of the electrolyte present in the 2-mm bore is high, so that any disturbance can be counterbalanced easily. A further advantage, of course, is that no adhesive is used with the membrane, so that a membrane can be changed and experiments in, e.g., methanol can be carried out more easily.
7.4. ECUIPMENT 7.4.1. Introduction
With the injection systems and the counter electrode compartments briefly discussed in this chapter, and the detectors discussed separately in Chapter 6, many types of instruments can be constructed. Moreover, the different components are connected in such a way that no adhesive need be applied and therefore the different parts are interchangeable. The means of thermostating can also be taken into consideration, e.g., the narrow-bore tube may be free-hanging in air that is thermostated with circulating water, a thermostated aluminium block can be applied with the narrow-bore tube mounted on it in a helix, or the narrow-bore tube may be thermostated directly with, e.g., circulating kerosene. The development and combination of electrode compartments, injection systems and auxiliary equipment has, of course, resulted in a continuous gradation of types of instruments and modifications, and it is sometimes difficult to distinguish one type from another. Therefore, in this section only three types of equipment will be discussed, Fig.7.9. Counter electrode compartment with a flat semipermeable membrane and a septum for experiments with a counter flow of electrolyte. 1, Perspex connection between the central bore of the counter electrode compartment and the narrow-bore tube of the electrophoretic equipment, provided with an O-ring; 2 = brass screw for clamping component (1); 3 = brass support for component (1); 4, 14 = Perspex units for mounting the counter electrode compartment on a rail (see Fig.7.16) and for clamping 8 and 11; 5, 1 5 = brass pen with screw-thread; 6, 16 = bolts; 7 = cap of the electrode compartment, provided with a hole; 8 = electrode compartment; 9 = flat cellulose polyacetate membrane; 10 = rubber O-ring; 11 = central housing with canals of 2 mm diameter that pass along the flat membrane and the septum; 12 = septum; 13 = screw-head for clamping the septum in the central housing; 17 = PTFE-lined Hamilton (1MMl) valve.
218
Fig.7.10. Counter electrode compartment with flat membrane.
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belonging to three clearly distinguishable types in the development of the instrument& tion of analytical isotachophoretic equipment with a narrow-bore tube. 7.4.2. Narrow-bore tube surrounded with a water-jacket Fig.7.11 shows a photograph of the isotachophoretic equipment with which experiments were carried out in the early days of isotachophoresis (1964). Instead of the PTFE narrow-bore tube, as in Fig.7.11, a narrow-bore tube made of Pyrex glass was used. The equipment consists of a narrow-bore tube, which is fixed with adhesive (shellac if a Pyrex or Araldite if a PTFE narrow-bore tube is used) in a type of Liebig condenser. On the left-hand side a four-way tap is mounted, as discussed in section 7.2.2. The electrode compartment, which contains the semipermeable membrane as discussed in section 7.3.2, is not mounted as a counter electrode compartment as is usually done, but is mounted behind the sample tap and contains the terminating electrolyte. The reason for this is the fact that we still use this equipment for measurements of mobilities by the moving-boundary method and it is easier t o rinse if the membrane compartment is mounted at the position shown in Fig.7.11. By means of the cylindrical membrane electrode compartment, hydrodynamic flow of electrolyte is prevented. The connection between the reservoir containing the terminating electrolyte and the cylindrical membrane electrode compartment is made with a PTFE tube and a PTFE-lined Hamilton (lMF1) valve in which the syringe fits. In the Liebig-type condenser, there are three holes into which the thermocouples (linear and differential) may be mounted. Because these thermocouples are so thin, the narrow-bore tube is fured by a small spring, which fits the tube and which is fixed to the wall of the Liebieg-type condenser with hot shellac. The thermocouples are finally soldered on copper wires, also fixed to the wall of the condenser with hot shellac. In Fig.7.11, three thermocouples, all of the linear type, are mounted. In order to reduce the influence of temperature differences in the laboratory (due to movement, draughts etc.), the holes in the wall of the condenser are sealed with adhesive foil that is covered with aluminium foil. For optimal results, the whole equipment is covered with a blanket of cotton-wool. Thermostated water is circulated through the outer space of the condenser to give a constant temperature inside. The reference junction of the thermocouple is therefore mounted with some adhesive on the inside of the condenser wall, protected with a heat-sink compound. For thermostating in our work, a Hacke thermostat with an accuracy of +O.l"C is used. However, if the variations in the temperature of the laboratory are not too large, no thermostat is needed and the outer space of the condenser can simply be filled with water. The capacity of the outer space and hence the volume of water are large enough to keep the temperature constant in the space where the thermocouples are mounted during the isotachophoretic run. The procedure for filing and cleaning this equipment was described in section 7.2.2. The total length of the narrow-bore tube of the equipment shown in Fig.7.11 is approximately 1 m, while the thermocbuples are mounted at distances of 25, 50 and 75 cm. In our work, the signals derived from the thermocouples are amplified with a h i c k amplifier (type A) and recorded with a potentiometric recorder. If only the linear
Fig.7.11. Electrophoretic equipment suitable for isotachophoretic analyses, constructed in 1964 by Everaerts. Detection is effected with thermocouples (copper-constantan), wound a o u n d the narrow-bore tube at three different positions and fixed with adhesive. I?le narrow-bore tube is mounted in a type of Liebig condenser, filled with thermostated water. The injection can be made via a four-way tap (Fig.7.1.). On the left-hand side is mounted the cylindrical electrode compartment with the cellulose polyacetate semipermeable membrane (Fig.7.8.), which was added at a later stage to the equipment.
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signal of the thermocouple is needed, no amplification is necessary if a 100-mV potentiometric recorder is available. 7.4.3. Narrow-bore tube thermostated with an aluminium block Fig.7.12 shows the main difference between this equipment and that described in section 7.4.2. A PTFE narrow-bore tube (O.D. 0.75 mm, I.D. 0.45 rnm) is embedded in a groove in an aluminium block, and is wound around the aluminium block in the form of a helix.
Fig.7.12. Exploded view of the basic components of an electrophoretic apparatus suitable for isotachophoretic analyses in which the narrow-bore tube is mounted on a thermostated aluminium block. 1 = Narrow-bore tube; 2,3 = thermocouples (copper-constantan); 4 = aluminium block; 5 = cap for the aluminium block; 6 = Pt resistor; 7 = load. Tap water can flow through the block through four canals.
222
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Fig.7.13. Electronic circuit for thermostating the aluminium block shown in Fig.7.12.
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No effect on the resolution of the fact that the narrow-bore tube is no longer straight could be observed on the thermometric detector. Later experiments with high-resolution detectors showed that the narrow-bore tube must be mounted as straight as possible, especially the last 2 cm before the detector. If even a small kink was present just before the detector, the resolution was decreased. Gaps between the narrow-bore tube and the aluminium block are carefully filled with a heat-sink compound (zinc oxide powder in silicone oil). Because the heat produced in the narrow-bore tube is transferred so quickly to the aluminium block, a special compartment (see Fig.7.12) is created where the thermocouples are mounted in order to ensure that there will still be a signal to detect. If this compartment is too small, a noisy baseline results because a very high amplification has to be used. Of course, a compromise must be sought, because if this compartment is too big a situation similar to that described in section 7.4.2 results, and the narrow-bore tube is cooled only by thermostated air surrounding it. The temperature of the reference junctions of the thermocouples is always the same as that of the aluminium block, because a certain amount of heatsink compound is smeared on the junction that is insulated with a PTFE spray, which is glued to the aluminium block in order to guarantee good thermal contact with the aluminium block. The narrow-bore tube and the heat-sink compound are fixed by a thin layer of shellac spray (Krylon). For thermostating the aluminium block, thermostated water (accurate to +O.0loC) is used. A temperature sensor (100-L2 Pt resistor) is mounted in the neighbourhood of the detector compartment. Also here gaps are filled with the heat-sink compound. In the centre of the aluminium block a load of 60 W is mounted. The Pt resistor and the load are both connected to the temperature control unit, as shown in Fig.7.13. Rubber O-rings are employed to prevent contact of water, circulating inside the aluminium block, with the electrical circuits. The narrow-bore tube protruding from the thermostat is connected at one side with a type of injection block as shown in Fig.7.7. The narrow-bore tube is connected to the injection block, without adhesive, by means of the clamping device discussed in section 7.2.3. As the counter electrode compartment, the cylindrical construction shown in Fig.7.8 was used. The proportional temperature controller used in the thermostat is based on the relatively high temperature coefficient of a Pt resistor, a Pt resistor of 100 52 at 0°C being used. This Pt resistor forms an a.c. bridge (R5) together with the resistors R1, R 2 , R3 and %. The temperature coefficients of all resistors in the a.c. bridge, apart from the resistor R5,must be chosen to be as small as possible. The smaller these values are, the more accurate will be the thermostatic control. Of course, one of the resistors of the a.c. bridge is variable so as to permit the a.c. bridge to be balanced. If the bridge is unbalanced, a signal, the result of the unbalanced position, will be fed to a pre-amplifier, the phase of this signal being dependent on the polarity of the imbalance of the bridge. The preamplifier generates a sinusoidal voltage and this will be transformed by a voltage limiter into a symmetrical square wave. By means of the very high amplification of the preamplifier and the voltage limiter, the amplitude of the bridge voltage is transformed into a phase-shifted square wave. The leading edge of this square wave is amplified and triggers two antiparallel-connected thyristors that control the amount of heat dissipated in the load, which is mounted in the direct neighbourhood of the Pt resistor (Fig.7.12).
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If the bridge approaches its balanced condition, the output voltage of the bridge decreases and the phase shift of the thyristor trigger pulse will thus be reduced. The thryistor will trigger later and the heat produced in the load will also decrease, and a steady state will result. The temperature (T, "C) can be selected by the variable resistor & of the a.c. bridge, according to the equation
T = 2.59
(R4
- 0.5835)
(7.1) (temperature coefficient R s = 0.003916). Some possibilities are shown in the Table 7.1. An RC filter in front of the input of the pre-amplifier corrects the phase of the trigger pulse, and the proportional band (system gain) can be changed by varying the a.c. voltage over the bridge. Incorrect temperature regulation may result if the temperature coefficients of the other resistors of the a.c. bridge are poor, leading to instabilities if the thermal resistance between the load and the Pt resistor is large or if the heat capacity of the object to be thermostated is too high. A photograph of the equipment with indirect thermostating via the aluminium block is shown in Fig.7.14, which also shows the power supply. A pressure system has been developed for rinsing and re-filling the different compartments of the equipment with the chosen electrolytes. In order to prevent the dissolution of air in these electrolytes, the surfaces of the electrolytes were covered with a layer of kerosene. An additional advantage is that negligible amounts of carbon dioxide dissolve in the electrolytes if a 'high' pH is chosen in performing the analysis (even pH 7). If experiments are to be carried out in parallel-mounted narrow-bore tubes, this method of mounting the narrowbore tubes on a thermostated aluminium block is recommended. 7.4.4. Equipment with high-resolution detectors
Fig.7.15 shows a schematic diagram of isotachophoretic equipment for use with a highresolution W absorption detector and a conductimeter, and a photograph is shown in Fig.7.16. The equipment consists of a PTFE narrow-bore tube in which the analysis is performed, the length being about 25 cm, although a longer tube can easily be mounted. It is produced by Habia (Breda, The Netherlands), with O.D. c.a 0.7-0.75 mm and I.D. ca TABLE 7.1 SOME VALUES FOR THE RESISTANCES (a)TO BE MOUNTED IN THE BRIDGE (FIG.7.13) OF THE TEMPERATURE-REGULATING UNIT TO SELECT A TEMPERATURE RANGE Resistors R, , R, and R, : 1%, 50 ppm/"C. Resistance
R , =R, R3 R,
Temperature range ('0 0-50
0-125
0-300
120 100
150 100 50
180 100
50
100
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Fig.7.14. Electrophoretic equipment suitable for isotachophoretic analyses, with an injection system comparable with the injection block described in section 7.2.5. A counter electrode compartment of the cylindrical type (Fig.7.8) is used. The narrow-bore tube is wound around a thermostated aluminium block (Fig.7.12.). Detection is performed with thermocouples (copper-constantan). A pressure system is applied for rinsing and re-filling the various compartments. This equipment was constructed in 1968 by Verheggen and Everaerts.
0.4-0.45 mm. The variations in diameter per unit length are negligibly small. This narrowbore tube is clamped by a special clamping device, as discussed in section 7.2.3, in the injection block, the counter electrode compartment and on both sides of the conductivity probe. The narrow-bore tube is uninterrupted in the W detector.
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/ I
1
d
I
/
/ ,
/
\
Fig.7.15. Exploded view of more advanced electrophoretic equipment suitable for isotachophoretic analyses in which the injection block shown in Fig.7.5 and the cylindrical counter electrode compartment shown in Fig.7.8 are used. For the detection of the various zones, a UV absorption meter, a potential gradient detector (d.c. method) and a conductivity detector (a.c. method) are applied (see Chapter 6).
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Fig.7.16. Photograph of the more advanced electrophoretic equipment based on that shown in Fig.7.15. This photograph shows the flexibility of the construction. Various injection systems, detectors and counter electrode compartments can easily be combined, In the equipment shown, the injection block shown in Fig.7.5 and the counter electrode compartment with a flat membrane shown in Fig.7.9 are used. The six-way valve shown in Figs.7.2-7.4 is fitted in order to make a simple introduction via either a micro-syringe or a tap possible. For the detection of the various zones, a UV absorption meter, a potential gradient detector (d.c. method) and a conductivity meter (a.c. method) are applied (see Chapter 6). The equipment was constructed by Verheggen and Everaerts.
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The W light is generated by a microwave-powered low-pressure mercury lamp. This W light is transported by an optical quartz rod and fed into a cylindrical slit of width 0.05-0.3 mm. As already mentioned, the PTFE narrow-bore tube is not interrupted and is clamped by the slit, which is made of brass, and the W light passes through the narrowbore tube and is again transported via an optical quartz rod to a set of filters (an interference filter in combination with an end filter). The UV quanta then illuminate a UV light-sensitive photodiode (S330; Hamamatsu, Hamamatsu City, Japan). The quality of the PTFE narrow-bore tube is not sufficiently constant for the UV detector, because the PTFE material itself has a high W absorption. On mounting a particular narrow-bore tube, the amount of light that passes through it and finally reaches the detector may vary by a factor of up to three compared with a previously used narrow-bore tube owing to the difference in the thickness of the two tubes, if they are filled with a non-UVabsorbing liquid. On one hand the high absorptivity of the PTFE material in the UV range is a disadvantage, while on the other hand the dark current, i.e., the current that is transported by the PTFE wall and reaches the detector without passing through the narrow-bore tube, is reduced to a minimum. The signals are handled electronically and result in a trace on a potentiometric recorder. The trace does not have a continuous stepwise character if the isotachophoretic zones pass the detector. At the position where the conductimeter is mounted, the narrow-bore tube is interrupted by a piece of insulating material (Perspex or TPX) in which the micro-sensing electrodes are mounted (Chapter 6). As a result, there is always a slight difference in cell volume between the conductimeter and the UV detector. The sequence of mounting these two detectors was tested and it proved to be of no importance; experiments were carried out to prove this only with components that were stable in the UV region, and possible deleterious effects due to W light were not studied. The conductivity detector can be applied for measurements of the conductivity (a.c. method) or for measurements of the potential gradient (d.c. method) via two microsensing electrodes (10-pm Pt-Ir foil) mounted axially and in direct contact with the electrolytes inside the narrow-bore tube. In Fig. 7.16 can be seen the position where the coil is mounted in order to give good galvanic separation of the high potential on the micro-sensing electrodes from the circuit for measuring the conductivity (potential gradient) at low potential. As discussed in Chapter 6, a leak current towards earth (even lo-” A) must be prevented. For this reason the conductivity probe is surrounded by PTFE insulation. Even the wires connecting the micro-sensing electrodes with the electronic measuring circuit are provided with extra insulation by means of a PTFE narrow-bore tube. The signals derived from the conductivity probe are fed to a field effect transistor (potential gradient measurement) or directly to a well insulated transformer for good galvanic insulation. If the measuring electrodes are mounted equiplanar, only the conductivity can be determined of course. For the measurement of the conductivity (a.c. method) with axially mounted electrodes, these electrodes must be separated from each other via a capacitor, otherwise an electric current will flow, due to the potential gradient, and electrode reactions will result, e.g. ,coating or gas production. Even when the micro-sensing electrodes were
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mounted equiplanar, we found it advantageous to have this capacitor between the measuring electrodes; possibly an exact equiplanar construction is not always possible. Owing to the high potentials applied, some leak current will decrease the resolution after a small series of experiments. The signals derived from the transformer are handled electronically and result in a trace on the potentiometric recorder. This trace has a continuous stepwise character if the isotachophoretic zones pass the detector. If the trace does not have a continuous stepwise character, e . g , if a drift is obtained or dips and/or overshoots are recorded, something is wrong. A drift of the base line is obtained if, for instance, impurities are present that are more mobile than the leading ion, the buffer capacity of the counter ion is not sufficient or some electrode reaction occurs at the micro-sensing electrodes. Dips (or negative steps) can be expected if the buffer capacity of the counter ion is not sufficient, if an enforced isotachophoretic system is obtained or if the electrodes are coated with a polymer as a result of an electrode reaction or the physical adsorption of any material. Overshoots can be expected if the buffer capacity of the counter ion is not sufficient, if the temperatures of two adjacent zones are too different or if an electrode reaction occurs. A modified Brandenburg (Thornton Heath, Great Britain) power supply of the alpha-series is used. It is modified in such a way that it not only can be applied as a constant-voltage source (+30 kV), but for the isotachophoretic experiments can also be applied as a current-stabilized power supply (lt30 kV). Various current-stabilized power supplies, however, are commercially available nowadays, even up to 60 kV. Between the injection block, shown in detail in Figs.7.5 and 7.6, a six-way tap (Figs.7.2-7.4), w h c h can easily be removed without changing the narrow-bore tube if necessary, is mounted. In the equipment shown, an injection can also be made with a normal commercially available micro-syringe, as the sample can be introduced via the tap. Thus this instrument combines all the advantages of taps and syringes. Also, instead of the cylindrical counter electrode compartment (Figs.7.8 and 7.1 5), a counter electrode compartment with a flat membrane (Figs.7.9 and 7.10) can be used. These electrode compartments can easily be changed if necessary without any problems or the need to fit a new narrow-bore tube. All components of the isotachophoretic equipment shown in Fig.7.15 are replaceable because no adhesive is applied, rubber O-rings and screw-threads being used for clamping. We found that it is sometimes necessary to replace the narrow-bore tube as their life was found to vary from several years to only a few months. A narrow-bore tube needs to be changed if a decreased resolution cannot be improved. Owing to differences in the behaviour of the various operational systems, or compounds of the sample, even the ‘inert’ PTFE can become coated with material that is not easy to remove, and the resolution may decrease. Impurities, possibly building up over a long period, that are adsorbed on the walls of the injection system or the counter electrode compartment have less influence on the detection or the separation itself, because the bores in these parts of the instruments are considerably greater. The conductivity probe, if washing with a non-ionic detergent gives no improvement, can easily be cleaned with some metal polish and a cotton thread.
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7.5. COUNTER FLOW OF ELECTROLYTE 7.5.1. Introduction
Many of the papers describing electrophoretic techniques have dealt with the electrolytic counter flow of electrolyte, and a large number of other papers could be cited, especially relating to equipment filled with various stabilizing media. In t h s field, experiments are carried out t o increase the length of the separation, especially for improving the separation of isotopes, and it has been found that mainly enrichment could be obtained. The electrophoretic techniques applied usually involved a movingboundary system, in w h c h a complete separation cannot be expected. However, if an isotachophoretic system is chosen for the separation of isotopes, the separation procedure is also a moving-boundary system that may result in a complete separation, ie., the steady state. In this section, some possible methods for regulated and non-regulated counter flows are given, and a newly developed pumping system is described in which the gas production is used for pumping hydrodynamically the liquid needed for the counterflow of electrolyte. The driving current can be regulated by signals from the isotachophoretic equipment, by means of which the zones can be stopped in the separation chamber (the narrow-bore tube) if counter flow is applied. Of course, it is beyond the scope of this book to discuss all possible systems for electrolytic counter flows. We can consider a regulated counter flow in terms of the main basic principles, as follows. (a) The electric current is constant during the analysis, and the hydrodynamic counter flow of electrolyte is regulated and controlled by signals derived from the electrophoretic apparatus. (b) The hydrodynamic counter flow of electrolyte is constant during the time the counter flow of electrolyte is required, and the electric current is adjusted to this counter flow by means of signals derived from the electrophoretic equipment. During the detection, the electric current is stabilized again. (c) The electric current is constant in the initial phase and the hydrodynamic counter flow of electrolyte is started as soon as a pre-set value of the voltage of the current-stabilized power supply has been reached. The counter flow of electrolyte is then adjusted until n o further increase in voltage is obtained. If for any reason a lower pre-set value is reached, the counter flow of electrolyte is stopped. It should be pointed out that although the length of separation is generally increased, the counter flow of electrolyte disturb the electrophoretic separation (Chapter 17). The method of producing the counter flow can vary widely, and syringe pumps, peristaltic pumps, level differences or ‘gas pumps’ can be applied. Two main reasons can be given for wanting a counter flow of electrolyte, both originating from the fact that the narrow-bore tube is not long enough for a particular separation: (1) the concentration differences between the ions to be separated are too laIge; and (2) the differences in (effective) mobility between the ions of interest are small. Of course, these two factors may be combined in a specific instance. In those instances when the difference in (effective) mobility is minimal, the use of a counter flow of electrolyte will generally fail. More research needs to be carried out in order to determine the effect of the ‘disturbance factor’. It is not unlikely that in specific
COUNTER FLOW OF ELECTROLYTE
231
instances this factor may be zero or even that the separation may be positively influenced. Also, when the difference in effective mobility is minimal, one cannot expect always a complete separation because in some cases the ions have a mutual adverse influence on the pH of the mixed zone and give a poorer separation. Once the ions are separated they will form discrete zones owing to the difference in the pH values in the two zones. We found the counter flow of electrolyte to be successful especially when samples need to be separated with large concentration differences between the various zones. The use of a counter flow of electrolyte has also proved of value in elucidating whether a separation is completed or not (i.e.,mixed zones are present or not). Although the use of a counter flow of electrolyte in isotachophoretic experiments can be seen to be a valuable tool, it also has disadvantages. If a counter flow of electrolyte is to be considered, the chemicals must be of the highest purity available, and even then they often are not pure enough. The impurities may sometimes be collected betwetn the leading and terminating zones and influence the analysis. Sometimes the zone still undergoes a small migration and cannot be stopped owing to impurities present. The impurities in the leading electrolyte and/or in the terminating electrolyte must be removed by recrystallization, zone refining or electrophoretic procedures, etc., if
Eqn. 7.2 relates to the leading electrolyte and eqn. 7.3 to the terminating electrolyte, are the effective mobilities of the terminating ion, where meff,T, meff.,I and impurity and leading ion, respectively. 7.5.2. Counter flow with level regulation Fig.7.17 shows schematically the equipment with which a counter flow of electrolyte can be applied, and the circuit for the regulation of the counter flow of electrolyte is shown in Fig.7.18. The moment at which the counter flow is to be started can be selected with the lO-kf2 potentiometer. The switch A is provided in order to have the possibility of selecting a high potential on the side of the injection block of chosen polarity. It has to be borne in mind that for optimal functioning of the conductimeter, the probe must be at a ‘low’ potential, Le., less than 10 kV. As soon as the voltage selected by the lO-kS2 potentiometer has been reached, the level is controlled by the plunger (Fig.7.17) by means of a coil. Before the experiment, this level is adjusted approximately t o the level in the compartment of the terminating electrolyte, such that the sample zones still migrate in the appropriate direction by means of the electric field strength (possibly a small flow in the direction of the movement of the zones is permitted). Owing t o the construction of the counter electrode compartment, the pH jump across the membrane is of minor importance. Experiments with a counter flow of electrolyte showed that it is important that the compartment in which the driving electrode is mounted should contain electrolyte also. The electrolyte, containing buffer ions, decreases the potential at the measuring electrodes of the conductivity probe and diminishes the pH jump across the membrane.
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Fig.7.17. Equipment for producing a counter flow of electrolyte via level regulation. 1 = Electronic regulation circuit (shown in Fig.7.18); 2 = coil with which a movement of the plunger can be effected; 3 = set of detectors.
The counter flow is stopped by switching the PTFE-lined Hamilton valve, mounted in the plunger reservoir, to the closed position, and the device for regulating the counter flow of electrolyte can then be switched off. It should be noted that the coil is fed by a rectified electric current that is not smoothed by a capacitor. It has been found experimentally that the vibration of the plunger by the unsmoothed current eliminates the mechanical friction that could disturb the analysis at the moment the regulation is started by an abrupt lowering of the plunger.
233
COUNTER FLOW OF ELECTROLYTE
p High V lOOMR
50
2
Fig.7.18. Electronic circuit for regulation of the counter flow of electrolyte via level regulation in isotachophoretic analyses. The resistances are given in kn unless stated otherwise.
This method of regulation can also be applied if a counter flow of electrolyte is required that is regulated by signals derived from the detectors mounted directly on the narrow-bore tube. In this instance the zones are stopped at the regulating detector, which usually gives a better result.
7.5.3. Counter flow with light-dependent resistor regulation This method of producing a regulated counter flow of electrolyte is shown schematically in Fig.7.19 and the circuit for regulation is given in Fig.7.20. A light-dependent resistor (LDR) is attached in series with the narrow-bore tube and a constant potential gradient is applied over the narrow-bore tube and the LDR. Because in isotachophoretic experiments the total potential gradient over the equipment is higher than 300 V, which is the LDR limit, a series of LDRs is used so that one is able to work at 1 0 kV. The series of LDRs can be considered as a voltage source. The amount of light given by a lamp (see Fig.7.20) is regulated by a thermocouple (copper-constantan) mounted around the narrow-bore tube. A change in the temperature of the narrow-bore tube will automatically involve a change in the electric current through it. As is normal in isotachophoretic analyses, the
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INSTRUMENTATION
Fig.7.19. Equipment for producing a counter flow of electrolyte with regulation via a light-dependent resistor. 1 = electronic circuit shown in Fig.7.20; 2 = light-dependent resistor; 3 = set of detectors.
total resistance of the electrolytes inside the narrowbore tube will increase in time owing to the progress of less conductive zones. The increase in the resistance of the narrow-bore tube during the analysis will produce a decrease in the current if a constant voltage is applied over it, and this decrease in current will cause a decrease in the temperature of the narrow-bore tube (quadratic relationship.) This decrease in temperature is recorded by the regulating thermocouple. Hence the total resistance of the LDR and indirectly the voltage drop over the narrow-bore tube are controlled by this thermocouple and a stabilized current will be the result. A means of obtaining a more stable regulation of the current is to arrange a resistor in series with the narrow-bore tube. The potential drop over this resistor can be used for current stabilization, and slowly moving concentration fronts, such as pH disturbances, will not influence the regulation of the current.
COUNTER FLOW OF ELECTROLYTE
235
Fig.7.20. ElecQonic circuit for stabilizing the electric current by signals derived from a thermocouple mounted around the narrow-bore tube in which the electric current flows. This circuit can also be applied for regulation of the various zones moving isotachophoretically in the narrow-bore tube in experiments with a counter flow of electrolyte. 1 , 2 = connections for the thermocouple (copperconstantan); 3 = + 15 V; 4 = common terminal; 5 = - 15 V,
Therefore, during the counter flow of electrolyte, a thermocouple mounted around the narrow-bore tube is applied and during the detection of the zones the current is stabilized by an extra resistor mounted in series with both the LDR and the narrow-bore tube. The counter flow of electrolyte can be produced in various ways, although only the syringe pump is shown in Fig.7.19. Particularly if the counter flow is produced by a difference in levels, a complication can arise because the level is not controlled, and the counter flow will thus change with time. As will be discussed later, there are two limits for the counter flow and if at a certain moment the lower limit is exceeded the counter flow of electrolyte is no longer able to stop the zones. For a counter flow over a long period of time, the electrode compartment that contains the counter flow electrolyte must be very large and it is preferable to use a pump, especially that discussed in section 7.5.5. It wdl be noticed immediately that the adjustment of the electric current as described here will automatically result in an oscillation of the zones around the regulating thermocouple. For thermometric recording, the zone must have passed the thermometric detector by about 1-2 cm for complete qualitative and quantitative determination, but for the regulation a much lower signal is needed. We found that this method of regulation gives a negligible oscillation; the experimental conditions were checked with coloured ions for which the sharpness of the boundaries was studied. Fig.7.21 shows two isotachopherograms for the separation of formate and acetate with and without a counter flow of electrolyte in order t o demonstrate LDR regulation
INSTRUMENTATION
236
-
Chloride min.
Time
Fig.7.21. Isotachophoretic separation of formate and acetate without (a) and with (b) a counter flow of electrolyte. The experiments were carried out in the operational system at pH 6 (Table 12.1) with glutamic acid as terminating electrolyte. Detection was carried out with a thermocouple mounted at a distance of about 50 cm from the injection point. The electric current was stabilized by the circuit shown in Fig.7.20. The thermocouple for regulation was mounted at a distance of about 25 cm from the injection point. The traces show that the electric current decreases (lower temperature) if a hot zone passes the regulating thermocouple. As soon as the terminating ion is below the regulation thermocouple, the electric current is stabilized at imin.. Trace (b) shows that equilibrium is achieved between the counter flow of electrolyte and the electric current. Traces (a) and (b) show that the isotachopherograms finally obtained are similar. These isotachopherograms are not given to show the usefullness of a counter flow of electrolyte, but only to demonstrate current stabilization via LDR and the possibility of using a counter flow of electrolyte (see Chapter 17).
and the isotachopherogram that can be expected. The recording is performed with a thermometric detector (copper-constantan thermocouple). In this experiment, therefore, two thermocouples were mounted around the narrow-bore tube, one at the beginning of the narrow-bore tube, which was used for the LDR regulation during the counter flow of electrolyte period, and the other at the end of the narrow-bore tube, which was used for the detection. Because more advanced systems are considered later, further isotachopherograms with this type of regulation will not be shown. The experimental conditions for the isotachopherograms shown in Fig.7.21, however, will be given. The analysis was performed in the operational system at pH 6 (Table 12.1) with chloride as the leading ion and glutamate as the terminating ion. The aluminium block
COUNTER FLOW OF ELECTROLYTE
231
around which the narrow-bore tube was mounted (section 7.4.3) was thermostated at 18°C. A 2-pl injection was made, containing 0.02 mole of sodium acetate and 0.02 mole of sodium formate. The current was 92 pA in the initial phase and the temperature of the zone of the leading ion was used as reference for the current stabilization (about 25°C). In the initial phase, the current is not yet stabilized, possibly owing to the movement of ions ahead of the zones of formate and acetate, which increase the conductivity. Subsequently the real zones of formate and acetate reach the regulation thermocouple. Because these zones are considerably hotter than the leading zone (see Fig.6.7), even if the aluminium block is applied as a thermostat, the electrophoretic driving current will decrease. Fig.7.21 shows clearly a drop in electric current from ima. = 9 2 p A towards imh. = 52 pA, because the temperature of the glutamate is used for stabilization of the electric current. In Fig.7.21 b, from the initial phase a counter flow of electrolyte is produced in such an amount that the zones still have a movement in the appropriate direction. Fig.7.21 shows that the temperature of the formate zone does not give such a low electric current that the zones are stopped by the counter flow chosen. Between the formate and acetate zones, however, a temperature is attained such that the zones are stopped. The counter flow produced was 200 pllh. After the counter flow of electrolyte has stopped, the current decreases further to the in,h. value and the experiment is completed, as shown in Fig.7.21a. It need not be explained that the thermocouple used for the detection of the various zones must be mounted as far as possible from the regulating thermocouple, otherwise some material may pass the recording thermocouple too soon, especially if components are present in the sample that normally have a temperature in the zone lower than that at which equilibrium is obtained.
7.5.4.Counter flow with direct control on the pumping mechanism via the power supply A counter flow of electrolyte can be obtained in this way if the initial and end voltage over the narrow-bore tube are known. If both of these values are known, the position of the zones as a function of the potential gradient and the approximate counter flow required in order to stop the zones can be calculated (Fig.7.22). A circuit such as that shown in Fig.7.23 can be applied, with which it is possible to select a voltage of the current-stabilized power supply at which the pump is started. Because the counter flow to be produced is calculated only roughly, a counter flow must be selected such that the zones are stopped and slowly pushed back. If the counter flow is insufficient, the zones are not stopped by the pump and finally reach the detector, while if the counter flow matches the movement of the zones the pump will be in action continuously. If the zones are pushed back, the voltage across the narrow-bore tube will decrease. As soon as a chosen lower limit has been reached, the counter flow of'electrolyte is stopped and the zones will again move in the required direction. It needs no further explanation that the range of voltage in which the operation of the pump is planned must be very small. Experiments with coloured ions showed that the zone boundaries are less sharp during the period when they are being pushed back, but as soon as the pumping was stopped sharp boundaries were recorded very rapidly.
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Fig.7.22. Equipment for producing a counter flow of electrolyte by means of on-off regulation of the pumping mechanism by signals derived from the current-stabilized power supply. 1 = Electronic circuit shown in Fig.7.23; 2 = set of detectors.
7.5.5. Counter flow with no regulation
This method of producing a counter flow is comparable with the method discussed briefly in section 7.5.3.In this instance also the initial and end voltages must be known, and the current-stabilized power supply must have a voltage limiter. The procedure is demonstrated in Fig.7.24. A represents an experiment with no counter flow of electrolyte. The electric current is constant and the potential gradient increases continuously with time, because fewer conductive zones move and occupy more of the narrow-bore tube. This potential gradient does not, of course, increase regularly, because the bore of the injection block does not have a diameter identical with the inside diameter of the narrow-bore tube and the bore of the conductivity probe.
COUNTER FLOW OF ELECTROLYTE
239
p high V
i
1OOGR
r-
Fig.7.23. Electronic circuit for the on-off regulation of the pumping mechanism in isotachophoretic experiments with a counter flow of electrolyte. The common terminal should not be mounted such that the stabilization of the current in the narrow-bore tube is influenced (see Fig.7.26).
In B an experiment with a counter flow of electrolyte is shown. The voltage of the current-stabilized power supply is limited to V1, which is higher than the initial voltage and much lower than the final voltage. As soon as V , has been reached (after a time t l ) , the power supply is no longer able to keep the electric current stabilized and as a result the current will decrease. Depending on the magnitude of the counter flow produced, an equilibrium current (Ieq, 1) can be reached at which the zones are stopped after a time (tl*).After the counter flow of electrolyte has stopped (after a time tl**), the voltage is no longer limited and a stabilized current will be the result. In C, a similar experiment is shown with a limited voltage V , and a greater counter flow of electrolyte. If a well chosen counter flow of electrolyte is applied, i.e., a flow such that the zones will move in the appropriate direction if the current I , has been chosen and the zones can be stopped before the detector, no further regulation need be used. Nevertheless, we found this method t o be difficult to apply in practice, particularly because the position at w h c h the zones are stopped is influenced by the size and c o m p o sition of the sample. If the sample consists of many ions with a high effective mobility, the increment in voltage is not great initially. If the regulation is not performed at a ‘low’ voltage, t!ie zones may be stopped if they have already passed the detector.
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V
INSTRUMENTATION
t “2
Fig.7.24. Isotachophoresis with a counter flow of electrolyte without direct regulation of the process. A, Experiment without a counter flow of electrolyte. The voltage increases because less mobile ions enter the narrow-bore tube. In practice, this increment is not as smooth as is shown here. The electric current is kept constant during the experiment at I, B, Experiment in which a counter flow of electrolyte is applied. The electric current is stabilized at I, up to V, (fJ, then the voltage is stabilized (limiter). This results in a decrease in the electric current to ieq, (t;). At time ff*, the counter flow of electrolyte is stopped, the current is stabilized at I , again and the voltage can increase steadily. C, Experiment with a greater counter flow of electrolyte t b n in B. The electric current is stabilized at I, up to V , ( t 2 ) , then decreases to ieqz) ( t z ) .The counter flow of electrolyte is stopped at fz* and the electric current is stabilized again at I,. This figure does not relate to actual experiments, all values being chosen arbitrarily. For further explanation, see text.
24 1
COUNTER FLOW OF ELECTROLYTE
7.5.6. Counter flow regulated by the current-stabilized power supply; the membrane Pump
This method is the most accurate and simple, and is therefore discussed in more detail. The principle is shown in Fig.7.25. Fig.7.26 can be used to explain the principle of the method and also the principle by which the electric current through the narrow-bore tube (Ic) is stabilized. If through the narrow-bore tube, filed with a suitable electrolyte (leading electrolyte), an electric current is stabilized at Ic, the total voltage needed (V,) is then increasing during
T
I
1
Fig.7.25. Equipment for producing a counter flow of electrolyte regulated by the currentstabilized power supply. This method of pumping and also the regulation were found to be optimal in combination with the narrow-bore tube, in spite of the fact that the membrane pump does not have linear characteristics. 1 = Electronic circuit shown in Fig.7.29; 2 = set of detectors. If the counter flow of electrolyte is also to be applied for micro-preparative purposes, another means of pumping can be sought (e.g., an electroendosmotic pump).
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INSTRUMENTATION
Fig.7.26. Principle of regulation of a counter flow of electrolyte, via a membrane pump (as shown in Fig.7.25). Attention should be paid to the common terminal and the earth, which prevent disturbances to the current stabilization (electrophoretic driving current) by the counter flow regulation. This could destroy, or at least obscure, the final result.
the isotachophoretic run. If gas is now produced in the electrolysis cell of the membrane pump, the volume of this electrolysis cell tends to expand. The volume can expand easily because between the electrolysis cell and a cell filled with leading electrolyte, mounted. next to it, a thin membrane (e.g., a rubber contraceptive) is mounted. This membrane is mounted with pre-stressing. In Fig.7.27, the construction of the membrane pump is shown in more detail, and a photograph is shown in Fig.7.28. The flow of liquid caused by the production of gas in the electrolysis cell of the membrane pump counteracts the increment in V,. This gas is produced by an electric current I,, in an electrolyte (e.g., 0.01NKC1). Because V, is of the magnitude of kilovolts, V, is reduced to a value B V, with the aid of two resistors of 100 Ma and 56 ka.An electronic circuit (Fig.7.29) compares this value B V, with an adjustable V, If BlV,l< V,, (V,,> 0), then I, = 0. If BlV,l> V&., then I, # 0 and the increment in V, is counteracted. The regulation is such that I. will reach a value such that BIG1 becomes and remains approximately equal to VEf.. Thus the relationship betweenI,,, BI V,l and V,, is:
BI Vc I Q Vmf.
