Frans_M_Everaerts_Isotachophoresis_378342.pdf

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MATHEMATICAL MODEL FOR THE STEADY STATE r- 1 4.3.2.5. Modified Ohm ’s law Working at a constant current density: IIG = constant = EL hL = E, X, The overall electrical conductivity of a zone is the sum of the values ci mi bil and consequently Substitution of eqns. 4.26 and 4.27 in eqn. 4.37 gives COH,L %H,L +CH,L~H,L +cAL r 1 61 (4.3 5) (4.36) (4.37) (4.38)
62 MATHEMATICAL MODEL FOR ISOTACHOPHORESIS 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 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 (4.39) 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 9 ‘AL, zAL can be calculated from the total concentration, and with eqn. 4.26 all 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
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Journal of Chromatogaphy Library -
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Journal of Chromatography Library -
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Dedicated to Pr0f.Dr.h. A.I.M. Keul
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Contents Preface ..................
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CONTENTS IX 6.4.2. The d.c. method
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CONTENTS XI 12.2.2. Applications ..
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It is very well known that charged
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Chapter 1 Historical review SUMMARY
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HISTORICAL REVIEW 3 Independently i
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THEORY
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Chapter 2 Principles of electrophor
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MOVINGBOUNDARY ELECTROPHORESIS a S
Page 26 and 27: MOVINGBOUNDARY ELECTROPHORESIS 0 iu
Page 28 and 29: ISOTACHOPHORESIS 13 2.4. PRINCIPLE
Page 30 and 31: ISOTACHOPHORESIS 15 As the anionic
Page 32 and 33: ISOTACHOPHORESIS velocities, so tha
Page 34 and 35: ISOTACHOPHORESIS 19 d.t ’.t I Fig
Page 36 and 37: ISOTACHOPHORESIS 21 t Fig.2.8. Isot
Page 38 and 39: ISOELECTRIC FOCUSING 23 The four is
Page 40 and 41: DISCUSSION 25 Fig.2.11. Survey of t
Page 42 and 43: Chapter 3 Concept of mobility SUMMA
Page 44 and 45: IONIC MOBILITY AND IONIC EQUIVALENT
Page 46 and 47: EFFECTIVE IONIC MOBILITY 31 obtain
Page 48 and 49: EFFECTIVE IONIC MOBILITY 33 compari
Page 50 and 51: EFFECTIVE IONIC MOBILITY Fig.3.4. R
Page 52 and 53: DETERMINATION OF IONIC MOBILITIES 3
Page 54 and 55: DETERMINATION OF IONIC MOBILITIES 3
Page 56 and 57: Chapter 4 Mathematical model for is
Page 58 and 59: GENERAL EQUATIONS 43 anionic specie
Page 60 and 61: GENERAL EQUATIONS 4.2.1. Equilibriu
Page 62 and 63: GENERAL EQUATIONS 41 i Similar equa
Page 64 and 65: GENERAL EQUATIONS 49 Uthzone (U-llt
Page 66 and 67: GENERAL EQUATIONS 4.2.4. Modified O
Page 68 and 69: GENERAL EQUATIONS TABLE 4.2 REDUCED
Page 70 and 71: MATHEMATICAL MODEL FOR THE STEADY S
Page 84 and 85: VALIDITY OF THE ISOTACHOPHORETIC MO
Page 92 and 93: CHECK OF THE ISOTACHOPHORETIC MODEL
Page 94 and 95: CHECK OF THE ISOTACHOPHORETIC MODEL
Page 96 and 97: REFERENCES 81 Fig.4.17. Relationshi
Page 98 and 99: Chapter 5 Choice of electrolyte sys
Page 100 and 101: CHOICE OF THE SOLVENT 85 In general
Page 102 and 103: CHOICE OF THE SOLVENT TABLE 5.2 THE
Page 104 and 105: CHOICE OF THE SOLVENT pH and pKvalu
Page 106 and 107: CHOICE OF THE SOLVENT 91 TABLE 5.4
Page 108 and 109: CHOICE OF THE pH OF THE LEADING ELE
Page 110 and 111: CHOICE OF THE pH OF THE LEADING ELE
Page 112 and 113: CHOICE OF THE TERMINATING AND LEADI
Page 114 and 115: ADDITIONS TO THE ELECTROLYTE SOLUTI
Page 116 and 117: EXAMPLES Choice of solvent. Can wat
Page 118 and 119: EXAMPLES 103 solvent, hoping that a
Page 120 and 121: EXAMPLES TABLE 5.11 STEP HEIGHTS OF
Page 122 and 123: EXAMPLES TABLE 5.12 STEP HEIGHTS OF
Page 124 and 125: Fig.5.9. Isotachopherograms of the
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EXAMPLES II 4 3 Fig.5.11. Isotachop
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REFERENCES 113 Example I. As exampl
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INSTRUMENTATION
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Chapter 6 Detection systems SUMMARY
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THERMOMETRIC RECORDING 6.1.3. Combi
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THERMOMETRIC RECORDING Potential gr
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THERMOMETRIC RECORDING /2 Fig.6.1.
