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List of Frequently Used Symbols (Volumes I-V)
LIST OF FREQUENTLY USED SYMBOLS (Volumes I-V) Symbols representing physical quantities are printed in italics. Thermodynamic functions: capital for macroscopic quantities, small for molecular or subsystem quantities (example: U = total energy, u = pair energy between molecules). Superscripts standard pressure t standard in general o * pure substance; complex conjugate inter facial (excess) a interaction at constant charge (a) interaction at constant potential (\|/) excess, X (real) -X (ideal) E S, L, G in solid, liquid or gaseous state 1 normal to surface parallel to surface // Subscripts m molar (sometimes molecular) a areal (per unit area) g per unit mass Recurrent special symbols 0( 1020) of the order of 1 O^o AX X (final) - X (initial). Subscript attached to A to denote type of process: ads (adsorption, diss (dissociation), hydr (hydration), mix (mixing), r (reaction), sol (dissolution), solv (solvation), subl (sublimation), trs (transfer), vap (vaporization, evaporation), etc. Some mathematical signs and operators Vectors bold face. Example: F for force, but F^ for z-component of force Tensors bold face with tilde ( ? ) complex quantities bear a circumflex in), the corresponding conjugate is n * I XI absolute value of x {x) averaged value of x 3c Fourier or Laplace transform of x (sometimes this bar is omitted) For vectorial signs and operators ( V, V^ , grad, rot, and x ), see I.appendix 7.
XXX
SYMBOL LIST
Latin a a^ a a^ a a a^ A A A ^ii(k) b B , B B2(T) B^{T) c c Cj, C2 C C^ C^ C Cj C2 C^ C Cy C^ C^ Ca d^ d d^^ d^ d^^^
activity {mol m""^) mean activity of an electrolyte (mol m"-^) attraction parameter in Van der Waals equation of state (N m'*) two-dimensional attraction parameter in two-dimensional Van der Waals equation of state (N m^) radius (m) radius of gyration (m) area per molecule (m^) area (m^) specific area (m^ kg~M Hamaker constant (J) Hamaker constant for interaction of materials i and j across material k (J) volume correction parameter in Van der Waals equation of state (m^) magnetic induction (T = V m~2 s) second virial coefficient (m^ mol"^ or m*^ molecule" M interfacial second virial coefficient (m^ mol~^ m^ molecule"^ or -) velocity of electromagnetic radiation in a vacuum (m s"^) concentration (usually mol m~*^, sometimes kg m"*^) principal curvatures (m~M (differential) electric capacitance (C V~^ or, if per unit area, Cm-2v-i) (differential) electric capacitance of diffuse double layer (Cm-2\r-^) (differential) electric capacitance of Stern layer (C m~^ V~M BET-transformed (-) first bending moment (N) second bending moment (J) (time-) correlation function of x (dim. x^ ) molar heat capacity at constant pressure (J K"^ mol~M molar heat capacity at constant volume (J K~^ mol~M interfacial excess molar heat capacity at constant area per unit area (J K~^ m"^ mol"M interfacial excess molar heat capacity at constant interfacial tension per unit area (J K"^ m~^ mol~M capillary number (-) fractal dimension (-) layer thickness (m) electrokinetic thickness (m) hydrodynamic thickness (m) ellipsometric thickness (m)
SYMBOL LIST
d^* D D^ Dj. Dg D, D De Du e E ,E E E. Egg^ Eg^j. / / / /.. F F Fj, Fjj^ F^ F^ F^, F^ / A F , F g{r) g^^^ g{q,t]
xxxi