(7.4)
then I,, = 0, and
BI VCl> V,f.
(7.5)
then I , = A (BI V, I - VXt). The optimal value for the amplification factor, dl,/dl V,l = BA, is dependent, among other factors, on the electrolytic system chosen (operational system) and on the cross-
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COUNTER FLOW OF ELECTROLYTE
I
I
31
I
Fig.7.27. Detailed diagram of the membrane pump. The pump can be used in isotachophoretic experiments with a counter flow of electrolyte. 1 = Cap for closing the electrolysis cell; 2 = electrolysis cell filled with a suitable electrolyte, e.g., 0.01 M KCl; 3 = nuts; 4 = the gas-producing electrodes; 5 = rubber O-ring; 6 = cap for closing the electrolysis cell; 7 = PTFE-lined Hamilton (1MM1) valve; 8 = cap for closing the compartment filled with leading electrolyte; 9 = rubber O-ring; 10 = electrode that can be used, if required, such that during the time the counter flow of electrolyte occurs, the electrode that is connected with the current-stabilized power supply is not separated from the narrowbore tube in which the analyses are performed by a semipermeable membrane; 11 = central body of the compartment filled with leading electrolyte; 12 = bolts for clamping components (11) and (2) together (in total four bolts and nuts are applied); 1 3 = needle; 14 = rubber membrane; 15 = rubber O-ring.
section of the narrow-bore tube, which may vary if a replacement narrow-bore tube is used. If BA has a too high a value, then the regulation will be unstable, while if BA is too small, the accuracy of the regulation will not be sufficient. Because the current, Z,., through the resistors of 100 MR and 56 ki2 may not influence the current through the narrow-bore tube (Ic), the resistors must be mounted as shown in Fig.7.26. Of course, the input current, Zi,of the electronic regulating circuit must be negligibly small compared with Z,. A galvanic separation of the electrodes of the electrolysis cell of the membrane pump with earth is arranged, because otherwise part of Z, would flow through the thm membrane. The membrane was found to be permeable for small
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Fig.7.28. Photograph of the membrane pump illustrated in Fig.7.27.
ions in a long run. In addition to the leak of the electric current, ions from the electrolyte of the electrolysis cell may also interfere if they can pass through the membrane due to poor galvanic separation of the electrodes of the electrolysis cell towards earth. The operational amplifiers (see Fig.7.29) ICl0, ICll and IClz form a differential amplifier with a high input impedance. The amplification factor of this differential amplifier is unity. With aid of a switch ‘polarity’, the output signal of the differential amplifier is always kept positive, depending on the polarity of V,. By means of a ten-turn potentiometer, the reference voltage Vref, can be adjusted. The trim potentiometer of 10 k n must have a value such that the output voltage of ICI3 is equal to zero if I V,I = 10 kV and V,, has its maximal value. If the absolute value of V, is greater than the selected value of VEf., a negative output voltage of IC13is obtained. The amplification factor of ICI3 is constant within 3 dB up to approximately 3 Hz. This frequency is sufficiently high to make stable regulation possible. By the low-pass characteristic of the amplifier, the eventual disturbance of the electric mains (50 Hz) is sufficiently suppressed. The transformer T, forms an oscillator with the two npn transistors. If the input voltage of ICI4 is negative, the sum of the average collector currents of both transistors is proportional to this voltage. The average value of the rectified current through L3, the electric current I, needed for the electrolysis cell of the membrane pump, is approximately proportional t o the input voltage of IC14. If this voltage is positive, I, is zero. By means of a resistor of 4.7 kSl between the connection points 4 and 5 of IC14, the offset voltage of ICI4 is changed in such a way that I , is certainly zero if the input voltage of IC14 is zero, in the case of manual regulation.
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COUNTER FLOW OF ELECTROLYTE
max. 15 kV hishVl-+
*
a: 2 N 4 124
-- common Fig.7.29. Electronic circuit that can be used for the regulation of the electrolytic counter flow in isotachophoretic experiments, with aid of the membrane pump shown in Figs.7.27 and 7.28. Components IC,,, IC,,, IC,, ,IC,, and IC,, are all of the type rA741. All diodes are 1N4148 or 1N914. The resistances are given in kR unless stated otherwise. The specifications for the transformer are: L, = two times 10 turns; L, = two times 50 turns; L, = 65 turns. For the wires enamelled copper Wire, diameter 0.4 mm, is used. The potcore is of the type P 36/22,3B7, ~e (permeability) = 2030.
By means of a switch ‘auto-manual’, automatic or manual regulation of the membrane pump can be selected. The maximal value of I , is approximately 2 mA, and the voltage needed is low (+ 3 V). The amplification factor BA of the circuit (Fig.7.29) for experiments in the operational system at pH 6 (see Table 12.1) with the equipment as described in section 7.4.4. (a PTFE narrow-bore tube of I.D.0.4-0.45 mm and O.D.0.7-0.8 mm and a total length of approximately 30 cm) is approximately 0.1 5 mA/V. We can therefore calculate that I Vcl changes by approximately 14V if I , changes from 0 to 2 mA. Of course, other values can easily be taken, although we found the above values to be optimal.
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APPLICATIONS
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Chapter 8
Introduction SUMMARY In t h s chapter some practical information is given on the Section Applications, and a scheme is given for ‘trouble-shooting’.
8. INTRODUCTION The Section Applications contains almost all of the practical information about isotachophoretic separations in narrow-bore tubes. In this section, applications and results are given for separations classified according to chemical compounds that belong to clearly distinguishable classes. The separations were carried out in so-called operational systems in which the electrolytes were shown to give optimal results. The operational systems are listed in tables, in order to make a comparison between them possible. The systems listed were chosen somewhat arbitrarily; many more possibilities could be given. Also, the separations considered were mainly chosen arbitrarily: many real problems from industry or hospitals proved to be much simpler. The separations are shown in order to indicate their possibilities and to make patterns recognizable. When a specific operational system is chosen, one always has to bear in mind that the pH in anionic separations by isotachophoresis tends to increase, while in cationic separations it tends to decrease, going from the leading zone towards the terminating zone. Therefore, the pH must always be chosen such that the optimal effect of the buffering counter ion is used. In some instances a buffering counter ion is not necessary, while in other instances two or more counter ions with overlapping buffer regions are needed. A difference of 0.5 pH unit can give an operational system that has completely different characteristics for a specific analytical problem, as shown in the following example. If a separation of anions is sought and the operational system at pH 6 (Table 12.1) is found to be suitable, one can adjust the pH of the leading electrolyte from its initial value of 6; the buffering capacity of histidine is sufficient until a pH of ca. 7. If, however, an anion is present with a very low effective mobility, which needs a terminator with an even lower effective mobility than the anion to be separated, it may be preferable t o adjust the pH of the leading electrolyte to 5.5. If the pH of the leading’electrolyte is decreased too much, sometimes difficulties can arise because too few counter ions are present and the buffering capacity may not be sufficient (see Fig.9.5). Experimentally, we found it best to adjust the pH of the leading electrolyte, with the chosen counter ion, to the selected value as accurately as possible and to check the pH of the solution again the following day. In most instances the pH is shifted (kO.1-0.2 pH unit). Step heights listed in the various tables are proportional to the effective mobilities of 249
The analysis can he carried out
The analysis of m e zest mixture of anions o r cations shows t h a t the step heights are n o t constant and/or the resolution is bad, and the base. line has a drift.
c
NO
I
I
The micro-sensing electrodes are coated. Depolarize the electrodes in 0 . 1 N HNOl. If this is not effective apply aqua regra. If this is not effective dismount the probe and apply metal polish. Wash the equipment after each procedure with a non-ionic detergent and thoroughly with douhledistilled water.
Perform an analysis c
NO
-
1
I
NO
NO
For the conductivity detector (n.c. method) only
detector (a.c. method).
The narrow-bore tube is
For the UV detector and t h e conductivity detector ( a x . method).
2
YES
YES
i 1
For the UV detector only
4
with a non-ionic detergent and rinse the entire equipment
If after several washings the analysis stlll does not improve, the entire equipment must be dismounted. Polish the various narrow bores with a suitable polish and use another narrow-bore tube. Before an analysis can he carried out, the entire equipment must be washed with a non-ionic detergent and rinsed with double-distilled water.
This easily can he checked. If the time hetween the start of the analysis and the appearance of the first sample zone varies (in our equipment dewrihed in section 7.4.4 the time is shorter). it indicates that a leak is present. Generally the time is constant within 10 sec in an average time of analysis of 15 min.
1
If only the resolution is had: (1)there IS not a liquid-tight connection between the Hamilton (1MM1) valve and the counter electrode compartment or between the counter electrode compartment and the narrow-bore tube; ( 2 ) the plunger of the Hamiltori (1MM1) valve is loose and leaks; (3)the semi-permeable membrane has a leak.
‘The instrument must be waslie; liiorougldy with a non-ionic aurfartant and then thoroughly rinsed with double.distilled water. 4
Fig.8.1. Flowsheet for ‘troubleshooting’. It is assumed that the electronics of the conductivity detector and UV absorption detector are perfect, and the electrolytes of the operational systems me pure and stable. For ‘trouble-shooting’,the electronics of the conductivity detector, the UV absorption detector and the UV source are as discussed in section 6.4.3 for the d.c. method, section 6.4.5 for the a.c. method, section 6.5.2 for the UV source and section 6.5.3 for the UV absorption detector. Later research shows that the sensitivity of the conductivity detector is improved if the complete equipment is rinsed with a solution of 5%silicon grease in pentadecane, followed by a normal washing procedure.
INTRODUCTION
25 1
the various ionic species in the operational systems and they indicate which ions can be separated in a given length of narrow-bore tube, assuming that the concentration differences are not too great. If the concentration differences are too great, a longer narrowbore tube or a counter flow of electrolyte must be used (see Chapter 17). It should be noted that no corrections for the temperatures of consecutive zones have been made to the results presented from either the thermometric or conductivity detector. If the influence of the counter ion chosen is great (high effective mobility in the operational system chosen), greater differences in effective mobility between the sample ions are needed for a complete separation. If the pH of the consecutive zones increases regularly (in anionic separations) or decreases regularly (in cationic separations), small differences in effective mobility are often sufficient because once the ions diffuse into the zone where the pH is higher (anionic separations) or lower (cationic separations), they may attain a greater effective mobility owing to dissociation. More attention is paid to this phenomenon in Chapter 9. It is sometimes easier and quicker to apply two or more operational systems, as the equipment can be rinsed in a few minutes and is then ready for another operational system, than to try to carry out a complete separation in one operational system. More attention is paid to this aspect in Chapter 11. Sometimes only the concentration of the operational system needs to be changed. The sulphate ion, for instance, in the operational system at pH 6 (Table 12.1) moves behind the chloride ion (concentration of the leading ion, C1- = 0.01 N), while it has a greater mobility than the chloride ion if the concentration of the ‘leading’ chloride ion is changed t o 0.001 N . Another example is given in Fig.12.7. In principle, we do not recommend the use of too long a narrow-bore tube, because the voltages needed are too high and electroendosmosis may dominate the separation. If two types of detectors are available, in many instances the analysis can be carried out, in spite of stable mixed zones (see Fig.6.33), in one operational system. From time to time the equipment used in isotachophoretic analyses must be washed well with a nonionic detergent followed by thorough rinsing with double-distilled water. Adsorption of many types of compounds may influence the detection (see Chapter 6), because amongst other effects the {-potential may be changed. Because the resolution of both the W absorption detector and the conductivity detector (ax. method) decreases in such instances, an electrode reaction only must be rejected. We prefer the a.c. method to the d.c. method because the detector indicates more quickly if something is going wrong and measures can be taken directly (see Chapter 6). We recommend that, before a series of analyses, a test mixture of anions or cations should be examined, because it can be seen very quickly if the resolution and reproducibility are adequate. If the test mixture indicates that non-reproducible data can be expected, appropriate measures must be taken, as shown in Fig.8.1. In our analyses, we pay special attention to the pH and the concentration of the terminating electrolyte, although from various papers one may obtain the impression that this is unnecessary. If too high a concentration of the terminating electrolyte is chosen, eluting effects due to the impurities can be expected, the sample zones may still migrate if a 100%counter flow of electrolyte is present (while the regulation is made via the
252
INTRODUCTION
current stabilizing power supply*) and sample ions can be flushed in the terminating electrolyte if the counter flow of electrolyte occurs too soon (Chapter 17). Moreover, quantitative results are non-reproducible if the injection is made at the boundary of the leading and terminating electrolytes because some of the sample is always mixed with the terminating electrolyte. Particularly if experiments are carried out at low concentrations (0.001 N C1-) problems can be expected (see Chapter 10). A wrongly chosen pH of the terminating electrolyte can cause eluting effects by H’ and OH- ions. Non-reproducible results can also be expected, especially if weak acids or weak bases are present in the sample and some of the sample is mixed with the terminating electrolyte. In the following chapters, much data are given on thermometric detectors, but also data obtained with conductivity and UV detectors are given. Data obtained with the thermometric detector can be applied directly, if a conductivity detector is available. However, the opposite is not true in some instances, because the resolution of the conductivity detector (and the W detector) is so much greater. So far, the information obtained with UV absorption detectors does not have qualitative uses. The electrolytes applied in the various compartments must not, of course, contain gas bubbles. Especially when the leading electrolyte is prepared, a surfactant (0.05% of Mowiol) is added, and as a result small gas bubbles can easily be formed. For de-gassing the electrolytes, in our laboratory we use an ultrasonic bath and still have a ‘trip unit’ on our current-stabilizing power supply, which cuts off the electric current immediately (faster than 0.1 sec) if the voltage increases too quickly. It was determined experimentally that the micro-syringes often need to be cleaned, because many impurities found in the isotachopherograms originate from dirty syringes. For washing the equipment and cleaning the syringes, we recommend the detergent Extran (E. Merck, Darmstadt, G.F.R.), which we purify by running it over a mixed-bed ion exchanger. The syringes are cleaned with this surfactant in an ultrasonic bath.
*For an extensive discussion, see the sections 7.5.5 and 17.1.
Chapter 9
Practical aspects SUMMARY
In experimental work on isotachophoresis, unusual effects are sometimes obtained. These effects can be caused when not all of the conditions that are required in order to obtain an isotachophoretic system are fulfilled. In this chapter, some of these phenomena are discussed and a method for comparing and converting results obtained with different types of apparatus is described.
9.1. INTRODUCTION In Chapter 8, some practical information was given concerning the use of the operational systems and the data presented in the Section Applications. It is difficult to give a complete survey of all phenomena that may obscure or disturb the analysis. It will be clear that, especially if narrow-bore systems are chosen, gas bubbles may affect the analysis if they occupy too much of the tube. Once present above a critical size, the temperature will increase, the gas bubbles will expand, and so on. Also, if small gas bubbles are present and if the narrow-bore tube is mounted horizontally instead of vertically, these gas bubbles may migrate, especially at the boundaries of two adjacent zones with a large temperature difference. Many obscure results in both qualitative and quantitative determinations can be expected if the operational systems are used in the wrong way and for the wrong application, e.g., if the buffer does not have a sufficient buffering capacity. Another possibility is that a leading electrolyte may be chosen of which the composition is not constant with time, e.g., owing to an increasing amount of carbonate in operational systems at high pH (if no precautions are taken), or an increasing amount of formic, acetic or propionic acid if the leading electrolyte consists of formaldehyde, acetealdehyde or propionaldehyde, respectively. This chapter summarizes some important general disturbances that can be found in almost all operational systems; specific disturbances are discussed in the chapters to which they belong.
9.2. DISTURBANCES CAUSED BY HYDROGEN AND HYDROXYL IONS 9.2.1. Disturbances from the terminator zone in unbuffered systems Sometimes disturbances can be caused by the presence of a large amount of H+ at low pH, especially in unbuffered systems. An unbuffered system for the separation of cationic species in isotachophoresis can consist of a strong acid as a leading electrolyte (e.g., hydrochloric acid) and a terminator such as Tris. After the introduction of a sample and 25 3
254
PRACTICAL ASPECTS
the separation of the sample ionic species, a series of zones is obtained containing one ionic species of the sample. Two kinds of separation boundaries can be distinguished, viz., a separation boundary between the leading ions (H') and the zone with ions of the sample (Ml), with the highest mobility (we shall call this boundary the 'HI-MI boundary'), and a separation boundary between two zones of sample cations (the 'MI-M,, boundary'). These two types of separation boundaries have different characteristics and are discussed below.
9.2.1.1. HI-MI boundary The zone of the cations M; will always contain H' ions, so that it is essentially a mixed zone of M; cations and H+ ions. The H+ ions are more mobile than the Mi ions and will therefore pass the HI-MI boundary. (In a buffered system they will be removed by the buffer, according to the equilibrium state.) Those H' ions which pass this boundary migrate into the leading electrolyte (hydrochloric acid) zone and create an H+ zone between the leading electrolyte zone and the first sample zone, Mi. Evidently the extra H+ zone has the same H' concentration as the leading electrolyte zone. In fact, this is a moving-boundary procedure. For the Mf zone, the isotachophoretic condition is no longer valid. The speed of this zone is lower than that of the leading electrolyte zone and the step heights will be smaller owing t o the effect of the H+ ions. If the H' concentration in the M; zone is low, the effect mentioned above is very small and almost no disturbances can be expected. If the pH is low in the M; zone, the original H' zone is elongated and the result is longer detection times and smaller step heights. Figs.9.la-9. Id show electropherograms for the situation with A13' as terminator after 0.01 N hydrochloric acid as the leading electrolyte in methanol, as obtained in practice. Fig.9.la shows the original situation, viz., the original leading ion zone H'(1) and the terminator solution A13+(3),which also contains H+. In Figs.9.lb-9.1 d, an increasing amount of H+(2) between the original solution of H'(1) and the mixed zone A13+-H+ is obtained after a longer time of analysis. The original concentration boundary, which will also be present, is neglected.
9.2.1.2. M,-M,, boundary Now two mixed zones are close together, both consisting of a cation of the sample and H' ions. The H' ions of the M;, zone will pass the boundary and will migrate into the M; zone. Calculation of the pH relationship for the two zones (for hypothetical values), including the mass balances for the H+ and OH- ions and the dissociation constant of water, gives imaginary data, assuming a stationary state. Hence no stationary state will exist. If the pH is about 7, the influence on a stationary situation will be small and almost no disturbances can be expected. If the concentrations of H' or OH- are high, elution phenomena will be dominant. If the pH of the second cation zone is low, the H+ concentration will pass the boundary and a mixed zone of Mf and the H+ coming from the Mi, zone is created.
DISTURBANCES CAUSED BY H+ AND OH
255
rt
Fig.9.1. (a)-(d): Simplified electropherograms of the leading electrolyte (HCl) and the terminator (A13') with methanol as solvent, obtained after different times. (e)-(h): Simplified isotachopherograms of the leading electrolyte (HCl) and the terminator (A13+),when a sample of K+ is introduced. Again the experiment is carried out in methanol and various phases are shown. (i)-(1): Simplified isotachopherograms of the leading electrolyte (KC1) and the terminator (A13+),when a sample of Na' is introduced. Again the experiment is carried out in methanol and various phases are shown. T = increasing temperature; t = time.
The step height in the electropherogram will decrease, which results in two zones of the cation M;, viz., the original M; zone and the mixed zone of H+ and M;. After some time, the H+ coming from the Mi, zone covers the whole Mi zone. A situation as described was obtained using a leading electrolyte of 0.01 N hydrochloric acid in methanol and a terminator of A13+.The sample K+ was introduced. Fig.9.le shows the original situation. The first zone is the leading zone consisting of H'( l), the second the original K' zone (2) and the last zone contains A13' plus H' ions (3). In Fig.9.lf the H+ ions have partially penetrated the K'(2a) zone, whereas in Fig.9.lg the H+ ions have nearly reached the leading zone. In Fig.9.lh an enlarged leading zone (la) can be seen. Zone 2 fits the isotachophoretic condition, while zone 2a does not. In Figs.9.li-9.11 a similar procedure is shown for a leading electrolyte of potassium chloride (l), a sample containing Na'(2) and a terminator of A13+(and H') (3). The H+ ions coming from the A13+zone enter the Na' zone (2a) and finally reach the K' zone (la). In order to check the influence of a low pH in the terminator quantitatively, experimental values are compared with theoretical values, as calculated with the model as described in Appendix A. As a terminator, mixtures of hydrochloric acid and potassium chloride at different pH values are used with a leading electrolyte of 0.01 N hydrochloric
256
PRACTICAL ASPECTS
acid. The current was 70 PA. The ratios f L / t Care i taken as a check*. In Fig.9.2, the relationship between the pH of the terminator and the r L / t U ratio is given for theoretical (solid line) and experimental (individual points) values. Good agreement is obtained, showing that a moving-boundary model provides a better description than isotachophoresis. If the influence of background electrolytes such as H' is too great, elution phenomena will appear after a certain time. The zone boundaries become less and less sharp and after a long time they release each other. The elution effects are often caused by electrode reactions when the electrode compartments are not renewed in time; using C1- as a counter ion in methanol (95%, wlw), the following reactions can be expected: 2C1-
* Clz + 2e
+HZO
HOCl HC1+
+CH30H
CHjOCl
In experiments with an unbuffered system, the H+ ions produced disturb the analyses. As an example, the separation of caesium, sodium and lithium with the leading electrolyte 0.01 N hydrochloric acid and terminator cadmium chloride is shown in Fig.9.3a. In Fig.9.3b, the separation of the same mixture in the same system after the terminator
Fig.9.2. Theoretical (line) and experimental (points) relationship between the pH of the terminator solution and the relative detection times for solutions of KCl applied as terminator, in a movingboundary system. * t ~ ' Time of appearance of a sample zone if no ionic species with the same charge as the species studied passes the separation boundary; tU = time of appearance of a sample zone if an ionic species with the same charge as the species studied passes the separation boundary. If tL/ru = 1, an isotachophoretic zone is obtained; if tL/tu< 1, a moving-boundary zone is obtained.
DISTURBANCES CAUSED BY H+ AND OH 5
4
3
2
1
25 I
5
4
3
2
1
1 T
Fig.9.3. Separation of a mixture of cations in an unbuffered electrolyte system. (a) With fresh terminating electrolyte; (b) with old solution the pH of which is changed by the electrode reaction. 1 = H'; 2 = Cst; 3 = Na+;4 = Li+; 5 = Cd". T = increasing temperature; r = time. A thermometric detector was used.
electrolyte has not been renewed for some time is shown. The terminator solution became increasingly acidic and a flow of r m i g r a t e s through all zones towards the cathode compartment. From the phenomena described above, it can be concluded that it is not advisable to work with unbuffered electrolyte systems, where regular renewal of the electrode compartments is necessary. The use of terminator solutions at low pH is undesirable in cationic separations. A similar disturbance can be expected in anionic separations in unbuffered systems as a terminator of high pH is used. A flow of OH- from the terminator zone penetrates all 7 n n ~ rr n i i r i n o rlirtiirhanrpq
RP
Clirriirwrl nhnvp
9.2.2. Disturbances from the leading zone in unbuffered systems In the previous section, disturbances caused by the presence of H' and OH- from the terminator zone and penetrating all preceding zones have been described. Sometimes disturbances can also be caused by H' and OH- from the leading zone penetrating all proceeding zones. Although it is sometimes difficult to recognize whether the disturbances originate from the terminator or from the leading zone, these disturbances have different characteristics. In order to recognize the difference, two detectors have to be used, and from the two signals obtained it can be concluded from which side the disturbance is coming. In this section we discuss the disturbances from the leading zone. In an anionic separation, this disturbance is due to a flow of H', whereas in a cationic separation it is caused by a flow of OH-. Some examples of the latter situation are considered below. If cations are separated in an unbuffered system, a leading electrolyte of, e.g., hydrochloric acid could be used. In such a case, hydrogen will be evolved at the cathode. OH-, possibly formed in the cathode compartment and migrating in the direction of the anode, will meet the H' ions of the leading electrolyte and will be neutralized because the
25 8
PRACTICAL ASPECTS
concentration of H' in the leading zone (normally about 0.01 N hydrochloric acid) is rather high. No disturbances can be expected. However, if a leading electrolyte that consists of a metal chloride, e.g., potassium chloride, is used, hardly any H+ is present in the cathode compartment and it can therefore be expected that OH- will be formed in the cathode compartment according to the equation 2 H z 0 + 2e + Hz + 2 OHThe OH- ions formed will migrate in the direction of the anode but will not meet H+ for neutralization to occur (the leading electrolyte is potassium chloride) and a flow of OHthrough the whole capillary tube, and all zones, will be the result. Of course, this disturbance will be visible if the concentration of the OH- formed is fairly high and if the time of analysis is sufficient for OH- to reach the detector. For a leading electrolyte of lithium chloride, an increase in pH from 6.7 to 10.7 in the cathode compartment could be measured after some experiments. In such a case, disturbances can be expected and renewal of the cathode compartment is necessary. An example of such a disturbance is shown in Fig.9.4. The isotachopherogram shows the disturbances of a flow of OH- from the cathode compartment, moving in an opposite direction to the migration of the sample zones. The
*
rim.
Fig.9.4. Disturbance due to the presence of OH- formed in the cathode compartment in cationic separations. The leading electrolyte is KCl and the terminator is LiCl (unbuffered system). Thermocouple (2) is mounted closer to the cathode compartment and therefore records the disturbance by OH- first (marked with an arrow). The amplification of the signal of thermocouple (1) is twice that of thermocouple (2). T = increasing temperature.
DISTURBANCES CAUSED BY H+ AND OH-
25 9
leading electrolyte was potassium chloride and the terminator was lithium chloride. The first thermocouple (close to the anode compartment) first detects the step height of lithium, but after some time this step height decreases because the flow of OH- has reached this thermocouple. A second thermocouple (close to the cathode compartment) first detects a decreasing step height of the leading electrolyte because OH- reaches this thermocouple first and after some time the step height of lithium appears. It is clear that the disturbance is coming from the cathode compartment, in contrast with the disturbances described in section 9.2.1. A similar disturbance can be expected in the separation of anionic species if H+ is formed in the anode compartment. Fig. 9.5 shows an example in which H' moves in the opposite direction to the anionic zones. Creatinine (pK = 4.88) was used as the 'buffering' counter ion. The leading electrolyte was 0.01 Nhydrochloric acid (pro analysi grade), adjusted to pH 4 by the addition of creatinine. Glutamic acid was used as the terminator. No sample was introduced. A UV absorption detector (256 nm) and a conductivity detector (a.c. method), both described in Chapter 6, were applied. The UV absorption detector was mounted closer to the reservoir of the terminating electrolyte, so that the isotachophoretic zones reached this detector first. As is well known, the W absorption of creatinine is influenced by the pH if it is approximately at its pK value, which is the reason why a disturbance by H' can be made visible. The length of the narrow-bore tube between the anode and cathode compartments
I.
2.
e -
pH<4!
Jb
A
Ilrn.
Ib
pHr4
Fig.9.5. Electropherogram of a glutamate zone moving behind a chloride zone in an insufficiently buffered system. 1, Chloride; 2, H' disturbance; 3, glutamate. (a) Conductivity detector; (b), UV absorption detector. The H' disturbance is generated in the counter electrode compartment, which is why it first reaches the conductivity probe, which is mounted closer to this Compartment. Conditions: leading electrolyte, 0.01 N HCI (pro analysi grade) adjusted to pH 4 by addition of creatinine; terminating electrolyte, (0.005 N glutamic acid adjusted to pH 4 by addition of Tris); current, stabilized at 70 PA. R = Increasing resistance;A = increasing UV absorption. For comparison with an experiment in a sufficiently buffered system with creatinine as the counter ion, see Fig.5.9.
260
PRACTICAL ASPECTS
is important and the ratio ZJZC is well chosen in order t o show the effect as illustrated in Fig.9.5. Because the buffer capacity of the creatinine is not sufficient, a front of H+ moves towards the cathode and hence reaches the conductivity detector first. It increases the conductivity of the leading electrolyte and is therefore recorded as a dip. If the H+ ions reach the U V absorption detector, it isindicated by a change in absorption of the creatinine. Shortly after this moving pH front has passed the UV detector, the glutamate reaches the detector, already adjusted to the ‘new’ leading electrolyte (mixed zone). For this, the pH of the glutamate is less than 4, which is abnormal if the conditions are chosen well (see Fig.S.9). It will be clear that the conductivity as measured under these circumstances may differ from experiment to experiment, because the disturbance is not exactly reproducible. By changing the length of narrowbore tube between the anode compartment and the set of detectors, another electropherogram could easily be obtained in which the glutamate has passed the UV detector before the H‘zone. 9.2.3. Disturbances due to the presence of hydrogen and hydroxyl ions in buffered systems
In sections 9.2.1 and 9.2.2, disturbances due to the presence of H’ and OH- at high and low pH for anionic and cationic species in unbuffered systems have been described. Disturbances can also be expected sometimes in buffered systems, especially at low pH for cationic species and at high pH for anionic species. The disturbances arise because at these low and high pH values the H+ and OH- ions, respectively, are present in such large amounts that they can carry the electric current and hence low step heights are obtained that are almost identical for all ionic species. Under such conditions, the isotachophoretic condition is n o longer valid, the zones can release and a type of zone electrophoresis is the result. Some examples are given below for cationic species. In section 4.3.3, we mentioned that sometimes no real values for pH, could be obtained because the isotachophoretic conditions were lost at low pH in cationic and at high pH in anionic separations. This can be caused because the pH increases in anionic separations and decreases in cationic separations until values at which ‘water’ acts as a background electrolyte. This phenomenon was observed when analyzing nucleic bases, which have low mobilities and low pK values. The step heights of some substances have been determined with a leading electrolyte consisting of a mixture of potassium acetate and acetic acid at different pH values (Table 9.1). In Table 9.1 it can be seen that at low pH of the leading electrolyte (in the sample zones the pH is even lower) all substances have the same step heights; some substances have double peaks. At higher pH, the substances have different step heights but the differences are too small to separate all of them together. Moreover, the step heights are, in fact, step heights of mixed zones of the substances obtained at a high concentration of H+,as the pH in the sample zone can be decreased substantially. It can be concluded that substances with low pK values and low mobilities cannot be separated at low pH. Some experiments were also carried out with amino acids, and similar results have *I,= Length of narrow-bore tube between the point of injection of the sample and the detector; 2, = length of narrow-bore tube between the semipermeable membrane in the counter electrode compartment and the detector.
26 1
DISTURBANCES CAUSED BY H+ AND OH TABLE 9.1 STEP HEIGHTS (mm) OF SOME CATIONS WITH A LEADING ELECTROLYTE OF 0.01 N POTASSIUM ACETATE AND ACETIC ACID AT DLFFERENT pH VALUES
Cations
4.0
4.3
4.5
Adenine Adenosine Guanine Uridine Cytidine Guanosine
-
30 12+37 13 12 12 t 40 12
69 + 90 85 + 120 85 77 103 80
12 11.5 12 12 12
4.91 ~
156 -
119 145 120
TABLE 9.2 CALCULATED pH VALUES O F THE SAMPLE ZONES FOR CATIONS WITH THE LEADING ELECTROLYTE (A) POTASSIUM FORMATE (0.01 m-FORMIC ACID AND (B) SODIUM FORMATE (0.01 N)-FORMIC ACID AT DIFFERENT pH VALUES Leading electrolyte
Cations
PHL
Mobility (10-5cm2/V sec)
pK
50 30 10 30 30 30 30 30
14 14 14 6 5 4 3 2
38.8 30 20
14 8 8
-
A
B
3.25
3.5
3.75
4.0
4.1
4.2
4.5
5.0
-
3.34
3.61
-
-
3.87 3.55
3.98 3.68
4.08 3.80
4.38 4.12
4.88 4.65
-
-
-
-
-
-
3.54 3.48
3.67 3.60
3.79 3.70
-
-
-
-
-
-
4.10 3.93 3.38
4.49 4.13 3.51
3.068
3.368
-
-
3.637 3.458
3.896 3.749
been obtained. At low pH, the amino acids had the same step heights. Van Hout [ 11 also found the same step heights for an electrolyte system at pH 5 (see also Chapter 13). Calculated pH values in the zones for some cationic species are shown in Table 9.2; where no pH is given, no real zero points were present. From Table 9.2, it can be seen that monovalent substances with low pK values ( 2 or 3 ) cannot be separated by isotachophoresis, whereas completely ionized cationic species can be analyzed even at low pH. In order to see what happens when separating these cations, experiments were carried out with Tris' as a terminator and Li' as a sample ion with leading electrolytes consisting of 0.01 N potassium formate-formic acid and 0.01 N sodium formate-formic acid at different pH values. In Table 9.2, Li' (mobility 3 8 . 8 lo-' cmZ/V sec) always shows real zero points with the leading electrolyte sodium formateformic acid, whereas Tris' (mobility about 3 0 * lo-' cmZ/V* sec) does not show real zero points at pH 3.25 and 3 . 5 .
-
-
262
PRACTICAL ASPECTS
lim. Fig.9.6. Electropherogram for Li' between Tris' (terminator) and Na'. The leading electrolyte was prepared by adjusting NaOH (0.01 N ) t o the pH values shown by addition of formic acid. The isotachopherograms show what happens if the counter ion does not buffer sufficiently. T = Increasing temperature. A thermometric detector was used.
263
DISTURBANCES DUE TO CO,
Electropherograms are given for these systems in Fig.9.6. Li' at these pH values has normal step heights,but Tris+ at pH 3.5 shows a retardation and at pH 3.25 a large and a lower step height are present between the Li' and Tris' zones (zone electrophoresis). Note that the traces at pH 4.25,4.0 and 3.75 are nearly identical, but at pH 3 . 5 and 3.25 the step heights of Li' are about the same whereas those of Tris' decrease owing to the presence of H+. Tris'already shows no real zero points at pH 3.75 in the system potassium formate-formic acid, and indeed at this pH the isotachopherogram (see Fig.9.7) shows a large and a low step height between Li' and Tris'. Similar results can be obtained at high pH in anionic separations.
9.3. DISTURBANCES DUE TO THE PRESENCE OF CARBON DIOXIDE* In section 9.2, some disturbances due to the presence of H+ and OH-, migrating through all zones according to the moving-boundary principle, have been described. A flow of HCO; ions can also cause such a disturbance, because of the presence of carbon dioxide in air and solvents (even if all carbon dioxide is removed from the solution, it can still diffuse through the capillary walls into the solution). Carbon dioxide can react in an aqueous solution as follows:
-
COZ + HzO =+ HzCO3
K , = 2.6 1 0 - ~
(9.1)
HzCO3 + H,O
K z = 1.72 *
(9.2)
=+
H 3 0 ++ HCO;
Fig.9.7. Electropherogram of Li' between Tris' (terminator) and K'. The leading electrolyte was prepared by adjusting KOH (0.01 N ) to pH 3.75 by addition of formic acid. T = Increasing temperature. A thermometric detector was used.
*See also Chapter 13.
264
PRACTICAL ASPECTS
The overall K as generally used is given by K,=KlK2=4.47-
(9.3)
According to the last equilibrium constant, carbonic acid will be characteristic of weak acids. It must be noted, however, that although the reaction between carbonic acid and water is instantaneous, the reaction between carbon dioxide and water is slow, which accounts for the well known ‘fading’ of the colour of phenolphthalein in the titration of an aqueous carbon dioxide solution. At higher pH, carbon dioxide can also react with OH- : C02
+ OH- + HCO;
(9.4)
This last reaction is faster than that with water. Because carbon dioxide is always present in water, especially at high pH, disturbances can be expected owing to the presence of HCO,. The ionic mobility of HCO; ions is about 44 cm2/V sec at 25°C. Especially for the separation of amino acids and proteins, which are normally carried out at high pH, disturbances due to this effect can be troublesome. At low pH, the effective mobility of HCOJ ions is very low and their presence is not troublesome. The step heights for carbonate zones generally have a typical form and are not as sharp as those of other substances owing to the slow equilibrium adjustment of eqn.9.1. In fact, carbonic acid does not migrate as a single homogeneous zone, but as a continuous series of zones of slightly different compositions.
-
-
9.4. ENFORCED ISOTACHOPHORESIS
The pH of the zones depends strongly on the pK values of the buffer ions and the sample ions. When separating strong acids the pH is nearly equal to the pH,, but for weak acids large pH shifts can occur. Problems can be expected when the pH of the zones does not increase regularly. When the pH of a zone is lower than the pH of the preceding zone in anionic separations, the effective mobility of the ionic species of the preceding zone will be smaller in that zone, i e . , if some of the ions are left behind* they cannot reach their own zone and the self-correction of the sharpness of the front is lost. In course of time the zone length will decrease and mixed zones are the result. An example of this phenomenon [2] is the HCO; zone before a zone of cacodylic acid. The pH in the cacodylic acid zone is lower than the pH of the HCO; zone, and the effective mobility of HCO; is higher in the pure HCOJ zone than in the cacodylic acid zone. The HCO; zone vanishes. Further, a pH can be chosen such that the ionic species in a particular zone has an effective mobility higher than that of the leading ion, but a smaller effective mobility in the leading electrolyte zone. The ionic species cannot pass the boundary with the leading electrolyte (pH shift) but has a larger effective mobility and therefore a smaller step height. T h s can be called an enforced isotachophoretic system, because the zones do not occur in order of decreasing effective mobility. *The pH is lower, so their extent of dissociation and hence their effective mobility decreases.
265
ENFORCED ISOTACHOPHORESIS
I
I 2 -
3
t
T
I
-
TI
1
f
t
a
b
Fig.9.8. Electropherogram of a hydrogen carbonate zone between the leading electrolyte potassium acetate (0.01 “-acetic acid (pH 4.75) and cacodylate. (a) Analysis by a second thermocouple about 15 min after (b). T = Increasing temperature; t = time. 1 = Acetate; 2 = hydrogen carbonate; 3 = cacodylate. The sample was introduced via a four-way sample tap (Fig.7.1).