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THERMOMETRIC RECORDING T t l Fig.6.
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THERMOMETRIC RECORDING 7 127 It-- I
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THERMOMETRIC RECORDING a concentrat
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HIGH-FREQUENCY CONDUCTIVITY DETECTI
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CONDUCTIVITY DETECTION 133 Fig.6.9.
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CONDUCTIVITY DETECTION 135 The d.c.
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CONDUCTIVITY DETECTION 137 Hi V 1kR
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CONDUCTIVITY DETECTION Fig.6.12. Co
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CONDUCTIVITY DETECTION Fig.6.14. Th
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CONDUCTIVITY DETECTION 143 6.4.4. T
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CONDUCTIVITY DETECTION 145 contact
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CONDUCTIVITY DETECTION 147 We can n
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CONDUCTIVITY DETECTION 149 N.Y., U.
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CONDUCTIVITY DETECTION 151 achieved
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UV ABSORPTION METER 153 -_-.- +- R
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UV ABSORPTION METER Fig.6.22. Contr
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W ABSORPTION METER r +15V -15V Mod
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W ABSORPTION METER 159 TABLE 6.4 PR
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W ABSORPTION METER 230 240 2% m zm
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to Mod (Fig 6.24) oscillator I sync
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UV ABSORPTION METER 165 dicular to
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Fig.6.31. Isotachopherograms for th
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UV ABSORPTION METER 169 50 Fig.6.33
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ADDITIVES TO THE ELECTROLYTES 171 6
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ADDITIVES TO THE ELECTROLYTES 173 e
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ADDITIVES TO THE ELECTROLYTES 175 a
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ADDITIVES TO THE ELECTROLYTES 177 o
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ADDITIVES TO THE ELECTROLYTES 179 d
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ADDITIVES TO THE ELECTROLYTES 181 T
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ADDITIVES TO THE ELECTROLYTES Fig.6
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ADDITIVES TO THE ELECTROLYTES 185 F
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ADDITIVES TO THE ELECTROLYTES 1 2 3
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ADDITIVES TO THE ELECTROLYTES 189 n
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COATING OF THE MICRO-SENSING ELECTR
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DETECTION LIMITS 193 electric drivi
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DETECTION LIMITS 195 Fig.6.48. Infl
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DETECTION LIMITS 197 TABLE 6.6 SURV
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CONCLUSION 199 average length of a
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REFERENCES 201 seen. Again it is cl
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Chapter 7 Instrumentation SUMMARY T
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INJECTION SYSTEMS I! I n Fig.7.1. P
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INJECTION SYSTEMS Fig.7.3. Exploded
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INJECTION SYSTEMS Fig.7.5. Injectio
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COUNTER ELECTRODE COMPARTMENTS 21 1
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COUNTER ELECTRODE COMPARTMENTS Even
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COUNTER ELECTRODE COMPARTMENTS 21 5
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EQUIPMENT the large bore, a more di
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EQUIPMENT 219 belonging to three cl
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EQUIPMENT 221 signal of the thermoc
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EQUIF'MENT 223 No effect on the res
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EQUIPMENT 225 Fig.7.14. Electrophor
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EQUIPMENT Fig.7.16. Photograph of t
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EQUIPMENT 229 mounted equiplanar, w
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COUNTER FLOW OF ELECTROLYTE 231 ins
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COUNTER FLOW OF ELECTROLYTE p High
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COUNTER FLOW OF ELECTROLYTE Fig.7.2
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COUNTER FLOW OF ELECTROLYTE 231 aro
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COUNTER FLOW OF ELECTROLYTE p high
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COUNTER FLOW OF ELECTROLYTE 24 1 7.
