General index

General index

Batchelor equations, 260-261, 351 Batchinski equation, 287, 297 Blanc's law, 283, 365 Bloch equation, 220, 243 Boundary formation, for diffusion measurements, 126, 127, 147-149 Brownian motion, 5, 72, 208, 240, 262, 333, 336, 394 Bulk flow, 45, 73 Bulk velocity, 64

Conductivity (cont.) thermal, 3, 24, 26, 265, 268 and heat flux correlation function, 19 Consolute points, diffusion near, 296, 353, 356-358, 371 Convective mixing in ternary diffusion, 183-184 Correlated m o t i o n , a n d diffusion, 12, 280 Correlation functions (see also Distribution functions), concentration, 297 force, 265 heat flux, 19 time, 12-19, 313-314 velocity, 18, 265, 268-269, 283, 313 long time tails, 269 diffusion coefficient and, 19, 296 Correlation time, rotational [see also Rotational diffusion coefficient), 333-335 Coupled chemical reactions, 31 Curie principle, 4 1 , 48-49

C a r n a h a n - S t a r l i n g equation, 267, 282 C h a p m a n - E n s k o g theory of dilute gases (see also Enskog theory), 8, 25, 36, 64, 266, 312, 315, 365 Chemical reactions, cyclic, and O R R , 2 8 - 3 3 , 36 C h r o m a t o g r a p h y , 193-199 C h r o n o a m p e r o m e t r y , Chronogalvametry, 191 C h r o n o p o t e n t i o m e t r y , 191, 426 Coefficient of sliding friction, rotational, 332, 336, 349 translational, 259, 323, 325, 336, 349 C o m p u t e r simulation, see Molecular dynamics a n d M o n t e Carlo c o m p u t e r simulations Conductivity, electrical, 14-15, 87, 97-98, 299, 305 and diffusion coefficients (see also Nernst-Hartley equation; Velocity correlation coefficients), 88-100

D a r k e n equation (see also H a r t l e y - C r a n k equation), 74, 85, 294, 356, 364 D e b y e - H i i c k e l - O n s a g e r theory of dilute electrolyte solutions, 8, 299 D i a p h r a g m cell, see Diffusion coefficients, m e t h o d s for measuring Diffusion (see also Interdiffusion; Intradiffusion; Tracer diffusion coefficient), binary systems, 56-64 free, 104 experimental m e t h o d s , 127-150 interacting flows, 6, 65, 116, 156, 367 m u l t i c o m p o n e n t systems (see also T e r n a r y systems), 6 4 - 7 1 , 369-381 pressure, effect on, 339-341, 345-347, 356 restricted, 105, 223 experimental m e t h o d s , 123-126 solute molecules, effect of association of, 360-361

Activated j u m p theory, 284-286, 295, 297, 316, 427-429, 430-431 conceptual difficulties with, 285-286 Airy integral in interpretation of G o u y fringe patterns, 165, 168, 177 Autocorrelation functions, defined, 14 from light scattering data, clipped, 205-206 field, 201, 208 intensity, 202, 204

438

Index Diffusion {cont.) solvent molecules, effect of dissociation, 388-389 steady state, 105-122 Diffusion coefficients {see also I n t r a - ; Inter-; Intrinsic-; Rotational-; Self-; Tracerdiffusion coefficients) electrochemical and intradiffusion coefficients, 192-193 estimation, empirical m e t h o d s , 290-298 from molecular diameters, 273-276, 345-346, 433 from refractive index gradient curves, area-height, 153, 164, 177, 180 m o m e n t - a r e a , 155 n o n G a u s s i a n systems, 159 polydisperse systems, 156 reduced fourth m o m e n t , 171 reduced second m o m e n t , 159, 180 skew curves, 156, 159 weight average, 156 z-average, 209 measurement in multicomponent systems, d i a p h r a g m cell, 115-117 G o u y interferometry, 176-180 Rayleigh interferometry, 178, 181-183 m e t h o d s for measuring, capillary, 213-217, 389-390, 423 c h r o m a t o g r a p h i c , 193-199 conductimetric H a r n e d , 123-125, 397-398 A g a r - L o b o capillary, 125-126 d i a p h r a g m cell, 105-120, 389-390, 426 calibration, 113 conditions of operation, 112-114 differential diffusion coefficients, calculation, 115 high pressure, 117-120 Millipore type, 109 ternary diffusion coefficient measurement, 115-117 electrochemical m e t h o d s , polarographic, 185-191 transient, 191-192 layer analysis, 123, 216-217 light scattering, 199-213, 237-239 N M R spin echo, 217-234 a p p a r a t u s , 218, 226-228 calibration, 227-228 field gradient coil design, 226-227 Fourier transform, 223-234 pulsed gradient, 230-233, 234 steady gradient, 224-228 optical interference techniques, G o u y , 127-129, 132-133, 160-168 holographic, 144-147 L a m m scale, 130, 150, 164 M a c h - Z e h n d e r , 133, 135-137 optical diffusion cell design, 147-150