An example of such a system is a leading electrolyte consisting of a mixture of 0.01 N potassium acetate and acetic acid at pH 4.75 and a sample of a hydrogen carbonate. The effective mobility of HCO; is higher than that of the acetic acid, but the pH of the leading electrolyte is such that the HCO, cannot pass that boundary. In Fig.9.8, electropherograms are given for a system showing both effects at two different times of detection. It can be seen that the step heights of the HCO; zones are smaller than the step heights of the leading zones, where its zone length decreases with time, because of the lower pH of the cacodylate zone. 9.4.1. Disc electrophoresis
In disc electrophoresis [3], the first stage of the separation consists of an isotachophoretic system whereby the sample introduced is concentrated in small zones. Generally the leading electrolyte consists of an acid (e.g., acetic acid) that buffkrs at a low pH (4.75) and a buffering counter ionic species (e.g., Tris) that does not act as a buffer in the leading zone (pK = 8). The counter ions buffer only in the following zones and they create high pH values where the proteins have a sufficient mobility. In the literature [4-71, different treatments for the calculation of the pH in the proteins zones have been considered and from comparisons with weak acids, pH values of 8-9 are assumed in the zones. We calculated for some weak acids (hypothetical pK values) the pH values in the sample zones for a system as described above at a pH, of 4.75; the pH values in the zones as a
PRACTICAL ASPECTS
266
d
9 I
I
I
1
10
20
30
40 M59m.ff.
*
Fig.9.9. Relationship between the pH in the sample zones and the effective mobilities of the sample ionic species for different pK values of the ionic species. The leading electrolyte was 0.01 N potassium acetate adjusted to pH 4.75 by addition of acetic acid. Tris (pK = 8) was used as the counter ion. pK values of ionic species: a = 10; b = 9; c = 8; d = 7.
267
WATER AS TERMINATOR
function of the effective mobilities are shown in Fig.9.9 for several pK values of the ionic species. It can be seen that the pHzonedepends strongly on the pK values and on the mobilities of the ionic species. Especially for mobile ionic species, large pH shifts can be obtained, while for low mobilities the shift in pH is not as high as is assumed in the literature. For some acids with charges of -10 to -100 and pK values of 7-8, pH values were calculated to be 5.72-6.4. If it is permissible to use the model for the calculation of the pH values, then the proteins do not move in an isotachophoretic way, but are in fact pushed along by the terminator solutions, where a high pH is present. This can also be called enforced isotachophoresis.
9.5. WATER AS TERMINATOR
As already described in section 9.2.3, disturbances can be caused by the presence of large amounts of H+ and OH- at low and high pH, even in buffered systems. These ions can carry the electric current, act as a background electrolyte, the isotachophoretic condition is no longer valid and zone electrophotetic phenomena can be the result. As H’ and OH- can carry the electric current and as they are present in all zones, the question arises of whether it is possible to use the ‘water’ as a terminator solution, without the presence of another substance. The advantage is clear. A suitable terminator is sometimes difficult to find owing to the requirements of mobility and purity, but if ‘water’ could be used these problems would be solved. Of course, it only can be used between certain pH values. If, for instance, with cationic species the pH is rather high, then ‘water’ cannot be used as its ‘effective mobility’ would be too low. At too low a pH, disturbances can be expected, as shown in section 9.2.3. In order to show the possibility and to determine the pH values if ‘water’ were used as a terminator, some experiments were carried out. In Table 9.3, step heights are given for the terminating zone ‘water’ on top of those of the leading zone. The step heights of Li’ and/or Tris’ are also given for comparison. TABLE 9.3
SOME STEP HEIGHTS FOR ‘WATER’ AS A TERMINATOR Leading electrolyte: (a) 0.01 N potassium formate-formic acid; (b) 0.01 N potassium acetate-acetic acid. Leading electrolyte
PH
a
b
Step height (in: lo-’) Water zone
Lit zone
Tris’ zone
4.1 4.2 4.25
16 16 20
20.5 21
35 35 31
4.25 4.5 4.15 5 .o
40 64 I5 81
-
~
23 21 -
35 39 -
-
268
PRACTICAL ASPECTS
It can be seen from Table 9.3 that the step heights of the Li’ and Tris’ zones are nearly constant (at this pH they are both strong ions), whereas the step heights of the terminating zone ‘water’ increase considerably with increasing pH. At pH values below about 4.25 (depending on the type of leading electrolyte used), ‘water’ cannot be used as a terminator because disturbances will occur. At these pH values, the step height of the pure ‘water’ zone is lower than that of, e.g., Tris’ and zone electrophoretic phenomena can be expected. Also, above a pH of about 5-5.5, ‘water’ cannot be used as a terminator because its effective mobility is too low. Therefore water can act as a terminator in the approximate pH range 4-5.2. In a similar way, water can act as a terminator in the approximate pH range 9-10 for anionic separations. Van Hout [ 11 used water as a terminator* in the separation of, e.g., amino acids at pH 9.2. An example is shown in Fig.9.10 for the separation of glutamic acid, taunne, serine, &cine, tryptophan and sarcosine. The terminator was water and the leading electrolyte was 0.01 N hydrochloric acid-ethanolamine at pH 9.2. Barium hydroxide was added to the terminator ‘water’ in order to suppress the amount of hydrogen carbonate present in the solution and to raise the pH in the terminating reservoir. In Fig.9.10, however, a small zone of hydrogen carbonate can be seen (see also Chapter 13). 9.6. PURIFICATION OF THE TERMINATOR
As already described in section 5.4, terminating electrolytes have to be very pure, because if small amounts of impurities are present in the terminating zone (a large voltage gradient), with higher mobilities than that of the terminating ions, they will be pushed forwards through all preceding zones until they reach a zone boundary in accordance with their effective mobilities. This procedure is a type of moving-boundary procedure and can cause disturbances. In addition to chemical methods for purifying terminators, such as recrystallization and distillation, an isotachophoretic method can also be used. TABLE 9.4 SOME STEP HEIGHTS MEASURED WITH TWO DIFFERENT THERMOCOUPLES The metals were measured in the operational system WKCAC: and the anionic species in the system MTris/HCI*i(A). The step heights are given in millimetres, and relate to 0 PA. Species
Thermocouple 1
Thermocouple 2
Species
Thermocouple 1
Thermocouple 2
Formate Acetate Caprylate Stearate Cacodylate Salicylate Butyrate Palmitate
162 186 223 26 0 298 172 202 253
170 197 234 27 6 312 183 216 272
Li Tris‘ Ni*+ cu2+ Pb’+ BaZ* Na’ (CJ N Cd’+
233 305 201.5 22 1 24 3 169 184 270 223
24 I 321 214 24 1 262 180 195 285 236
+
*WKCAC is listed in Table 11.4 and MTris/HCI in Table 12.4. *Later experiments show that often a terminating ion can better be added to the water (section 13.1.3).
PURIFICATION OF THE TERMINATOR
269
7 9 / 4
t
Fig.9.10. Isotachopherogram of the separation of a series of anions at high pH with ‘water’ as the terminating electrolyte. 1 = Chloride; 2 = hydrogen carbonate; 3 = glutamate; 4 = taurine; 5 = serine; 6 = glycine; 7 = trypthophan; 8 = sarcosine; 9 = OH-. A thermometric detector was used. T = Increasing temperature; r = time.
For a certain time, the terminator is allowed t o migrate after the leading electrolyte, with no sample ionic species present. During this period, the impurities will migrate forwards, out of the terminator solution. The terminating electrolyte will remain pure in a series of separations provided that it is not renewed.
210
PRACTICAL ASPECTS
9.7. CONVERSION OF DATA MEASURED WITH DIFFERENT DETECTORS When different apparatus are used at different times, it is sometimes difficult to compare the results. For thermocouples and conductivity detectors, however, a simple method can be used to interconvert the results. We can utilize the situation that the signals obtained from one detector, when represented graphically as a function of the signals of another, give a nearly straight line. After constructing a calibration graph, all results can then be converted by means of the conversion graph. This graph is independent of the different operational systems as it simply represents a conversion of measured temperatures and conductivities, and so it can be used for all systems.
D
Ir,
150
200
250
3&0
t.c.2
Fig.9.11. Conversion graph for two different thermocouples (t.c.1 and t.c.2). * = Anionic species given in Table 9.4; O = cationic species given in Table 9.4.
REFERENCES
271
AS an example, the conversion graph for two different thermocouples is shown in Fig.9.11. The line was constructed by measuring the step heights for several substances in different operational systems with two thermocouples in two different pieces of apparatus. It can be seen that a nearly straight line is obtained. All of the step heights used for constructing this conversion graph are listed in Table 9.4.
REFERENCES 1 2 3 4 5 6 7
P. van Hout, Graduation R e p . , University of Technology, Eindhoven, 1972. R. J . Routs, Thesis, University of Technology, Eindhoven, 1971. L. Omstein, Ann. N. Y. Acud. Sci., 121 (1964) 321. R. A. Alberty, J. Amer. Chem. SOC.,72 (1950) 2361. E. B. Dismukes and R. A. Alberty, J. Amer. Chem. SOC.,76 (1954) 191. J. C. Nicho1,J. Amer. Chem. Soc., 72 (1950) 2367. J. C. Nichol, F. B. Dismukes and R. A. Alberty, J. Amer. Chem. SOC.,80 (1958) 2610.
This Page Intentionally Left Blank
Chapter 10
Quantitative aspects SUMMARY A method is described for determining a calibration constant that simplifies quantitative determinations considerably, as a calibration graph for each ionic species need not be constructed. The calibration constant is a constant for each operational system, assuming that the electric current is precisely constant between the analyses considered. The reproducibility of both the equipment with a thermometric detector (section 7.4.2) and the equipment with a high-resolution detector (section 7.4.4) has been determined experimentally. The use of a calibration constant has been verified experimentally.
10.1. INTRODUCTION In Chapters 1-5, the theory of isotachophoresis was described and quantitative aspects were considered. Experiments have been carried out to check both the accuracy and the reproducibility of this analytical method, using both a thermometric and a conductivity detector (a.c. method) as their resolutions are different [ 1, 21 . For the experiments in which a thermometric detector was used, the equipment with the four-way tap (section 7.4.2) and the equipment with the injection block (section 7.4.3) were applied in order to compare the differences between the four-way tap and sampling via a microsyringe. For the experiments with the conductivity detector, the equipment described in section 7.4.4 was applied. In the equipment, the six-way valve was also used as the injection block, mounted both as a single unit and in combination. No differences were found in the isotachopherograms if they were both mounted in the equipment so that there is therefore no mutual effect. In the thermometric experiments, the reproducibility was found to be better if the sampling was performed via a micro-syringe instead of with a four-way tap. Most of the differences found must be ascribed to the better construction of the equipment described in section 7.4.3. Moreover, the use of an injection block facilitates work with different concentrations. The six-way valve was found t o be excellent, especially when different workers inject an identical sample. The reproducibility was found to be better than 99.5%, which means that the differences found were less than 0.5%. The six-way valve was found to be better than sampling via a micro-syringe and the injection block (section 7.2.4). It should be noted that the concentration of the terminating electrolyte must be prepared more accurately if the injection is made via a micro-syringe. The order of arrangement of the UV absorption detector and the conductivity probe did not influence the quantitative results for the ions tested. Because the thermometric detector needs a minimum zone length of approximately 100 sec for a full qualitative and quantitative analysis, relatively large samples must be 213
214
QUANTITATIVE ASPECTS
introduced compared with experiments in which a high-resolution detector is applied. The greatest linearity and reproducibility were found, however, when small amounts of sample were introduced in low concentrations, resulting in small zone lengths. For the experiments in which small amounts of sample are introduced in the narrow-bore tube, an instrument was applied for automatic recording of the zone lengths, which enabled small time intervals to be used between successive peaks, as found in the differential traces of the linear conductivity trace (0.3 sec). We did not follow the principles of chromatography, where internal standards are sometimes applied, because the accuracy was found to be high enough without such a procedure. Moreover, the variations in sample size, if any, can be compensated for by using the sample taps. It will be recalled that if a UV detector is available for ionic material that has W absorption, the so-called mixed-zone method can be applied. The sample to be analyzed is diluted with a non-W-absorbing ion with an effective mobility that is the same, in the operational system chosen, as that of the W-absorbing ion of interest. The step height in the trace of the W absorption detector will give the necessary quantitative information, after calibration.
10.2. THEORETICAL
For the quantitative determination of ionic species by isotachophoresis, calibration graphs can be obtained experimentally. Theoretically, there should be a linear relations h p between the length of the zone of a specific ionic species and the amount of the ionic species introduced. Calibration graphs for all ionic species present in a sample that are required to be separated must be measured, however. The introduction of a calibration constant, characteristic for all ionic species in the chosen system, simplifies the quantitative determinations considerably. The calibration constant can be determined as follows. The amount of an ionic species introduced into the apparatus is given by
Q = y.c
(10.1)
where Q (mole) is the total amount of the ionic species, V j (ml) is the volume of the sample injected and c (mole/ml) is the concentration of a particular ionic species present in the sample. The amount of a particular ionic species in the narrow-bore tube will therefore be Q = Ac*L
(10.2)
where A (cm2) is the cross-sectional area of the narrow-bore tube, c* (mole/ml) is the actual concentration of the ionic species in the zone that is adapted to the leading electrolyte and L (cm) is the zone length of a particular ionic species. Combining eqns. 10.1 and 10.2, we obtain
y.C
A =c*L or
(1 0.3)
THERMOMETRIC MEASUREMENTS
vjc
Kcl=
c*L"
215
(10.4)
where Kcd is the calibration constant and L* (sec) is the zone length as detected between two successive signals obtained from the equipment if a zone boundary passes the detector. By means of a computer program (Chapter 4), the actual concentrations of the ionic species in the zone can be calculated in a well defined operational system. This means that once the calibration constant is known, the concentration of all ionic species in a sample can be calculated from the zone length. Not all calibration graphs for each ionic species have to be measured separately. In order to check the reproducibility and to determine simultaneously the calibration constant, K,,, quantitative experiments were carried out in different electrolyte systems with water as the solvent. The calibration constant is not a constant for all systems. Some factors, such as variations in the concentration of the leading electrolyte, temperature and changes in the current density, result in different potential gradients and hence affect the migration speed in the system. This effect produces different zone lengths for the same amounts of ionic species in different systems.
10.3. THERMOMETRIC MEASUREMENTS 10.3.1. Reproducibility In order to estimate the reproducibility, the zone length of formic acid (injected volume 3 p1 of a 0.05 Nsolution) was measured ten times in different experiments. The leading electrolyte was 0.01 Nhistidine and 0.01 N histidine hydrochloride. The pH of the solution was thus 6.02. The current was stabilized at 70 FA. The terminator was 0.005N glutamic acid (adjusted to pH 6 by addition of Tris). The average zone length found was I* = 31 1 sec from ten experiments and the average deviation was 4 sec. Owing to the asymmetry of the step response, the zone length depends on the terminator used. Some experiments were therefore carried out with the same sample but with a different terminator (acetic acid). The average zone length then found was i* = 307 sec from five experiments and the average deviation was 3 sec. No significant differences were found when the values found in the experiments with glutamic acid and acetic acid were compared. Glutamic acid was therefore used as the terminating ion in the other experiments. Later experiments showed that one has to be careful if glutamic acid is used as a terminating ion because it is a strong acid and hence mixed zones can easily be formed, which cannot be separated further.
10.3.2. Calibration constant The calibration constant was determined from experiments carried out with histidine (0.01 N)/histidine hydrochloride (0.01 N)(pH 6.02) as the leading electrolyte. The current was stabilized at 70pA. All zone lengths are given in Table 10.1. The third
276
QUANTITATIVE ASPECTS
TABLE 10.1 CALIBRATION CONSTANTS, K,,l,AND ZONE LENGTHS WITH HISTIDINE/HISTIDINE HYDROCHLORIDE AS THE LEADING ELECTROLYTE The experimental values were measured with a thermometric detector. Ionic species
Concentration in the sample (mole/l)
Concentration in the zone (rnolell)
Injected volume 011)
Succinic acid
0.01
0.0051
4
Acetic acid Adipic acid Formic acid Iodic acid Lactic acid p-Chloropropionic acid Succinic acid Sulphamic acid Tartaric acid
0.05 0.025 0.05 0.05 0.031
(set)
CalibraDeviation from tion average KCa1 constant ( ~ , , , . 1 0 ~ ) AKC,1.1O6 %
163
0.481 2
-1.73
-3.5
0.0085 0.0046 0.0093 0.0085 0.0081
358.5 335 311 350 222
0.4923 0.4867 0.5186 0.5042 0.5172
-0.62 -1.18 2.01 0.57 1.87
-1.2 -2.4 4.0 1.1 3.7
0.05 0.01 0.05 0.025
0.0081 0.0051 0.0090 0.0048
370 119 335 320
0.5005 0.4943 0.4975 0.4883
0.20 -0.42 -0.10 - 1.02
0.4 -0.8 -0.2 -2.0
Acetic acid Adipic acid Iodic acid Maleic acid Tartaric acid
0.05 0.025 0.05 0.05 0.025
0.0085 0.0046 0.0085 0.0057 0.004 8
234 223 231 349 21 3
0.5028 0.4874 0.5093 0.5027 0.4891
0.43 -1.11 1.08 0.42 -0.94
0.9 -2.2 2.2 0.8 -1.9
Acetic acid Formic acid
0.05 0.05
0.0085 0.0093
120 105
0.4902 0.5120
-0.83 1.35
-1.7 2.7
0.4985
0.93
1.9
Average
1 1
Detected zone length
column in Table 10.1 shows the actual concentrations of the ionic species, calculated with the computer program given in Chapter 4.The last two columns show the deviations from the average K values. Reasonable values were obtained, which can be improved al if more accurate vafues are available for the ionic mobilities. A similar determination of the calibration constant was carried out with imidazole/ imidazole hydrochloride (0.01 N ) at pH 7.05 as the leading electrolyte (with water as the solvent). The current was stabilized at 70 HA. All zones measured are given in Table 10.2. The last two columns show the deviations from the average K,, value. Reasonable constancy of the calibration constant was obtained. It should be remembered that the influence of the activity coefficients is neglected in the calculations of the actual concentrations of the ionic species. From our experiments, we can state that a minimum detectable zone length in the PTFE narrow-bore tube (I.D. 0.45 mm, O.D. 0.7 mm) is about 5 mm, using a thermo-
277
THERMOMETRIC MEASUREMENTS TABLE 10.2 CALIBRATION CONSTANTS, Kcal, AND ZONE LENGTHS WITH IMIDAZOLE/IMIDAZOLE HYDROCHLORIDE AS THE LEADING ELECTROLYTE The experimental values were measured with a thermometric detector. lonic species
Concentration in the sample (mole/l)
Concentration in the zone (mole/l)
Ace tic acid Adipic acid Formic acid Hydrofluoric acid Iodic acid Lac tic acid Maleic acid
0.05 0.025 0.05 0.05 0.05 0.0343 0.05
Tartaric acid Acetic acid Formic acid Maleic acid Acetic acid Formic acid
Deviation from average Kca,
(set)
Calibration constant to4)
w~~,.
A K ~1 0 ~6 ~ %-
0.0075 0.0042 0.0087 0.0087 0.0074 0.0069 0.0046
467 407 398 409 465 340 735
0.4283 0.4388 0.4327 0.4215 0.4364 0.4386 0.4437
-0.82 0.23 -0.38 -1.50 -0.01 0.21 0.72
-1.9 0.5 -0.8 -3.4 0.0 0.5 1.6
0.025 0.05 0.05 0.05
0.0042 0.0075 0.0087 0.0046
416 308 255 491
0.4290 0.4329 0.4508 0.4428
-0.75 -0.36 1.43 0.63
-1.7 -0.8 3.3 1.4
0.05 0.05
0.0075 0.0087
154 129
0.4329 0.4455
-0.36 0.90
-0.8 2.1
0.4365
0.64
1.5
Average
lnjected volume (bl)
1
1
Detected zone length
metric detector'. This value can vary, depending on the heat production in the adjacent zones, the electric current, the type of solvent used and the cross-section of the narrowbore tube. The concentration of an anionic species in the narrow-bore tube is about 0.01 g-equiv./l under the conditions used and the cross-section of the narrow-bore tube is about 1.6 10-3 cmz . This means the minimum amount of an ionic species that can be detected is about 8 * g-equiv. If the volume of the sample injected is 3 pl, the minimum concentration in the sample that can be detected is about 2.7 * g-equiv./l. In order to illustrate this, the separation of a mixture of 0.005Noxalate, 0.01 N formate, 0.01 N acetate and 0.015NP-chloropropionate in the system described above at pH 6.02 was carried out. The results are shown in Fig.lO.1. Traces (a), (b) and (c) correspond to injected volumes of 1,2 and 31.11, respectively. The amounts detected were 5* and 1.5 lo-' g-equiv., respectively, for the different anions, when 1 1.11was injected. It can be stated that a complete separation of the mixture is obtained, both qualitatively and quantitatively, in traces (b) and (c). All quantitative information can be deduced from trace (a), for it should be remembered that for quantitative analyses the transition of zone boundaries is required, once the sequence is known. Trace (a) shows
-
-
*This means that a difference of about 100 sec is needed between two successive peaks, the differential trace of the linear temperature response.
QUANTITATIVE ASPECTS
7
7
I
L
h
I
1 II
c- t i m e
Fig.lO.1. Isotachopherogramof the separation of some anions in the operational system at pH 6 (see Table 12.1). Volumes injected: (a) 1, (b) 2 and (c) 3 p1 of a solution of 0.005N oxalate, 0.01 N formate, 0.01 Nacetate and 0.015 NP-chloropropionate. Detection was carried out with a thermometric detector.
a complete separation of a mixture of anions. It should be remembered that the smaller the amount of ionic species introduced into the separation chamber, the shorter is the time of analysis required for a complete separation. If the isotachopherogram in Fig. 10.1a should have been a chromatogram, it should have represented an incomplete separation. Of course, normally an isotachopherogram as shown in Fig.lO.la would not have any value. The detection limit can be decreased by using a leading electrolyte with a lower concentration. If the concentration of the leading electrolyte is decreased to N, the minimum detectable amount of an ionic species will theoretically decrease by a
CONDUCTIMETRIC MEASUREMENTS
219
factor of 10. Other factors, e.g. , electroendosmosis and temperature profiles, place limits on the dilution of the leading electrolyte. Moreover, the pH range in which the analysis can be carried out will be considerably smaller if dilute solutions are applied. Elution effects due t o O H and H’soon appear. Also impurities, especially those present in the terminating electrolyte, may play a dominant role. For correct sampling, especially with a micro-syringe, the concentration of the terminating electrolyte must be adjusted to the low concentration of the leading electrolyte. More attention must be paid to the pH*. The detection limit can be decreased by injecting a larger sample, and a sample tap is particularly suitable for ths. Of course the availability of a counter flow of electrolyte can also decrease the detection limit. The time required for the analyses depends on the length of the narrow-bore tube needed for separation, the electric current used, the type of leading and counter io;r;s present, the pH, the differences in effective mobility of the most difficult pair of ions that need to be separated, the volume injected, the concentrations of the various sample ions, etc. The time required for the analyses discussed above was cu. 45-60 min.
10.4. CONDUCTIMETRIC MEASUREMENTS 10.4.1. Reproducibility Experiments are often carried out at low concentration regions in which it is impossible to use a thermometric detector. Experiments with thermometric detectors have shown, however, that the greatest reproducibility and linearity are obtained if low concentrations and small amounts of sample are used. For the experiments with the conductivity detector, the improved injection block (section 7.2.4) can be used and the injection of the sample made in the leading electrolyte, the terminating electrolyte or at the boundary between them. The effects of the terminators applied can be studied more precisely. The experiments showed that the best terminator is a component with a suitable pK value and that its concentration must be made as similar as possible to the adjusted concentration inside the narrow-bore tube. Also, the pH must be adjusted to an appropriate value. However, all of these precautions with respect to the terminating electrolyte need not be taken in all experiments. Not only the injection block, but also the use of a high-resolution detector improves the reproducibility. The experiments here were also carried out in the operational system at pH 6 (Table 12.1.). Again formic acid was injected ten times with glutamic acid and acetic acid as the terminators. The terminator solution was carefully prepared, the pH being adjusted to that of the leading electrolyte by addition of recrystallized Tris. The average zone length was found to be L* = 65 sec for both series of experiments, with an average deviation of 0.4 sec. *An isotachopherogram of a separation at a low concentration of the leading electrolyte is shown in Chapter 6, where the thermometric detector is discussed (section 6.2.4, Fig.6.6).
QUANTITATIVE ASPECTS
280
10.4.2. Calibration constant
In Tables 10.3-10.5, the results are shown of analyses with nitrate, chlorate and acetate. In addition to the pure components, mixtures of them were also injected. The concentration was chosen such that a 0.5-pl volume could be injected each time. The current was stabilized at 70 MA.Glutamic acid was applied as the terminator, at a concentration of 0.01 N . The average results of two experiments are given. The actual concentrations of the ionic species in the zones, in the steady state, moving behind the leading electrolyte were again calculated with the computer program given in Chapter 4. As expected, a linear relationship between zone length and amount of component injected was found at low concentrations. For the calculation of the calibration constant, an average of the values listed in
TABLE 10.3 ZONE LENGTHS FOUND EXPERIMENTALLY AT A CONCENTRATION OF 0.0125NIN THE SYSTEM HISTIDINE/HISTIDINE HYDROCHLORIDE WITH A CONDUCTIVITY DETECTOR Ion
I. *
K,,, .1 o4
NO,-
13.5
-
-
Cl0,-
-
13.5
-
14.1 13.8
CH, COO-
-
-
15.6
-
-
13.8
14.1 15.9
-
16.2
14.1 13.8 16.2
0.448 0.461 0.462
TABLE 10.4 ZONE LENGTHS FOUND EXPERIMENTALLY AT A CONCENTRATION OF 0.025NIN THE SYSTEM HISTIDINE/HISTIDINE HYDROCHLORIDE WITH A CONDUCTIVITY DETECTOR K,d’ lo4
Ion
L*
NO,-
21.9
-
(30,CH, COO-
-
28.5
-
28.2 28.2
-
32.1
-
-
21.9
21.9 31.8
-
31.8
28.2 28.2 31.8
0.448 0.451 0.459
TABLE 10.5 ZONE LENGTHS FOUND EXPERIMENTALLY AT A CONCENTRATION OF 0.05 N IN THE SYSTEM HISTIDINE/HISTIDINE HYDROCHLORIDE WITH A CONDUCTIVITY DETECTOR Ion
L*
NO,-
51.3
Cl0;
-
CH,COO-
-
K , ~ , 104 56.1 -
-
63.6
56.1 51.3 -
-
51.6 62.1
56.1 -
62.1
51.3 51.9 64.8
0.443 0.452 0.460
28 1
CONCLUSION
Tables 10.3-10.5 was taken. The deviations* from the average calibration constant must be ascribed to the use of the micro-syringe for sample introduction. These values are listed in Table 10.6. The tables show that the zones do not have a mutual influence on each other, which means that the buffer capacity of the counter ion chosen is sufficient. TABLE 10.6 CALIBRATION CONSTANTS, Kca,, DETERMINED FROM THE VARIOUS EXPERIMENTS LISTED IN TABLES 10.3-10.5 Ion
Concentration
-
K , ~lo4
(N)
Deviation in KcaI * l o 7
Deviation
(%I
NO,(30; CH, COO-
0.0125
0.448 0.467 0.462
-7 t12 +7
1.4 2.6 1.3
NO,-
0.025
0.448 0.457 0.459
-7 +2 +4
1.4 0.4 0.9
0.05
0.443 0.452 0.461
-12 -3 +6
2.7 0.7 1.3
c10; CH,COONO,(30; CH,COOAverage
0.455
1.43
10.5. CONCLUSION With an automatic device for recording zone lengths, a high-resolution detector and injection via a micro-syringe (a sample valve, as described in section 7.2.3, was even better), good linearity can be obtained between the amount injected and the distance in the isotachopherogram between the differential traces of the linear signal of the conductivity detector. If the experiments are carried out with care and good equipment is available, no internal standard need be applied. If the detection of even smaller zones than those in the tables is required, the profiles as shown in Fig.17.2 must be taken into account. Among other factors, impurities and different profiles for different zone boundaries may obscure the quantitative results. The zone boundary of, for instance, acetate with glutamate is different from that of acetate with morpholinoethanesulphonate, which has a considerably smaller effective mobility in the operational system at pH 6 (Table 12.1) than has glutamate. If a specific detector is available, e.g., the W absorption detector, one can use the *As already mentioned in section 10.3.2, more accurate data, used for the calculation of the actual concentrations of the various ionic species via the computer program in Chapter 4, will also improve the accuracyof Kcal.
282
QUANTITATIVE ASPECTS
curvature of the boundary profile for the determination of very small amounts of UVabsorbing material [3]. The W-absorbing compound must be sandwiched between two non-UV-absorbing ions, the UV-absorbing ion ‘coating’ the profile with a small layer. Because the parabolic profile is about 0.1-0.4 mm, even a layer of 0.01 mm of Wabsorbing component can be detected. Of course, a calibration graph must be constructed for each component and disturbances by electroendosmosis of unwanted hydrodynamic transport influence the quantitative results enormously. Another problem may occur if one is interested in the quantitative determination of the ion which is the most mobile in the system, i.e., the leading ion. Reproducible measurements can be carried out if a sample tap is available. Because the time of appearance of the leading electrolyte-sample boundary is constant (if the injection of the sample is reproducible), the retardation in the time of the appearance of the first sample zone, with an effective mobility smaller than that of the leading ion, can be used to obtain the quantitative information. A reproducibility of better than 98% can easily be obtained.
REFERENCES 1 J.L. Beckers and F.M. Everaerts, J. Chromatogr., 7 1 (1972) 329. 2 F.M. Everaerts, J. Chromatogr., 91 (1974) 823. 3 M. Svoboda and J. Vaci’k, J. Chromatogr., 119 (1976) 539.
Chapter 11
Separation of cationic species in aqueous solutions SUMMARY As mentioned in earlier chapters, the effective mobilities of cations can easily be influenced. This can be an advantage, especially if the cations to be separated have the same or almost the same effective mobilities in an electrolyte system. By changing the system, it may be possible to separate such ionic species. In this chapter, the qualitative simultaneous separation of some cations using both water and deuterium oxide as a solvent are described, using buffered and unbuffered systems. Results obtained with thermometric, conductivity and UV detectors are given. For these experiments, the equipments described in sections 7.4.2 and 7.4.4 were used. The time of analysis, from the start of the experiment to the detection of the last zone, is about 3 0 4 5 min with the thermometric detector and about 15 min for the high-resolution detectors.
11.1. SEPARATION OF CATIONIC SPECIES IN AQUEOUS SOLUTIONS USING A THERMOCOUPLE AS DETECTOR
The experiments were carried out with the equipment described in section 7.4.2. The sample was introduced via a four-way tap, as described in section 7.2.2. A constant d.c. power source with a maximum potential of 20 kV was used. We used a Micrograph BD 5 recorder (Kipp & Zonen, Delft, The Netherlands), which is especially useful because of its automatic zero suppression module. The effective mobilities of some cations were sometimes very low and the increment in electrical resistance during the analyses, due to the movement of the zones with small conductivities, required the use of higher potentials than those which were available; in this section, the term ‘not sufficiently mobile’ is used for these cations. Sometimes the length of the capillary tube was too short for complete separation of the cations. Also, the zones, although separated, sometimes could not be detected because the resolving power of the thermometric detector was too low to detect small lengths of zones or small differences in temperature between two zones; in these instances, the term ‘not separated’ is used. The volume of the sample tap (about 20 pl) is rather large and corresponds to the contents of about a 14-cm length of the capillary tube. If the concentration of the sample ionic species is chosen to be too high, complete separation according to the isotachophoretic principle cannot be expected. The average time for all analyses was about 45 min. In Tables 11.1-1 1.5, the conditions of the systems used are listed; these are the socalled operational systems. The abbreviations given in the tables are used in the text of t h s chapter. For some systems, a scheme can be given to show which series of cations can be separated simultaneously. The interpretation is as follows. Ions placed in one circle and ions placed in circles directly connected by lines cannot be separated simultaneously, 283
SEPARATION OF CATIONIC SPECIES IN AQUEOUS SOLUTIONS
284 TABLE 11.1
OPERATIONAL SYSTEM AT pH 2 SUITABLE FOR CATIONIC SEPARATIONS Solvent: H, 0. Electric curent &A): Ca. 50-100. Electrolyte Leading Cation Concentration Counter ion PH Additive
H+ 0.01 N c12 0.05% Polyvinyl alcohol (Mowiol)*
Terminating Tns+ Ca. 0.01 N
c1Ca. 6 None
*For experiments with a thermometric detector, this additive is not necessary.
TABLE 11.2 OPERATIONAL SYSTEM AT pH 1.9 SUITABLE FOR CATIONIC SEPARATIONS (WHIO,)
H, 0. Solvent: Electric current &A): Ca. 50-100. Electr olyte Leading Cation Concentration Counter ion PH Additive
H+ Ca. 0.01N 10,- (0.01 N ) 1.5 0.05% Polyvinyl alcohol (Mowiol)*
Terminating Tris+ Ca. 0.01 N
c1-
Ca. 6 None
*For experiments with a thermometric detector, this additive is not necessary.
e.g., in Fig.ll.1 (the system WHCl) BaZ+and +’%F
cannot be separated because they are placed in the same circle, and CaZ+and A13+cannot be separated because they are connected directly by a line, whereas Ba" and A13+can be separated because they are not directly connected by a line. If BaZ+,CaZ+and A13+are present, they form mixed zones together. I.i+ and (C, H5)4N’can be separated because they are not connected by a line. AU step heights* found in the isotachopherograrns of the experiments in
*The step height in an isotachopherogram is a qualitative measure 101the ionic species, where the distance between two successive peaks (the differential signal of the linear thermocouple signal) gives all necessary quantitative information.
SEPARATION USING A THERMOCOUPLE AS DETECTOR
285
TABLE 11.3 OPERATIONAL SYSTEM AT pH 5.4 SUITABLE FOR CATIONIC SEPARATIONS (WKAC) H, 0. Solvent: Electric current h A ) : Ca. 50-100.
Electrolyte
Cation Concentration Counter ion PH Additive
Leading
Terminating
K+
Tris+ Ca. 0.01 N CH,COOCa. 5 None
0.01 N CH, COO-
5.4 0.05% Polyvinyl alcohol (Mowiol)*
*For experiments with a thermometric detector, this additive is not necessary.
TABLE 11.4 OPERATIONAL SYSTEM AT pH 6.4 SUITABLE FOR CATIONIC SEPARATIONS (WKCAC) Solvent: H, 0. Electric current hA) : Cu. 50-100. Electrolyte
Cation Concentration Counter ion PH Addit.ive
Leading
Terminating
K+ 0.01 N (CH,),AsOO6.4 0.05% Polyvinyl alcohol (Mowiol)*
Tns+ Ca. 0.01 N CH,COOCa. 6 None ~~
~
*For experiments with a thermometric detector, this additive is not necessary
water measured by means of a thermocouple are given in Table 11.6. All these step heights refer to 0 PA. 11.1.1. The system WHCl
The leading electrolyte used is hydrochloric acid in water and Tris in water is used as the terminator. Many mono-, di- and trivalent cations have about the same step heights. Their effective mobilities are nearly equal so that separations are impossible with the apparatus available. Ions can be separated if they differ in step height by about 20 mm in this system (see Table 11.6).
SEPARATION OF CATIONIC SPECIES IN AQUEOUS SOLUTIONS
286 TABLE 11.5
OPERATIONAL SYSTEM AT pH 7.4 SUITABLE FOR CATIONIC SEPARATIONS (WKDF) Solvent: H, 0. Electric current &A): Ca. 50-100 Electrolyte
Cation Concentration Counter ion PH Additive
Leading
Terminating
K+
Tris' Ca. 0.01N CH,COO-
0.01 N I,-L-Tyr- (diiodo-Ltyrosine) 7.4 0.05% Polyvinyl alcohol (Mowiol)*
Ca. 7
None
*For experiments with a thermometric detector, this additive is not necessary.
Fig.ll.1. Simultaneous separation of some cations in the system WHCI. Guan = Guanidine; Im = imidazole; S.C. = succinyl choline; Tea = (C,H,), N; Tma = (CH,), N.
Separations of mixtures containing cationic species with low pK values are difficult, as explained in Chapter 9. Figure 11.1 shows which cations can be separated simultaneously in this system. Fig.ll.2 shows the isotachopherogram for the separation of a ’l La3+,Ca*+, Fez+CdZ+and Liz, with H+ as the leading ion and mixture consisting of , Tris' as the terminating ion. 11.1.2. The system WHI03
In this system, the leading electrolyte is M 0 3 in water and the buffering effect is small. The sequence of the step heights of the cations is similar to that in the system WHCI. The most important shifts in step heights are those of Cr3+, Ce3+and La3+. Pbz+ does not migrate noticeably.
287
SEPARATION USING A THERMOCOUPLE AS DETECTOR TABLE 11.6 QUALITATIVE INFORMATION ON SOME CATIONS OBTAINED IN THE OPERATIONAL SYSTEMS LISTED IN TABLES 11.1-11.5
The values given are the step heights as found in the isotachopherogram in the Linear trace of the thermocouple signal. The values are given in millimetres and refer to 0 /.LA.About 20 mm is sufficient for a complete qualitative and quantitative separation by isotachophoresis. The current was stabilized at 100 MA. WHCl
WHIO,
WKAC
WKCAC
WKDIT
H+ K+ Na+ Li+ NH: Ag+
60 216 292 352 215
72 290 400 492 292
-
-
220 302 378 220 260
280 384 476 282 338
300 410 504 303 . n.s.m.0
TI+
217 302 400 n.s.m. 4 34 306 208 21 3 285 324 290 291 294 290 266 285 318 294 248-2 70* 250 255 294 n.s.m. 241 246 312* 272
295 437 560 n.s.m. 625 412
Cation
.
(CH, 14 N’ (C, H, N+ (C, H, I., N+ Tris+ Imidazole’ cs+ Rb+ Guanidine+ Succinyl choline’ CO’+ Ni + Mg2+
cu I+ Ca” MnZ+ Cd’+ Fez+ Sn’+ Pb2+ Baz+ 2n2+ Fe 4t LaN Ce Cr 3+ AIw
-
391 450 416 415 408 4 04 372 412 420 410 n.s.m. 352 404 n.s.m. 366 368 498 380
-
340 432 n.s.m. 490 310 294 343 318 318 314 387 284 320 341 312 1276** 371 264 320 1128** 322 325 390 360
*Double step. **Estimated value from experiment at a lower current density. *The step height for imidazole at pH 6.53 is 472 mm. 5n.s.m. = not sufficiently mobile.
-
-
-
430 540 808 610 432-
442 568
-
372 434 407 403 396 442 362 420 446 508 n.s.m. 486 338 415 n.s.m. 402 416 n.s.m. n.s.m.
-
680 551 399 477 n.s.m. 430 n.s.m. 388 440 n.s.m. n.s.m. n.s.m. 368 n.s.m. n.s.m. 634 834 n.s.m.
-
288
SEPARATION OF CATIONIC SPECIES IN AQUEOUS SOLUTIONS
Fig.ll.2. Isotachopherogramof the separation of some cations in the system WHCl, using a thermometric detector: 1 = W; 2 = lI+;3 = La"; 4 = Caz+;5 = Fez+;6 = CdZ+;7 = Li+;8 = Tris+.T = Increasing temperature; t = time.
