Frans_M_Everaerts_Isotachophoresis_378342.pdf

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GENERAL EQUATIONS 49 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 Ay which is not present in the (U-1)th zone. uniform substance with an effective mobility given by ii = aimi = $ /cimi/ct> (4.1 5) i= 0 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 EufiA (fiA, > fiA2 > . . . . > fiA > r71 ). For the anionic species A,-,, for u-1 Au 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 So to S1. 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
50 MATHEMATICAL MODEL FOR ISOTACHOPHORESIS 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 EU-l~Au-l, The amount of ions between P and So (at time t=O) is oc~u-l, U (psI-sO sl) = ocAu-l, U(EUriiAu-l, U-EUriiA, U) where 0 is the cross-sectional area of the narrow-bore tube and ci is the total 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 The amount of the anionic species between P and So (at time r = 0) reaches the 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-i (EU-l fiAu-l,U-l-EUfiAu,U) The general expression for the mass balance of an anionic species is ‘A,., U WEUfiAu, U) = A,., U-1 (EU-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) (4.18) (4.20)
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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 ..
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 60 and 61: GENERAL EQUATIONS 4.2.1. Equilibriu
Page 62 and 63: GENERAL EQUATIONS 41 i Similar equa
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
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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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