439

Diffusion coefficients (cont.) Rayleigh, 133-135, 168-172 schlieren, 130-131, 150 shearing interferometers (Savart plate), 139-144, 173-176, 426 wedge, 138 p o r o u s frit, 423 'pulsation' technique, 199 stabilized inverse density gradient, 120-122 tracer, 213-217 Diffusion thermo-effect, see Dufour effect Digital autocorrelator, 204 Dissipation function, 7, 23, 28, 31, 40, 42, 47-49, 49-50, 65 Distribution functions, 8-10, 13, 300, 348 radial, 257, 263, 282 D o u b l e diffusive convection, see Convective mixing in ternary diffusion D r o p p i n g mercury electrode, 185 Dufour effect, 6

Einstein equation, 10-11, 268 Electron paramagnetic resonance (EPR), 245-248, 349 Electrophoretic effect, 299, 301, 387, 396-400, 408, 411 Enskog theory, t r a n s p o r t in dense gases, 266-268, 279, 291 E n t r o p y production (see also Dissipation function), 7, 27-32, 32-37, 3 7 - 4 1 , 42-48

Fick's laws of diffusion, first, 2, 23, 56, 104 second, 3, 6 1 , 72, 105, 157, 203 Flux densities (see also Phenomenological equations), 7, 4 1 , 87 Flow equations, linear, 2, 7, 30, 4 1 , 87 F o k k e r - P l a n c k equation, 10 Forces, thermodynamic, 7, 41 Fourier's law (see also Conductivity, thermal), 2, 3, 23, 26, 33, 203 F r a m e s of reference, 2, 42, 51, 72, 194 barycentric or mass-fixed, 42, 44, 48, 57, 65-66, 79, 100 bulk flow and, 64, 73 cell-fixed or laboratory, 62, 72 conditions for equivalence of cell- and volume-fixed (see also Volume changes during diffusion), 63, 100 'convective', 75 'intrinsic', 72, 74-75 Kirkendall, 74 mole-fixed, 58 relationships between, 58-61 resistance coefficients and, 51 solute-fixed, model for m e m b r a n e transport, 77

440

Index

F r a m e s of reference (cont) solvent-fixed, 58, 60, 69-70, 87, 88-89, 100, 412 volume-fixed, 56-58, 65, 68, 80, 369 Free volume theories, 268-290 Frictional coefficients, see Resistance coefficients

G i b b s - D u h e m equation, 7, 48, 50, 65, 78, 81, 102 Glass transition temperature, 287, 289 G o r d o n equation, 262, 294, 304, 351, 355, 405 Hamiltonian function, operator, 8, 12, 313-314 Hard-sphere fluid model {see also Diffusion coefficients, estimation from molecular diameters; Molecular dynamics), 267-284 tests of, 342-344, 433-434 hard discs, 269 rough hard-sphere model, 272, 276-277, 284 tests of, 345, 356-357 H a r t l e y - C r a n k equation {see also D a r k e n equation),'294, 364 Heat conduction {see also Conductivity, t h e r m a l ; Fourier's law), 3 analogy between diffusion and, 1 High pressure techniques, see Diffusion coefficients, m e t h o d s for measuring H y d r a t i o n numbers, 304 H y d r o d y n a m i c theories {see also Batchelor e q u a t i o n s ; Stokes-Einstein equation), 259-266 tests of, 322-339, 349, 355 Ilkovic equation, 187-190 Interdiffusion, aqueous electrolytes, 396-406 aqueous nonelectrolytes, 349-355 molten salts, 423-434 multicomponent systems, 361-381 n o n - a q u e o u s electrolytes, 106, 398-399 n o n - a q u e o u s nonelectrolytes, 355-361 Interdiffusion coefficients {see also Diffusion coefficients), 4, 57, 280-284 apparent molar volumes and, 354 differential, 62-64 'effective' diffusion coefficients, light scattering, and, 208, 213 frames of reference and, 57-61 integral, 62, 104, 110, 112, 158 intradiffusion coefficients and {see also Darken equation; Hartley-Crank equation), 363-369 relations between, in multicomponent systems, 66-69