11.1.3. The system WKAC
The leading electrolyte is a solution of potassium acetate in water, adjusted to pH 5.39 by adding acetic acid. This pH is chosen because in the following zones the pH of the zones decreases almost to the pK value of acetic acid, producing a maximum buffering effect. The differences in step heights of the cations, for a complete separation, must be 20 mm in this system. Fig.11.3 shows which ions can be separated simultaneously. Comparing the step heights in this system with those of the other systems, some shifts in the step heights must be explained. The most important are those of F'b2+, Ce3+,La3+, A13' and Cr3+,which are all polyvalent ions. The reason for the shifts can be found in the higher pH of the system and stronger complex formation. Figure 11.4 shows the isotachopherogram for the separation of a mixture of Ba2+, Ca'+, Na', Ni2+,Cd2+, Pbz+and (C2H,),N+. K+is the leading ion and Tris+the terminating ion.
SEPARATION USING A THERMOCOUPLE AS DETECTOR
289
Fig.ll.3.Simultaneous separation of some cations in the system WKAC. Abbreviations as in Fig.11.1.
9
-
i,
f
Fig.ll.4. Isotachopherogram of the separation of some cations in the system WKAC, using a thermometric detector. 1 = Kt; 2 = Ba”; 3 = Ca? 4 = Na’; 5 = Ni”; 6 = Cd2+;7 = Pb2+;8 = (C,H,), W; 9 = Trist. T = Increasing temperature; t = time.
11.1.4. The system WKCAC
The leading electrolyte is potassium hydroxide in water, adjusted to pH 6.37 by adding cacodylic acid Tris’ is used as the terminating ion. This higher pH was chosen so as t o investigate the effect of increased pH. In the system WKCAC, all ions have lower effective mobilities owing to the higher pH (some cationic species have pK values between 5 and 7) and to complex formation. The effective mobilities of N3+,Cr3+ and Fe3+are too low. Imidazole shows a typical shift in step height. It has a pK value of 6.95 and at higher pH its effective mobility will decrease.
290
SEPARATION OF CATIONIC SPECIES IN AQUEOUS SOLUTIONS
In order to check this effect, some experiments were carried out with the same buffer at pH 6.53. For some cations of strong electrolytes the step heights were nearly identical, while the step height of imidazole increased (see Table 1 1.6). Figure 1 1.5 shows which ions can be separated simultaneously. In Fig.ll.6, the isotachopherogram is given for the separation of the cations Ba2+, Ca2+.N$. Ni2+,Mnz+, Cu2+ and (C2H,),N+. The leading ion was K'and terminator was Tris'.
Ni
Fig.ll.5. Simultaneous separation of some cations in the system WKCAC. Abbreviationsas in Fig.11 . l .
Fig.ll.6. Isotachopherogram of the separation of some cations in the system WKCAC, using a thermometric detector. 1 = K+;2 = Ba2+;3 = Ca"; 4 = Na+;5 = Ni2+;6 = Mn2*;7: Cu"; 8 = (C, H 5 )4 N+; 9 = Tris+. T = Increasing temperature; t = time.
SEPARATION USING A THERMOCOUPLE AS DETECTOR 72 __
h i- 1
-1
12
29 1
I
f,
-1
Fig.ll.7. Isotachopherogram of a test mixture of cations carried out in the operational system at pH 5.4 with water and deuterium oxide as solvents (Table 11.3). A conductivity detector (a.c. method) and a W adsorption detector (256 nm) were applied 1 = K+; 2 = BaZ+;3 = Na+;4 = (CH,), N+; 5 = Pb2+; 6 = C,H,N+-CH,-CO-NH-NH, ;7 = Tris'; 8 = h i s t i d i d ; 9 = creatinine*; 10 = bemidine+; 11 = e-aminocaproic acid+; 12 = raminobutyric acid+. The amplification of both the UV absorption detector and the conductivity detector was not changed. A = Increasing U V absorption, R = increasing resistance; t = time. TABLE 11.7 DIFFERENCES IN THE EFFECTIVE MOBILITIES OF SOME CATIONS IN THE SOLVENTS WATER AND DEUTERIUM OXIDE The values (h) refer to the step heights (mm) as measured in the linear trace of the conductivity detector.
Ionic species K+ Baa+ Na Tma' Pb2+ C,H,N'-CH,-CO-NH-NH, +
hHZO 0
8.8 14.2 20.8 25.4 39.4
hDzO
Ionic species
hH,O
hD,O
0 9.1 16.9 23.8 34.8 44.8
Tris' Histidine' Creatinine' Benzidine' e-Aminocaproic acid+ y-Aminobutyric acid+
51.0 58.5 65.6 81.3 109.2 115.6
54.8 65.6 78.0 98.1 130.6 149.2
292
SEPARATION OF CATIONIC SPECIES IN AQUEOUS SOLUTIONS
TABLE 11.8 RELATlVE STEP HEIGHTS OF CATIONS IN THE OPERATIONAL SYSTEM LISTED IN TABLE 11.3 WITH WATER AND DEUTERIUM OXIDE AS THE SOLVENTS For the experiments with deuterium oxide, the same amounts of electrolytes as in the experiments with water were dissolved. The accuracy is better than 4%. The values given are t o be used only for the identification of cations in isotachophoretic analyses in the operational systems given. The potassium ion (leading ion) has a relative step height of 0, while the sodium ion has a relative step height of 100. The current was stabilized at 90 pA. - - = No UV absorbance; - = not measured.
Ionic species
H*O lOOh
-
uv absorbance
D,O lOOh
-
hNa Amine, butyl Amine, diethanol Amine, ethanol Amine, Zethylaminoethyl Amine, octyl Amine, triethanol Amine, triethyl 2-Amino-2-methyl-1,3-propanediol Amphetamine Arginine Ammonium, tetrabutyl Ammonium, tetraethyl Ammonium, tetramethyl Barium(I1) Benzidine Benzidine, 3,3-methoxy Butyric acid, 3-amino Cadmium(I1) Calcium(I1) Caproic acid, 2-amino Chromium(II1) Cobalt(I1) 2,4,6-Collidine Copper(1I) Creatinine Diamine, trimethylene Diamine, o-phenylene Girard reagent D Girard reagent P Girard reagent T Guanidine Histidine Hydrazine Hy droxylamine Imidazole Iron(I1) Lanthanum(II1) Lead(I1)
225 29 2 159 51 367 290 290 343 350 422 635 304 147 59 576 814 813 142 86 772 175 114 315 169 462 35 557 280 277 280 83 411 59 134 119 108 109 179
_
165 350 -
313 335 409 590 29 1 142 54 580 881 154 81 768 197 124 290 237 460 20 550 260 265 252 95 388 64 132 122 128 138 210
uv absorbance
293
SEPARATION USING CONDUCTIVITY AND UV DETECTORS TABLE 11.8 (continued)
HZ0 100 h
Lithium(1) Lysine Magnesiurn(I1) Manganese(I1) Nickel(I1) Phenazone, 4-amino 3-Picoline Piperidine Piperidine, 1-methyl Purine, 6,8-dihydroxy Pteridine,2,4-diamino-6,7-dimethyl F'yridine Sitver(1) Sodium(1) Strontium(I1) Tetramine, hexamethylene Tin(I1) o-Tolidine Tris (hydroxymethy1)aminomethane Zinc(1I)
uv
-
absorbance
hN,
(%I
194 400 102 114 115 1014 217 214 252 1051 439 24 2 18 100 73
196 395 110 120 130 221 21 5 231
461
476
1083 816 358 130
-
432 232 -
100 -
__ -_
__ __
__ -
88 __
-_
98 92 -
__
-
-_
-
-
807 333 134
96
_-_
11.1.5. The system WKDIT
The leading electrolyte is potassium hydroxide in water, adjusted to pH 7.39 by adding diiodo-Ltyrosine, and the terminator is Tris. At this pH, many ions do not migrate at all and sometimes precipates are formed. While all possible step heights were measured, the above effects were such that no separations could be achieved in this system. For some special purposes, however, this sytem can be useful, e.g., in combination with other systems.
1 1.2. SEPARATION OF CATIONIC SPECIES IN WATER AND DEUTERIUM OXIDE USING A CONDUCTIVITY DETECTOR (a.c. METHOD) AND A UV ABSORPTION DETECTOR (256 nm)
As already shown in section 11.1, cations can be separated in aqueous systems and the mobilities can be influenced by changing the operating conditions. Also, with these types of detectors all types of systems can be prepared and analyses can be performed. For the reasons mentioned in Chapter 8, only the operational system listed in Table 11.3
294
SEPARATION OF CATIONIC SPECIES IN AQUEOUS SOLUTIONS
(potassium acetate-acetic acid at pH 5.4), will be discussed*. Both water and deuterium oxide were used as solvents. During a long series of analyses, it was found that, in spite of the fact that the electric leak to earth of the conductivity probe can be neglected (Chapter 6), a layer is formed on the micro-sensing electrodes (Kolbe electrolysis). Owing to this layer, irreproducible results can be expected if no precautions are taken. Therefore, between analyses, the electrodes were depolarized (by connecting the anode of a power supply with the micro-sensing electrodes) for approximately 5 sec with an electric current of approximately 5 PA. For a reproducible analysis, the base line must show no drift (less than 1%). In Fig. 11.7, a separation of cations in water and deuterium oxide is shown. This mixture can be used as a test mixture of cations, as discussed in the Chapter 8 (Fig.8.1). The differences obtained in the systems with water and deuterium oxide are listed in Table 11.7. Because the operational conditions are comparable, except for the solvent, the shift is due to two main factors: the solvation and the difference in the pH and pD scale. In Table 11.8, some step heights are listed for some cations obtained in the operational system in Table 11.3 with water and deuterium oxide as the solvents.
*Many data are given from thermometric registration (Table 11.6), which can be used. The values given in Tables 11.6 and 11.8 can be compared.
Chapter I 2
Separation of anionic species in aqueous solutions SUMMARY Separations of anionic species in water and deuterium oxide solutions are discussed. In the first section, two operational systems using a thermometric detector with measurements in aqueous solutions are considered. In the second section, the results obtained using a conductimeter (a.c. method) and a UV absorption detector are given, with experimental data for separations in deuterium oxide. The time of analysis with the thermometric detector is approximately 30-45 min and with the high-resolution detectors approximately 15 min from the start of the experiment till the detection of the last zone.
12.1. SEPARATION OF ANIONIC SPECIES IN AQUEOUS SOLUTIONS USING A THERMOMETRIC DETECTOR The results given in this section were obtained in the equipment briefly discussed in section 7.4.2. The systems were measured in the two operational systems listed in Tables 12.1 and 12.2. Most of the organic acids have pK values not higher than about 5.5 and will therefore be almost completely ionized at the pH values chosen, i.e., pH 6 and 7. In fact, only separations according to mobilities are carried out, not according to the pK values. 12.1.1. Operational system histidine/histidine hydrochloride (pH 6 ) Step heights* measured in this system are listed in Table 12.3 and refer to 0 PA. Many anions have the same or almost the same step heights, because their effective mobilities are almost identical, le., they cannot be separated. In our experiments we found that anions can be separated in these systems if their step heights differ by about 10%when using a thermometric detector (thermocouple). It will be shown in section 12.2 that commonly, if a separation according to mobilities fails, a separation according to pK values will be successful. In Fig. 12.1, a separation is shown of a mixture of anions carried out in this operational system using a thermocouple as detector. Fig.12.2 shows the separation of another mixture of anions. From the combination of anions chosen, it will be clear that, e.g. , nitrate and sulphate cannot be separated under these conditions, le., with this operational system and detector.
*The step height in an isotachopherogram is a qualitative measure for the ionic species, where the distance between two successive peaks (the differential signal of the linear thermocouple signal) gives all necessary quantitative information.
295
SEPARATION OF ANIONIC SPECIES IN AQUEOUS SOLUTIONS
296 TABLE 12.1
OPERATIONAL SYSTEM AT pH 6 SUITABLE FOR ANIONIC SEPARATIONS Solvent: H,O and D,O. Electric current &A): Cu. 50-100. Purification: Morpholinoethanesulphonic acid (MES) is recrystallized three times and the crystals are washed with acetone. Electrolyte
Anion Concentration Counter ion PH Additive
Leading
Terminating
cl-
E.g., MESCu. 0.01 N Tris+ Cu. 6 None
0.01 N Histidine' 6.02 0.05% Polyvinyl alcohol (Mowiol)*
*For experiments with a thermometric detector, this additive is not necessary.
TABLE 12.2 OPERATIONAL SYSTEM AT pH 7 SUITABLE FOR ANIONIC SEPARATIONS Solvent : Electric current hA): Purification:
H, 0. Cu. 50-100.
Morpholinoethanesulphonic acid (MES) is recrystallized three times and the crystals are washed with acetone. Electrolyte
Anion Concentration Counter ion
PH Additive
Leading
Terminating
c10.01 N Imidazole+ 7.05 0.05% Polyvinyl alcohol (Mowiol)*
E.g., MESCa. 0.01 N Tris' Ca. 6 None
*For experiments with a thermometric detector, this additive is not necessary.
12.1.2. Operational system imidazole/imidazole hydrochloride (pH 7) In this operational system, the absolute mobility of the counter ion (imidazole) is greater than in the operational system listed in Table 12.1 in which histidine is the counter ion. This means that all zone resistances are lower and consequently all step heights are smaller. The resolution will also be decreased by the more mobile counter ion. Thls was found particularly in experiments with a conductivity detector.
SEPARATION USING A THERMOMETRIC DETECTOR
29 7
TABLE 12.3 STEP HEIGHTS FOR SOME ANIONS OBTAINED IN THE OPERATIONAL SYSTEMS LISTED IN TABLES 12.1 and 12.2 The values are the step heights found in the isotachopherograms in the linear trace of the thermocouple signal. The values are given in millimetres and refer to 0 fiA. The experiments were carried out with a current stabilized at 70 @A. -
Ionic species
Adipic acid Acetic acid Acetylsalicylic acid Allomucic acid Azelaic acid Benzoic acid Benzoic acid, rn-amino Benzoic acid, o-amino Benzoic acid, p-amino Benzyl-dl-aspartic acid Benzoic acid, 5-bromo2,3-dihydroxy Butyric acid Cacodylic acid Caffeic acid Capric acid Caproic acid Caprylic acid Carbonic acid Chloric acid Chromic acid Cinnamic acid Citric acid Crotonic acid Dichromic acid 2,4-Dihydroxybenzoic acid EDTA Formic acid D-Galacturonic acid Glucuronic acid Glutamic acid Glycolic acid Glyoxylic acid Guanidoacetic acid Hippuric acid Hydrofluoric acid a-Hydroxybutyric acid 4,5-Imidazoledicarboxylic acid Indolylacetic acid Iodic acid Isovaleric acid
System*
Ionic species
A
B
334 366 474 319 365 430 454 408 454 531
252 281 380 250 274 340 340 350 440
460 428 620 526 51 1 478 510 520 sl.* 24 3 259 500 292 416 249 459 3 34 276 n.s.m.509 476 360 399 n.s.m. 490 271 470 326
316 356 400 420 400 386 400 320 sl. 190 173 368 200 326 174 354 285 216 420 386 286 290 n.s.m. 391 218 375 240
n.s.m. 358 460
n.s.m. 290 360
System*
2-K&ogulonic acid Kynurenic acid Lactic acid Laevulinic acid Maleic acid dl-Malic acid Malonic acid Mandelic acid Methacrylic acid Molybdic acid Naphthalene-2sulphonic acid Nicotinic acid Nitric acid rn-Nitrobenzoic acid p-Nitrobenzoic acid Nitrous acid Orotic acid Orthophosphoric acid Oxalic acid Pelargonic acid Periodic acid Peroxodisulphuric acid Phenidon Phenylacetic acid o-Phthalic acid Picric acid Pimelic acid Propionic acid, p-chloro Pycrolonic acid
A
B
496 470 391 430 312 286 280 456 4 04 335
395 383 314
496 436 220 440 442 217 454 408 236 494 358 212 n.s.m. 44 8 328 446 345 399 n.s.m.
358 342 174 340 345 170 310 266 180 393 250 162 n.s.m. 366 246 350 264 316 -
298
-
301 -
235 204
224 224 408 304 304 420 283
172 323 224 244 344 228
-
216 222 204 364 312 185
Pyrazine-2,3-dicarboxylic acid Pyrazole-3,5-dicarboxylic acid F'yrophosphoric acid Pyrosulphuric acid Pyrosulphurous acid Salicylic acid Succinic acid Sulphamic acid Sulphanilic acid Sulphosalicylic acid
-
(Continued on p.298)
298
SEPARATION OF ANIONIC SPECIES IN AQUEOUS SOLUTIONS
TABLE 12.3 (continued) Ionic species
Sulphuric acid Sulphurous acid Tartaric acid Tartronic acid Tiglic acid Trichloroacetic acid Trimethylacetic acid
sys tem* A
B
224 286 280 256 410 399 470
169 170 216 195 332 316 363
Ionic species
System* B A
Uric acid 7-Oxoiminovaleric acid Vanadic acid Vitamin C Xanthurenic acid
424 466 320sl. 510 484
*Systems: A = histidine/histidine hydrochloride; B = imidazole/imidazole hydrochloride. sl. = An indefinite step height was obtained. The signal slopes slowly to an end-point. *n.sm. = Not sufficiently mobile. *Ir
n t
Fig.12.1. Isotachopherogam of the separation of some anions in the operational system listed in Table 12.1 (pH 6). 1 = Chloride; 2 = nitrate; 3 = oxalate; 4 = tartronate; 5 = formate; 6 = citrate; 7 = maleate; 8 = adipate; 9 = iodate; 10 = trichloroacetate; 1 1 = mandelate; 12 = ascorbate. The current was stabilized at 70 rk T = Increasing temperature; t = time.
360 382 184 390 353
SEPARATION USING A THERMOMETRIC DETECTOR
299
Fig.12.2. Isotachopherogram of the separation of some anions in the operational system listed in Table 12.1 (pH 6). 1 = Chloride; 2 = sulphate; 3 = chlorate;4 = chromate; 5 = malonate; 6 = pyrazole3,5-dicarboxylate; 7 = adipate; 8 = acetate; 9 = p-chloropropionate; 10 = phenylacetate; 11= ascorbate. The current was stabilized at 70 PA. T = Increasing temperature; t = time. This isotachopherogram is used in several places in this book for comparison of the various detectors and the various solvents.
The smaller steps in the system imidazole/imidazole hydrochloride correlate correctly with the calculated zone resistances (see section 4.5). Some step heights are low, which can be ascribed to a dissociation that is more complete in this system. Some compounds that show these very large shifts are citric acid (pK3 = 6.4), orthophosphoric acid (pK, = 7.21) and chromic acid (pKz = 6.49). Fig.12.3 shows aa isotachopherogram of the separation of some anions carried out in the operational system listed in Table 12.2. Although the resolution is lower than in the operational system at pH 6, in general anions can be separated if the step heights given in Table 12.3 differ by about 10%. The disadvantage of this operational system is the relatively high pH, which soon gives a disturbance due to carbonate.
300
SEPARATION OF ANIONIC SPECIES IN AQUEOUS SOLUTIONS
t
\
n I1
rc--
t
Fig.12.3. Isotachopherogram of the separation of some anions carried out in the operational system listed in Table 12.2 @H 7). 1 = Chloride; 2 = sulphate; 3 = oxalate; 4 = chlorate; 5 = formate; 6 = pyrazole-3,5-dicarboxylate;7 = adipate; 8 = iodate; 9 = P-chloropropionate; 10 =nicotinate; 11 = ascorbate. The current was stabilized at 70 PA. If this isotachopherogram is compared with those in Figs.12.1 and 12.2, it can be seen that the resolution is smaller, although separations are still possible.
12.2. SEPARATION OF ANIONIC SPECIES IN AQUEOUS SOLUTIONS USING A CONDUCTIVITY DETECTOR (a.c. METHOD) AND A UV ABSORPTION DETECTOR (256 nm) 12.2.1. Introduction In this section, we consider isotachophoretic separations in four operational systems with water and deuterium oxide. The pH values were chosen arbitrarily as 7.5 (Table 12.4), 6 (Table 12.1), 4.5 (Table 12.5) and 3 (Table 12.6). The results obtained in these systems are listed in Table 12.7 for water and Table 12.8 for deuterium oxide. The analyses discussed in section 12.2.2 were carried out mainly in these operational systems, although the pH, for optimal separation, may be chosen to be higher or lower than those given in the tables. The analyses were carried out with the equipment described in section 7.4.4.
SEPARATION USING CONDUCTIVITY AND W DETECTORS
30 1
TABLE 12.4 OPERATIONAL SYSTEM AT pH 7.5 SUITABLE FOR ANIONIC SEPARATIONS Solvent: H,Oand D,O Electric current &A): CQ.50-100. Purification: Morpholinoethanesulphonic acid is recrystallized three times and the crystals are washed with acetone. Electrolyte Leading Anion Concentration Counter ion
PH Additive
Terminating
a-
MES-
0.01 N Tris+ 7.5 0.05% Polyvinyl alcohol (Mowiol)
Ca. 0.01 N
Tris+ Ca. 6 None
TABLE 12.5 OPERATIONAL SYSTEM AT pH 4.5 SUITABLE FOR ANIONIC SEPARATIONS H, 0 and D, 0. Solvent: Electric current (PA): Cu. 50-100. Morpholinoethanesulphonic acid (MES) is recrystallized three times and the Purification: crystals are washed with acetone. c-Aminocaproic acid is recrystallized.
Electrolyte
Anion Concentration Counter ion PH Additive
Leading
Terminating
c10.01 N COOH-C,H,-CH,N+H 4.5 0.05% Polyvinyl alcohol (Mowiol)
MESCa. 0.01 N Tris' CQ,4 None
12.2.2. Applications
As described in Chapter 11, we can change from one operational system to another if a complete separation between various ionic species is sought. It is almost always more convenient to perform the analyses in two or more operational systems than to lengthen the narrow-bore tube, which involves the use of higher potential gradients. Less attention is paid here to the influence of the activity on the effective mobility (the concentration of the leading electrolyte must be changed), because if the concentration is decreased*, higher potential gradients must be used, the effect of electroendosmosis is difficult to suppress and higher demands are placed on the purity *If the concentration is increased, many substances are no longer soluble.
SEPARATION OF ANIONIC SPEClES IN AQUEOUS SOLUTIONS
302 TABLE 12.6
OPERATIONAL SYSTEM AT pH 3 SUITABLE FOR ANIOMC SEPARATIONS
H, 0 and D, 0. Solvent Electric current (PA): Ca. 50-100. Purification : p-Alanine must be purified by recrystallization from a methanol-water mixture and the crystals are washed with acetone. Electrolyte
Anion Concentration Counter ion PH Additive
Leading
Terminating
c1-
E.g., CH,COOCa. 0.01 N Tris+ Ca. 3 None
0.01 N COOH-CH, -CH, WH 3 0.05% Polyvinyl alcohol (Mowiol)
of the chemicals used in the operational systems. An example of the use of two operational systems is given in Fig. 12.4, where the separation of the oxidation products of acetylsalicylic acid is shown. The oxidation was performed by heating the compound in solution to 90°C and blowing air through it. The separations shown in Fig. 12.4a and b were carried out in the operational system at pH 6 (Table 12.1), while the analysis in Fig.12.4~was performed at pH 3.2 (Table 12.6). It is clear that a complete separation can be achieved at low pH. The isotachopherograms in Fig.12.5 were obtained in the operational system at pH 6 (Table 12.1), with water and deuterium oxide as the solvents. This mixture is nowadays applied as the test mixture of anions suitable for ‘trouble-shooting7(Fig.8.1). The sequence of the compounds is given in Table 12.9, where the shifts obtained by the use of water and deuterium oxide are listed. Again, these shifts are due mainly to the differences in solvation and differences in the pH and pD scales. Large shifts occur for the components for which the pH of the operational system chosen has a significant effect on the dissociation (pK values pHoperationalsystem). Fig. 12.6 shows that solvation really plays a role. In these isotachopherograms, the separation of nitrate and sulphate is shown in the operational system at pH 6 (Table 12.1). Wtiilc a separation could be achieved only with difficulty when water was used as the solvent (here the concentration of the leading electrolyte plays an important role), the separation in deuterium oxide posed no problems. One should note the linear trace of the UV absorption detector, which shows that nitrate has a small W absorption, clearly visible in the experiments with deuterium oxide, while this W absorption is spread over the total mixed zone when water was used as the solvent. The isotachopherograms in Fig.12.6b and c are given in order t o show the reproducibility. In Fig.12.7, two important phenomena are shown. A research group working mainly on peptide synthesis, asked us for very reproducible quantitative information about the amount of chloride in their samples. As discussed in the conclusion of Chapter 10, this can be achieved by measuring the retardation of the appearance of the first sample zone
-
303
SEPARATION USING CONDUCTIVITY AND UV DETECTORS
-6
-5
-4
-3 -2
i
-1
Fig.12.4. Isotachopherograms of the separation of the oxidation products of acetylsalicylic acid in two different operational systems. (a), Reaction mixture before oxidation, analysis carried out in the operational system at pH 6 (Table 12.1); (b), reaction mixture after oxidation, analysis carried out in the operational system at pH 6 (Table 12.1); (c ),reaction mixture after oxidation, analysis carried out in the operational system at pH 3.2 (Table 12.6). The current was stabilized at 80 PA. 1' = Chloride; 2' = acetate; 3' = salicylate and phosphate; 4' = acetylsalicylate; 5 ' = MES; 1 = chloride; 2 = phosphate; 3 = salicylate; 4 = acetylsalicylate; 5 = acetate; 6 = propionate. A = increasing UV absorption; R = increasing resistance; t = time.
with a smaller effective mobility than that of the leading ion, in this particular instance the chloride ion. The reproducibility of these analyses, performed with a sample tap, proved t o be better than 2%. Nevertheless, a more mobile ion than chloride was sought. The literature indicates that the Fe(CN6)& ion is a fast moving ion at infinite dilution and is much faster than the chloride ion. For this reason, three operational systems we re prepared : for Fig.12.7a: 0.01 N Fe(CN6)4- with 0.02 N histidine; for Fig.12.7b: 0.005 N Fe(CN6)" with 0.01 N histidine; for Fig.12.7~:0.001 N Fe(CNJ4- with 0.002 N histidine.
SEPARATION OF ANIONIC SPECIES IN AQUEOUS SOLUTIONS
304
15
H O 2
I
I
I
c _
ii
20 s e c
~
1
15 -t \
YY-
Fig.12.5. Separation of a test mixture of anions in the operational system at pH 6 (Table 12.1) with water and deuterium oxide as solvents. The sequence of the anions is listed in Table 12.9, where the differences in step height are compared. The current was stabilized at 70 PA. A = Increasing UV absorption;R = increasing resistance; r = time.
305
SEPARATION USING CONDUCTIVITY AND UV DETECTORS
An injection was made of an industrial sample that contained the chloride ion and the isotachopherograms shown in Fig.12.7 were obtained. No attention will be paid to the mixture of anions (x). In Fig.l2.7a, it is clear that the chloride ion is more mobile than the Fe(CN6)4- ion. This can be seen in the UV trace and the linear trace of the conductivity detector. - . It should be noted that the concentration of the original Fe(CN6)& thistidine is not changed after the passage of the chloride ion, which can be seen in the linear trace of the conductivity detector and the linear trace of the W absorption detector [Fe(CN,)4- has a W absorption]. In Fig.12.7b, a mixed zone between Cl- and Fe(CN6>e can be seen. In Fig. 12.7c, Fe(CN6)4- is moving in front of Cl-.
"f
2+3+ I--
-
-+t
c
!
t
r
I
: I
t Ib
1"
C
Fig.12.6. Separation of nitrate andsulphate in the operationalsystemat pH 6 (Table 12.1) withwater and deuterium oxide as the solvents. The difference in solvation of these two solvents is clearly visible. 1 = Chloride; 2 = nitrate; 3 = sulphate; 4 = acetate. The current was stabilized at 7 0 PA. A = Increasing W absorption;R = increasing resistance; t = time.
306
SEPARATION OF ANIONIC SPECIES IN AQUEOUS SOLUTIONS
3 @ 2+i
1
3 0
2
Fig.12.7. Isotachopherograms with Fe(CN,)4- as the leading ion at concentrations of (a), 0.01 N; (b), 0.005 N; (c), 0.001 N. Histidine was used as the buffering counter ion. (a) shows that C1- is more mobile than Fe(CN,)4-, but that the original concentration is not changed if this mobile chloride passes the first separation boundary; (b) shows that a mixed zone is obtained; (c) shows that Cl- is less mobile than Fe(CN,)4-. The current was stabilized at 70 MA.A = Increasing W absorption; R = increasing resistance; t = time. 1 = Fe(CN,)4-; 2 = C1-; 3 = MES-; 4 = mixture of anions.
Quantitative analyses could easily be performed, although the leading electrolyte must be freshly prepared each time as it is unstable. It should be repeated that the concentration change in the leading electrolyte of the operational system may give this system completely different properties. The concentration adjustment is not influenced if impurities with a higher mobility than that of the leading ion pass the first separation boundary. The test mixture of anions (Fig.12.5) was also analyzed in the mixture urea-water (1: 1). Differences similar to those in the isotachopherograms shown in Chapter 16 were obtained. Because of the high concentration of urea, these operational systems are difficult to work with, for practical reasons as the eqhpment soon becomes covered with urea. Nevertheless, this system can be used, because many organic substances are more soluble in it and it is not aggressive.
SEPARATION USING CONDUCTIVITY AND UV DETECTORS
307
TABLE 12.7 RELATIVE STEP HEIGHTS OBTAINED IN THE OPERATIONAL SYSTEMS LISTED IN TABLES 12.1, 12.4,12.5 and 12.6 FOR VARIOUS ANIONIC SPECIES The accuracy is better than 4%. The values given are to be used only for the identification of anionic species in isotachophoretic analyses in the operational systems considered. The chloride ion (leading ion) has a relative step height of 0, while the chlorate ion has relative step height of 100. At pH 3.0 the current was stabilized at 90 w A ;at pH 4.5 the current was stabilized at 80 MA;at pH 6.0 the current was stabilized at 70 PA; at pH 7.5 the current was stabilized at 80 MA.h = step height. - _ -- No UV absorbance; - = not measured. Ionic species
pH = 3.0
lOOh hchlorate
Aspartic acid, dl. benzyl Acetic acid Acetic acid, monochloro Acetic acid, dichloro Acetic acid, trichloro Benzoic acid Benzoic acid, p-amino Benzoic acid, 2,4-dihydroxy Benzoic acid, pnitro Butyric acid Cacodylic acid Capric acid Caproic acid Caprylic acid Chlorate Chromic acid Chromic acid, hi Citric acid Enanthic acid Formic acid E'umaric acid Glucaric acid Glucuronic acid Glu tamic acid Glycerinic acid Glycolic acid Gluconic acid Hippuric acid
pH = 4.5 UV absorption
lOOh
pH = 6.0
UV
lOOh
pH UV
7 absorp- 7 absorpchlorate tion chlorate tion
=
100h
hchlorate tion
-
3880
1090
1150 484
1139 466
745
516
487
465
578
537
542
524
656 2810
699 1200
620 726
596 7 23
6290
1780
836
768
1460
930
803
734
1600 5280 n.s.m.* n.s.m. 6520 7280 100 184
890 1240 6610 6260 1930 2320 100 173
771 751 1509 1486 905 1062 100 134
759 725 940 1410 859 1011 100 33
210 1370 6750 1010 980
1370
1180
132 259 988 208 217 355 1033 927 629 456 1023 962
35 178 94 8 209 230
2200 3750 1670 1620
168 51 9 2040 285 338 1310 1510 760 587
-
-
UV
-absorp-
-
-
7.5
_
1019 887 61 1 469 412
308
SEPARATION OF ANIONIC SPECIES IN AQUEOUS SOLUTIONS
TABLE 12.7 (continued) Ionic species
Iodic acid orKetoglutaric acid Lactic acid Laevulinic acid Maleic acid Malic acid Malonic acid Me thacrylic acid Naphthalene-2sulphonic acid Nicotinic acid Nitric acid Nitrous acid Orotic acid Oxalic acid Pelargonic acid Perchloric acid Phenylacetic acid Phosphoric acid Phthalic acid Picric acid F’imelic acid Pivalic acid Propionic acid Propionic acid, p-chloro Pyrazine, 2,3dicarbox ylic acid Pyrazole, 33dicarboxylic acid Salicylic acid Succinic acid Sulphamic acid Sulphanilic acid Sulphuric acid Sulphurous acid Tartaric acid Tartronic acid
pH = 3.0
pH = 4.5
lOOh
uv
‘chlorate
absorp tion
lOOh
pH = 6.0
uv
lOOh
pH = 7.5
w
100h
498
17
500
464
460
915 1910 4220 508 1460 750
__
__
505 1060 1390 491 5 24 469
259 609 744 305 259 209
250 593 719 207 253 169
3360
8
1100
619
6 24
830 5040 20 32 970 400 5970 69
89 100
910 1570 21 31 810 120 1880 63
798 731 35 25 738 93 1150 75
779 667 33 19 720 83 1023 72
823 614 382 766 450 859 635
814
-_ __ __
1210 750 5 00 890 1270 1910 1460
326 346 753 412 821 604
__
820
6 29
565
3680 840 1280 820 4330 7090 4480 1820
__-
50 __
__
__ 90 5
__ __
12
__
72 100
616
73
368
296
290
876 1060 2720 308 1260 33 364 1000 696
65 30
303 686 84 1 311 7 87 49 332 321 274
293 647 301 294 688 60 284 233 157
288 667 279 303 719 48 172 226 142
__ __
100 __
--
__ -_
*n.s.m. = not sufficiently mobile.
w
7 absorp- 7 absorp- - absorpchlorate tion chlorate tion %hlorate tion
SEPARATION USING CONDUCTIVITY AND UV DETECTORS
309
TABLE 12.8 RELATIVE STEP HEIGHTS OBTAINED IN THE OPERATIONAL SYSTEMS AT pH 6 (TABLE 12.1) FOR VARIOUS ANIONIC SPECIES WITH WATER AND DEUTERIUM-OXIDE AS SOLVENTS The accuracy is better than 4%. The values are given for comparison of the two solvents. The experiments with water were carried out at 70 PA and those with deuterium oxide at 80 PA*. In both solvents the chloride ion (leading ion) has a relative step height of 0, while the chlorate ion has a relative step height of 100. h = step height. -- = No UV absorbance. lonic species
40 100 h hchlorate
Aspartic acid, dl-benzyl Acetic acid Acetic acid, monochloro Acetic acid, dichloro Acetic acid, trichloro Benzoic acid Benzoic acid, p-amino Benzoic acid, 2,4-dihydroxy Benzoic acid, p-nitro Butyric acid Cacodylic acid Capric acid Caproic acid Caprylic acid Chlorate Chromic acid Chromic acid, bi Citric acid Enanthic acid Formic acid Furnaric acid Glucuronic acid Glutamic acid Glycolic acid Hippuric acid Iodic acid a-Ketoglutaric acid Lactic acid Laewlinic acid Maleic acid Malic acid Malonic acid Methacrylic acid Naphthalene-2-sulphonic acid Nicotinic acid Nitric acid Nitrous acid Orotic acid
1150 4 84 487 542 620 7 26 836 803 771 751 1509 1486 905 1062 100 134 132 259 988 208 217 1033 927 456 962 464 259 609 744 305 259 209 619 798 731 35 25 7 38
uv absorption (%)
100 h hchlorate
uv absorption
(%I
1244 519 526 583 669 7 86 923 873 840 818 1787 1814 998 1170 100 146 145 277 1099 217 225 1143 1015 503 1060 486 268 643 801 323 27 2 224 680 858 817 28 17 808
(Continued on p. 310)
310
SEPARATION OF ANIONIC SPECIES IN AQUEOUS SOLUTIONS
TABLE 12.8 (continued) Ionic species
HZ0 lOOh -
hcMorate
D*O
uv
lOOh
absorption (%)
&hlorate
W absorption (%)
88 1252 915 677 410 819 972 699 701 321 316 703 314 313 736 57 319 167
93 1150 823 614 382 766 859 635 6 29 296 293 647 301 294 688 60 284 157
Oxalic acid Pelargonic acid Phenylacetic acid Phosphoric acid Phthalic acid Picric acid Pivalic acid Propionic acid Propionic acid, p-chloro Pyrazine, 2,3-dicarboxylic acid Pyrazole, 3,5-dicarboxylic acid Salicylic acid Succinic acid Sulphamic acid Sulphanilic acid Sulphuric acid Sulphurous acid Tartronic acid
-
*The step height is not influenced by this difference in electric current, if conductivity detection is applied (a.c. method). TABLE 12.9 DIFFERENCES IN THE EFFECTIVE MOBILITIES OF SOME ANIONS IN THE OPERATIONAL SYSTEM AT pH 6 (TABLE 12.1) WITH WATER AND DEUTERIUM OXIDE AS THE SOLVENTS The values ( h )are the step heights (mm) that can be measured in the linear trace of the conductivity detector. Ionic species
'H,O
hD,O
Ionic species
hH,O
hD,O ~~
Sulphate Chlorate Chromate Malonate Pyrazole-3,5-dicarboxylate Adipate Acetate
5.6 9.3 12.4 18.8 27.5 37.2 44.9
5.6 9.8 14.2 21.8 30.8 42.8 51.4
p-chloropropionate Benzoate Naphthalene-2sulphonate Glutamate Enanthat e Benzyl-dl-aspartate
58.4 67.5 74.0 86.1 92.2 107.4
69.5 76.6 83.7 99.0 102.2 121.6
Chapter 13
Amino acids, peptides and proteins SUMMARY The separation of amino acids in aqueous solutions at low pH, at high pH and at ‘neutral’ pH when propionaldehyde is added to the electrolytes is discussed. Experimental data for the amino acids in several operational systems are given. The separation of proteins in an operational system at neutral pH is discussed. The addition of a mixture of amphiprotic substances, by which the proteins are diluted in their zone, stabilizes proteins of high moleculer weight, although this technique deviates from the originiil principle of isotachophoresis as discussed in Chapter 4. For small peptides, the addition of amphiprotic substances is not necessary. The time of analysis is approximately 15 min from the start of the experiment to the detection of the last zone.