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COUNTER FLOW OF ELECTROLYTE I I 31
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COUNTER FLOW OF ELECTROLYTE max. 15
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APPLICATIONS
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Chapter 8 Introduction SUMMARY In t
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INTRODUCTION 25 1 the various ionic
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Chapter 9 Practical aspects SUMMARY
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DISTURBANCES CAUSED BY H+ AND OH 25
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DISTURBANCES CAUSED BY H+ AND OH- 2
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DISTURBANCES DUE TO CO, 263 Electro
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ENFORCED ISOTACHOPHORESIS 265 t T T
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WATER AS TERMINATOR 267 function of
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PURIFICATION OF THE TERMINATOR 7 4
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REFERENCES 271 AS an example, the c
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Chapter 10 Quantitative aspects SUM
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THERMOMETRIC MEASUREMENTS 215 vj c
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THERMOMETRIC MEASUREMENTS TABLE 10.
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CONDUCTIMETRIC MEASUREMENTS factor
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CONCLUSION 28 1 Tables 10.3-10.5 wa
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Chapter 11 Separation of cationic s
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SEPARATION USING A THERMOCOUPLE AS
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I SEPARATION USING A THERMOCOUPLE A
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SEPARATION USING CONDUCTIVITY AND U
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Chapter I2 Separation of anionic sp
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SEPARATION USING A THERMOMETRIC DET
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SEPARATION USING CONDUCTIVITY AND W
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Chapter 13 Amino acids, peptides an
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AMINO ACIDS TABLE 13.1 OPERATIONAL
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AMINO ACIDS 8- ?- 6- 5- 4- 3- 2- f-
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AMINO ACIDS 317 TABLE 13.5 STEP HEI
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AMINO ACIDS Fig.13.3. Schematic dia
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AMINO ACIDS TABLE 13.6 DETERMINATIO
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SEPARATION OF PROTEINS IN AMPHOLYTE
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SEPARATION OF SMALL PEPTIDES reprod
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Chapter I4 Separation of nucleotide
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Chapter 15 Enzymatic reactions SUMM
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ENZYMATIC CONVERSION OF GLUCOSE (FR
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ENZYMATIC CONVERSION OF PYRUVATE 35
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Chapter 16 Separations in non-aqueo
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SEPARATION OF ANIONIC SPECIES IN ME
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SEPARATION OF CATIONIC SPECIES IN M
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EXPERIMENTS IN AQUEOUS METHANOLIC S
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Chapter I7 Counter flow of electrol
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INTRODUCTION 317 In various operati
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EXPERIMENTAL 0% 10 % a b 60 % a b a
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EXPERIMENTAL 381 caused by the coun
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CONCLUSION 383 c t r ’r; I I"
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APPENDICES
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Appendix A Simplified model of movi
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PROCEDURE OF COMPUTATION A.3. PROCE
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EXPERIMENTAL 39 1 TABLE A1 THEORETI
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DISCUSSION E I I Fig.A2. Graphical
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Appendix B Diameter of the narrow-b
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Appendix C Literature 1897-1966 F.
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LITERATURE 399 B.P. Konstantinov an
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LITERATURE 401 1971 L. Arlinger, Is
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LITERATURE 403 1973 L. Arlinger and
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LITERATURE 405 A. Chrambach and J.S
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LITERATURE 407 M. Coxon and M.J. Bi
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Symbols and abbreviations SYMBOLS A
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SYMBOLS AND ABBREVIATIONS SUPERSCRI
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Subject index A Absorption meter, U
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SUBJECT INDEX 41 5 Detection limit
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SUBJECT INDEX 41 7 --_ , separation
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