steric thickness (polymeric adsorbates) (m) diffusion coefficient (m^ s~M surface diffusion coefficient (m^ s~M rotational diffusion coefficient (s~M self-diffusion coefficient (m^ s"M dielectric displacement (C m^^) Deborah number (-) Dukhin number (-) elementary charge (C) electric field strength (V m - ^ Young's modulus (N m~2) irradiance (J m~2 s~^ = W mr^) sedimentation potential (V m~M streaming potential (V m^ N~M friction coefficient (kg s~l) activity coefficient (mol fraction scale) (-) fraction of free counter ions (-) Mayer function for interaction between particles i and j (-) Faraday constant (C mol"M Helmholtz energy (J) partial molar Helmholtz energy (J mol~M molar Helmholtz energy (J mol~M interfacial (excess) Helmholtz energy (J) interfacial (excess) Helmholtz energy per unit area (J m"^) force (N) radial distribution function (-) hth order distribution function (-) time correlation function, if real (light scattering usage) (dimensions
asCJ g G G G., Gj^. G^ G^ G^, G^ / A G{z) G{z,s) h n h
standard acceleration of free fall (m s"^) Gibbs energy (J) one of the nine components of the bulk modulus (N m"^) partial molar Gibbs energy (J mol~M molar Gibbs energy (J mol-M interfacial (excess) Gibbs energy (J) interfacial (excess) Gibbs energy per unit area (J m^^) segment weighting factor in polymer adsorption theory (-) endpoint distribution in a segment of s segments (polymer adsorption (-) Planck's constant (J s) h/2K{Js) (shortest) distance between colloidal particles or macrobodies (m) (half distance in ch. V. 1)
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SYMBOL LIST
h ,H h h^^ h{r) H H., Hj^. Hj^ H^ H^, H^ /A H ,H H[p,q) i i^ IQ ig I /g^ / / I^ico) j j ,J j^, j ^ J J ,J J^ J^ J k k /Cj /C2 fc k X K[R) K{o)) K K K^ K K K^
height (m) film t h i c k n e s s (m) critical film thickness for rupt ure (m) total correlation function (-) enthalpy (J) partial molar enthalpy (J mol~M molar enthalpy (J mol~M interfacial (excess) enthalpy (J) interfacial (excess) enthalpy per unit area (J m"^) magnetic field strength (C m"! s'M Hamiltonian (J) intensity of radiation (V^ m~2) incident intensity (V^ m~^) intensity in a v a c u u m (V^ m"^) scattered intensity (V^ m"^) unit vector in x-direction (-) (not in chapter 1.7) s t r e a m i n g c u r r e n t (C m^ N"^ s"M ionic strength (mol m"^) r a d i a n t intensity (J s"^ s r "^ = W s r "M spectral density of x (dim. x^ s ) unit vector in y-direction (-) (not in chapter 1.7) (electric) current density (A m"^ = C m"^ s~M surface current density (C mr^ s~M compliance (m^ N"M flux (mol m~2 s-i or kg m"^ s"M surface flux (mol m~^ s"^ or kg m"^ s~M interfacial compliance (mN~M first, or mean, curvature (m~M Boltzmann's constant (J K~M rate c o n s t a n t (dimensions depend on order of process) bending modulus (J) saddle splay modulus (J) unit vector in y-direction (-) (not in chapter 1.7) wave vector (m~M optical constant (m^ kg"^ or m^ mol"^) optical constant (V^ C-2 m ' ^ ) absorption index (-) chemical equilibrium constant (general) on p r e s s u r e b a s i s (-) on concentration basis (-) second, or G a us s , curvature (m"^) (integral) electric capacitance (C V"^ or C m"^ V~^) (integral) electric capacitance of diffuse layer (C m~2 v~M
SYMBOL LIST
K^ Kpj k^ K. KL K K
L L.j^ £g C m M
Ma n n n^ N N
xxxiii
(integral) electric capacitance of Stern layer (C m"^ V~M Henry constant (m) Huggins constant (various dimensions) distribution (partition) coefficient (-)
Langmuir constant (m^ mol~M compression modulus (N m"^) conductivity (S m"! = C V"! mr^ s'M K^ surface conductivity (S = C V~^ s~M K^ interfacial dilational modulus (N m"M contour length (polymers) (m) cross coefficients in irreversible thermodynamics (varying dimensions) Bjerrum length (on surfaces) = 2r^ (m) bond length in a polymer chain (m) mass (kg) (relative) molecular mass (-) ( M ) ^ , M^ ibid., mass average (-) {M)^,M^ ibid., Z-average (-) ( M ) ^ , Mjj ibid., number average (-) Marangoni number (-) refractive index (-) number of moles (-) n^ (excess) number of moles in interface (-) unit vector in x-, y- or z-direction (-) (chapter 1.7 only) number of segments in a polymer chain number of molecules (-) Nj^^ Ng