13.1. AMINO ACIDS 13.1.1. Introduction
The analysis of amino acids is extremely important and nearly all separation techniques have been applied to them. Good results have been obtained by various research workers who analyzed these substances by liquid chromatography [ 1,2] , gas chromatography and electrophoresis. Many references can easily be found and they are not cited here because only an incomplete list could be given. So far, little attention has been paid to the separation of amino acids by isotachophoresis [3-51. In this section, we discuss various systems in which amino acids can be analyzed by isotachophoresis. The application of t h s technique to amino acids is particularly interesting because in theory they can be separated both as cations and as anions. The possibility of achieving a complete separation according to pK values (Chapter 5) is, of course, considered first. It is clear that n o systems at a neutral pH can be chosen, because most amino acids have their pZ values at neutral pH and hence will have a negligible migration in an electric field. It is also well known that amino acids form stable complexes, e.g, with metals and aldehydes. If such a complex is formed, not only the molecular size and solvation change, but also the pK values, and the effective mobility therefore changes in an operational system chosen. Several operational systems are considered below in order to show complex formation and the variations in the effective mobilities. Much more research, however, needs to be carried out. In particular, solvents or a combination of solvents in which the amino acids are more soluble than they are in aqueous systems must be sought. Unusual combinations of systems may be obtained e.g., a combination of urea and water to increase the solubility of the amino acids, to which an aldehyde must be added to decrease the p l 31 1
312
AMINO ACIDS, PEPTIDES AND PROTEINS
values of the amino acids (Schiff base formation) and methanol to stabilize the aldehyde (e.g , propanal). In this section, however, these solvent systems are not discussed as this topic is beyond the scope of this book. The analyses were carried out with the equipment described in Chapter 7, using the modified injection block, the counter electrode compartment with a flat membrane and hgh-resolution detectors. The conductivity detector (a.c. method) and the UV absorption detector (256 nm) were combined. The operational systems considered represent only a few of many possible combinations, and were chosen arbitrarily, although optimal characteristics were sought. Because the operational systems in the equipment can be changed quickly (it usually does not take longer than the normal rinsing and re-filling procedure) and the time of analysis is relatively short (10-1 5 min), sometimes a complete separation between the amino acids in a given mixture can be better achieved by applying two or more systems rather than by optimizing a single system. It will be recalled that a small difference in effective mobility will increase drastically the time of analysis and longer narrow-bore tubes or a counter flow of electrolyte must be applied. The last technique is effective only if the difference in the effective mobilities of the various amino acids is still sufficiently large (see Chapter 17). 13. I .2. Separation at low pH values in aqueous systems
At low pH, most amino acids will migrate as cations. However, most amino acids also have a low effective mobility, so that the pH of the amino acid zone will be lower than that of the leading electrolyte zone. Soon so many H ions are present that a significant proportion of the electricity is carried by the protons. As a result, the amino acids show only small differences in step height as measured in the linear trace of the conductimetric signal*. Only the amino acids L-lysine, L-arginine and L-histidine have a sufficiently high mobility that they can be separated without a visible disturbance of the protons. It does not need further explanation that the pH of the leading electrolyte cannot be decreased too far, because soon zone electrophoretic phenomena occur, e.g., ‘elution’ by the protons. For basic amino acids, an operational system is given in Table 13.1. 13.1.3. Separation at high pH values in aqueous systems
If the pH of the leading electrolyte is above 8, most amino acids will have an effective mobility suitable for a separation according to the isotachophoretic principle. A disadvantage is that at such pH values disturbances from carbon dioxide from the air can be expected. More information on this aspect is given in Chapter 9. If suitable precautions are not taken, the carbonate (hydrogen carbonate) may even obscure the analysis. For optimal results, we found that the electrolytes of the operational systems must be prepared under an atmosphere of nitrogen and stored in polyethylene bottles under *The step height is a measure of the qualitative information in isotachophoretic measurements. It indicates whether a complete separation can be expected, as it is a measure of the effective mobility.
31 3
AMINO ACIDS TABLE 13.1 OPERATIONAL SYSTEM AT pH 5.4 SUITABLE FOR CATIONIC SEPARATIONS
H, 0. Solvent: Electric current @A): Ca. 50-100. Electrolyte -~
Cation Concentration Counter ion PH Additive
Leading
Terminating
K+ 0.01 N CH, COO5.4 0.05% Polyvinyl alcohol (Mowiol)
DL-Ala’ Ca. 0.01 N OH- [added as Ba(OH),]
>I None
nitrogen. Moreover, barium hydroxide of pro analysi quality must be added to the terminating electrolyte in order to prevent any carbonate (hydrogen carbonate) from penetrating into the narrow-bore tube via the reservoir filed with the terminating electrolyte. The addition of barium hydroxide to the leading electrolyte did not improve the separation, however. Because of the high mobility of Ba2+,less sharp boundaries can be expected. If suitable precautions are taken, some carbonate (hydrogen carbonate) may still be detected if an anion with a lugher effective mobility is used as the leading ion. This carbonate (hydrogen carbonate), however, did not obscure both the qualitative and quantitative results. Only a leading ion with an effective mobility higher than or equal to that of the carbonate (hydrogen carbonate) ion can be used, otherwise the carbonate may no longer be visible but may still disturb or at least obscure the analytical result, if it is supported continuously. The resolution will decrease and zone electrophoretic phenomena can soon be expected e.g., ‘elution’ by the carbonate (hydrogen carbonate) ions. Several suitable buffers are commercially available that enable one to work at high pH. Some of them, including bis(3-aminopropyl)amine, trime thylenediamine, L-arginine, 1-methylpiperidine, octylamine, ethanolamine and L-lysine, were tested for purity and effective mobility*. Some of the compounds were found to be very impure and even could not be purified satisfactorily by the usual methods such as distillation, recrystallization or ion exchange. Some of the counter ions show unexpected phenomena, e.g., enforced isotachophoretic systems or undesirable complex formation. Of the compounds mentioned above, only 1 -methyl piperidine, L-arginine, L-lysine, octylamine and ethanolamine gave good results. In Tables 13.2 and 13.3, two operational systems are given in which analyses were performed and for which more data will be given later.
*If a counter ion (buffer) is too mobile, a considerable proportion of the electricity is carried by this counter ion, which results in less sharp zone boundaries and a decrease in resolution.
AMINO ACIDS, PEFTIDES AND PROTEINS
314 TABLE 13.2
OPERATIONAL SYSTEM AT pH ABOUT 9 SUITABLE FOR ANIONIC SEPARATIONS Solvent: H, 0. Electric current (/.LA):CQ. 50-100. Electrolyte Leading
Terminating __-
Anion
5-Br-2,4-diOH-C6H, COO-
Concentration Counter ion PH Additive
0.004 M HOC, H, NH ' 9.0, 9.2, 9.4, 9.6 0.05% Polyvinyl alcohol (Mowiol)
0-Ala- (recrystallized from waterethanol) CQ. 0.01 M Baa+[added as Ba(OH),] Ca. 10.5 None
TABLE 13.3 OPERATIONAL SYSTEM AT pH ABOUT 9 SUITABLE FOR ANIONIC SEPARATIONS Solvent: H, 0. Electric current (fiA): Ca. 50-100. Electrolyte Leading
Terminating
Anion
5-Br-2,4-diOH-C6H, COO-
P- Ala- (recrystallized
Concentration Counter ion PH Additive
0.004 M L-Lys+ 9.1, 9.2, 9.4 0.05% Polyvinyl alcohol (Mowiol)
from wa tere thanol) Ca. 0.01 M Ba2+[added as Ba(OH), J Ca. 10.5 None
The leading ion in these systems was chosen because its effective mobility is almost identical with the effective mobility of the carbonate (hydrogen carbonate) ion. In the linear trace of the conductivity detector, the carbonate (hydrogen carbonate) step is n o longer visible*. The leading ion, however, has a W absorption. If too much carbonate (hydrogen carbonate) is present, it is present in the UV trace, which is used only to mark the UV-absorbing zones and has so far not been applied for qualitative determinations. The carbonate (hydrogen carbonate), if present, is enriched just before the zones of the isotachophoretic 'train', as can be seen in Fig. 13.1. *This simplifies the qualitative information considerably.
315
AMINO ACIDS
20 5.c
8?-
I
654-
32-
f-
1"
Fig.13.1. Isotachopherogram of the separation of a mixture of amino acids obtakled with the operational system listed in Table 13.3. 1 = Chloride; 2 = Asp; 3 = Cys; 4 = I,-Tyr; 5 = Asn; 6 = Ser; 7 = Tyr; 8 = Gly; 9 = Trp; 10 = Ile; 11 = P-Ala. All are L-amino acids. R = Increasing resistance; A = increasing UV absorption; t = time.
AMINO ACIDS, PEPTIDES AND PROTEINS
316
TABLE 13.4 STEP HEIGHTS (mm) FOUND IN THE LINEAR TRACE OF THE CONDUCTIVITY DETECTOR SIGNAL IN THE ISOTACHOPHEROGRAMS OBTAINED WITH THE OPERATIONAL SYSTEM LISTED IN TABLE 13.2. Amino acid
L-Asp L-cys L-Glu I, -L-Tyr L-Ser L-Thr DL-Tyr DL-Met Gly L-His L-Phe L-Ma L-Val L-Trp 3-L-Hyp L-Ile L-Leu P-Ala
PH
9.00
9.20
9.36
9.55
40.5 51.5 49.5 76 112.5 113 135 133 138.5 145 147.5 180 184 191 185 203.5 205 239
33 39.5 40 63 88 98.5 114.5 116 119 124 127.5 154 159 161.5 162 172.5 172.5 210
30.5 35.5 34 59 84 90 107 112.5 106 118 121 147 151 157 151 162.5 164.5 20 1
38.5 34.5 35.5 58 85 94.5 105 117.5 110.5 123 126.5 149 155 161 154 167 170 190
The results obtained when using the operational systems specified in Tables 13.2 and 13.3 are given in Tables 13.4 and 13.5. Differences in step heights of about 15-20 mm are sufficient for a complete separation of the various amino acids. The differences found in the two operational systems considered must be ascribed mainly to the difference in effective mobility of the counter ion used. While in the operational system specified in Table 13.2 about eight amino acids can be separated in a single run, in that specified in Table 13.3 about ten amino acids can be separated simultaneously. L-Lysine has a very small effective mobility at the pH of the leading electrolyte chosen, while the effective mobility of ethanolamine is considerably greater. The idea that pure water, adjusted to a high pH by adding barium hydroxide, can be used as an optimal terminating electrolyte in operational systems at high pH is nearly always wrong. If double-distilled water adjusted to a high pH is applied as the terminating electrolyte*, one can expect the buffer capacity of the counter ion to be insufficient. If, instead, a suitable terminator, e.g., p-alanine, is added to the water, also adjusted to a high pH, the pH of the zone of the terminating electrolyte does not need to be increased so *OH- may carry the electricity because the pH in the zone is increased sufficiently as water is a weak acid in this electrolytic system. This, in combination with the high absolute mobility, will give OHa sufficient high effective mobility.
317
AMINO ACIDS TABLE 13.5
STEP HEIGHTS (mm) FOUND IN THE LINEAR TRACE OF THE CONDUCTIVITY DETECTOR SIGNAL IN THE ISOTACHOPHEROGRAMS OBTAINED WITH THE OPERATIONAL SYSTEM LISTED IN TABLE 13.3. Amino acid
L-Asp L-cys L-Glu I, -L-Tyr L-Ser L-Thr DL-Tyr DL-Met GlY L-His L-Phe L-Ala L-Val L-Trp 3-L-Hyp L-Ile L-Leu
p-Ala
PH
9.01
9.22
9.42
32 40.5 37.5 61 93 95.5 122 118.5 135 122 130 176 169 171 170 188 190 24 0
29 36 33.5 58 82 87.5 111.5 110.5 124.5 128.5 121 165 160 162 161.5 180 178 233
27.5 31 33.5 51 78 88 104 106 117 109 116 155
153 156 152.5 171 170 205
much because 0-alanine is a stronger acid than water under the conditions chosen. Conductimetric recordings of analyses in which double-distilled water, adjusted to a high pH, and analyses in which water plus a suitable terminator are applied, showed that the zone boundaries were less well defined and that the conductivity finally attained is smaller. An isotachopherogram obtained in the operational system specified in Table 13.2 is shown in Fig.13.2. Fig.13.1 and 13.2 also show the differences that can be found in Tables 13.3 and 13.4. Fig.13.3 illustrates the possible mixed zones that can be expected if a mixture of amino acids is analyzed. Two amino acids with close effective mobilities were injected in the system specified in Table 13.3, at a pH of the leading electrolyte of 9. A black square indicates that a mixed zone can be expected in a time of analysis of about 12 min (70pA). A decrease in the concentration of the leading electrolyte did not result in substantial differences in the effective mobilities of the various amino acids. An increase must be avoided because the amino acids are not sufficiently soluble. So far in our laboratory no research has been carried out to find electrolyte systems in which the amino acids are more soluble. Combinations of non-ionic substances with water seem to have good prospects, as the amino acids are not sufficiently soluble in methanol.
AMINO ACIDS, PEPTIDES AND PROTEINS
318 9-
8-
1
20 Sm2
7-
6-
54-
3-
2-
Fig.13.2. Isotachopherogram of the separation of a mixture of amino acids obtained with the operational system listed in Table 13.2. 1 = Chloride; 2 = Asp; 3 = I, -Tyr; 4 = Ser; 5 = Tyr; 6 = Phe; 7 = Ala; 8 = Leu; 9 = p-Ala. All are L-amino acids. A = Increasing UV absorption; R = increasing resistance: t = time.
13.1.4. Separation by use of complex formation
It is well known that amino acids form complexes with metal ions, e.g., Cu*+.In an aqueous solution of copper(I1) sulphate, the addition of various amino acids cause a colour change, which indicates that a complex is formed. Isotachophoretic experiments have shown that only a few of these complexes are sufficiently stable to be detected as real complexes. An isotachopherogram of a copper-histidine complex is shown in Fig.13.4C. In the isotachopherogram in Fig.13.4A, 0.2 pl of 0.01 M L-histidine solution was injected, in Fig.13.4B 0.2 pl of 0.005 M copper(l1) sulphate solution was injected and in Fig.13.4C 0.4 pl of the solution obtained by mixing equal volumes of these two solutions was injected, with the operational system specified in Table 13.1. When other amino acids were examined, however, their complexes were found to be too unstable. No further research was carried out on this aspect. It may be that the field strength applied in isotachophoretic analyses is too great or the complexation constants
AMINO ACIDS
319
Fig.13.3. Schematic diagram illustrating that mixed zones are found in isotachophoretic analyses if the differences in effective mobilities are too small. A black square indicates that a mixed zone is obtained between that pair of amino acids if they are present in one sample. The experiments were carried out in the operational system listed in Table 13.3.
are too small. If so, a method may be found for determining complexation constants in isotachophoretic analyses by varying the field strength in various experiments. 13.1.5. Separation in aqueous propanal solutions
It is well known that amino acids easily form complexes (Schiff bases) with aldehydes. If amino acids are dissolved in a solution that contains an aldehyde, differences in mobility can be expected because the solvent property changes, the amino acid molecule is larger after complex formation and its pZ value changes because the complex is formed with the amino group(s). The first two effects result in a small difference and the last effect in a large difference in mobility. The last effect occurs at very low concentrations of the aldehyde, assuming that the aldehyde character is great enough. Experiments with sugars did not show substantial differences in the effective mobilities of the various amino acids, especially if they were added in relatively low concentrations. Formaldehyde, which has a strong aldehyde character, and acetaldehyde were found to be very unstable. Even during analysis, formic acid and acetic acid, respectively, are formed. Research is continuing to find a suitable combination of a non-ionic stabilizer(s) in order to work reproducibly with formaldehyde and acetaldehyde.
AMINO ACIDS, PEPTIDES AND PROTEINS
320
/
c
/
B
A
Cu-His complex
His +
t
t
Fig.13.4. Isotachopherogramobtained with the operational system listed in Table 13.1. Species injected: A, histidine; B, CuSO,; C, a mixture of the two. R = Increasing resistance; f = time.
With propionaldehyde, experiments could be carried out satisfactorily, although it must be distilled several times under nitrogen. Even after distillation, propionic acid is present in small amounts, but it was found that the amount of propionic acid did not increase during the analysis. A similar disturbance to that discussed briefly in section 13.1.3, due to carbonate (hydrogen carbonate), can be expected; this disturbance does not obscure the analytical results either qualitatively or quantitatively. For optimal information, before the analyses were carried out, the pK values of the various amino acids were determined in aqueous propionaldehyde solutions of various concentrations, and the results are given in Table 13.6. It can be seen that the pK values of the acidic groups decrease, because the amino groups are blocked. The analysis of some amino acids was carried out in a solution containing 3% of propionaldehyde, with the operational system specified in Table 13.7. The leading electrolyte was adjusted to pH 7.2 because it was found that the pK value of ethanolamine was 7.2 in a 3%propionaldehyde solution. Only measurements at ‘neutral pH: are possible with an aqueous solution containing 3% of propionaldehyde. At a pH of the leading electrolyte, which contains propionaldehyde, of above 8, a white insoluble component is formed after some time. In Table 13.8, some step heights of amino acids obtained in the operational system
321
AMINO ACIDS TABLE 13.6 DETERMINATION OF pK VALUES IN AQUEOUS PROPIONALDEHYDE SYSTEMS Propionaldehyde concentration (mole%)
Amino acid
L-His L-G~U* L-AS~* L-Ile L-Leu L-Val L-Phe DL-Ala L-Met L-Ser L-Thr 3-L-Hyp L-Trp L-Tyr GlY L-Arg L-Lys
0.0
2.5
4.0
8.0
9.18 9.47 9.82 9.758 9.744 9.719 9.24 9.866 9.21 9.15
7.81 8.53 8.87 8.38 8.83 8.57 8.17 9.03 8.10 7.60 7.28 9.36 8.50
7.70 8.47 8.58 8.33 8.41 8.45 7.90 8.50 7.90 7.35 7.23 8.95 8.24 8.05 8.31 7.22 8.20
7.93 8.38 8.50 8.15 8.26 8.20 7.88 8.37 7.90 6.35 6.15
9.73 9.39 10.07 9.778 12.48 10.53
8.95 7.62 8.42
8.10 8.00 8.17 7.98
~
* P K ~value.
specified in Table 13.7 are given. Table 13.8 shows that the analysis can be performed at a relatively low pH. By this means, the disturbance due to the carbonate (hydrogen carbonate) is prevented, although in its place a disturbance due to propionic acid has to be dealt with. For the operational system specified in Table 13.7, the possibility of the formation of TABLE 13.7 OPERATIONAL SYSTEM AT pH ABOUT 7.5 SUITABLE FOR ANIONIC SEPARATIONS IN AQUEOUS PROPANAL' SOLUTIONS Solvent: H,0 + 3% C, H , CHO. Electric current k A ) : < 50. Electrolyte
Anion Concentration Counter ion PH Additive
Leading
Terminating
c10.01 N HOC, H, N+H
DL-Ma-
7.2, 7.8 0.05% Polyvinyl alcohol (Mowiol)
c4. 7 (<8)
c4. 0.01M Tris+ None
AMINO ACIDS, PEPTIDES AND PROTEINS
322
TABLE 13.8 STEP HEIGHTS (mm) FOUND IN THE LINEAR TRACE OF THE CONDUCTIVITY DETECTOR SIGNAL IN THE ISOTACHOPHEROGRAMSOBTAINED WITH THE OPERATIONAL SYSTEM LISTED IN TABLE 13.7 Amino acid
PH 7.30
L-cys L-His L-Ser L-Thr L-Glu L-Asp L-Asn L-Met L-Ile Gly L-Val L-Trp L-Tyr I, - L - T ~ I L-Phe DL-Ala
55 67.5 46 43 29.5 24.5 43.5 115 175 170 168 147 135 51 128 190
7.80 29.0 60 41.5 39 13.5 13 30 84
128 108 32 103 175
mixed zones has been studied. Pairs of amino acids with comparable effective mobilities, determined experimentally, were injected simultaneously into the system at pH 7.2. The results are given in Fig.13.5. This figure, amongst others, shows that histidine can be separated completely from the other amino acids, which was not possible in the aqueous systems considered. The disadvantages of using propionaldehyde are its instability, the extra work involved in preparing the operational system and its relatively low boiling point (48 C). Because of the last property, one can work only with relatively mobile components or at low current densities. In Fig.13.6, an isotachopherogram is shown of some amino acids obtained in the operational system specified in Table 13.7. The UV trace is of lower quality than those with comparable systems in aqueous solutions because propionaldehyde shows a significant absorption at 256 nm.
13.2. SEPARATION OF PROTEINS IN AMPHOLYTE GRADIENTS 13.2.1. Introduction While small peptides can usually easily be analyzed by isotachophoresis, the analysis of proteins is often troublesome. If the proteins are not denatured, they are stacked in small zones that have a high density, which is not ideal for isotachophoretic separations.
SEPARATION OF PROTEINS IN AMPHOLYTE GRADIENTS
323
Fig.13.5. Schematic diagram illustrating the formation of mixed zones in isotachophoretic analysis if the differences in effective mobilities are too small. A black square indicates that a mixed zone is obtained between that pair of amino acids if they are present in one sample. The experiments were carried out in the operational system listed in Table 13.7.
The detection of these zones with a thermometric detector is difficult, because a zone length of at least 5 mm in the narrow-bore tube is required for a complete qualitative and quantitative determination. Even the resolution of a conductivity or U V detector (Chapter 6) is often not sufficient. Moreover, the proteins adhere to the wall of the electrophoretic equipment, even to the ‘inert’ PTFE wall of the narrow-bore tube, so that the electroendosmosis changes and hence the profile of the boundaries may also change. Owing to this effect, the profile finally detected may vary from one analysis to another if no precautions are taken (a rigorous washing procedure between analyses) or if one is not aware that these changes are taking place. Another drawback, if proteins are being analyzed, is that the micro-sensingelectrodes of the conductivity probe can easily become coated with a film of proteins that is not caused by an electric leak to earth (see Chapter 6). If a film of protein adheres t a t h e wall of the micro-sensing electrodes the final signals from the conductivity detector (a.c. method) may give non-reproducible results that are difficult to interpret. It will be recalled that the potentiometric detector (d.c. method) is less sensitive to these effects (Chapter 6). Special components can be added to the sample of the proteins, which may both dilute the protein zone (carrier function) and space the protein zones from each other. If
AMINO ACIDS, PEPTIDES AND PROTEINS
3 24
\
20 Sec
i
6-
5-
4-
3-
I 1.
2-
1t -
Fig.13.6. Isotachopherogramof the separation of a mixture of amino acids obtained in the operational system listed in Table 13.7. 1 = Chloride; 2 = propionate; 3 = Asp; 4 = I,-Tyr; 5 = His; 6 = Met; 7 = Tyr; 8 = Val; 9 = Ala. All are L-amino acids. A = Increasing UV absorption;R = increasing resistance; t = time.
these samples are analyzed, one can say that they are being analyzed in isotachophoretic operational systems, but owing to the presence of the additives isotachophoresis as strictly defined (see Chapters 2 and 4) does not take place. The proteins are much more stable if these additives are included, because not only are they present as a single substance with the counter ion in a specific zone (as is common in isotachophoretic analyses), but also the density is much lower. Hence the electric current can pass much more easily and excessive temperatures do not occur. These two effects were verified experimentally. Ampholines (LKB, Bromma, Sweden) so far seem to be compounds that can be applied both for the dilution of the various zones (carrier function) and €or spacing the various zones (spacer function), because they consist of numerous amphiprotic compounds. The ampholines are mixtures of polyamino polycarboxylic acids of general structure -
CH2 -N-(
I
C Hz )x -N-( CH2 )x-NR2
I
where x = 2 or 3 and R = H or -CHz -CHz -COOH. These compounds are commonly applied in isoelectric focusing experiments in order to create a stable pH gradient. In Fig. 13.7, the space function and the carrier function are shown schematically. As already said, the ampholyte mixtures will give both characteristics to the separation in
SEPARATION OF PROTEINS IN AMPHOLYTE GRADIENTS I
325
I
I
Fig.13.7. [llustration of carrier and spacer functions. If an ionic species S is added to a sample consisting of ions A and B such that m A > ms > m g , and the differences in mobility are sufficient for a complete separation, S acts as a ‘Spacer’ for ions A and B. If a component C is added to a sample consisting of ions A and B such that the effective mobility of C is equal to the effective mobility of B in the operational system chosen, component C acts as a ‘carrier’ for ion B. In specific instances it is possible for a component to be added such that a mixed zone is formed between the ions A, B and the component added, although generally an enrichment of A in front and an enrichment of B a t the rear can be expected.
question. One has to bear in mind that although the differences in effective mobility between the compounds of interest remain constant, the separation capacity decreases because compounds are added that have effective mobilities between those of the compounds of interest. The final result of the detection of the various zones, which really move with equal speed, will be less sharp than under ideal isotachophoretic conditions because the self-sharpening effect is much lower. Apart from the addition of, e.g., ampholytes to the leading electrolyte, the terminating electrolyte can also be doped with a suitable ion with an effective mobility higher than that of the most mobile protein. However, in some instances the elution effect due to the substance added may play a dominant role (i.e., isotachophoresis will gradually become zone electrophoresis). Experiments along these lines will not be discussed in this book, because they lie far outside its scope. 13.2.2. Experimental
All experiments described in this section were performed in the operational system specified in Table 13.9. Various operational systems can be used, depending mainly on the particular proteins to be separated. Only a general discussion is presented here but we hope it will be sufficient for scientists interested in the separation of proteins. Glutamic acid was chosen as the leading ion because it is commercially available in a very pure form (‘isotachophoretically pure’) and its mobility is sufficiently high in comparison with that of the most mobile protein at a pH of the leading electrolyte of 7.2. As already indicated in the analyses discussed in section 13.1, the influence of carbonate (hydrogen carbonate) on both the qualitative and quantitative results are negligible,
AMINO ACIDS, PEF'TIDES AND PROTEINS
326 TABLE 13.9
OPERATIONAL SYSTEM AT pH 7.2 SUITABLE FOR ANIONIC SEPARATIONS Solvent:
Electric current @A): Length of narrow-bore tube (cm): UV absorption detector wavelength (nm):
H, 0. Ca. 30-50. Ca. 15. 256.
Electrolyte
Anion
Leading
Terminating
Glu-
Gly- (adjusted to
a sufficiently Concentration Counter ion PH Additive
0.005 M Tris' 7.2 0.05%Polyvinyl alcohol (Mowiol)
high pH) Ca. 0.005M
Tris+ Ca. 9 None
assuming that the necessary precautions as mentioned in section 13.1.I are taken. These precautions must be taken because a less mobile ion is used as the termimator (low effective mobility) and hence the pH will increase considerably. In Fig. 13.8, isotachopherograms for several commercially available ampholytes (LKB) are given. The ampholytes were diluted with double-distilled water (dilution factor 1:20). In each instance 0.2 pl of ampholytes with the pZ ranges (b) 3 . 5 4 , (c) 4-6, (d) 5-8 and (e) 6-8 were injected, and the leading-terminating electrolyte boundary is shown in (a) when no sample was introduced. Fig.13.8a also shows the impurities in the electrolytes. Because the ampholytes were specially developed for use in experiments on isoelectric focusing, it would be fortuitous if they could be applied directly to experiments based on isotachophoretic principles. In order to obtain a better gradient between the leading and terminating electrolytes that would be more suitable for experiments with serum proteins, various commercially available ampholytes were mixed and several of the mixtures were found to be suitable. Obviously, if one is interested in the separation of mobile albumins the most suitable gradient will be completely different from one suitable for the separation of globulins. In the remainder of this section we show some isotachopherograms obtained in the analysis of normal serum and pathological human sera obtained from the St. Josef Hospital, Eindhoven, The Netherlands. The separations were carried out with the gradient shown in Fig. 13.9. The differential trace of the conductivity detector is given in order to show the amount of substances present, which is not so easy to see if only the linear trace is given. The gradient, as already mentioned, was determined experimentally by injecting 0.1 pl of a mixture of ampholytes with different pI ranges in the ratio indicated in Fig.13.9, using the operational system at pH 7.2 (Table 13.9). It proved to be important to include a larger proportion of the ampholytes with low p1 ranges.
SEPARATION OF PROTEINS IN AMPHOLYTE GRADIENTS
327
t
Fig.13.8. Isotachopherogram obtained with the operational system listed in Table 13.9. (a) Boundary between leading and terminating electrolytes; (b) separation of 0.2 rl (dilution 1:20) of ampholyte mixture of PI3.5-4; (c) separation of 0.2 pl (dilution 1:20) of ampholyte mixture of pI4-6; (d) separation of 0.2 pl (dilution 1:20) of ampholyte mixture of PI5-8; (e) separation of 0.2 p1 (dilution 1:20) of ampholyte mixture of PI6-8. A = Increasing UV absorption;R =increasing resistance; t = time.
In order to compare the results obtained from the analyses of sera, a zone electrophoretic separation was also carried out. The experiments were carried out on a porous cellulose polyacetate strip in veronal buffer, the separated proteins subsequently being rendered visible with amido black, washed with acetic acid solution and prepared for a densitometric scan. The results are shown in Fig.13.10 for both normal and pathological sera. The ratios of the proteins present in these sera are given in Table 13.10.
AMINO ACIDS, PEPTIDES AND PROTEINS
328
\
\
30sec
I
R
Fig.13.9. Isotachopherogramobtained with the operational system listed in Table 13.9. A 0.1-p1 volume of a mixture of ampholytes (LKB) with a ratio of pI3.5-4: PI4-6: PI6-8: water of 1:1.5:0.5:20 was injected. A = Increasing UV absorption;R = increasing resistance; 1 = time.
Figs.13.11 and 13.12 show the separations of the sera in Table 13.10 in a narrow-bore tube using a conductivity and a UV absorption detector (256 nm). The UV traces are not shown in Figs.13.1 l a and 13.12a as they do not give much useful information, but if they are of interest Fig.13.8a should be consulted. Fig.13.llb and 13.12b must be compared with Fig.13.10 in order to obtain a comparison of the isotachophoretic and zone electrophoretic separations of serum proteins. In order to obtain Figs.13.1 l c and 13.12c, the sera were diluted with the ampholytes by first injecting 0.2 p1 of the serum to be analyzed into the injection block (Fig.7.5) and then 0.2 p1 of the ampholyte mixture. This procedure was compared with a procedure in which the sera were diluted before the analysis, in a small bottle. The reproducibilities of both dilution techniques were identical, but in the first procedure only a small amount of ampholyte mixture is needed.
329
SEPARATION OF PROTEINS IN AMPHOLYTE GRADIENTS
i
A
l l
5
WL ~
....
--+
..--
Fig.13.10. Separation of a normal serum (A) and a pathological serum (B) by zone electrophoresis. The analysis was carried out on cellulose polyacetate, the proteins subsequently being coloured with amido black. The electropherogram was obtained with a Kipp (Delft, The Netherlands) densitometer. 1 = Albumin; 2 = 01, -globulin; 3 = a,-globulin; 4 = p-globulin; 5 = yglobulin. These sera were used in the analyses in the narrow-bore tubes. TABLE 13.10 COMPOSITIONS OF NORMAL AND PATHOLOGICAL SERA DETERMINED BY ZONE ELECTROPHORESIS ON CELLULOSE POLYACETATE STRIPS This mixture wasused in the analyses presented in Figs.13.11-13.15. Composition (%)
Protein
Albumin 0 1 ~-Globulin ~~,-Glob~~lin p-Globulin y-Globulin
___
Normal serum
Pa thological serum
45 4
47 6
12 17 22
5 4
38
At present it is difficult to draw a conclusion from the results shown in Figs.13.11 and 13.12 because the conditions can vary so easily, resulting in completely different isotachopherograms. The isotachopherograms in Figs. 13.1 1 and 13.12, especially the W traces, must be interpreted in a completely different manner to the traces in Fig.13.10. Although ampholytes are added to the serum proteins in the analysis shown in Figs.13.11 and 13.12, a relationship still exists between the amount of a species introduced into the system and the zone length finally occupied by it, with or without the presence of a supporting
330
AMINO ACIDS, PEPTIDES AND PROTEINS
Fig.13.11. Isotachopherogram of normal serum (Fig.13.10) in an ampholyte gradient (Fig.13.9) obtained with the operational system listed in Table 13.9. (a) Boundary between leading and terminating electrolytes; (b) 0.2 pl of normal serum injected; (c) 0.2 MI of normal serum and 0.2 pl of ampholyte mixture (Fig.13.9) injected. A = Increasing W absorption;R = increasing resistance; t = time.
electrolyte, assuming that it occupies a position between the boundary of the leading and terminating zones. Too easy the W traces in Figs.13.11 and 13.12 will be interpreted in a similar manner to the zone electrophoretic traces in Fig. 13.10. The differential trace from the conductivity detector is not given because it is rather complex and does not give any additional information. The application of a micro-preparative instrument will indicate if the isotachophero-
SEPARATION OF PROTEINS IN AMPHOLYTE GRADIENTS
331
Fig.13.12. Isotachopherogram of pathological serum (Fig.13.10) in an ampholyte gradient (Fig.13.9) obtained with the operational system listed in Table 13.9. (a) Boundary between leading and terminating electrolytes; (b) 0.2 pl of pathological serum injected; (c) 0.2 pl of pathological serum and 0.2 pl of ampholyte mixture (Fig.13.9) injected. A = Increasing W absorption;R = increasing resistance; r = time.
grams shown in Fig.13.11 and 13.12 have a practical value, because by applying specific techniques after the separation more information can be obtained. The isotachopherograms shown in Fig.13.11 and 13.12 may also be the result of the reproducible degradation of the various proteins. Fig.13.13 illustrates the reproducibility of the analysis. In order to show the difference if another ampholyte mixture is applied, the composition was changed, 0.2 pl of
332
AMINO ACIDS, PEPTIDES AND PROTEINS
Fig.13.13. Isotachopherograms of normal serum (Fig.13.10) in an ampholyte gradient obtained with the operational system listed in Table 13.9. The ampholyte mixture had the following composition: PI3.5-4: PI4-6: PI6-8: water = 1 : 1 :0.25 :20. In both A and B, 0.2 pl of normal serum and 0.2 p1 of ampholyte mixture were injected. A = Increasing UV absorption; R = increasing resistance; t = time.
serum* being diluted with 0.2 pl of the ampholyte mixture. The reproducibility in Fig.13.13 is acceptable. Fig. 13.14 demonstrates the effect of a variation in the amount of proteins, in an identical sample, on the shape of an ampholyte gradient. First 0.1 pl of the ampholyte mixture was injected and then (a) 0.1 pl, (b) 0.2 p1 and (c) 0.3 pl of normal serum*. Finally, we present some isotachopherograms that can be compared with those in Fig. 13.14. These isotachopherograms (Fig. 13.1 5) show that an optimum must always be sought in the dilution of the serum with the mixture of ampholytes. If too little ampholyte is added, the sample zones are small and denaturation will soon occur. Separate experiments in which a microscope was used to observe the narrow-bore tube showed that even with human albumin small solid particles are formed (denaturation) that move between the leading and terminating electrolyte zones, and the particles show convection. Under isotachophoretic conditions, thermal degradation of the albumin can soon be expected, as can be understood from Fig.6.7, where the temperatures of zones *The serum for which an analysis is shown in Fig.13.11 was used.
333
SEPARATION OF PROTEINS IN AMPHOLYTE GRADIENTS
t
i.
Fig.13.14. Isotachopherograms of normal serum (Fig.13.10) in an ampholytegradient obtained with the operational system listed in Table 13.9. The ampholyte mixture had the following composition: PI3.5-4: PI4-6: PI6-8: water = 1 : 1 : 0.5: 20. In each instance 0.1 pl of ampholyte mixture was injected, and (a) 0.1 pl, (b) 0.2 pl and (c) 0.3 p1 of normal serum. A = Increasing UV absorption; R = increasing resistance; t = time.
334
AMINO ACIDS, PEPTIDES AND PROTEINS
1 Fig.13.15. Isotachopherogram of normal serum (Fig.13.10) in an ampholyte gradient obtained with the operational system listed in Table 13.9. The ampholyte mixture had the following composition: pI 3.5-4: pI4-6: PI6-8: water = I : 1.5: 0.5 : 20. In each instance 0.2 pl of ampholyte mixture was injected and (a) 0.2 pl, (b) 0.05 pl and (c) 0 p1 of normal serum. A = Increasing UV absorption; R = increasing resistance; t = time.
in a narrow-bore tube, hanging free in air, are plotted. However, in another system than applied for the experiments with proteins. In the terminator zone of the operational system in which the proteins can be separated even higher temperatures can be expected. If too much ampholyte is added to the serum to dilute the protein zone, the resolution is decreased. The isotachopherograms presented in this section show that much more work must be carried out in this field. The compositicils of the ampholyte mixtures and their
SEPARATION OF SMALL PEPTIDES
335
reproducibility are very important, because with the ampholyte mixture a constant gradient, i.e., constant in slope and constant in length, between the leading and terminating electrolyte zones must be maintained. This is the most important rule in this typical version of isotachophoretic analysis. More information can be found in ref. 6.
13.3. SEPARATION OF SMALL PEP'IIDES 13.3.1. Introduction
Less attention will be paid to the separation of small peptides, because most of them can be analyzed both in the system in which amino acids can be separated (Table 13.3) and in the system in which the analyses with the proteins were performed (Table 13.9). A single isotachopherogram will be presented.
Fig. 13.16. Isotachopherogramof the analysis of some small peptides obtained with the operational system listed in Table 13.3. 1 = 5-Bromo-2,4-dihydroxybenzoicacid; 2 = chloride; 3 = glutathione; 4 = glycylglycine; 5 = glycylglycylglycylglycine; 6 = D-leucyl-L-tyrosine; 7 = L-alanine.
336
AMINO ACIDS, PEPTIDES AND PROTEINS
13.3.2. Experimental The operational system used was that specified in Table 13.3. L(+)-Alanine was used as the terminating electrolyte, adjusted to pH 9.8 by addition of barium hydroxide. The leading ion, 5-bromo-2,4-dihydroxybenzoic acid (0.004 M), was adjusted to pH 9.05 by addition of L-lysine. The current was stabilized at 100 MA,and the time of analysis was approximately 8 min. About 0.01 mole of glutathione (Merck, Darmstadt, G.F.R.), glycylglycine hydrochloride, glycylglycylglycylglycine and D-leucyl-L-tyrosine (Nutritional Biochemicals, Cleveland, Ohio, U.S.A.) was injected. The isotachopherogram of the analysis is shown in Fig.13.16. One should note the chloride*, which is more mobile than the 5-bromo-2,4-dihydroxybenzoic acid, which has passed the first separation boundary. Because the chloride is coming from the cathode compartment, it is not a pH disturbance, which may originate from the semi-permeable membrane, especially as the zone is reasonably well defined. It can clearly be seen in the linear traces of both the conductivity detector and the W absorption detector that the concentration of the leading electrolyte is not changed after the passage of the mobile chloride ion.