Interferometric techniques, F a b r y - P e r o t , 238 G o u y , 127-129, 132-133, 160-168, 176-180 M a c h - Z e h n d e r , 133, 135-137 Rayleigh, 133-135, 168-172, 178, 181-183 Intradiffusion, a q u e o u s electrolytes, 389-396 aqueous nonelectrolytes, 349-355 molten salts, 423-434 multicomponent systems, 361-381 n o n - a q u e o u s nonelectrolytes, 355-361 Intradiffusion coefficients {see also Diffusion coefficients; Self-; Tracerdiffusion coefficients), 71-72, 210, 213-234 equality with interdiffusion coefficient at infinite dilution, experimental evidence for, 351, 363-366 mathematical proof, 84 electrochemical tracer diffusion coefficients and, 192-193 in binary systems, treated as ternary diffusion, 8 1 - 8 4 in electrolyte solutions, 91-100 interdiffusion coefficients and, 74, 213 ionic, a n d viscosity, 394-396 measurement, 213-234 'Intrinsic' diffusion coefficients {see also D a r k e n e q u a t i o n ; F r a m e s of reference; H a r t l e y - C r a n k equation), 71-75 Ion-pairing effects, 408, 412-418, 420, 422 Isotope effects, see Mass effects; M o m e n t of inertia effects

J o n e s - D o l e equation, 122 J o u l e - T h o m s o n experiment, 22

Kohlrausch's law, 90

Langevin equation, 10, 262, 337 Lattice theories of diffusion, 75 Legendre polynomial, 235 Levich equation, 188, 191 Linear response theory, 12-19 Liouville equation, 9, 18 operator, 313-314

Macromolecules, diffusion of, 259-261, 322-323 rotational diffusion of, 235, 336-338 techniques of measurement of diffusion of, 121, 154, 156, 174, 207, 212-213

Index Mass effects, as function of pressure, 321 self-diffusion and, 311-318 separation of isotopes due to, 318 tracer diffusion and, 279-280, 290, 316, 318-322 viscosity and, 322 Microscopic reversibility, principle of, 29, 33, 37 Mobilities, from intradiffusion coefficients, 73 from 'intrinsic' diffusion coefficients, 72 ionic, 298, 302-303 Mobility coefficients, 7, 2 2 - 2 3 , 2 9 - 3 1 , 48, 68, 77-80, 88, 258, 387 determination from diffusion coefficients, 6 5 - 7 1 , 78-79, 82 for electrolyte solutions, 306, 407-418 for molten salts, 424-425 relationship with correlation functions, 17, 33, 36, 85-86, 9 9 - 1 0 0 ternary, 372-381 prediction from binary data, 379-381 Molecular diameters, from hard-sphere kinetic theory, 272-284, 342 use in prediction of diffusion coefficients, 273-276, 345-346, 433 Molecular dynamics c o m p u t e r simulations, 12, 19, 261, 318, 425, 429, 432, 434 argon, 12, 315 binary mixtures, 279-280, 315-316, 361-363 hard-disc fluid, 269 hard-sphere fluid, 268-269 L e n n a r d - J o n e s fluid, 288, 316 mass effect studies, 315-316 methane, 344 rough hard-sphere fluid, 272 square-well fluid, 272, 342 Molten salts, 108, 216, 318, 387, 423-434 M o m e n t of inertia, effect on diffusion (see also Mass effects), 321 M o n t e C a r l o c o m p u t e r simulations, 348, 425 M u t u a l diffusion coefficient, see Interdiffusion coefficient

N a v i e r - S t o k e s equation, 46 Nernst diffusion layer, 185-186, 191 N e r n s t - H a r t l e y equation, 9 1 , 298, 390, 396 and O R R , 91 N o m e n c l a t u r e , 26 Nonequilibrium thermodynamics, fundamental hypotheses, 25 Nuclear magnetic resonance ( N M R ) (see also Diffusion coefficients; Relaxation times), 217-234, 242-245 C a r r - P u r c e l l pulse sequence, 229 Fourier transform, 233-234

441

Nuclear magnetic resonance ( N M R ) (cont.) H a h n spin-echo, 223 spin-spin coupling, 234

O h m ' s law, 2, 23 O n s a g e r coefficients, see Mobility coefficients O n s a g e r - F u o s s theory (see also Inter- and Intra-diffusion of electrolytes), 299-305, 379-381 Pikal version, 407-408 O n s a g e r reciprocity relationship (ORR), 7, 24, 32-37, 50, 64, 90, 92, 96, 258, 370, 371 chemical reactions and, 2 8 - 3 3 , 48 confirmation, 36-37, 90, 96, 371-381, 407 e q u a t i o n for testing, from diffusion coefficients, 71 for system in magnetic field, 35 symmetry of, under transformation, 35-36, 41 O s m o t i c pressure, 211

Peltier effect, 6 P e r t u r b a t i o n theory, 262-263 P h a s e plate, 132 Phenomenological coefficients, see Mobility coefficients Phenomenological equations (see also Flow equations) binary systems, 78-81 correct choice of conjugate forces and flux densities for, 24, 36-37, 40, 47 electrolyte solutions, 87 tracer diffusion, 81 P h o t o n correlation spectroscopy, 200-208, 237 Poisson equation, 163-165 Polarizability, 225-236 Polarization anisotropy, 240