p p Ap p p ,p ^ind'Pind p ,p P P{q) P ,P Pe Pe^ Pe^ q q(isost)
Avogadro constant (mol"M number of sites (-) bound fraction (of polymers) (-) pressure (N m"^) capillary pressure (N m~2) stiffness (persistence) parameter (polymers) (-) dipole moment (Cm) induced dipole moment (Cm) {= m V ] momentum (J m"^ s) probability (-) form factor (-) polarization (C m~^) Peclet number (-) translational (-) rotational (-) heat exchanged (incl. sign) (J) isosteric heat of adsorption (J)
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SYMBOL LIST
q q q q q ,q Q Q{N,V,T) Q^Q^ 9^Q J r, r fg r
generalized parameter indicating place coordinates in Hamiltonian subsystem canonical partition function {-) electric charge (on ions) (C) persistence length (polymers) (m) scattering vector (m~M electric charge (on colloids, macrobodies) (C) canonical partition function (-) electro-osmotic volume flow per unit field strength (m"^ V"^ s"M electro-osmotic volume flow per unit current (m^ C~M distance (m) Bjerrum length (in bulk) (m) number of segments in a polymer (-)
R R R
gas constant (J K~i mol~M (principal) radius of curvature (m) Poynting vector (W m~2)
KQ Re s
Rayleigh ratio (m"M Reynolds number (-) sedimentation coefficient (s) relative standard deviation of x (-) supersaturation ratio (-) entropy (J K-l) partial molar entropy (J K"^ mol~M molar entropy (J K"^ mol~M inter facial (excess) entropy (J K~M interfacial (excess) entropy per unit area (J K"^ m~^) spectral density as a function of co^ - co^ = H (V^ m"^ s) structure factor (-) ordering parameter of s (-) time (s) transport (or transference) number (-) temperature (K) Taylor number (-) Trouton number (-) (internal) energy per subsystem (J) (electric) mobility (m^ V~^ s"M (internal) energy, general (J) partial molar energy (J mol"M
s^ s S Sj, S^j S^ S*^ S^, S^ /A S(q,R,i3) S{q,c), S{q) S{s) t t T Ta Tr u u U LT., Uj^. U^^ U^ U^,U^ /A u V, V
molar energy (J mol~M interfacial (excess) energy (J) interfacial (excess) energy per unit area (J m"^) excluded volume parameter (polymers) {= 1-2/) velocity (m s"M
SYMBOL LIST
v^^ v^^ Ug Y v., V^^ V^ w w u;^.^ We X X X X, X y y z z z Z{N,p,T) Z^ Greek a a a a a, a fi^2 fi /3^ j3^ /3^ fl /3 Y y Y Y r 5 Sx
xxxv
electrophoretic velocity (m s~M electro-osmotic velocity (m s~M slip velocity (m s~M volume (m^) partial molar volume {m-^ mol~M molar volume (m^ mol~M work (incl. sign) (J) interaction parameter in regular mixture theory (J mol"^) interaction energy between pair of molecules or segments (landJ) (J) Weber number {-) mol fraction (-) distance from surface (m) dimensionless line charge parameter (-) generalized force in irreversible thermodynamics (varying units) activity coefficient (molar scale) (-) dimensionless potential {Fy//RT] (-) coordination number (-) distance from surface (m) valency (-) isobaric-isothermal pairtition function (-) configuration integral for N particles (-)
linear expansion coefficient (-) real potential {V) degree of dissociation (-) contact angle (-) polarizability (C V"^ m^ = C^ J-i m^) twice binary cluster integral (-) Van der Waals constant (molecular) (J m~^); Debye-Van der Waals constant (molecular) (J m"^) Keesom-Van der Waals constant (molecular) (J m~^) London-Van der Waals constant (molecular) (J m~^) Esin-Markov coefficient (-) damping coefficient (m~M interfacial or surface tension (N m~^ or J m"^) activity coefficient (molal scale) (-) shear strain (-) rate of shear (s"i) surface (excess) concentration (mol m"^) diffusion layer thickness (m) small variation of x (dim. x )