REFERENCES 1 A. Niederwasser and H. Curtius, Z. Klin. Chem. Klin. Biochem., 5 (1969) 4G4. 2 D.H. Spackman, W.H.Stein and S. Moore, Anal. C h e m , 30 (1958) 90. 3 F.M. Everaerts and A.J.M. van der Put, J. Chromatogr., 5 2 (1970) 415. 4 A. Kopwillem, J. Chromatogr., 82 (1973) 407. 5 A.J. de Kok, Graduation Rep., University of Technology, Eindhoven, 1975. 6 F.E.P. Mikkers, Graduation Rep., University of Technology, Eindhoven, 1974.
*The chloride is derived from the sample component glycylglycine hydrochloride.
Chapter I4
Separation of nucleotides in aqueous systems SUMMARY Experiments were carried out in order to separate nucleotides comprising the mono-, di- and triphosphates of adenosine, cytidine, guanosine and uridine with water as solvent. The time of analysis is approximately 30-45 min for the thermometric detector and approximately 15 min for the high-resolution detectors, from the start of the experiment to the detection of the last zone.
14.1. INTRODUCTION
The nucleotides are amphiprotic substances and at intermediate pH values they are negatively charged and show a behaviour similar to that of acids. As examples, the structures of the 5-monophosphates of the nucleotides adenosine, cytidine, guanosine and uridine are given in Fig. 14.1. This group of substances form the basis of the nucleic acids and play an important role in carbohydrate, lipid and vitamin metabolisms. The adenosine and guanosine phosphates are derived from the purine bases adenine and guanine, and the cytidine and uridine phosphates are derived from the pyrimidine bases cytosine and uracil. Exact data on the pK values and mobilities of these nucleotides are not known but it would be expected that a separation according to pK values would be the most successful. The pH of the electrolyte system regulates the extent of dissociation of the nucleotides and is therefore an important factor affecting the effective mobilities. In the first section some operational systems and data are given for the separation of nucleotides, using thermometric detection, and in the second section data are given for separations using a conductivity detector and a UV absorption detector. In this chapter, the abbreviations A, C, G and U are used for adenosine, cytidine, guanosine and uridine, respectively, and MP, DP and TP for mono-, di- and triphosphate, respectively.
14.2. SEPARATION USING A THERMOMETRIC DETECTOR
The experiments for the determination of the optimal pH of the operational system at which the analyses are performed gave a series of operational systems as specified in Tables 14.1-14.7. These systems were used only with thermometric recording of the various zones. Later a UV absorption detector became available and this precludes the use of strongly W-absorbing counter ions. For the experiments in which a thermometric detector was used, the equipment described in section 7.4.2 was applied. In Table 14.8, all of the step heights measured for the different systems are given. They were all obtained with the same thermocouple. In Fig.14.2, the step heights for the different systems are shown graphically. 331
SEPARATION OF NUCLEOTIDES IN AQUEOUS SYSTEMS
338
U-SLMP
G-<-MP
C-5'-MP
Fig.14.1. Structures of nucleotide 5'-monophosphates. Left to right: uridine, guanosine, cytidine and adenosine.
TABLE 14.1 OPERATIONAL SYSTEM AT pH 3.4 SUITABLE FOR ANIONIC SEPARATIONS (WAdCl) This operational system was used only in experiments in which only a thermometric detector was available.
H, 0 Solvent: Electric current &A): Cu. 70. Electrolyte
Anion Concentration Counter ion PH Additive
Leading
Terminating
cl-
C,H,,COOCu. 0.01 N Tris+ ch. 3 None
0.01 N A+ 3.4 None
TABLE 14.2 OPERATIONAL SYSTEM AT pH 3.7 SUITABLE FOR ANIONIC SEPARATIONS (WaNC1) This operational system was used only in experiments in which only a thermometric detector was available. Solvent: H, 0. Electric current bA): Ca. 70. Electrolyte
Anion Concentration Counter ion PH Additive
Leading
Terminating
cl-
C,H,, COOCu. 0.01 N TriG Ca. 3 None
0.01 N C,,, H, N+H 3.7 None
SEPARATION USING A THERMOMETRIC DETECTOR
339
TABLE 14.3 OPERATIONAL SYSTEM AT pH 4.2 SUITABLE FOR ANIONIC SEPARATIONS (WAnCl I) This operational system was used only in experiments in which only a thermometric detector was available.
Solvent: H, 0. Electric current @A): Ca. 70. Electrolyte Leading Anion Concentration Counter ion PH Additive
Terminating
a-
(CH ) CCOO-
0.01 N C, H , W H 4.2 None
Ca. 0.01 N
Tris+ Ca..4 None
-
--
___--
01
.
3.4
5
6
Cytidine Adenosine
Guanosine Uridine
I
phosphates
7
8 PH
*
Fig.14.2. Graphical representation of the step heights obtained with a thermometric detector in the operational systems listed in Tables 14.1-14.7 at 7 0 PA. 1 = CMP; 2 = AMP; 3 = GMP; 4 = CDP; 5 = UMP; 6 = ADP; 7 = GDP; 8 = ATP; 9 = CTP; 10 = UDP; 11 = GTP; 12 = UTP.
SEPARATION OF NUCLEOTIDES IN AQUEOUS SYSTEMS
340
\
j’! I,
t
Fig. 14.3. Isotachopherogram of the separation of (A) adenosine phosphates and (B) uridine phosphates in the operational system listed in Table 14.6. (A): 1 = Chloride; 2 = pyrophosphate; 3 = ATP; 4 = ADP; 5 = AMP; 6 = cacodylate. (B): 1 = Chloride; 2 = UTP; 3 = UDP; 4 = UMP;5 = cacodylate. A thermocouple was used for detection.
TABLE 14.4 OPERATIONAL SYSTEM AT pH 4.6 SUITABLE FOR ANIONIC SEPARATIONS (WAnc1II)
This operational system was used only in experiments in which only a thermometric detector was available.
H,0. Solvent: Electric current b A ) : Ca. 70. Electrolyte
Anion Concentration Counter ion PH Additive
Leading
Terminating
cl-
(CH, ) 3 CCOOCa. 0.01 N Tris+ ca. 4 None
0.01 N
C,H,N*H 4.6 None
SEPARATION USING A THERMOMETRIC DETECTOR
341
At higher pH (5-7), the differences in step heights are rather small and it can be concluded that these systems are less suitable for the separation of complicated mixtures. TABLE 14.5 OPERATIONAL SYSTEM AT pH 5 SUITABLE FOR ANIONIC SEPARATIONS (WPyrC1) This operational system was used only in experiments in which only a thermometric detector was
available.
H, 0. Solvent: Electric current @A): Ca, 70. Electrolyte
Anion Concentration Counter ion PH Additive
Leading
Terminating
cl-
(CH,),AsOOCu. 0.01 N Tris+
0.01 N NC5H5+ 5.0 None
Ca. 5
None
TABLE 14.6 OPERATIONAL SYSTEM AT pH 6 SUITABLE FOR ANIONIC SEPARATIONS (WHiscl) H, 0. Solvent: Elechc current @A): Ca. 70. Electrolyte
Anion Concentration Counter ion PH Additive
Leading
Terminating
a-
(CH, AsOOCa. 0.01 N Tris+ Ca. 6 None
0.01 N His+
6 None
TABLE 14.7 OPERATIONAL SYSTEM AT pH 7 SUITABLE FOR ANIONIC SEPARATIONS (WIrncl) Solvent : H, 0. Electric current @A): Ca. 70. Electrolyte Leading
Anion Concentration Counter ion PH Additive
Terminating
cl-
Benzyl-dl-Asn-
0.01 N Imidazole+ 7 None
Ca. 0.01 N
Tris+ Ca. 6 None
SEPARATION OF NUCLEOTIDES IN AQUEOUS SYSTEMS
342
The separation of the mono-, di- and triphosphates of every nucleotide is, however, possible in each operational system, Fig.14.3 shows the isotachopherograms for the separations of (A) adenosine phosphates and (B) uridine phosphates at pH 6; in the former sample pyrophosphate was also present. The time of separation was about 20 min. At lower pH, the step heights diverge and larger differences are obtained, because many of them have pK values in this pH range. These systems are more suitable for the separation of the nucleotides in complicated mixtures. As an example, the isotachopherogram of the separation of the nucleotides UTP, UDP, GDP, ADP, UMP, GMP, AMP and CMP is shown in Fig.14.4. A complete separation could be obtained in 30 min at pH 3.7. Lower pH values can rarely be used because the low effective mobilities at these pH values require a higher potential than can be attained and disturbances due to the presence of H’ ions can be expected.
14.3. SEPARATION USING A CONDUCTIVITY DETECTOR (a.c. METHOD) AND A W ABSORPTION DETECTOR (256 nm)
While in the previous section various operational systems in which the separations of the nucleotides can be carried out were given, here only one isotachopherogram is given for comparison. These components are very easy to separate at both low and neutral pH and a separation according to pK values can easily be performed. Moreover, the nucleotides
TABLE 14.8 STEP HEIGHTS (A QUALITATIVE MEASURE IN THE ISOTACHOPHORETIC ANALYSES) OF THE NUCLEOTIDES FOR THE DIFFERENT OPERATIONAL SYSTEMS LISTED IN TABLES 14.1- 14.7 The step heights (mm) were determined in the linear trace of the thermocouple signal, and refer to the temperature of the leading zone at 70 PA and not at 0 F A as in Chapters 11 and 12. Ionic species
WAdCl
WaNCl
WAnCl I
WAnCl I1
WPyrQ
WHisCl
WImCl
AMP ADP ATP
5 36 318 204
476 26 8 184
400 224 150
310 170 118
304 164 100
290 186 146
162 108 82
GMP GDP GTP
388 230 172
350 210 160
352 176 120
290 152 104
290 140 100
300 192 160
162 112 88
CMP
740 356 176
624 312 188
472 276 168
346 192 124
300
250 184 142
100 68
3 28 172
318 164 120
3 24 168 104
264 136 98
270 178 130
100 78
CDP CTP UMP UDP UTP
-
108
SEPARATION USING CONDUCTIVITY AND UV DETECTORS
343
have a strong UV absorption, which makes it possible to determine very small amounts as discussed in Chapters 10* and 6**.
I---
Fig. 14.4. Isotachopherogram of the separation of some nucleotides in the operational system listed in Table 14.2. 1 = Chloride; 2 = UTP; 3 = UDP; 4 = GDP; 5 = ADP; 6 = UMP; 7 = GMP; 8 = AMP; 9 = CMP; 10 = caproate. A thermocouple was used for detection.
*The UV-absorbing component can be sandwiched between two non-UV-absorbing ions. Due to the profiles that are always present one can determine very small amounts, even in the picomole region. ** The UV-absorbing component can be ‘diluted’ with a non-UV-absorbing ion. The component added has an effective mobility identical with that of the nucleotide of interest. The step height of the linear trace of the UV detector gives all necessary quantitative information.
SEPARATION OF NUCLEOTIDES IN AQUEOUS SYSTEMS
344 TABLE 14.9
RELATIVE STEP HEIGHTS OF A SERIES OF NUCLEOTIDES IN THE OPERATIONAL SYSTEMS LISTED IN TABLES 12.5 and 12.6 The accuracy is better than 4%. The values given are to be used only for the identification of the ionic species in isotachophoretic analyses in the operational systems indicated. The chloride (leading ion) has a relative step height of 0, while the chlorate has a relative step height of 100. The current was stabilized at 90 PA for the experiments at pH 3 and at 80 PA for the experiments at pH 4.5. - = No UV absorption. Ionic species
pH 3.0
100 h
pH 4.5
uv
hchlorate
A-2 ',3'-MP A-3',5'-MP A3',MP A-S'-MP A-2',5'-DP A-3',5'-DP A-S'-DP A-S'-DP-glucose A-5'-DP-mannose A-S'-DP-ribose A-5'-TP
Chlorate C-5'-MP C-5'-DP (2-5'-TP Deox y thymidine-MP Deoxythymidine-DP Deoxythymidine-TP G5'-MP G-S'-DP GS'-TP I-S'-MP I-S'-DP 1-5'-TP U-S'-MP U-S'-DP U-S'-TP
2989 3178 3132 3610 1484 1469 1441 1807 1809 1786 728 100 55 10 1628 811 1579 726 4 18 1826 953 621 1621 738 457 1543 6 86 404
100 h
w
hchlorate
99 99 99 99 99 99 99 99 99 99 99 -
94 87 77 99 94 90 99 100 99 99 98 96 98 96 94
1365 1463 1525 1628 799 808 782 977 1038 987 496 100 1872 950 550 1383 664 374 1494 731 444 1438 693 407 1360 668 3 86
100 100 100 100 100 100 99 100 100 99 99 -
98 93 86 99 96 92 100 99 99 100 99 98 100 98 95
SEPARATION USING CONDUCTIVITY AND UV DETECTORS
4
I
3
2
345
1
Fig.14.5. Isotachopherogram of the separation of AMP, ADP and ATP in the operational system at pH 6 (Table 12.1). An amount of 10 nmole of each component was injected. The current was stabilized at 100 PA. The time of analysis is 8 min; however, this analysis can easily be carried out in 2 min. 1 = Chloride; 2 = ATP; 3 = ADP; 4 = AMP; 5 = MES. A = Increasing W absorption; R = increasing resistance; t = time.
In Fig.14.5, the separation of AMP,ADP and ATP in the operational system at pH 6 (Table 12.1) is shown. One can refer to Chapter 12 for operational systems that are suitable for the conductivity detector in combination with the W absorption detector. In Table 14.9, experimental data obtained with both the conductivity detector (a.c. method) and the W absorption detector (256 nm) are given. The equipment used is described in section 7.4.4.
This Page Intentionally Left Blank
Chapter 15
Enzymatic reactions SUMMARY The possibility of using isotachophoresis for the determination of non-ionic compounds via enzymatic reactions has been shown experimentally. The method for determining the initial velocity of an enzymatic reaction is shown, although it is a disadvantage that the reaction cannot be followed continuously. Two enzymes, representing two different classes, were chosen arbitrarily: hexokinase and lactate dehydrogenase. In principle, all enzymatic reactions can be studied in the operational systems specified in t h s chapter. The time of analysis is approximately 15 min from the start of the experiment to the detection of the last zone.
15.1. INTRODUCTION
Isotachophoresis can be applied in many instances to the study of enzymatic reactions, because ionic constituents are involved. Both enzymatic conversions and kinetics can be studied. Because enzymatic conversions can be analyzed, many organic substances that have no or a low effective mobility, e.g., glucose, fructose and urea, can be determined quantitatively by the isotachophoretic separation technique. While the spectrophotometric detection of enzymatic reactions sometimes needs a second reaction, isotachophoresis can be carried out with a single reaction. Moreover, the purity of the reaction constituents can be checked before the reaction; the purity of the starting materials is very important, especially if activities need to be measured [ 11 . Two types of reactions are considered in this chapter. The choice was made such that the two types cover all of the main classes of enzymatic reactions. Firstly, the enzymatic conversion of glucose into glucose-6-phosphate, followed by the conversion of glucosedphosphate into gluconate-6-phosphate is discussed. All enzymatic reactions that make use of ATP, ADP, AMP, NADP and NADPH can be studied*. Secondly, the enzymatic conversion of pyruvate into lactate is discussed, because in this reaction NAD (NADH) is involved. A disadvantage if isotachophoresis is applied to the study of enzymatic reactions is that the reaction cannot be followed continuously, especially if kinetics are being studied. The analyses were performed in the equipment as described in section 7.4.4.
*Abbreviations used: ADP = adenosine-5’-diphosphate; ATP = adenosine-5’-triphasphate; LDH = lactate dehydrogenase; MES = morpholinoethanesulphonic acid; NAD = nicotinarnide-adenine dinucleotide (oxidized); NADH = nicotinamide-adenine dinucleotidc (reduced); NADPH = nicotinamide-adenine dinucleo?ide phosphate (reduced); NADP = nicotinamide-adenine dinucleotide phosphate (oxidized). 341
348
ENZYMATIC REACTIONS
15.2. ENZYMATIC CONVERSION OF GLUCOSE (FRUCTOSE) INTO GLUCOSE-6PHOSPHATE (FRUCTOSE-6-PHOSPHATE) WITH HEXOKINASE FROM YEAST
Many papers have dealt with the enzymatic conversion of glucose and fructose into glucose-6-phosphate and fructose-6-phosphate by hexokinase (e.g., refs. 2-4). Apart from ATP and the enzyme hexokinase, the reaction can be performed only if sufficient Mgz+ or Ca2+is present. Singly charged ions mostly inhibit the reaction [5] . Mg2+forms a suitable complex with ATP, but it is beyond the scope of this book to go into too much detail concerning the complexity of the enzyme reaction itself. Kinetics and conversions are commonly studied via analyses of the substrate and product concentrations, especially the changes that occur during the reaction in the former instance. This is often effected by utilizing a physical property of one of the reaction constituents: the UV absorption at an appropriate wavelength. This measurement gives all necessary qualitative and quantitative information and is very sensitive. The reaction discussed briefly in this section, however, can be studied only if it is followed by a second reaction because ATP and ADP have almost identical UV spectra and glucose-6-phosphate and glucose have negligible UV absorption. The overall reaction can be expressed as follows: Glucose
+ ATP
hexokinase
Glucose-6-phosphate
glucosed-phosphate + ADP
+ NAPD
G6PDH 6-phosphogluconate
(15.1)
+ NADPH
(15.2)
The difference in UV absorption between the ions NADP and NADPH at 340 nm gives information about the conversion of glucose given in eqn. 15.1. In principle, by means of isotachophoresis all ionic constituents can be determined, both qualitatively and quantitatively. Suitable operational systems are listed in Tables 15.1 and 15.2. The conditions listed in Table 15.1 are used for measurements at ‘hgh’ concen-
TABLE 15.1 OPERATIONAL SYSTEM AT pH 3.8 SUITABLE FOR ANIONIC SEPARATIONS Solvent: H, 0. Electric current @A): Ca. 50-70. Purification: The buffer was purified by recrystallization in water-ethanol, the crystals being washed with acetone. The terminator was purified by recrystallization. Electrolyte
Anion Concentration Counter ion PH Additive
Leading
Terminating
c10.01 N pAla+ 3.8 0.05%Polyvinyl alcohol (Mowiol)
p NH, -C, H, -COOCa. 0.01 N
H+ r4 None
ENZYMATIC CONVERSION OF GLUCOSE (FRUCTOSE)
349
TABLE 15.2 OPERATIONAL SYSTEM AT pH 5 SUITABLE FOR ANIONIC SEPARATIONS Solvent : H, 0. Electric current (PA): Ca. 50-70. e-Aminocaproic acid was purified by recrystallization. Purification: Electrolyte
Anion Concentration Counter ion PH Additive
Leading
Terminating
c1-
GluCa. 0.005 N Tris’ ca. 5 None
0.005 N HOOC-C,H, -CH, N+H 5 0.05%Polyvinyl alcohol (Mowiol)
trations of the reaction constituents, while those listed in Table 15.2 make analyses at ‘low’ concentrations of the reaction constituents possible. Fig. 15.1 shows the analyses of all of the anionic constituents given in eqns. 15.1 and 15.2 after the conversion. In Fig. 15.2, the anionic constituents before the conversion are shown. The impurities present in the biochemically pure chemicals were not further identified, as’they did not disturb or obscure the final analytical results. Fig.15.1 and 15.2 show that it is possible to study the reactions given in eqns. 15.1 and 15.2 simultaneously or separately. For kinetic measurements via isotachophoresis the reaction must be stopped at a chosen time, in order to analyze the composition of the reaction mixture. The enzymatic reaction is stopped by injecting a small amount (50 pl) of the reaction mixture into a small glass tube (melting-point tube) that is wrapped with a Kanthal spring. The tube is placed in a high-frequency field for cu. 8 sec, when the temperature of the spring reaches the Curie point and the temperature of the contents of the tube reaches about 80°C. The enzyme is denatured at this temperature, and a reproducible analysis of the reaction mixture was achieved. Other techniques for stopping the enzymatic reaction were less reproducible, e.g., adding inhibitors t o the reaction mixture, rapidly changing the ‘optimal’ pH or filtering off the enzyme over a protein filter. In Table 15.3, six solutions are given with which the conversion of glucose was followed. The concentration of Mg2+was chosen to be twice that of ATP so as to ensure that the ATP was present as MgATP’ . All solutions were buffered to pH 8 by addition of Tris. The enzyme suspension used in the experiments described in this section was prepared by mixing in a bottle 1 p1 of yeast hexokinase (10 mgfml; 140 U/mg), 20 pl of glucosedphosphate dehydrogenase (1 mg/ml; 140 U/mg) and 29 pl of a 2 mg/ml solution of serum albumin in double-distilled water. Although the reaction in eqn. 15.2 was not followed, glucose-6-phosphate dehydrogenase was added in order to compare results under reaction conditions that were as similar as possible. The experiments showed that the results obtained in instances when only hexokinase was added to the reaction mixture were similar to those when glucose-6-phosphate was consumed by glucose-6-phosphate dehydrogenase and converted into 6-phosphogluconate.
ENZYMATIC REACTIONS
350
7
2
Fig.lS.l. Isotachopherogram of the separation of a reaction mixture in which the enzyme hexokinase (from yeast) and the enzyme G6 PDH are involved. 1 = Chloride; 2 = ATP; 3 = 6-PG; 4 = NADPH; 5 = ADP; 6 = NADP; 7 = glutamate. A = Increasing UV absorption, R = increasing resistance; t = time.
ENZYMATIC CONVERSION OF GLUCOSE (FRUCTOSE)
351
1
I
A
3
I’ Fig.15.2. Isotachopherogram of the reaction mixture before the enzymatic conversion. 1 = Chloride; 2 = ATP; 3 = NADP; 4 = glutamate. Various impurities from the chemicals are present, but these do not interfere with the separation. A = Increasing UV absorption; R = increasing resistance; r = time.
Fig. 15.3 shows an isotachopherogram of the reaction mixture after only hexokinase had been added. The enzymatic reaction was performed with the six solutions specified in Table 15.3, using 1.5 ml in the reaction flask each time. This flask was thermostated in a metal block at 25"C, a heat-sink compound being applied between the flask and the metal block for
352
ENZYMATIC REACTIONS
TABLE 15.3 COMPOSITION OF THE SOLUTIONS APPLIED FOR THE DETERMINATION OF THE INITIAL REACTION VELOCITY
4 chemicals were purchased from Boehringer (Mannheim, G.F. R.) Solution No.
Concentration (mmole/l) Glucose
ATP
MgC1,
ADP
1.00 2.00 2.00 2.00 1.oo 0.50
3.29 3.39 0.97
6.00 6.00
0.10 0.09 0.08 0.07 0.07
0.54 0.56 0.53
2.00 1.oo
1.oo 1 .00
0.03
good thermal contact. To the solution was added 1 p1 of the mixed enzyme suspension mentioned above. Under the conditions chosen, a maximum of 0.028 U of hexokinase is present. During the first 20 min, several samples were taken and the reaction stopped by thermal denaturation of the enzyme, as described above. After the denaturation, the melting-point tubes were quickly cooled and kept in an ice-bath until required for analysis. The analyses were carried out in the operational system specified in Table 15.2, about 5 pl of sample being analyzed each time. The results are given in Table 15.4. The concentrations of ATP, ADP and glucose-6-phosphateare in acceptable agreement. The measurements at high concentrations of ATP were less reproducible; possibly at these concentrations the degradation of ATP plays an important role. The initial reaction velocity, determined graphically from the values in Table 15.4, are given in Table 15.5. If smaller amounts of glucose need to be studied, then the ‘mixed-zone’method must be applied. The ATP or ADP must be diluted in its zone with a suitable non-UV-absorbing component. Therefore an anion must be sought that has, in the operational system chosen, an effective mobility identical with that of ATP. The quantitative information can now be obtained via a calibration graph, from the linear trace in the UV (see Fig.6.33). For ADP, hydroxybutyric acid can be applied at a pH of about 4, although analyses at pH > 6 show that the influence of the pH of the zone is less important. Another six solutions were prepared for the determination of the enzymatic conversions and are listed in Table 15.6. The analyses were carried out in the operational system specified in Table 15.1,0.5 pl being injected into the system each time. To 900 pl of the solution specified in Table 15.6,30 p1 of yeast hexokinase (10 mg/ml; 140 U/mg) were added. The solution was maintained at room temperature, the pH of the reaction mixture being adjusted to 8 by addition of Tris. The results of the conversions are shown graphically in Figs.15.4 and 15.5 for glucose and fructose, respectively. All enzymatic reactions in which ATP, ADP, AMP, NADP, NADPH are involved can be studied by isotachophoresis in the operational system given [6] .
ENZYMATIC CONVERSION OF GLUCOSE (FRUCTOSE)
6
4
t
Fig.15.3. Isotachopherogram of the reaction mixture (Fig.15.2) after the addition of the enzyme hexokinase. 1 = Chloride; 2 = ATP; 3 = ADP; 4 = NADP; 5 = G6P; 6 = glutamate. A = Increasing UV absorption; R = increasing resistance; t = time.
353
354
ENZYMATIC REACTIONS
TABLE 15.4 COMPOSITIONS OF THE SOLUTION LISTED IN TABLE 15.3 AFTER THE ADDITION OF THE ENZYME HEXOKINASE. ~
Solution No.
~~
Reaction time (min)
ADP
G6P
0.10 0.12 0.14 0.17 0.19 0.25
0.04 0.05 0.13 0.17 0.20
4
4 7 11 15
3.29 3.30 3.35 3.22 3.11 3.16
0 2 4 7 9.5 11 15
3.39 3.25 3.24 3.28 3.13 3.26 3.21
0.09 0.10 0.10 0.17 0.19 0.21 0.28
0.03 0.05 0.07 0.12 0.10 0.17
5
0 2 4 6 15 20
0.97 0.92 0.94 0.94 0.88 0.85
0.08 0.09 0.12 0.12 0.17 0.21
0.01 0.02 0.05 0.10 0.12
6
0
2
3
~~
Solution No.
ATP
1
2
Concentration (mmole/ 1)
~
Reaction time (min)
~
~~
Concentration (mmole/l) ATP
ADP G6P
0 2 4 6 10 16
0.54 0.51 0.52 0.49 0.46 0.42
0.07 0.07 0.11 0.12 0.14 0.20
0 2 4 6 10 15 21
0.56 0.52 0.49 0.49 0.48 0.47 0.39
0.07 0.09 0.10 0.13 0.15 0.20 0.27
0 2 4 8 10
0.58 0.52 0.48 0.47 0.45
0.03 0.06 0.09 0.10 0.05 0.10 0.04
-
_
-
-
0.05 0.09 0.13 -
0.02 0.08 0.08 0.10
_
TABLE 15.5 INITIAL REACTION VELOCITY OF THE SOLUTIONS LISTED IN TABLE 15.3 DETERMINED GRAPHICALLY FROM THE DATA IN TABLE 15.4 Solution No.
"conversion (lo* mcle!l- min:
1 "conversion (10' 1 * min/mole)
1 2 3 4
1.00 1.18 0.6 0.8 0.85 0.87
1.00 0.85 1.67 1.25 1.17 1.16
5 6
ENZYMATIC CONVERSION OF PYRUVATE
355
TABLE 15.6 COMPOSITION OF THE SOLUTIONS APPLIED FOR THE DETERMINATION OF THE EXTENT OF CONVERSION Solution No.
Concentration (mmole/l) .-
ATP
MgSO,
Glucose
1.5 1.5 1.5 1.5 1.5 1.5
2 1.45 0.5 -
Fructose
-
2 1 0.5
TABLE 15.7 OPERATIONAL SYSTEM AT pH 4.7 SUITABLE FOR ANIONIC SEPARATIONS Solvent: Electric current (PA): Purification:
H, 0. Ca. 70-100.
MES is purified by recrystallization three times from water-ethanol, the crystals being washed with acetone. e-Aminocaproic acid is purified by recrystallization. Electrolyte
Anion Concentration Counter ion* PH Additive
Leading
Terminating
c10.01 N HOOC-C, Ha CH, N'H and His+ 4.5 (c-Aminocaproic acid); 4.7 (His) 0.05% Polyvinyl aIcohol (Mowiol)
MESCa. 0.01 N Tris+ Ca. 4.5
None
*The leading electrolyte is prepared as follows: first, 0.01 N hydrochloric acid; secondly, eaminocaproic acid is added till a pH value of 4.5 has been reached; and finally, histidine is added till a pH value of 4.7 has been reached.
15.3. ENZYMATIC CONVERSION OF PYRUVATE INTO LACTATE WITH LACTATE DEHYDROGENASE FROM PIG HEART This type of enzymatic reaction was chosen because NAD (NADH) is involved. The reaction is: Pyruvate
+ NADH+ + H+
LDH
NAD + lactate*
(15.3)
A reaction mixture was prepared by mixing 25 ml of buffer solution (0.01 Nhydrochloric *At pH 7.5 lactate is formed; at pH 8.9 pyruvate is formed.
356
ENZYMATIC REACTIONS
E
Fig.15.4. Relationship between the lengths of the zones of the various reaction constituents, as found in the isotachopherograms,and the amount of glucose converted. c = concentration of glucose (mmole/l).
acid adjusted to pH 7.6 by addition of Tris), 195.3 mg of NADH .and .. 109 mg of pyruvic acid in a reaction flask. In this instance also the enzymatic reaction was stopped at chosen time intervals for kinetic measurements. The same procedure is followed as described in section 15.2. Each time 0.3 pl was injected and analyzed in the operational system
357
ENZYMATIC CONVERSION OF PYRUVATE
ADP F6P
ATP
0.5
I
1.5
2
c*
Fig.15.5. Relationship between the lengths of the zones of the various reaction constituents, as found in the isotachopherograms, and the amount of fructose converted. c = Concentration of fructose (mmole/ 1).
specified in Table 15.7. The example in Fig.lS.6 shows two isotachopherograms that illustrate the reaction mixture before and after the conversion (80 min). The composition of the reaction mixture as a function of time is given in Fig.15.7 and the data are listed in Table 15.8. From Fig.15.7, it can be seen that lactate and NAD fit a straight Iine exactly, while the pyruvate and NADH lines are curved of the beginning, possibly due to the impurities
ENZYMATIC REACTIONS
35 8
I1
c-
t-
t
Fig.15.6. Isotachopherograms showing the enzymatic conversion of pyruvic acid into lactic acid b y LDH (pig heart). Left, reaction mixture after the conversion; right, reaction mixture before the conversion. 1 = Chloride; 2 = sulphate; 3 = pyruvate; 4 = lactate; 5 = NADH; 6 = NAD; 7 = MES. A = Increasing UV absorption; R = increasing resistance; f = time.
359
ENZYMATIC CONVERSION OF PYRUVATE
I0
50
40
30
20
ca
70
time
Fig.15.7. Zone lengths of the various reaction constituents as a function of the reaction time in an enzymatic reaction in which LDH is involved. TABLE 15.8 CHANGE IN COMPOSITION OF A REACTION MIXTURE CAUSED BY THE ENZYME LACTATE DEHYDROGENASE Reaction time (min)
Zone length (mm) Pyr uvate
Lactate
NADH
NAD
0 10 30 40 60 70 80 90 100 120
27.4 27.3 24.3 23.3 22.0 21.7 20.9 21.1 25.0 20.4
1.4 2.7 4.2 4.9 6.5 7.3 7.9 7.1 2.9 8.7 _
17.6 16.2 11.3 9.5 6.1 5.0 3.7 5 .O 14.1 2.1
2.3 4.5 5.8 8.3 9.3 10.2 9.0 2.5 11.1
~ -
_ _ _
that are always present in the chemicals. For this series of experiments, a mass balance was made for all reaction constituents. In order to determine the amounts of pyruvate and NADH in nanomoles that fit a zone length of 1 mm, the values obtained at t = 0, the reaction mixture before the conversion, were applied, as these amounts are known exactly at this time. For lactate and NAD, a calibration graph was constructed, which is quicker* than using the calibration constant *Moreover, accurate data are not available for the determination of the calibration constant.
360
ENZYMATIC REACTIONS
TABLE 15.9 MASS BALANCE OF: THE REACTION CONSTITUENTS Reaction time (min)
40 60 70 80
Amount (nmole)
-~___
Pyruvate
Lactate
NADH
NAD
- 148.4 - 195.5 -206.3 -235.3
134.8 196.4 227.2 250.3
- 127.2 - 180.6 - 197.8 -218.2
128.2 183.4 205.5 225.4
method (Chapter 10) because only two componentsneed to be quantitatively determined. The results of these experiments are given in Table 15.9. Table 15.9 shows that an acceptable agreement is obtained, although it is not clear why the values for pyruvate and lactate on the one hand and for NADH and NAD on the other are so similar. The reason may lie in impurities in the standards used for the calibration, and especially impurities present in NAD and NADH. All enzymatic reactions in which NAD or NADH are involved can be analyzed by isotachophoresis [7].
REFERENCES 1 A.J. Berry, A.J.M. Lot and G.1:. Grannis, Clin. Chem., 19 (1973) 1255. 2 H.J. Fromm and V. Zewe,J. Biol. Chern., 237 (1962) 3027. 3 H.J.Frornm, J. Biol. Chem., 239 (1964) 3045. 4 P. Ottolenghi, C.R. Trav. Lab. Carlsberg, 34 (1964) 237. 5 N.C. Melchior and J.B. Melchior, J. Biol. Chern., 231 (1958) 609. 6 J. Hoenkamp, Graduation Rep., University of Technology, Eindhoven, 1975. 7 T. Willemsen, Graduation Rep., University o f Technology, Eindhoven, 1974.
Chapter 16
Separations in non-aqueous systems SUMMARY Experimental data are mainly presented for isotachophoretic separations with methanol as solvent. Data are given only for experiments in which a thermometric detector was used because, especially for the conductivity detector, the sharpness is poor, possibly owing to electroendosmosis, if concentrated methanol solutions are applied. The time of analysis is approximately 30-45 min for the thermometric detector and approximately 15 min for the high-resolution detectors from the beginning of the experiment to the detection of the last zone. Some isotachopherograms are shown of a standard mixture of ions obtained with a conductivity detector and a UV absorption detector when methanol-water mixtures were applied.
16.1. INTRODUCTION
As already mentioned in Chapter 5, solvents other than water can be used for isotachophoretic analyses. In this chapter, some examples of other solvents are considered, especially methanol and also a mixture of methanol and water. In section 16.2 results are given for separations of anionic species using a thermometric detector and in section 16.3 the separation of cationic species in methanol is considered. The results obtained when a conductivity detector (a.c. method) and a UV absorption detector were applied are discussed in section 16.4. No results are given for methanol (95%) as solvent with these detectors because the resolution is bad, possibly owing to electroendosmosis. No surfactant, e.g., polyvinyl alcohol as used in the aqueous experiments, could be found that would suppress the electroendosmosis. The isotachopherograms lack sharpness with both detectors, although the UV detector can be applied in numerous experiments. As will be shown, the influence of other dielectric constants and differences in solvation, resulting in different pK values and mobilities, allows numerous possibilities compared with isotachophoretic experiments in aqueous solutions. The 95% methanol (technical grade) used for the separations described in sections 16.2 and 16.3 were purified by running it through a column filled with a mixed-bed ion exchanger (Merck V). The equipment used for the experiments with the thermometric detector is discussed in section 7.4.2, while for the experiments discussed in section 16.4 the equipment with high-resolution detectors described in section 7.4.4. was used.
361
362
SEPARATIONS IN NON-AQUEOUS SYSTEMS
16.2. SEPARATION OF ANIONIC SPECIES IN METHANOL USING A THERMOMETRIC DETECTOR For experiments with anionic species in methanol, the pH, and pK values of the substances involved in the separation are very important. Some pK values are presented in Chapter 5 and from these data we chose as the leading electrolyte a mixture of Tris and hydrochloric acid in methanol at pHC 9, the concentration of chloride ions being 0.01 N(Tab1e 16.1). This means that a combination of a ‘separation based on pK values’ and a ‘separation based on mobilities’ was used, as most acids have p K z values of 8-9. The step heights measured in this system are given in Table 16.2. Simultaneous separations are possible in this system if the differences in step heights are about 7% (relative to 0 PA). As discussed in Chapter 12, some fatty acids have been measured in aqueous systems, but many of them have similar effective mobilities and some are not sufficiently soluble for them to be separated. Their solubility in methanol is much better and also the differences in mobility seem to be greater. A separation of fatty acids in methanol has already been shown in Fig.5.8. In the separation of some dicarboxylic acids, it is remarkable that often different step heights were obtained when they were measured after various times. In particular, for fresh and old solutions of oxalic acid different step heights were obtained. It was found that fresh solutions of oxalic acid gave a step height of 300 mm, whereas a 2-day-old solution gave a step height of 112 mm. Between these times, isotachopherograms were obtained showing two step heights, one at 112 and one at 300 mm, where the zone lengths were different according to the time of preparation. These steps were stable, i.e., when a mixture of oxalic acid and another substance, with a step height between the two for oxalic acid, was introduced the electropherogram showed three peaks in accordance with those of oxalic acid and the other substance. In Fig.16.1A the isotachopherogram of dl-malic acid is shown, in Fig.16.lB that of oxalic acid (two steps) and in Fig.16.1C that of a mixture of dl-malic acid and oxalic
TABLE 16.1 OPERATIONAL SYSTEM AT pH* 9 SUITABLE FOR ANIONIC SEPARATIONS Solvent: CH OH. Electric current (PA): Ca. 50-70. Purification: Methanol (95%, technical grade) was purified by running it through a column filled with a mixed-bed ion exchanger (Merck V). Electrolyte Leading
Terminating
Anion
c1-
Concentration Counter ion PH* Additive
0.01 N Tris’ 9 None
E.g., (CH,),AsOO-, C, H ,,COOCa. 0.01 N Tris’ Ca. 8 None
363
SEPARATION OF ANIONIC SPECIES IN METHANOL TABLE 16.2
QUALITATIVE INFORMATION (STEP HEIGHTS) FOR SOME ANIONS IN THE OPERATIONAL SYSTEM LISTED IN TABLE 16.1 The step heights H refer to the step height of the leading zone (173 rnrn is the step height from 0 t o 70 pA for the zone of the leading electrolyte). Ionic species
H(mrn)
Ionic species
Acetic acid Acetic acid, phenyl Acetic acid, trichloro Adipic acid Azelaic acid Benzoic acid Benzoic acid, o-amino Benzoic acid, p-amino Benzoic acid, rn’-amino Benzoic acid, 5-bromo3,4-dihydroxy Benzoic acid, 2,4 dihydroxy Butyric acid Cacodylic acid Capric acid Caproic acid Caprylic acid Crotonic acid Hydrofluoric acid Formic acid Hippuric acid Lactic acid Lauric acid
88 240 76 260 212 216 304 412 308 264 224 176 800 380 296 336 180 148 37 256 232 408
Linoleic acid Maleic acid Malic acid, dl Malonic acid Mandelic acid, dl Myristic acid Oleic acid Oxalic acid Palmitic acid Pelargonic acid Pimelic acid Pyruvic acid Salicylic acid Salicylic acid, acetyl Salicylic acid, sulpho Stearic acid Suberic acid Succinic acid Sulphanylic acid Sulphonic acid, 2-naphthalene Valeric acid
Hhm) 508 176 t 344* 244 120 + 188* 210 440 504 112 t 300* 480 360 264 96 + 298* 112 108 t 220* 108 508 280 224 200 162 2 74
*Double step.
acid. The isotachopherograms were measured I day after the preparation of the sample solutions. pK measurements on oxalic acid showed the disappearance of one pK step during the time involved. A fresh solution gave two pK values, while a 2-day-old solution gave only one. A large proportion of the methanol in the solutions of oxalic acid in methanol was evaporated off and, after the subsequent addition of water, the resulting solution was also measured in an aqueous operational system. Here the products of the old methanolic solution gave a higher step height than normal, while the product from the fresh methanolic solution gave the normal step height of oxalic acid in water. Old solutions of oxalic acid in methanol gave, after several hours in water, two step heights, but after about 1 day they gave only one step height (the normal step height of oxalic acid). It can be concluded from these experiments that oxalic acid undergoes spontaneous conversion into its monoester in methanolic solutions. Other dicarboxylic acids showed similar effects, but on a smaller scale. Dicarboxylic acids such as dihydroxymaleic acid showed a large number of step heights and it is clear that the analyses of such substances will be difficult. In Fig.16.2, the
SEPARATIONS IN NON-AQUEOUS SYSTEMS
364
3
i t
T
t
c _
t
Fig.16.1. Isotachopherograms of the separation of dl-malic acid (A), oxalic acid (B) and a mixture of oxalic and dl-malic acids C. A: 1 = Chloride; 2 = dl-malate; and 3 = cacodylate. B: 1 = Chloride; 2 , 3 = components that belong to the oxalate [the oxalate ( 2 ) and possibly an ester (3)] ;4 = cacodylate. C: 1 = Chloride; 2 = oxalate; 3 = malate; 4 = the ester of oxalate and methanol (?); 5 = cacodylate.
isotachopherogram of pure dihydroxymaleic acid is given. The terminator was cacodylic acid. The substances listed in Table 16.2 are almost all organic acids; in general, inorganic acids were sparingly soluble in methanol. Because of its lower dielectric constant, complex formation occurs to a much greater extent in methanol than in water, and also the greater effect of the activity coefficients and the decreasing effect on the mobility make methanol unsuitable for isotachophoretic experiments with inorganic ionic species. For the halides, however, which have almost identical effective mobilities in water and cannot be separated, some experiments were carried out in methanol. As with alkali metals (see section 16.3.1), the halides have greater differences in mobilities in methanol and can easily be separated. In Table 16.3, the absolute ionic mobilities and measured step heights in water and methanol are given. The leading electrolyte in water was 0.01 N hydrobromic acid and in methanol 0.01 N hydriodic acid. In Fig.16.3, the separation of the halides is shown, with sodium dihydrogen orthophosphate as terminator. In the sample used to obtain Fig.16.3, formate was added in order to have the possibility of comparing the step heights with those in Table 16.2.