Q u a d r u p o l a r coupling constant, 244 Q u a t e r n a r y systems, 117, 184

Radioactive labelling, 214 Radius of gyration, 291 R a m a n scattering, 238-239 Rayleigh scattering, 199, 237 Regular solutions, 264 Relaxation times, 234 dielectric, 235-236, 336 ESR, 245, 349 fluorescence depolarization, 235 from infrared F T spectroscopic measurements, 338, 349

442

Index

Relaxation times (cont.) NMR, spin-lattice (7\), 219, 221, 242-245, 334, 336, 349 spin-spin (T ), 219, 221, 232, 233 2 Resistance (frictional) coefficients, 9-10, 4 9 - 5 3 , 77-80, 222, 258-266, 387 calculation of, from diffusion data, 80, 365 comparison with mechanical friction coefficients, 51-52 D u n l o p convention for, 52, 409 electrolyte solutions a n d , 93-95, 409-410, 412-413 geometric mean rule, 85, 366-367 hydrodynamic theory a n d , 259-266, 355 independence of frame of reference, 51 intradiffusion, 83-84, 365-366 K l e m m - L a i t y , 52, 79-80, 84, 259 L a m m , 52, 79-80, 84, 291 and viscosity, 292 multicomponent systems, 6 9 - 7 1 , 370-371 molten salts, 423-425 O n s a g e r - M i l l e r convention, 4 9 - 5 1 rotational, 234, 261, 332, 338, 349 Rice-Allnatt theory, 264-266 Rotational diffusion coefficient, 5, 261, 332 measurement of, dielectric relaxation, 235-237, F a b r y - P e r o t interferometry, 238 fluorescence depolarization, 239-242 light scattering, 237-239 N M R a n d E P R , 242-248 tests of h y d r o d y n a m i c theories for, 332-336 Rotating disc electrode, 185, 189

Salting-out effect in multicomponent diffusion, 371, 373 Sand equation, 192 Savart plate, see Diffusion coefficients, m e t h o d s of measuring, optical interference techniques, shearing interferometers Second law of thermodynamics, 2 1 - 2 3 , 28, 39, 46 Seebeck effect, 6 Self-diffusion coefficient (see also Intraand Tracer-diffusion coefficient), 267-278, 339-349 Siegert relationship, 204 Soret effect, 6, 7, 126 Statistical thermodynamics, nonequilibrium, 8 Steady state, 2, 7, 24, 185 Stokes-Einstein, equation, 259, 270, 278, 291, 293, 315, 318, 322-323, 327, 331, 347, 354, 433 number, 324-329, 433-434

Stokes law, 299, 301, 303 Stokes p a r a d o x , 336

Taylor dispersion technique, see Diffusion coefficients, m e t h o d s of measuring, chromatographic Ternary systems, d i a p h r a g m cell measurements on, 115-117, 371 diffusion in, 96-97, 154, 233, 353, 369-381, 394-396 optical interference fringe measurements of, 176-183 predictive equations for, 297, 379-381 T h e r m a l diffusion, 64, 126 T h e r m a l diffusivity, 3, 203, 210 T h e r m o m e t r i c conductivity, see Thermal diffusivity T h o m s o n ' s hypothesis, 6, 37 Time of relaxation effect, 299, 304, 388, 408 Tracer diffusion coefficient (see also Intraand Self-diffusion coefficient), 4, 192 ionic, 304-305, 389-396, 426, 433 T r a n s p o r t (transference) n u m b e r , 299 definition of, 87, 425 diffusion coefficients a n d , 88-100 Hertz, 98 in molten salts, 425 O R R and, 90 Transition state theory, see Activated j u m p theory T r a n s l a t i o n a l - r o t a t i o n a l coupling, 272, 283, 291, 314, 343 constants, 272-273, 275, 276-277, 284, 318, 345 composition dependence, 355-356

Vacancy flux in solid state diffusion, 74 Velocity correlation functions, see Correlation functions Velocity correlation coefficients, 86, 97-101, 368-369, 387, 418-422 'standard', 100, 369, 418 Vignes equation, 295, 297 Viscosity (see also G o r d o n e q u a t i o n ; Stokes-Einstein e q u a t i o n ; H y d r o dynamic theories), 197, 243, 247, 265, 268, 270, 284-285 bulk (volume), 266 diffusion coefficients a n d , 259-266, 367-368 hard-sphere models a n d , 276-278 isotope effects on, 322 L a m m resistance coefficients a n d , 292 Viscous flow, 22, 49 Volume changes during diffusion (see also F r a m e s of reference), 113, 160 Vortex m o t i o n , 269