Frans_M_Everaerts_Isotachophoresis_378342.pdf

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GENERAL EQUATIONS 4.2.1. Equilibrium equations The thermodynamic equilibrium constant for an equilibrium d A-B+C can be defined as aBaC K, =- aA where aA, aB 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 45 (4.3) (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+: and, in a similar way: (4.6a)
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 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, +C +. . . zAr ‘“A,,, U, zA,l A,., V, ~ ~ - 2 Substitution of eqn. 4.7 gives or (4.7)
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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 ..................
Page 10 and 11: CONTENTS IX 6.4.2. The d.c. method
Page 12 and 13: CONTENTS XI 12.2.2. Applications ..
Page 14 and 15: It is very well known that charged
Page 16 and 17: Chapter 1 Historical review SUMMARY
Page 18 and 19: HISTORICAL REVIEW 3 Independently i
Page 20 and 21: THEORY
Page 22 and 23: Chapter 2 Principles of electrophor
Page 24 and 25: 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 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
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CHOICE OF THE pH OF THE LEADING ELE
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CHOICE OF THE TERMINATING AND LEADI
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ADDITIONS TO THE ELECTROLYTE SOLUTI
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EXAMPLES Choice of solvent. Can wat
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EXAMPLES 103 solvent, hoping that a
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EXAMPLES TABLE 5.11 STEP HEIGHTS OF
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EXAMPLES TABLE 5.12 STEP HEIGHTS OF
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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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