16.3. SEPARATION OF CATIONIC SPECIES IN METHANOL USING A THERMOMETRIC DETECTOR Some cationic species were measured in three different systems, viz., the unbuffered system MHCl, listed in Table 16.4, and the buffered systems MKAC and MTMAAC listed in the Tables 16.5 and 16.6 respectively.
SEPARATION OF CATIONIC SPECIES IN METHANOL
365
-3
Fig. 16.2. Isotachopherogram of dihydroxymaleic acid in methanol. The leading ion is chloride and the terminating ion is cacodylate. Numerous ‘impurities’ are obtained. 1 = Chloride; 2 = dihydroxymaleate; 3 = cacodylate.
16.3.1. The operational system MHCl
The step heights of the cations in the methanolic systems are given in Table 16.7. The differences in step heights required for a complete separation must be about 8-10 mni. In comparison with the aqueous systems, especially for monovalent cations, separations can be achieved much more successfully in methanol. Trivalent cations are difficult to separate as their isotachopherograms show very wide, sometimes double, steps because
366
SEPARATIONS IN NON-AQUEOUS SYSTEMS
TABLE 16.3 MOBILITIES AND STEP HEIGHTS OF HALIDES IN WATER AND METHANOL The step heights refer to 0 PA. These values indicate the possibility of effecting separations. Anion
Water
Methanol
-
-
m - 1 0 5 (cm2/V*sec)
h (mm)
m lo5 (cmz/V sec)
h (mm)
BrICIF-
81.3 79.8 79.0 56.6
105 106 107 135
58.6 66.1 54.1 42.2
153 138 164 196
HCOO-
56.6
136.5
51.7
176
6-
Fig.16.3. Isotachopherogram of the separation of h.alidesin the operational system listed in Table 16.1. Formic acid is included for comparison. 1 = I-; 2 = Br-; 3 = C1-; 4 = CHOO-; 5 = F-; 6 = H, PO, *-.
clusters can be formed. For this reason, only the separations of monovalent and divalent cations were investigated. Fig. 16.4 shows which cations can be separated simultaneously and, in Fig.16.5, the isotachopherogram for the separation of alkali metals is given, the
SEPARATION OF CATIONIC SPECIES IN METHANOL
367
TABLE 16.4 OPERATIONAL SYSTEM (UNBUFFERED) SUITABLE FOR CATIONIC SEPARATIONS (MHCI) Solvent: CH,OH. Electric current (MA): Ca. 50. Purification: Methanol (95%, technical grade) was purified by running i t through a column filled with a mixed-bed ion exchanger (Merck V). Electrolyte
Cation Concentration Counter ion PH Additive
Leading
Terniinating
H+ 0.01 N
CdZ C'. 0.01 N c1-
c1-
+
-
-
None
None
TABLE 16.5 OPERATIONAL SYSTEM AT pH 7.4 SUITABLE FOR CATIONIC SEPARATIONS (MKAC) Solvent: CH,OH. Electric current (MA): Ca. 50. Purification: Methanol (9576, technical grade) was purified by running i t through a column filled with a mixed-bed ion exchanger (Merck V). Electrolyte
Cation Concentration Counter ion PH Additive
Leading
Terminating
K+ 0.01 N
Cd" Ca. 0.01 N c1-
CH, COO7.4 None
-
None
leading ion being W and the terminating ion Cuz+.In Fig.16.6, the isotachopherogram is given for the separation of a mixture of (CH3)41V, (C2H5)4N+,NH;, K', Na', Ca2+,Li+, Co2+,Mn2+and Cu2+,the leading ion being H’and the terminating ion Cd2+. 16.3.2. The operational system MKAC
In this system, the leading electrolyte is potassium acetate in methanol adjusted to a pH of 7.4 by adding acetic acid. The pH is measured with a glass electrode and a calomel electrodel filled with an aqueous saturated solution of potassium chloride, as a reference electrode; The terminator used is cadmium chloride in methanol. There are large differences in clornparison with the step heights of the cations in the system MHC1, particularly
368
SEPARATIONS IN NON-AQUEOUS SYSTEMS
TABLE 16.6 OPERATIONAL SYSTEM AT pH 6.9 SUITABLE FOR CATIONIC SEPARATIONS (MTMAAC) CH OH. Solvent : Electric current (PA): Ca. 50. Methanol (95%, technical grade) was purified by running it through a column Purification: filled with a mixed-bed ion exchanger (Merck V). Electrolyte
Cation Concentration Counter ion PH Additive
Leading
Tcrminating
(CHJ4 N+ 0.01 N CH, COO6.9 None
Cd” Ca. 0.01 N
clNone
TABLE 16.7 QUALITATIVE INFORMATION (STEP HEIGHTS) OF SOME CATIONIC SPECIES IN THE OPERATIONAL SYSTEMS LISTED IN TABLES 16.4-16.6 The step heights (mm) refer to 0 wA. Cation
H (mm) MHCl
Cation MKAC
Ag+ NK Tris+
124 195 222 25 7 180 168 179 292
TI
-
(CH3),+ (C, H, +,). (C, H, ),+ Guanidine+ Succinyl choline’ Imidazole’
154 170 265 192
195 230 270 1031 321 218 151 177 260 203
209 176
191 599
H+ K+ Na+ Llt Rb+
cs+
*n.s.m. = not sufficiently mobile.
MTMAAC
198 230 260 188 173
184
193 317 150 186 250 198
NiZ+ MgZ+ Zn2+ PbZ+ BaZ* Caz+ CdZi co2+ cuz+ Mn2+ Fez+ Fe3+ A13+ Cr3+ Ce3+
La3+
H (mm) MHCl
MKAC
MTMAAC
26 2 240 n.s.m.* n.s.m. 232 24 1 628 272 383 296 390 340 256 290 310 330
510 397 821 946 335 425 1025 497 n.s.m. 483 n.s.m. n.s.m. n.s.m. n.s.m. n.s.m. n.s.m.
560 436 960 1080 350 456 540 -
5 20 -
SEPARATION OF CATIONIC SPECIES IN METHANOL
369
Fig.16.4. Simultaneous separation of some cations in the operational system MHCl (Table 16.4.). Cations in a circle or in a circle connected to another circle by a line cannot be separated. Abbreviations: Guan = guanidine; Im = imidazole; S.C. = succinyl choline; Tba = (C,H,),N; Tea = (C,H,),N; Tma = (CH,),N.
Pig.16.5. Isotachopherogram of the separation of the alkali metals in the operational system listed in 3 = Rb+;4 = K+; 5 = Na+; 6 = Li'; 7 = Cua+. Table 16.4 1 = H+; 2 = CS+;
SEPARATIONS IN NON-AQUEOUS SYSTEMS
370 1,
C
\
t
Fig.16.6. Isotachopherogramof the separation of some cations in the operational system listed in Table 16.5. 1 = H+;2 = (CH,),N+; 3 = (C,H,),N+; 4 = NH:; 5 = K ’ ; 6 = Na'; 7 = Ca2+;8 = Li'; 9 = Co"; 10 = MnZ+;11 = Cu2+;12 = Cd*+.
for divalent cations. The trivalent cations have such a low effective mobility that they do not migrate in an appropriate way. Fig.16.7 shows which cations are simultaneously separated in this system and Fig.16.8 shows the isotachopherogram of the separation of some cations. The most important metals in blood can easily be separated in this operational system. Qualitative separations are more difficult because large differences in concentrations exist
SEPARATION OF CATIONIC SPECIES IN METHANOL
Fig.16.7. Simultaneous separation of some cations in the operational system listed in Table 16.5. Cations in the same circle cannot be separated. Abbreviations as in Fig.16.4.
r
Fig.16.8. Isotachophoretic separation of a mixture of anions carried out in the operational system listed in Table 16.5. A thermometric detector was used. 1 = K+; 2 = guanidine+; 3 = Na'; 4 = Li+; 5 = Baz+. 6 = MgZ+. 7 = CaZ+;8 = NiZ+;9 = Zn2+,
371
SEPARATIONS IN NON-AQUEOUS SYSTEMS
312
B
A
70% CH3OH
,J
:
r-
I!
Fig. 16.9.
B 3 0 % .CH30H
Fig. 16.10.
0% CH30H
A
EXPERIMENTS IN AQUEOUS METHANOLIC SYSTEMS
313
between the various ionic species and the resolution of the thermometric detector, as discussed in Chapters 6 and 10, is low. 16.3.3. The operational system MTMAAC In the preceding system, the leading ion is ’ K and cationic species with mobilities less than that of K' cannot be determined. Because many ions are more mobile than K’, we carried out some experiments with the leading electrolyte tetramethylammonium acetate, the tetramethylammonium ion being the most mobile cationic species used in our experiments. In Table 16.7 it can be seen that most step heights agree with those in the system MKAC. All divalent cations are slightly slower, possibly owing to the higher pH.
16.4. EXPERIMENTS IN AQUEOUS METHANOLIC SYSTEMS USING A CONDUCTIMETRIC DETECTOR (a.c. METHOD) AND UV ABSORPTION DETECTOR (256 nm) More detailed research must be carried out with methanol-water mixtures as solvents before conclusive results can be given; it is always difficult to recommend specific proportions of these two solvent components because they depend mainly on the substances to be analyzed. Therefore, only four experiments will be briefly discussed here, carried out in 100%water and 9: 1,4:1 and 7:3 water-methanol mixtures. The methanol (95%, technical grade) was purified by running it through a mixed-bed ion exchanger (Merck V). Double-distilled water was applied. The experiments were carried out in the operational system at pH 5.0 (Table 11.3), except for the solvent. The current has been stabilized at 70 PA, the amplifications of the conductivity detector (a.c. method) and the UV absorption detector were not changed and the speed of the recorder paper was 6 cm/min for all analyses. Fig.16.9 shows the results of the analyses for 100%water and 9:1 water-methanol, and Fig.16.10 shows those for 4:1 and 7:3 water-methanol. From the isotachopherograms shown, it is clear that the effective mobilities of the various constituents of the sample are influenced in different ways. Moreover, it can be seen that the resolution of both detectors is sufficient. Fig.16.9. Isotachophoretic separation of a standard mixture of cations (Fig.ll.7) carried out in the operational system at pH 5 (Table 11.3) in (A) water and (B) 9: 1 water-methanol. 1 = K'; 2 = Ba2+; 3 = Na+;4 = (CH,),N*; 5 = PbZ+;6 = Girard reagent D+; 7 = Tris'; 8 = histidine'; 9 = creatinine+; 10 = benzidine'; 11 = e-aminocaproic acid+; 12 = y-aminobutyric acid'. The amplifications of the detectors were not changed. A = Increasing UV absorption; R = increasing resistance; t = time. Fig.16.10. Isotachophoretic separation of a standard mixture of cations (Figs.11.7 and 16.9) in water-methanol systems (A, 4 : l ; B, 7:3) carried out in the operational system at pH 5 (Table 11.3). A = Increasing UV absorption; R = increasing resistance; t = time.
This Page Intentionally Left Blank
Chapter I 7
Counter flow of electrolyte SUMMARY It has been found that a counter flow of electrolyte can be used if the concentration differences between the ionic species of the sample are large. If the effective mobilities of the ionic species of the sample are too small, no counter flow of electrolyte can be chosen that will give a complete separation in the available length of narrowbore tube. More attention must be paid to all types of disturbances to the boundary profiles.
17.1. INTRODUCTION
As already discussed in Chapter 7, a counter flow of electrolyte can be applied in isotachophoretic analysis in order to increase the effective length available for the separation of a given sample into its constituent ionic species. In zone electrophoresis, of course, a counter flow of electrolyte cannot be applied. In moving-boundary experiments, only the first zone can be stopped, which may be advantageous if one is interested only in the ion following,the leading ion, or if two ionic species are to be separated. Two main reasons can be given why counter flow of electrolyte is wanted [ 1 , 2 ] : (1) the difference in concentration of the various ions of the sample is too great to achieve a complete separation (Fig.4.5); (2) the differences in the effective mobilities of the various ions of the sample are too small (for the length of narrow-bore tube chosen) [3-91. It is logical that the first reason is chosen when studying the disturbances to the various zone profiles, because a sufficiently large difference in effective mobility is assumed to be present between the various ions for a complete separation to be expected. The second reason places more stringent demands on the resolution of the technique. A counter flow of electrolyte can be applied succesfully only if the disturbances to the profile of the zone boundary are suppressed sufficiently. The suggestion that the length of the narrow-bore tube simply needs to be increased for an improved separation is also of doubtful validity if the influence of electroendosmosis is not sufficiently well understood and the disturbances are not suppressed; more experiments need to be performed in order to elucidate these phenomena. In this section we shall consider the effect of a counter flow of electrolyte, given as a percentage of the electrophoretic migration, on disturbances to the profiles. We shall define a 100%counter flaw of electrolyte to be such that the zone boundaries n o longer move. Hence the electrophoretic migration is equal to the hydrodynamic counter flow of electrolyte. The regulation of the counter flow of electrolyte via signals derived from a detector, at which the zones are stopped, was found to be the most stable, although the regulation as given in section 7.5.5. was found to be a good alternative because an extra high-resolution 315
316
COUNTER FLOW OF ELECTROLYTE
detector is not needed. This regulation, however, places demands on the electrolytes of the operational system, which must be of high purity and also of carefully selected concentration. If the terminating electrolyte is impure, an impurity may influence the final recording if its effective mobility is greater than that of the terminating ion (see eqn. 7.4.). Both the pH and the concentration of the terminating electrolyte may have an influence on the regulation of the counter flow of electrolyte. At the position where the terminator is present in the narrow bore (1 mm) of the injection system (see Fig.7.5.), a well defined potential gradient is obtained as a result of the electrophoretic driving current chosen and the concentration of the electrolyte present (Ohm’s law). In isotachophoretic experiments without a counter flow of electrolyte, the concentration of the terminator has hardly an influence, assuming that it is present in such a concentration that it is able to adapt to the isotachophoretic concentration, which is determined by the concentration of the leading electrolyte chosen (ratio of the anion and cation concentrations). If a counter flow of electrolyte is now applied that is regulated by the total potential gradient between the electrodes, the total resistance over the bore (1 mm) filled with terminating electrolyte changes, owing to the counter flow of electrolyte applied, if the composition of the terminating electrolyte is not already that which it would finally attain as a result of the isotachophoretic conditions. If the concentration of the terminating electrolyte is too low, then in a long run the potential gradient will decrease, because the final conductivity* is higher. This results in a movement of the sample zones in the direction of the detector. If the Concentration of the terminating electrolyte is too high, then the sample zones will be pushed back, although this effect is much smaller and generally has a less important effect on the final results. If a later experiment with a counter flow of electrolyte is to be carried out, it is preferable to rinse the reservoir fdled with terminating electrolyte and to re-fill it with a fresh solution, although this is not always necessary in experiments without a counter flow of electrolyte**. Moreover, it was found experimentally to be preferable to fill the reservoir at least three-quarters full with the terminating electrolyte, otherwise impurities can penetrate into the narrow-bore tube more easily. If impurities are present in the leading electrolyte, they may influence the final recording (see eqn. 7.3). Particular attention should be paid to the electrolyte present in the counter electrode compartment at the side of the semi-permeable membrane where the electrode is mounted. In experiments without a counter flow of electrolyte, double-distilled water is suitable because the membrane is not polluted by the counter ion chosen. Especially if the equipment is used for various operational systems, the mutual effect of the various counter ions is minimal. If experiments with a counter flow of electrolyte are considered, the pH shift due to the membrane and the electrode reaction may influence the final result more quickly. If double-distilled water is still preferred, this compartment must be rinsed continuously during the analysis. If leading electrolyte is present, this compartment must still be rinsed and re-filled after each experiment, assuming that the time of analysis is not excessive, otherwise it must also be supplied continuously with fresh electrolyte. *The buffer ions are flushed into the canals filled with terminating ions. **If experiments are carried out at a low concentration (0.01 M),it is preferable to start each experiment again with a fresh solution of the terminating electrolyte.
INTRODUCTION
317
In various operational systems, the reaction products formed by the electrode reaction* may influence and obscure the final result. As a result, the concentration and/or composition of the leading electrolyte changes during the time the counter flow of electrolyte is applied. Consequently, the concentration of the sample zones changes (qualitative information) and the length of the narrow-bore tube occupied by these various zones also changes (quantitative information), which is in contradiction to the experiments shown in Figs.12.7 and 13.16 (see also Chapter 9). The shift in the step height often found in the trace of the linear signal of the conductivity detector (ax. method) or the potential gradient detector (d.c. method) can be caused by changes in the concentration and composition of the leading electrolyte**, and also by impurities that may possibly be present in the leading electrolyte and/or the terminating electrolyte. In the last instances, the zones are particularly obscure, depending on the effective mobility of the various impurities, as can be seen from eqns. 7.3 and 7.4. If the counter flow of electrolyte occurs too soon, i.e., if sample zones are present that have not reached the isotachophoretic concentration (note that ‘mixed’ zones also have the isotachophoretic concentration), problems can be expected because the sample can be flushed (partly) into the terminating electrolyte present in the narrow bore (1 mm) or even in the reservoir filled with the terminating electrolyte. Problems can particularly be expected if the sample is injected at too high a concentration, which leads t o a high conductivity at the position where the sample is injected. The various ions in this region have a much lower velocity than would be expected in the narrow-bore tube according to the isotachophoretic conditions. Fig.17.1 summarizes the situation at the moment when the counter flow of electrolyte must be applied, and illustrates the ‘dilution’ effect and the ‘concentration’ effect of isotachophoresis. In Fig.l7.la, the sample AB is introduced, already sandwiched between the leading electrolyte (L) and the terminating electrolyte (T). In the steady state, the zone length of A + B is less than the length of narrow-bore tube they originally occupied. Therefore, (1 7.1 )*** v,> V L , In this case, the counter flow of electrolyte can be applied at the beginning of the experiment. In Fig. 17.1 b, the ‘dilution’ effect is shown. Now, (17.2)*** If in this instance the counter flow of electro1:rte is applied at the beginning of the experiment, the sample is flushed back, resulting in a disturbance.
*E.g., in experiments carried out in the operational system at pH 6 (Table 12.1), where histidine is used as the buffering counter ion, a reddish component is formed. **This may also occur in experiments without a counter flow of electrolyte if the electrolyte (doubledistilled water) in the compartment at the side of the membrane where the electrode is mounted is not replenished regularly (see Chapter 9). m V;Cand V p are the velocities of the front B/T. Visot is the velocity of the front L/A.
COUNTER FLOW OF ELECTROLYTE
378
,
I
I
I
I
I
1 1
1
B
1 I
A
, ,
I v I ,
6 Fig.17.1. Diagram to illustrate the 'concentration' (a) and 'dilution' (b) principles of isotachophoretic analyses.
17.2. EXPERIMENTAL If the disturbance caused by the counter flow ofelectroIyte is to be studied, a scanning detector is needed or dyes must be applied. We studied the disturbance by using the dyes amaranth red, bromophenol blue and fluorescein. Acetate and glutamate were found to be suitable for spacing the dyes. The separations were carried out in the operational system at pH 6 (Table 12.1) and the results are shown in Fig.17.2 and 17.3. The photographs in Fig.17.2 were obtained in a fluoroethylene polymer (FEP) narrow-bore tube of I.D. approximately 0.5 mm, while the isotachopherograms in Fig.17.3 were obtained with a conductivity detector (a.c. method) that had a probe made almost completely of Perspex (see Chapter 6) with I.D. 0.4 mm. It can be seen that the optimal sharpness of zones is obtained if a small counter flow of electrolyte is applied. This optimal counter flow depends on, amongst other things, the viscosity of the electrolyte, the diameter of the bore, the temperature inside the bore and the material of which the narrow bore is made. This is why the recording of the zones by the a.c. method (Fig.17.3) indicates another optimum for the sharpness of the zone boundaries, ~
~
~.
~
Fig.17.2. Results of experiments carried out in the operational system at pH 6 (Table 12.1) to show the disturbance of the profiles by a counter flow of electrolyte (indicated in percentages). In (a) a free solution was applied, while in (b) an electrolyte in which the viscosity was increased by addition of 2%of hydroxyethylcellulose (purified by shaking it with a mixed bed ion exchanger) was used; the viscosity of the solution was approximately 100 cP. 1 = Chloride; 2 = amaranth red; 3 = acetate; 4 = bromophenol blue; 5 = glutamate; 6 = fluorecein; 7 = MES. It can clearly be seen that the zone boundaries are first sharpened, and then are disturbed. The disturbance is a function of the viscosity. In the two photographs in the bottom right-hand corner, two examples are given of the disturbance of the zune boundary as a function of the effective mobilities of the consecutive zones: (a) shows the boundary amaranth red/MES and (b) shows the boundary amaranth red/glutamate (loo%* counter flow of electrolyte).
EXPERIMENTAL
319
0%
a
b
10 %
a
60 %
a
b
b
70 %
a
b
20 %
a
b
80 %
a
b
30 %
a
b
90 %
a
b
40%
a
b
100 %
a
b
50 %
a
b
loo%*
a
b
380
COUNTER FLOW OF ELECTROLYTE
d
C
b
a
t R I
/
6
5
-f
Fig.17.3. Isotachophoretic separation of the mixture of components indicated in Fig.17.2, recorded with a conductivity detector (a.c. method) when a counter flow of electrolyte was applied. As shown in Fig.17.2, the zone boundaries become sharper if a small counter flow of electrolyte occurs. R = Increasing resistance; f = time. 1 = Chloride; 2 = amaranth red; 3 = acetate; 4 = bromophenol blue; 5 = glutamate; 6 = fluorescein; 7 = MES.
EXPERIMENTAL
381
caused by the counter flow of electrolyte, than the photographic registration shown in Fig.17.2. It should be noted that the zones shown in the isotachopherogram in Fig.17.3d move more slowly than those in Fig.17.3a, that the speed of the recorder paper was the same in both analyses, and that nevertheless the zones shown in Fig.17.3d are sharper. Moreover, Fig.17.3d shows that an impurity is present that is difficult to see in Fig.17.3a. This shows once more the risk involved when zone profiles are used for the quantitative determination of small amounts of components (see section 10.5). Both Figs.17.2 and 17.3 show that the thickness of the electrodes is sufficient, if the disturbances of the zone boundaries are not suppressed, assuming that the electrode reactions do not play an important role. Moreover, the suppression of the boundary disturbance by a counter flow of electrolyte can only be used for specific boundaries, because the consecutive boundaries all have their own curvature. From the photographs in Fig.17.2 (both the experiments in which 2% of hydroxyethylcellulose was added and those carried out in the free solution), the profile disturbances were photographically enlarged. The results are given in Fig.1 7.4: a t higher rates of counter flow of electrolyte, the disturbance proved to be no longer a function of the viscosity. Another series of experiments was carried out in order to investigate the disturbance of the zone boundary profile when the difference in effective mobilities is small.
Fig.17.4. Disturbance of the zone profiles by a counter flow o f electrolyte. (a) Experiments in a free solution; (b) experiments with 2%of hydroxyethylcellulose added to the leading electrolyte (viscosity = 100 cP). V, = electrophoretic velocity; V , = hydrodynamic velocity (counterflow of electrolyte).
382
COUNTER FLOW OF ELECTROLYTE
Amaranth red was used as the sample in the operational system at pH 6 (Table 12.1). Various terminators with different effective mobilities were applied. The results are shown graphically in Fig.17.5. These experiments indicated that the disturbance is greater;the smaller are the differences in effective mobilities. In Fig.17.2 (loo%*), two examples of these boundary disturbances are shown: (a) the boundary when MES was applied as the terminator and (b) the boundary when glutamate was applied as the terminator. Experiments with acetate as the terminator showed that the amaranth red is flushed back into the terminating reservoir. From these series of experiments, we can conclude that a ‘slow’ terminator is needed in order to prevent too much sample from being flushed back.
Fig.17.5. Disturbance of the zone boundary as a function of the effective mobility of the following zone. ah = Difference in effective mobility; L = length of the disturbance of the zone boundaries (mm). This figure can be compared with Fig.17.2 (loo%*). In these experiments hMES = 139; hglutamate = 77.5; hacetate = 17.5; hamarant,, red = 0; hence Ah refers to the step height of the amaranth red zone. Fig.17.6. Isotachopherogram of a standard mixture of anions (Fig.12.5) without (A) and with (B) a counter flow of electrolyte, showing that several mixed zones disappear. The experiments were carried out in the operational system at pH 6 (Table 12.1). The differences in heights of the peaks (impurities) in the linear trace of the W detector should be noted. These zones are marked with asterisks. They are enriched during the time that the counter flow of electrolyte is applied (see section 10.5). A slight difference between the recordings from the W absorption detector and the conductivity detector is always obtained because the diameters of the probe and the PTFE narrow-bore tube are not the same. Moreover, differences between the traces of the conductivity and the UV absorption detectors can be expected in (A), because the W absorption detector is mounted closer to the injection point. The zone of carbonate, marked with a large asterisk, increases with time (see Chapter 9). A = Increasing UV absorption; R = increasing resistance; t = time.
383
CONCLUSION
c
t
r ’r;
I
I"
COUNTER FLOW OF ELECTROLYTE
384
17.3. CONCLUSION
From section 17.2, we found that the disturbances are not as small in experiments in narrow-bore tubes as was emphasized from the results of earlier experiments. If boundaries were found t o be less sharp, both the regulation and the construction of the equipment were always found to be the cause. We now know that for enrichment of substances, a very mobile leading ion and a much less mobile terminating ion is needed. Fig.17.6 shows two analyses (with and without a counter flow of electrolyte) in order to illustrate when the optimal effect of a counter flow of electrolyte can be expected. The experiments were performed in the operational system at pH 6 (Table 12.1), the test mixture of anions (Fig.12.5) being injected. AU experimental conditions were the same except for the time for analysis: in (B) a counter flow of electrolyte was applied, which doubled the time of analysis (from 15 to 30 min). A complete separation could be achieved. The experiments were carried out with a membrane pump (section 7.5.5) in the equipment described in section 7.4.4.
REFERENCES 1 2 3 4 5 6 7 8 9 10
F.M. Everaerts, J. Vacik, Th. P.E.M. Verheggen and J. Zuska, J. Chromatogr., 49 (1970)262. F.M. Everaerts, J. Vacik, Th.P.E.M. Verheggen and J. Zuska,J. Chromatogr., 60 (1971)397. J.W. Westhaver, J. Res. Nut. Bur. Stand., 38 (1947) 137. S.L. Madorsky and S. Straus, J. Res. Nut. Bur. Stand., 38 (1947)169. S.L. Madorsky and A.K. Brewer., US. Put., 2,645,610,1953;C.A., 47 (1953) 10374a. B.P. Kostantinov and V.B.Fiks., Rum. J. Phys. Chem., 38 (1964)1038. B.P.Kostantinov and E.A. Bakulin, Russ. J. Phys. Chem., 39 (1965)315. W. Preetz, Talanta, 13 (1966)1649. W. Preetz and H.L. Pfeifer, Tulanta, 14 (1967) 143. J. van de Venne, Graduation Rep., University of Technology, Eindhoven, 1975.
APPENDICES
This Page Intentionally Left Blank
Appendix A
Simplified model of moving-boundary electrophoresis for the measurement of effective mobilities A. 1. INTRODUCTION If the separation in isotachophoresis is complete, only one ionic species of the sample is present in each sample zone and the parameters of each zone are related to those of the preceding zone. Calculations of the pH, concentrations of the ionic species in the zone and other parameters are possible and a mathematical model for the buffered systems is given in Chapter 4. If the separation is not complete, Le., if mixed zones are present and/or the influence of the background ions is too great, the conditions for real isotachophoresis are lost and the model described is no longer valid. In particular, the influence of the background will dominate in unbuffered systems. Sometimes the separation procedure can be better understood by using a model similar to that for the movingboundary technique. Several workers [ 1-61 have given mathematical models for the moving-boundary system, but it is very difficult to work with an exact model and some simplifications have to be made. All zones do not contain one ionic species of the sample, but the number of ionic species in the zones increases to the rear side. Only the first zone, following the leading electrolyte zone, contains one ionic species of the sample. All zones have correlations with both their preceding and following zones, which explains the difficulties involved in computations (see Chapter 4). A simpler model was used by Brouwer and Postema [ 7 ] , who described a model for the separation procedure during isotachophoresis, which in principle is moving-boundary electrophoresis. Concentration effects, the influence of pH and the differences in temperature were neglected. Although this is not a general model, it can be used for unbuffered systems of monovalent, fully ionized ionic species for the calculation of effective mobilities. In this Appendix, we describe a model comparable to that of Brouwer and Postema [7]. With the equations presented, a computer program was developed and the calculations carried out with it are compared with the results of experiments. Further, we describe the procedure for the determination of effective mobilities of strong electrolytes using the moving-boundary principle. Also, the effective mobilities of, for example, weak fatty acids can be determined working at high pH where they are fully ionized, for it is assumed that the influence of pH or pK values can be neglected.
A.2. MODEL OF MOVINGBOUNDARY ELECTROPHORESIS When carrying out experiments on moving-boundary electrophoresis, the capillary tube can be filled with an electrolyte of a strong acid if the separation of, for example, cations is desired. The cation present has a mobility that is higher than that of any other cation of the sample. The sample is situated at one end of the capillary tube, in the anode compartment. For the derivation of the equations, the following assumptions are made: 387
388
SIMPLIFIED MODEL OF MOVINGBOUNDARY ELECTROPHORESIS
fully ionized cations and anions are considered; the contribution of the background ions to the conductance of a zone is negligible; the influence of differences in pH and concentrations are neglected; the electric current is stabilized; diffusion, hydrodynamic flow and electroendosmosis are neglected; and the solution initially present in the capillary tube and anode compartment has a well known, constant composition. The equations that need to be considered are the electroneutrality equations, the modified Ohm’s law and the mass balances for all catioaic species.
A.2.1. Electroneutrality equations If the influence of the background ions can be neglected and when all ionic species are fully ionized, the concentration of the counter ions will always be identical with the concentrations of the cations present in a zone, if monovalent ions are considered.
A.2.2.Modified Ohm’s law
if the influence of the presence of the hydrogen and hydroxyl ions is neglected.
A.23. Mass balances for all cationic species In the stationary state, the amount of each ionic species passing a separation boundary is equal to the amount reaching the separation boundary. For each ionic species and all separation boundaries we can write (see also section 4.2.3): CA,.,V-I(EU-lmAr-vV)=
‘Ar,lJ (EVmAr-vV)
Substituting for uu:
*The subscript U refers to the Uth zone, which contains Uionic species of the sample.
389
PROCEDURE OF COMPUTATION
A.3. PROCEDURE OF COMPUTATION For a separation boundary between the zones U- 1 and U , eqn. A1 gives
u- 1 ~ u - *i
2
r= 1
U
(mA,+mB)cA,,U-i
=E,*
C (mAr+mB)cAr,U
(A71
r=l
Combining eqns. A7 and A6 gives
J I
In fact, this is a modification of the ‘Dole polynomals’ [ 1,8] and solutions for the equations are valid if
If the composition of the leading electrolyte and the sample solution are known, all parameters can be computed with the equations given above. The velocity of the concentration boundaries can be neglected. In the first instance, the concentrations of the ionic species in the last sample zone are taken to be equal to the original concentrations in the sample. Although this assumption is not correct, the ratio between the concentrations in the sample remains constant in the zones, according to eqn. A2, which gives
(It is assumed that the velocity of the concentration boundary can be neglected.) Using eqns. AS and A9, flu-] ,u can be calculated if all mobilities are known. With flu- ,u and eqn. A6, all concentrations of the zone U- 1 can be calculated, and thus all concentrations and values can be calculated for all zones. The concentration of the ionic species in the first sample zone can be calculated in two ways, either with the equations given above or using the isotachophoretic condition as described in Chapter 4. In the first computation, we chose arbitrarily as concentrations for the ionic species in the last sample zone those concentrations present in the original sample solution, and all quantities could be obtained. If the parameters of the first zone obtained in this way did not agree with those obtained by the isotachophoretic method, we re-computed from the first to the last zone with the quantities obtained with the isotachophoretic condition, using the 0 values from the moving-boundary procedure. By this calculation, new concentrations for the sample zones can be proposed and new /3 values can be calculated. This procedure of ‘iteration’ must be repeated until the P values and concentrations fit.
390
SIMPLIFIED MODEL OF MOVINGBOUNDARY ELECTROPHORESIS
A.4. EXPERIMENTAL
With the equations presented above, a computer program was developed and experiments were carried out in order to check this model. To this end, all concentrations should be determined in all zones. However, as this is difficult, another possibility is to measure the velocities of the zones by means of a detector. Each zone has a specific constant velocity, vu = EumAU;for practical reasons, we use relative velocities instead of absolute velocities* :
If the distance between the point of injection and the point of detection is P,the time needed for a particular ionic species to be detected will be
or
P = VUtU The correlation between vu and vL will be P = VUtU= V L t L
and hence v
U
= V U / V L = tL/tU
The times of detection can be measured from the time of the starting point of the analysis up to the time of the appearance of the zone of a particular ionic species. Because the velocity of the leading electrolyte is equal to the velocity of the first sample zone (isotachophoretic condition), we use the relationship v' = t L / t U = t J t " U
In this way, the measured ratio tl/tUfrom the electropherograms can be used to check the computed ratio vu/vL In order to check the model, some experiments were carried out. The values of t l ItU were measured from the electropherograms for different mixtures of P, Na+, Li+,(CH3)4NC and (CzHS)4M. The leading electrolyte was 0.01 Nhydrochloric acid and the current was stabilized at 70 PA. Experimental and theoretical values are given in Table A l . In Fig.Al these values are represented graphically (the broken lines represent the experimental values). The experimental values agree very well with the calculated values and it can be concluded that this model is suitable in many instances. Because the relative time of detection for a mixture of two ions of known concentrations is constant in a given system and depends only on the mobilities, it can be used for the determination of the effective mobility of an ion. In order to demonstrate this
(vh).
*The relative velocity of a moving-boundary zone is related to the isotachophoretic velocity of the leading zone (isotachophoretic condition).
39 1
EXPERIMENTAL TABLE A1 THEORETICAL AND EXPERIMENTAL VALUES OF THE RELATIVE TIME OF DETECTION FOR SOME CATIONS IN A MOVING-BOUNDARY ELECTROPHORETIC SYSTEM System
Value
K'
Na'
(CH,),N'
Li'
(C,H5)4N'
A
Concentration (N) fL/tv, theoretical t L / f u , measured
0.01 1.ooo 1.00
0.01 0.904 0.90
0.01 0.863 0.85
0.01 0.793 0.79
0.01 0.717 0.70
B
Concentration (N) tL/tv, theoretical f L / t U ,measured
0.02 1.000 1.00
0.01 0.848 0.84
0.0 1 0.805 0.79
0.01 0.736 0.73
0.01 0.664 0.65
C
Concentration (N) f L / t u ,theoretical f L / t U ,measured
0.02 1.ooo 1.oo
0.02 0.889 0.88
0.02 0.845 0.83
0.01 0.753 0.75
0.01 0.671 0.66
D
Concentration (N) fL/f u, theoretical r L / tu, measured
0.02 1.000 1.00
0.01 0.872 0.87
0.01 0.837 0.83
0.02 0.793 0.78
0.02 0.723 0.71
E
Concentration (N) t L / tu, theoretical f L / t Umeasured ,
0.02 1.000 1.00
0.01 0.877 0.87
0.02 0.845 0.84
0.01 0.767 0.76
0.02 0.708 0.70
effect, the theoretical values of all relative detection times as a function of the mobility of a cation are shown in Fig.A2. The concentrations of the cations varied from 0.01 N to infinite dilution and the leading electrolyte was 0.01 N hydrochloric acid. From the experimental values for the relative time of detection given in Fig.A2, the mobility can be derived. Measurements were carried out with samples of Na', (CH3)4N+ and (CzH5)4N+and the results are shown in Table A2. It can be seen that the theoretical and measured values agree. In Fig.A2 a linear relationship is obtained for a zero concentration of a cation mixed with 0.01 N potassium chloride in a sample. This corresponds with the theory, because TABLE A2 THEORETICAL AND EXPERIMENTAL MOBILITIES OF SOME CATIONS
Ion
Concentration
Ion
W)
(N)
Theoretical
Measured
K+
0.01 0.01
Na'
0.01 0.005
0.8375 0.7930
50.5
51.25 51.5
K'
0.01 0.01
(CH,),N+
0.0 1 0.005
0.7900 0.7200
45.0
45.7 45.5
K'
0.01 0.01
(C,H,),N+
0.01
0.6770 0.6000
30.0
32.2 33.2
0.005
392
.t
SIMPLIFIED MODEL OF MOVINGBOUNDARY ELECTROPHORESIS
r
1
2
3
4
2
3
4
5
5
1
2
I 1
2
3
3
4
4
5
1
-I
5
Fig.Al. Graphical representation of the theoretical and experimental values for the times of detection for some cations in a moving-boundary system (see Table Al.). r = ratio I , ItU. s = ionic species: 1 = K'; 2 = Na+; 3 = (CH,),N'; 4 = Li+;5 = (C,H,),N+. A, B,C, D and E refer to A, B,C, D and E in Table A l .
now elution phenomena prevail (a uniform voltage gradient is present over the whole of the capillary tube and consequently the relative times of detection show a Iinear relationship with the mobility).