xxxvi
SYMBOL LIST
Six] A AX « APX a
« AV ^ A^y/^^Q £ e^ € £ f 0 6 K K S /I A 1 A A A A //Q ^ ju ju jU J] 77^ T/g [r]] [;;] V V ^ ^ (J TT n 77°^ /7(h)
Dirac delta function of X (dim. x~^) displacement (m) X (final)-X(initial) X (phase (3) - X (phase a) (Galvani) potential difference (V) (Volta) potential difference (V) liquid Junction potential (V) relative dielectric permittivity (dielectric constant) (-) dielectric permittivity of vacuum (C^ N"^ m"^ or C m~^ V~M porosity (-) strain (-) electrokinetic potential (V) surface coverage = F/ F (saturated monolayer) (-) angle, angle of rotation, loss angle (-) reciprocal Debye length (m~M capillary length (m) grand (canonical) partition function (-) wavelength (m) charging parameter (-) ionic (or molar) conductivity (C V~^ m^ s~^ mol"^ = S m^ mol~M reciprocal Gouy-Chapman length (m"M molar conductivity (S m^ mol~M thermal wavelength (m) penetration depth of evanescent waves (m) magnetic permeability in vacuum (V m~^ C~^ s^) magnetic dipole moment (C m^ s~M chemical potential (J mol~^ or J molecule"M kinematic viscosity (m^ s~M Poisson ratio (-) dynamic viscosity (N s m~^) interfacial shear viscosity (N m~^ s) interfacial dilational viscosity (N m"^ s) intrinsic viscosity (concentration-based) (m^ kg'M intrinsic viscosity (volume fraction-based) (-) frequency (s"^ = Hz) linear charge density (C m"M correlation length (m) coupling parameter (Kirkwood) (-) grand (canonical) partition function of subsystem (-) surface pressure (N m~^ or J m"^) osmotic pressure (N m"^) osmotic pressure (N m"^) (ch. V. 1) disjoining pressure (N m"^)
SYMBOL LIST
p
xxxvii
a^ r T r
density (kg m"^) number density [N/V) (m~^) space charge density (C m~^) hard sphere radius (m) surface density of brushes (m"^) surface charge density (C m"^) contribution of ionic species i to surface charge (C m"^) surface charge density diffuse layer (C m"^) surface charge density Stern layer (C m~^) standard deviation of X (dim. X ) characteristic time (s) interfacial stress (N m~M line tension (N)
r 7
turbidity (m'M stress tensor (N m"^)
p^ p
T^ r
(p (j) (j) 0Q X
interfacial stress tensor (N m~M flux of x-momentum in L/-direction (kg m"^ s"^) = shear stress (N m~2), one of the nine components of the stress tensor rotational correlation time (s) rotational relaxation time (reorientation time) (s) yield stress (N m"^) volume fraction (-) o s m o t i c coefficient (-) p h a s e (-) Flory-Fox c o n s t a n t (-) excess interaction energy parameter (-)
^cr' ^cr XiX^^"^ X^ X^ X^^^^ y/ 0) Q)^ 0)^ CO co[r] a)[z) CO n Q Q Q
critical values of x and (p at phase separation interfacial potential jump (between phases (3 and a ) (V) electric susceptibility (-) adsorption energy parameter (-) critical value of x^ at the adsorption/desorption point (-) electric potential (V) angular frequency (rad s~^ or s~M angular frequency of incident radiation (rad s~^ o r s~M angular frequency of scattered radiation (rad s"^ o r s~M pair interaction (J) (ch. IV.5) local g r a n d potential density ( J m"^) (ch. V.4) local g r a n d potential density ( J m~^) (ch. V. 1) degeneracy of s u b s y s t e m (-) degeneracy of a s y s t e m or n u m b e r of realizations (-) co^-co^ (rad s"^ or s~M solid angle (sr) grand potential (J)
T^ Tj. r
xxxviii
Q^ D^ Q[N,V,U)
SYMBOL LIST
inter facial (excess) grand potential (J) interfacial (excess) grand potential per unit area (J m"^) number of realizations = microcanonical partition function (-)
XXX
SYMBOL LIST