A S . DISCUSSION
As shown in section A.4, a theoretical relationship between the relative time of detection and mobility can be used for the determination of effective mobilities, although of course an experimentally obtained relationship between mobility and relative times of detection can also be used. Sometimes, disturbances during isotachophoretic analyses can be understood better by using a moving-boundary model instead of an isotachophoretic model, and an example was given in section 9.2.1.2. In Fig.9.2, the relationship between the pH of the terminator and the ratio tl ItU ( v b ) is given for theoretical and experimental values. This is, in fact, the separation of a mixture of two cations, viz., a mixture of H' and K: and it will be clear that different pH values (different concentrations of H’)will cause different relative velocities of the K' zones. Moving boundary electrophoresis can hardly be used as an analytical technique. Of course, separations can be carried out in this way and Fig.A3 shows an electropherogram
DISCUSSION
E
393
II
Fig.A2. Graphical representation of the calculated relative times of detection as a function of the mobilities for different concentrations of the cations, mixed with 0.01 N KCl, after the leading electrolyte (0.01 N HCl). rn = mobility (10-5.cm2/V-sec).
I
Fig.A3. Separation of a mixture of cations in moving-boundary electrophoresis. All initial concentrations were 0.01 M. The current was stabilized a t 70 PA. The leading electrolyte was 0.01 M HC1 in methanol (95%, w/w). 1 = H+; 2 = (CH,),N+; 3 = (CH,),N+ + NH;; 4 = (CH,)," + NH,' + K+; 5 = (CH,),N+ + NH,' + K' + Na'; 6 = (CH,),N' + NH,' + K' + Na' + Caz+;7 = (CH,),N' + NH: + K' + Na+ + Caz++ Li'; 8 = (CH,),N' + NH,' + K' + Na+ + Ca2' + Li+ + CozC;9 = (CH,),N' + NH,' + K' + Na' + Ca ’+ + Lit + Coz++ MnZ+;10 = (CH,),N' + NH,* + K+ + Na' + Ca" + Li' + Coz+ + Mnzt + Cuz+.
394
SIMPLIFIED MODEL OF MOVINGBOUNDARY ELECTROPHORESIS
for the separation of a mixture of (CH3)41V+, NH;, K’, Na”, Ca2’, Li’, Co , Mn” and Cu2+in narrow-bore tubes, with H+as the leading ion and methanol as solvent. The separation is reasonable but an interpretation will be very difficult if the sample is unknown, as both the retention times (time of appearance of a ‘moving-boundary’ zone) and step heights depend on both the mobilities and the concentrations of the ionic species in the sample. Moving-boundary electrophoresis can thus hardly be used, unless the mixture has a simple composition. For simple routine analyses, however, this method can probably be used, because much simpler apparatus (compared with ‘isotachophoretic’ equipment) can be constructed.
REFERENCES 1 2 3 4 5 6 7 8
V.P. Dole, J. Amer. Chem. SOC., 67 (1945) 1119. R.A. Alberty, J. Amer. Chem. SOC., 72 (1950) 2361. J.C. Nichol, J. Amer. Chem. SOC., 72 (1950) 2367. J.C. Nichol, E.B. Dismukes and R.A. Alberty,J. Amer. Chem. SOC., 80 (1958) 2160. E.B. Dismukes and R.A. Alberty, J. Amer. Chem. Soc., 76 (1954) 191. D. Tondeur and J.A. Dodds., J. Chim. Ph,ys., 3 (1972) 441. G. Brouwer and G.A. Postema, J. Electrochem. SOC.,117 (1970) 7 and 874. M. Bier, Electrophoresis, Vol. 1, Academic Press, New York, 1959.
Appendix B
Diameter of the narrow-bore tube, applied for separation In Chapters 6 and 7 , equipment is described in w h c h a narrow-bore tube with an I.D. of 0.45 mm was used. The current density in the equipment discussed was about 500 pA/mm2. From experiments conducted in 1970, it was well known that, if glass narrow-bore tubes with 1.D.s of 0.2 and 0.1 mm were used for isotachophoretic experiments, very small temperature differences could be measured between the various zones with the micro-sensing thermocouples (section 6.2). Moreover, the increase in electroendosmotic flow even made analyses with dyes, as described in Chapter 17 (Fig.17.2), impossible. No additives, e.g., Mowiol (polyvinyl alcohol) were applied at that time. As soon as the equipment and detectors described in Chapters 6 and 7 had been developed and tested, some research was carried out so that the I.D. of the narrow-bore tube could be decreased. Three main reasons for desiring this reduction can be given: (a) With a smaller I.D. of the narrow-bore tube, the total detectable amount of the ionic species to be separated can be decreased, because the length of the zones increase on decreasing the diameter of the narrow-bore tube. (b) If comparable current densities are applied, the temperature differences between the successive zones is less if the narrow bore-tube has a smaller 1.D. A smaller profile of the zone boundary is thus obtained, especially between zones with ionic species that have very low effective mobilities. (c) If higher current densities can be permitted, the time of analysis will decrease. A conductimeter (Fig.6.10) was therefore constructed, with the electrodes (10 pm Pt-Ir) glued in a manner similar t o that discussed for the probe (Fig.6.16). In t h s instance, the linear conductimeter, as discussed in section 6.4.4, can still be used. The I.D. of the probe was made t o be 0.2 mm. A PTFE narrow-bore tube, with an I.D. of 0.2 mm and an O.D. of 0.45 mm, was mounted between the injection block (Fig.7.5) and the conductivity probe. A similar narrow-bore tube was mounted between the probe and the counter electrode compartment (Fig.7.9). The slit of the W absorption detector (Fig.6.30) was also adapted. Although the diameter of the narrow-bore tube is much smaller, the UV absorption detector can still be used because the wall thickness of the narrow-bore tube is much smaller. It is well known that PTFE has a great W absorption. Experimentally, it was found that the electroendosmotic flow could be decreased by addition of, e.g., Mowiol (polyvinyl alcohol). The current density applied could be increased up to at least 1500 pA/mm2. The sharpness of the zones increased by decreasing the diameter of the narrow-bore tube, partly owing t o the small differences in temperature between the adjacent zones. The main advantage of decreasing the diameter is the small heat production. Even between the leading electrolyte and terminating electrolyte the increment is small, compared with experiments in w h c h a narrow-bore tube of I.D. 0.45 mm was used. This effect can easily be seen if terminating ions that have a very low effective mobility are applied and the electric current is switched off. Because the conductivity is a function of temperature, the shift in the linear signal of the conductivity detector (a.c. method) gives 395
396
DIAMETER OF THE NARROW-BORE TUBE
an impression of the temperature of the electrolytes inside the probe. With the probe with an I.D. of 0.2 mm, the shifi is 0.4% of the total signal for ACES in the operational system listed in Table 12.1 if a current density of 500 pA/mm* is applied. With the probe with an I.D. of 0.45 mm, the shift is 2% under similar conditions. In addition, the drift in the signal (warming up of the probe) after the terminator has passed tile micro-sensing electrodes, again at a current density of 500 pA/mm*, can be neglected for probes with a small J.D. Whether or not I.D. can be decreased further depends on, among other factors, the possibility of suppressing the electroendosmotic flow, stable regulation of the currentstabilized power supply (I < 10 pA) and the technology involved in making probes with such a small I.D.
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406
LITERATURE
A.J. Mulder and J. Zuska, Isotachophoresis. Conductivity measurement and signal handling, J. Chromatogr., 9 1 (1 974) 8 19. T.W. Nee, Theory of isotachophoresis (displacement electrophoresis, transphoresis), J. Chromatogr., 93 (1974) 7. Z. Prusik, Free-flow electromigration separations, J. Chromatogr., 9 1 (1974) 867. M.Y. Rosseneu, V. Blaton, H. Caster, H. Peeters and A. Kopwillem, Isotachophoresis of human APO-HDL polypeptides, Protides Biol. Fluids, Proc. Colloq., 22 (1974) 697. B. Sjodin, A. Kopwillem and J. Karlsson, Isotachophoresis: A new technique for determination of tissue metabolite concentrations, Protides Biol. Fluids, Proc. Colloq., 22 (1974) 733. B.F. Sunden, Automatic sample futation in counterflow isotachophoresis, Ger. Offen Pat. 2,363,195 (C1.B. Olk,G.Oln) June 27, 1974; Swed. Appl. 16, 594/72. K. Uyttendaele, M. de Groote, H. Peeters and F. Alexander, Detection of traces of proteins by isotachophoresis, Protides Biol. Fluids, Proc. Colloq., 22 (1974) 743. J. Vacik and J. Zuska, Capillary isotachophoresis with electrolyte counter-flow. Temperature and concentration profiles of the zone boundary, J. Chromatogr., 9 1 (1974) 795. B. Vocisek, Some remarks about W-detection in capillary isotachophoresis, Graduation Report, Charles University, Prague, 1974. A.J. Willemsen, Enzymatic reactions followed via isotachophoresis, Graduation Report, University of Technology, Eindhoven, 1974. 1975
L. Arlinger, Apparatus for isotachophoretic separation, Ger. Offen Pat. 2,454,105, May 15, 1975; Swed. Appl. 73 15,417 (14 Nov. 1973). L. Arlinger, Analytical isotachophoresis in capillary tubes: Analysis of proteins in spacer gradients, in P.G. Righetti (Editor), Progress in Isoelectric Focusing and Isotachophoresis, North-Holland, Amsterdam, Oxford and Elsevier, New York, 1975, p. 33 1. G. Baumann and A. Chrambach, Gram preparative isotachophoresis of proteins, Fed. Proc., Fed. Amer. SOC.Exp. Biol., 34 (1975) 685. P. BoEek, M. Deml and J. Janik, Instrumentation for high-speed isotachophoresis, J. Chromatogr., 106 (1975) 283. T.C. BQg-Hansen,P.J. Svendsen and O.J. Bjerrum, On the biospecific interaction of Con A and glycoproteins in preparative isotachophoresis, in P.G. kghetti (Editor), Progress in Isoelectric Focusing and Isotachophoresis, North-Holland, Amsterdam, Oxford and Elsevier, New York, 1975, p. 347. C.-H. Brogren, P.J. Svendsen and T.C. Bdg-Hansen, On the purification of proteins b y neuraminidase treatment and preparative isotachophoresis, in P.G. Righetti (Editor), Progress in Isoelectric Focusing and Isotachophoresis, North-Holland, Amsterdam, Oxford and Elsevier, New York, 1975, p. 359. J.F. Brown and J.O.N. Hinckley, Electrophoretic thermal theory. 11. Steady-state radial temperature gradients in circular section columns, J. Chromatogr., 109 (1975) 218. J.F. Brown and J.O.N. Hinckley, Electrophoretic thermal theory. 111. Steady-state temperature gradients in rectangular section columns,J. Chromatogr., 109 (1975) 225.
LITERATURE
407
M. Coxon and M.J. Binder, Transverse temperature distributions in isotachophoresis columns of rectangular cross-section, J. Chromatogr., 107 (1975) 43. A.C.G. de Kok, The analysis of amino acids via isotachophoresis, Graduation Report, University of Technology, Eindhoven, 1975. M. Deml. P. BoCek and J. Jan&, High-speed isotachophoresis: Current supply and detection system. J. Chromatogr., 109 (1975) 49. F.M. Everaerts and Th.P.E.M. Verheggen, Analytical isotachophoresis: some practical and funadmental aspects, in P.G. Righetti (Editor), Progress in Isoelectric Focusing and Isotachophoresis, North-Holland, Amsterdam, Oxford and Elsevier, New York, 1975, p. 309. B. Gas, A mathematical model for isotachophoretic separation processes, Graduation Report, Charles University, Prague, 1975. J.O.N. Hinckley, Electrophoretic thermal theory. I. Temperature gradients and theii. effects. J. Chromatogr., 109 (1975) 209. J.C.M. Hoenkamp, The enzymatic phosphorylation, studied via isotachophoresis, Graduation Report, University of Technology, Eindhoven, 1975. A. Kopwillem, Analytical isotachophoresis, Fed. Proc., Fed. Amer, SOC.Exp. Biol., 34 (1975) 685. A. Kopwillem, U. Moberg, G. Westin-Sjodahl, R. Lundin and H. Sievertsson, Analytical isotachophoresis in the analysis of synthetic peptides, Anal. Biochem., 67 (1975) 166. M. Kovai, Isotachophoresis. Separation and analysis of some organic acids, Graduation Report, Comenius University, Bratislava, 1975. A.J.P. Martin and F. Hampson, The analytical isotachophoresis of insulin, in P.G. Righetti (Editor), Progress in Isoelectric Focusing und Isotachophoresis, North-Holland, Amsterdam, Oxford and Elsevier, New York, 1975, p. 327. R. Mollby, S.G. Hjalmarsson and T. Wadstrom, Separation of Escherichia co2i heat-labile entero toxin by preparative isotachophoresis, Febs Lett., 56 (1975) 30. G.T. Moore, Theory of isotachophoresis. Development of concentration boundaries, J. Chromatogr., 106 (1975) 1. Z. RySlav?, J. Vacik and J. Zuska, Temperature profiles in capillary isotachophoresis, J. Chromatogr., 114 (1975) 315. F. Schonhofer and F. Grass, Beitrage zur Theorie der elektrophoretischen Ionen fokussierung anorganischer Ionen mit schwachen Komplexbildnern, J. Chromatogr., 110 (1975) 265. A.J.K. Smolka and M. Bier, Isotachophoresis of living cells, Fed. Proc., Fed. Arner. SOC. Exp. Biol., 34 (1975) 685. S. Stankoviansky, P. b m a n e c and D. Kaniansky, Conductivity detection of zones in isotachophoresis with a high-frequency bridge, J. Chromatogr., 106 (1 975) 131. M. Svoboda, The combination of conductrometric detection and UV-absorption detection in capillary isotachophoresis, Graduation Reporf, Charles University, Prague, 1975. M. Svoboda, Some theoretical and practical aspects of photometric theory and spectrophotometric detection in capillary isotachophoresis, Zkesis, Charles University, Prague, 1975. K. Uyttendaele, V. Blaton, F. Alexander, H. Peeters, M.de Groote, N. VinaimontVandecasteele and J. Chevalier, Agarose isotachophoresis of human sweat, in P.G.
408
LITERATURE
Righetti (Editor), Progress in Isoelectric Focusing and Isotachophoresis, North-Holland, Amsterdam, Oxford and Elsevier, New York, 1975, p. 341. J.L.M. van de Venne, Some aspects of isotachophoretic analyses, Graduation Report, University of Technology, Eindhoven, 1975. J. Vozkova, Determination of dissociation constants via capillary isotachophoresis, Graduation Report, Charles University, Prague, 1975. A.J. Willemsen, Application of isotachophoresis in enzymology, J. Chromatogr., 105 (1975)405.
1976
J. Akiyama and T. Mizuno, Sensitivity of newly designed potential gradient detector for isotachophoresis, J. Chromatogr., 119 (1976) 605. L. Arlinger, Preparative capillary isotachophoresis. Principle and some applications, J. Chromatogr., 119 (1976) 9. P. BoEek, K. Lekova and J. Jan& Separation of some typical Krebs cycle acids by highspeed isotachophoresis, J. Chromatogr., 117 (1976) 97. F.M. Everaerts, M. Geurts, F.E.P. Mikkers and Th.P.E.M. Verheggen, Analytical isotachophoresis, J. Chromatogr., 119 (1976) 129. A. Kopwillem, W.G.Merriman, R.M. Cuddeback, A.J.K. Smolka and M. Bier, Serum protein fractionation by isotachophoresis using amino acid spacers, J. Chromatogr., 118 (1976) 35. H. Miyazaki and K. Katoh, Isotachophoretic analysis of peptides,J. Chromatogr., 119 (1976) 369. M. Svoboda and J. Vacik, Capillary isotachophoresis with ultraviolet detection. Some quantitative aspects, J. Chrornatogr., 119 (1976) 539.
Symbols and abbreviations SYMBOLS A A a
B b C C
'act C* D L 7
D
E e
F fc
G
H h I
i
MI N n ni
0
P Q 4 R r
S S
T
increasing UV absorption; empirical constant for a given series of ions of the same charge ionic species A activity buffer ionic species B, ionic species B; empirical constant for a given series of ions of the same charge distance of closest approach (A) capacity (F) concentration (molell) actual concentration of the ionic species in the narrow-bore tube (molell) equivalent concentration (g-equiv./l) dielectric constant of the solvent dielectric constant of a solution electric field strength (V/cm); electromotive force (V) charge on an electron (C) Faraday constant (C/g-equiv.); force (N) friction factor constant step height (qualitative information) (generally mm) step height (qualitative information) (generally mm) electric current (d.c.) (A); ionic strength (g-equiv./ml) electric current (a.c.) (A) equilibrium constant (in general, K is written for Ka) calibration constant gas constant per mole (erg/"K) constants length of a zone (cm) length of a zone (sec) migration distance of ion A (cm) mobility (cm' /V * s); molality (mole/l) molecular weight of the solvent Avogadro's number number of pKa values of a molecule number of ions i per ml cross-section of the narrow-bore tube (cm’) distance between point of injection and point of detection (cm) total amount of an ionic species (mole); volume transport (ml/sec) charge on an ion (e.s.e.; C) gas constant (erg/"K); electric resistance (sym. increasing resistance) (a) radius (A) entropy electrolyte constant; migration way absolute temperature ( O K ) ; increasing temperature 409
410 1
V
v
oi
a*
P Y
f 1) K
A A*
x x* IJe
w
SYMBOLS AND ABBREVIATIONS time (sec); transport number d.c. voltage drop (V); increasing voltage; molecular volume (A') velocity (cm/sec); a.c. voltage drop volume injected (pl) function of K h function of K b maximum number of positive charges for an ionic species; valency of an ion extent of dissociation; constant real extent of dissociation; constant ratio of two electric field strengths activity coefficient; correction factor according to Onsager potential (V) viscosity (g/cm sec) function of the concentration molar conductance (cm2 / a * mole) equivalent conductance (cm2/ a equiv.) electric conductivity of a zone [(Q crn)-'] equivalent conductance of an ionic species (cm'/s2 magnetic permeability frequency (Hz)
-
-
SUBSCRIPTS A B C
corn H
i ind isot
i L OH0
r ref rel. ret.
ionic species A ionic species B concentration computed ionic species H' a number indicating the step of dissociation; summation index indicator electrode isotachophoretic a number indicating the step of dissociation; liquid junction leading ion/zone ionic species OHat zero concentration type of ionic species reference electrode; reference value relaxation retardation
-
equiv.)
SYMBOLS AND ABBREVIATIONS
41 1
standard solution terminating ion/zone Uth zone Vth zone sample solution maximum possible charge
SUPERSCRIPTS t o the ith degree relative total maximum number of positive charges of an ionic species refers t o equivalents instead of molar quantities; refers t o quantities in a certain solution
EXAMPLES 'A,,lJ,z-i
concentration of the ionic species A, with z-i positive charges in the Uth zone
('H, CJ)’
the concentration of H' in the Uth zone to the ith degree
ABBREVIATIONS AMP, ADP, ATP CMP, CDP, CTP E'EP GMP, GDP, GTP G6P G6PDH GABA Guan HNP I. C. Im LDh MES MKAC NADP NAD 6 PG PTI:E S.C.
Tba Tea Tma Tris TPX UMP, UDP, UTP WKAC
adenosine mono-, di- and triphosphate cytidine mono-, di- and triphosphate fluoroethylene polymer guanosine mono-, di- and triphosphate. glu co se-6-ph ospha t e glucose-6-phosphate dehydrogenase y-aminobutyric acid guanidine half-neutralization point integrated circuit Imidazole lactate dehydrogenase morpholinoethanesulphonic acid an example of an operational system, listed in a table, with methanol as the solvent nicotinamide-adenine dinucleotide phosphate nicotinamide dinucleotide 6-phosphogluconic acid polytetrafluoroethylene succinyl c h o k e tetrabutylammonium tetraethylammonium tetramethylammonium trishydroxymethylarninornethane methylpentene polymers uridine mono-, di- and triphosphate an example of an operational system, listed in a table, with water as the solvent
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Subject index A Absorption meter, UV 153-170 a.c. conductivity detector, differentiator 154 Acidic media 87 Acidic solvents 86 a.c. method, calibration of conductimeter 15 1 _ _ _ , circuit suitable for determination of the conductivity 146, 148 _ _ _ , linearity of two conductimeters 152 a.c. method of resistance determination 135, 143 Activity coefficients 76 Adaptation in concentrations 44 Adapted zones 18 Additives 180-190 _-_ ,effect on electroendosmotic flow 171-173 --- , effect on micro-sensing electrodes 174- 180 --_ , influence.on isotachophoretic separation 183 Additives to the electrolytes 171-190 Alkali metals, determination 102 Alkali metals in methanol 104 Aluminium block, isotachophoretic equipment with thermostating via 221-224 Amino acids, peptides and proteins 31 Iff Amino acids, qualitative information 316, 317, 322 Amphiprotic media 87 Ampholyte gradients, separation of proteins 322-335 Analytical isotachophoresis, survey of detectors used 122 Anionic species, separation in aqueous solutions using a conductivity detector (a.c. method) and a UV absorption detector (256 nm) 300-310 ---, separation in aqueous solutions using a thermometric detector 295-300 --_ , separation in methanol using a thermometric detector 362-364 Anions, qualitative information 297, 298, 307-310,363 Aqueous methanolic systems, separations using a conductimetric detector (a.c. method) and UV absorption detector (256 nm) 373
Aqueous solutions, separation of anionic species using a conductivity detector (a.c. method) and a UV absorption detector (256 nm) 300-310 _-_ ,separation of anionic species using a thermometric detector 295-300 _ _ _ , separation of cationic species using a conductivity detector (a.c. method) and a UV absorption detector (256 nm) 293, 294 _ _ _ , separation of cationic species using a thermocouple as detector 283-293 Aqueous systems, separation of nucleotides using a conductivity detector (a.c. method) and a UV absorption detector (256 nm) 342-345 _ _ _ , separation of nucleotides using a thermometric detector 337ff Axial temperature differences 75, 76
B Background electrolyte 7 Basic media 87 Basic solvents 86 Beharrliche Funktion 2, 41 Boundary, concentration 44 _ _ _ , separation 44 - _ _ , _ _ _ ,velocity 48 Buffering capacity 94, 249
C Calibration constant 273,275,280, 281 Calibration of concentrations 99 Calibration of conductimeter, ax. method 151 Calibration of d.c.-a.c. converter 141 Carrier functions 325 Carriers 99, 100 Cationic species, separation in aqueous solutions using a conductivity detector (a.c. method) and a UV absorption detector (256 nm) 293,294 _ _ _ , separation in aqueous solutions using a thermocouple as detector 283-293 _ _ _ , separation in methanol using a thermometric detector 364-373
413
414
SUBJECT INDEX
Cations, qualitative information 287, 292, 293, 368 Choice of buffering counter ionic species 92,93 Choice of electrolyte system 83ff Choice of electrolyte system, scheme 101 Choice of pH of the leading electrolyte 93-96 Choice of solvent 84-92 Choice of terminating and leading ionic species 96-99 Circuit for counter flow regulation via the membrane pump 242, 245 Circuit for d.c. method 137 Circuit suitable for determination of the conductivity, a.c. method 146, 148 Circuit for differentiating thermometric signals 123 Circuit for on-off regulation of the pumping mechanism during counter-flow 239 Circuit for potential gradient detector 137 Circuit for regulation of the counter-flow of electrolyte via level regulation 233 Circuit for thermostating 222 Circuit of UV source 157 Coating of micro-sensing electrodes 191-193 ---,effect 192, 194 Combination of systems 11 1 Compartment, counter electrode 21 1-217 --- -__ ,cylindrical 213-215 -_- --_ , with flat membrane 215-217 Complex formation 33-35 Computation procedure for isotachophoresis 62 Computation procedure in moving-boundary electrophoresis 389 Computer program (steady-state in isotachophoresis) 74 Concept of mobility 27ff Concentration adaption 18, 19 Concentration boundary 44 ‘Concentration’ principle of isotachophoretic analyses 378 Concentrations, calibration 99 Conductance, equivalent 29,36, 86 Conductimeters, calibration, a.c. method 151 -_- , two, linearity, a.c. method 152 Conductimetric detector (a.c. method) and UV absorption detector (256 nm), separations in aqueous methanolic systems 373 Conductivity, ionic equivalent 29-31 Conductivity detection 133 -1 52 -_- ,high-frequency 130-133 ---, __- , construction 131-133 Conductivity detector 133 Conductivity detector (a.c. method) and UV absorption detector (256 nm), separation of anionic species in aqueous solutions 300-310 ~
Conductivity detector (a.c. method) and UV absorption detector (256 nm), separation of cationic species in aqueous solutions 293,294 Conductivity detector (a.c. method) and UV absorption detector (256 nm), separation of nucleotides in aqueous systems 342-345 Conductivity probe 136 Conductivity probe with equiplanar-mounted measuring electrodes 144 Conductivity probe with equiplanar-mounted sensing electrodes 143-152 Construction, high-frequency conductivity detection 131-1 33 Construction of thermocouples 119-1 25 Conversion, enzymatic 348-360 Conversion of data 270, 271 Corrosion inhibitors 184 Coulomb’s law 85 Counter electrode compartment 211-217 _ _ - ,cylindrical 213-215 - _ _ ,with flat membrane 215-217 Counter flow, 100% 375 Counter flow of electrolyte 230-245, 375ff -_- ,influence of impurities 231 ---,via level regulation, circuit 233 Counter flow regulated by the current-stabilized power supply 241-245 Counter flow regulation, via the membrane pump, circuit 242,245 Counter flow with direct control on the pumping mechanism via the power supply 237,238 Counter flow with level regulation 231-233 Counter flow with light-dependent resistor regulation 23 3-23 7 Counter flow with no regulation 238-240 Counter flow with on-off regulation of the pumping mechanism, circuit 239 Counter ionic species, buffering, choice 92,93 Current, leak 188 Current density, influence on the isotachopherogram 195 Current stabilized power supply 229 Cylindrical counter electrode compartment 213-215
D Data, conversion 270, 271 d.c.-a.c. converter 140-142 _ _ - , calibration 141 d.c. method, circuit 137 d.c. method of resistance determination 135 De-gassing of electrolytes 252
41 5
SUBJECT INDEX
Detection limit 129, 278 --_ , high-resolution detectors 193-199 _ _ _ , improvements 195 Detectors, specific 118 --_ , synchronous, UV detection 163 --_ ,universal 1 18 Detectors used in analytical isotachophoresis, survey 122 Determination of conductivity circuit suitable, ax.-method 146, 148 Determination of effective mobilities 392 Determination of trace amounts 168 Diameter of the narrow-bore tube 395ff Differential signal peaks 20 Differentiating thermometric signals, circuit 123 Differentiator for the a.c. conductivity detector 154 Diffusion, influence on the zone boundaries 74,75 ‘Dilution’ principle of isotachophoretic analyses 378 ‘Dilution’ technique 352 --_ , UV detector 169 Disc electrophoresis 17, 265-267 Disc electrophoretic system 67 Dissociation, partial 3 1-35 Disturbances caused by hydrogen and hydroxyl ions 253-263 Disturbances due to the presence of carbon dioxide 263, 264 Disturbances due to the presence of hydrogen and hydroxyl ions in buffered systems 260-263 Disturbances from the leading zone 257-260 ‘Dole polynomals’, modification 389
E Electrode, activated 187 -_ _ , bipolar sensing 176 --_ , charge-transfer 175, 176 _-- , ‘ideally’ polarized 175, 176 _-- , metallic 174 - _ _ , micro-sensing, coating 191- 193 _ - _ , --_ , effect of coating 192, 194 --- , (partially) passivated 186 --_ , passivated 185 - - _ , polarized 174 --_ , reversible 174 Electrode reactions 256 Electroendosmosis 171, 173
Electroendosmotic flow, effect of additives 171-173 Electrolyte, background 7 _ _ _ , de-gassing of 252 --- , leading 13 _ _ - , supporting 7 _ _ _ , terminating 13 Electrolyte systems, choice 83ff -__ ---,scheme 101 Electroneutrality, principle 15,60 Electroneutrality equations 47, 48, 388 Electrophoresis, disc 17, 265-267 _ _ - , moving-boundary 9-12, 387ff --- , - _ _ , procedure of computation 389 _ _ - , stacking 18 -_- ,zone 7 Electrophoretic system, disc 67 Enforced isotachophoresis 264-267 Enzymatic conversion 348-360 Enzymatic reactions 347ff Equilibrium equations 45-47,58 Equipment 217-229 Equivalent weight 29
F Fatty acids 103 _-- , separation in a methanolic system 108 Friction factor 27, 38 Friction force 27 Funktion, beharrliche 2, 41
Galvanic separation 150 Gas bubbles 252, 253
H Halides, qualitative information 366 Heights, step 20 Henderson-Hasselbalch equation 33 High-frequency conductivity detection 130-133 _ _ - , construction 131-133 High-resolution detectors, detection limits 193-199 , isotachophoretic equipment with 224-229
416
I Identification 20 --_ ,reference materials 99 Impurities, influence on counter-flow of electrolyte 23 1 --_ ,marking a zone boundary 165 --_ , zones of 96 Indirect UV method 166 Inhibitors, corrosion 184 Injection block 208-211 ---, simplified 211, 212 Injection systems 203-21 1 --_ ,four-way tap 204, 205 --_ ,six-way valve 205-208 Ionic atmosphere 28 Isoelectric focusing 23, 24 Isoelectric point 23 Isotachopherograms 20-22 ---,influence of current density 195 Isotachophoresis, computation procedure 62 ---, enforced 264-267 , mathematical model 41ff, 58-62 --_ , principle 13-23 -_- ,steady state 55-69 ---, _-_ , computer program 74 Isotachophoretic analysis, resolution 189 Isotachophoretic condition 14, 15, 58, 260 Isotachophoretic equipment 117 Is0tachophoretic equipment with high-resolution detectors 224-229 Isotachophoretic equipment with thermostating via aluminium block 221-224 Isotachophoretic equipment with water-jacket 219-221 Isotachophoretic model, check 76-81 Isotachophoretically separated system 13, 57 Isotachophoretic separations, concept 5 5 -5 8 ---,influence of additives 183 --_ ,influence of surfactants 189 Isotachophoretic separations in non-aqueous systems 361ff Iteration procedure 62-69
SUBJECT INDEX
Leak current 188 Length of a zone 18 Linearity of two conductimeters, a.c. method 152
M Mass balance of the buffer 59, 60 Mass balances 48-50, 388 Measurement of effective mobilities 387ff Mechanical construction of the UV source 158 Membrane pump 24 1-245 -__ ,circuit for counter flow regulation via 242, 24 5 ‘Memory’ effect 182 Methanol, alkali metals in 104 _-- , separation of anionic species using a thermometric detector 362-364 --_ , separation of cationic species using a thermometric detector 364-373 Methanol as solvent 87-92 Methanolic system, separation of some fatty acids 108 Micro-sensing electrodes, coatinq 191-193 --_ , effect of additives 174-1 80 ---, effect of coating 192, 194 --_ , polarization 176 Migration, independent, law 3 1 Migration paths 50 Mixed zones 9,13 Mobility, absolute ionic 30, 31 --_ , concept 27ff -__ ,ionic 29-31 --- _-- ,effective 31-37,49, 83, 86 --- - -- ---, determination 392 -- - - --, ---, measurement 3 87ff ---, ---,relationship with entropy 39 ---, __- , relationship with volume 37, 38 -__ , separations according to 83, 98, 100 Mobility at infinite dilution 30 Moving-boundary electrophoresis 9-12, 387ff - _ _ , procedure of computation 389 Moving-boundary procedure 13
L N Law of independent migration 31 Leading electrolyte 13 -_- ,pH, choice 93-96 Leading ionic species, choice 96-99 Leading zone, enlarged 255
Narrow-bore tube; diameter 395ff Non-aqueous systems, isotachophoretic separations 361ff Nucleotides, qualitative information 342, 344
41 7
SUBJECT INDEX
--_ , separation
103
- _ _ , separation in aqueous systems using a
conductivity detector (a.c. method) and a UV absorption detector (256 nm) 342-345 _ _ ,separation ~ in aqueous systems using a thermometric detector 337ff
Qualitative information of nucleotides 342, 344 Quantitative aspects 273 Quantitative determination 21, 23 Quantitative information 21-23
R 0 Ohm’s law 1 7 - - _ , modified 51, 61,62, 388 Operational system 249 Overpotential 176 Overshoot 177, 178
P Parabolic profile 199 Peptides, amino acids and proteins 311ff _ _ _ , small, separation 335, 336 pH, determination 90 --_ , operational definition 89 pK values, determination 89-92 _ _ _ , separations according to 83, 94, 98, 100 Polarization of micro-sensing electrode 176 Potential gradient detector 135 _ _ - , circuit 137 Potentials, acidity 86 Power supply, current stabilized 229 Procedure of computation in moving-boundary electrophoresis 389 Profile of a zone boundary 172 Proteins, amino acids and -peptides 311ff _ - _ _ , separation in ampholyte gradients 322-335 Protolysis 33
Q Qualitative information 21-23 Qualitative information of amino acids 316, 317, 322 Qualitative information of anions 297, 298, 307-310, 363 Qualitative information of cations 287, 292, 293, 36 8 Qualitative information of halides 366
Radial temperature differences 75, 76 Reference materials for identification 99 Regulating function 42 Relaxation 36, 37 Relaxation effect 28 Reproducibility 275, 279 Resistance determination, a.c. method 135, 143 --_ , d.c. method 135 Resolution of isotachophoretic analysis 189 Retardation, electrophoretic 28, 36, 37 R ~ v a l u e s8
S Self-conductance 85 Self-correcting effect 11 Self-correction 15 Separation, partial 9 _ _ _ , time needed 56 Separation boundary 44 _ _ _ ,velocity 4 8 Separation of anTonic species in aqueous solutions using a conductivity detector (ax. method) and a UV absorption detector (256 nm) 300-310 Separation of anionic species in aqueous solutions using a thermometric detector 295-300 Separation of anionic species in methanol using a thermometric detector 362-364 Separation of cationic species in aqueous solutions using a conductivity detector (ax. method) and a UV absorption detector (256 nm) 293,294 Separation of cationic species in aqueous solutions using a thermocouple as detector 283-293 Separation of cationic species in methanol using a thermometric detector 364-373 Separation of fatty acids in a methanolic system 108 Separation of nucleotides 103 Separation of nucleotides in aqueous systems using a thermometric detector 337ff
418
SUBJECT INDEX
Separation of nucleotides in aqueous systems using a conductivity detector (a.c. method) and a UV absorption detector (256 nm) 342-345 Separation of peptides 335, 336 Separation of proteins in ampholyte gradients 322-335 Separations according to mobilities 83, 98, 100 Separations according to pK values 83, 94, 98, 100 Separations in aqueous methanolic systems using a conductimetric detector (a.c. method) and UV absorption detector (256 nm) 373 Solvents, choice 84-92 ---,methanol 87-92 --_ ,acidic 86 ---,basic 86 --_ ,classes 87 Spacer functions 325 Spacers 99,100 Stabilizers 99 Stacking electrophoresis 18 Stationary state 48 Steady state 13,57 Steady-state in isotachophoresis, computer program 74 Supporting electrolyte 7 Surface-active chemicals 99 Surface-active compounds used in isotachophoretic analyses 181 Surfactants, influence on the isotachophoretic separation 189 Synchronous detector, UV detection 163 Systems, combination 11 1
UV absorption detector (256 nm) and a conductimetric detector (a.c. method), separations in aqueous methanolic systems 373 UV absorption detector and conductivity detector (a.c. method), separation of anionic species in aqueous solutions 300-310 UV absorption detector (256 nm) and ccnductivity detector (a.c. method), separation of cationic species in aqueous solutions 293, 294 UV absorption detector (256 nm) and conductivity detector (a.c. method), separation of nucleotides in aqueous systems 342-345 UV absorption meter 153-170 W cell 164, 165 UV detector, dilution technique 169 W detector combination with modulated UV source 162 UV detector combination with non-modulated UV 160 W method, indirect 166 UV source, circuit 157 _-- , construction 155-159 _-_ , mechanical construction 158
T
V
Tailing 8 Tap, four-way 204,205 Terminating electrolyte 13 Terminating ionic species, choice 96-99 Thermocouple, construction 119-1 25 ---, differential 121, 124 Thermocouple as detector, separation of cationic species in aqueous solutions 283-293 Thermometric detector, separation of anionic species in aqueous solutions 295-300 ---, separation of anionic species in methanol 362-364 --_ , separation of cationic species in methanol 364-373 --_ , separation of nucleotides in aqueous systems 337ff Thermometric recording 119-1 30 Thermometric signals, differentiating, circuit 123
Valve, six-way 205-208
Thermostating, circuit 222 Trace amounts, determination 168 Transport number 30 Trouble-shooting 249, 250
U
W Water-jacket, isotachophoretic equipment with 219
Z Zone boundary, influence of diffusion 74 -__ ,profile 172 Zone electrophoresis 7 Zone length 18 Zones, mixed 9, 13 _-_ ,adapted 18 Zones of impurities 96