Latin a a^ a a^ a a a^ A A A ^ii(k) b B , B B2(T) B^{T) c c Cj, C2 C C^ C^ C Cj C2 C^ C Cy C^ C^ Ca d^ d d^^ d^ d^^^
activity {mol m""^) mean activity of an electrolyte (mol m"-^) attraction parameter in Van der Waals equation of state (N m'*) two-dimensional attraction parameter in two-dimensional Van der Waals equation of state (N m^) radius (m) radius of gyration (m) area per molecule (m^) area (m^) specific area (m^ kg~M Hamaker constant (J) Hamaker constant for interaction of materials i and j across material k (J) volume correction parameter in Van der Waals equation of state (m^) magnetic induction (T = V m~2 s) second virial coefficient (m^ mol"^ or m*^ molecule" M interfacial second virial coefficient (m^ mol~^ m^ molecule"^ or -) velocity of electromagnetic radiation in a vacuum (m s"^) concentration (usually mol m~*^, sometimes kg m"*^) principal curvatures (m~M (differential) electric capacitance (C V~^ or, if per unit area, Cm-2v-i) (differential) electric capacitance of diffuse double layer (Cm-2\r-^) (differential) electric capacitance of Stern layer (C m~^ V~M BET-transformed (-) first bending moment (N) second bending moment (J) (time-) correlation function of x (dim. x^ ) molar heat capacity at constant pressure (J K"^ mol~M molar heat capacity at constant volume (J K~^ mol~M interfacial excess molar heat capacity at constant area per unit area (J K~^ m"^ mol"M interfacial excess molar heat capacity at constant interfacial tension per unit area (J K"^ m~^ mol~M capillary number (-) fractal dimension (-) layer thickness (m) electrokinetic thickness (m) hydrodynamic thickness (m) ellipsometric thickness (m)
SYMBOL LIST
d^* D D^ Dj. Dg D, D De Du e E ,E E E. Egg^ Eg^j. / / / /.. F F Fj, Fjj^ F^ F^ F^, F^ / A F , F g{r) g^^^ g{q,t]
xxxi
steric thickness (polymeric adsorbates) (m) diffusion coefficient (m^ s~M surface diffusion coefficient (m^ s~M rotational diffusion coefficient (s~M self-diffusion coefficient (m^ s"M dielectric displacement (C m^^) Deborah number (-) Dukhin number (-) elementary charge (C) electric field strength (V m - ^ Young's modulus (N m~2) irradiance (J m~2 s~^ = W mr^) sedimentation potential (V m~M streaming potential (V m^ N~M friction coefficient (kg s~l) activity coefficient (mol fraction scale) (-) fraction of free counter ions (-) Mayer function for interaction between particles i and j (-) Faraday constant (C mol"M Helmholtz energy (J) partial molar Helmholtz energy (J mol~M molar Helmholtz energy (J mol~M interfacial (excess) Helmholtz energy (J) interfacial (excess) Helmholtz energy per unit area (J m"^) force (N) radial distribution function (-) hth order distribution function (-) time correlation function, if real (light scattering usage) (dimensions
asCJ g G G G., Gj^. G^ G^ G^, G^ / A G{z) G{z,s) h n h
standard acceleration of free fall (m s"^) Gibbs energy (J) one of the nine components of the bulk modulus (N m"^) partial molar Gibbs energy (J mol~M molar Gibbs energy (J mol-M interfacial (excess) Gibbs energy (J) interfacial (excess) Gibbs energy per unit area (J m^^) segment weighting factor in polymer adsorption theory (-) endpoint distribution in a segment of s segments (polymer adsorption (-) Planck's constant (J s) h/2K{Js) (shortest) distance between colloidal particles or macrobodies (m) (half distance in ch. V. 1)
xxxii
SYMBOL LIST
h ,H h h^^ h{r) H H., Hj^. Hj^ H^ H^, H^ /A H ,H H[p,q) i i^ IQ ig I /g^ / / I^ico) j j ,J j^, j ^ J J ,J J^ J^ J k k /Cj /C2 fc k X K[R) K{o)) K K K^ K K K^
height (m) film t h i c k n e s s (m) critical film thickness for rupt ure (m) total correlation function (-) enthalpy (J) partial molar enthalpy (J mol~M molar enthalpy (J mol~M interfacial (excess) enthalpy (J) interfacial (excess) enthalpy per unit area (J m"^) magnetic field strength (C m"! s'M Hamiltonian (J) intensity of radiation (V^ m~2) incident intensity (V^ m~^) intensity in a v a c u u m (V^ m"^) scattered intensity (V^ m"^) unit vector in x-direction (-) (not in chapter 1.7) s t r e a m i n g c u r r e n t (C m^ N"^ s"M ionic strength (mol m"^) r a d i a n t intensity (J s"^ s r "^ = W s r "M spectral density of x (dim. x^ s ) unit vector in y-direction (-) (not in chapter 1.7) (electric) current density (A m"^ = C m"^ s~M surface current density (C mr^ s~M compliance (m^ N"M flux (mol m~2 s-i or kg m"^ s"M surface flux (mol m~^ s"^ or kg m"^ s~M interfacial compliance (mN~M first, or mean, curvature (m~M Boltzmann's constant (J K~M rate c o n s t a n t (dimensions depend on order of process) bending modulus (J) saddle splay modulus (J) unit vector in y-direction (-) (not in chapter 1.7) wave vector (m~M optical constant (m^ kg"^ or m^ mol"^) optical constant (V^ C-2 m ' ^ ) absorption index (-) chemical equilibrium constant (general) on p r e s s u r e b a s i s (-) on concentration basis (-) second, or G a us s , curvature (m"^) (integral) electric capacitance (C V"^ or C m"^ V~^) (integral) electric capacitance of diffuse layer (C m~2 v~M
SYMBOL LIST
K^ Kpj k^ K. KL K K
L L.j^ £g C m M
Ma n n n^ N N
xxxiii
(integral) electric capacitance of Stern layer (C m"^ V~M Henry constant (m) Huggins constant (various dimensions) distribution (partition) coefficient (-)
Langmuir constant (m^ mol~M compression modulus (N m"^) conductivity (S m"! = C V"! mr^ s'M K^ surface conductivity (S = C V~^ s~M K^ interfacial dilational modulus (N m"M contour length (polymers) (m) cross coefficients in irreversible thermodynamics (varying dimensions) Bjerrum length (on surfaces) = 2r^ (m) bond length in a polymer chain (m) mass (kg) (relative) molecular mass (-) ( M ) ^ , M^ ibid., mass average (-) {M)^,M^ ibid., Z-average (-) ( M ) ^ , Mjj ibid., number average (-) Marangoni number (-) refractive index (-) number of moles (-) n^ (excess) number of moles in interface (-) unit vector in x-, y- or z-direction (-) (chapter 1.7 only) number of segments in a polymer chain number of molecules (-) Nj^^ Ng
p p Ap p p ,p ^ind'Pind p ,p P P{q) P ,P Pe Pe^ Pe^ q q(isost)
Avogadro constant (mol"M number of sites (-) bound fraction (of polymers) (-) pressure (N m"^) capillary pressure (N m~2) stiffness (persistence) parameter (polymers) (-) dipole moment (Cm) induced dipole moment (Cm) {= m V ] momentum (J m"^ s) probability (-) form factor (-) polarization (C m~^) Peclet number (-) translational (-) rotational (-) heat exchanged (incl. sign) (J) isosteric heat of adsorption (J)
xxxiv
SYMBOL LIST
q q q q q ,q Q Q{N,V,T) Q^Q^ 9^Q J r, r fg r
generalized parameter indicating place coordinates in Hamiltonian subsystem canonical partition function {-) electric charge (on ions) (C) persistence length (polymers) (m) scattering vector (m~M electric charge (on colloids, macrobodies) (C) canonical partition function (-) electro-osmotic volume flow per unit field strength (m"^ V"^ s"M electro-osmotic volume flow per unit current (m^ C~M distance (m) Bjerrum length (in bulk) (m) number of segments in a polymer (-)
R R R
gas constant (J K~i mol~M (principal) radius of curvature (m) Poynting vector (W m~2)
KQ Re s
Rayleigh ratio (m"M Reynolds number (-) sedimentation coefficient (s) relative standard deviation of x (-) supersaturation ratio (-) entropy (J K-l) partial molar entropy (J K"^ mol~M molar entropy (J K"^ mol~M inter facial (excess) entropy (J K~M interfacial (excess) entropy per unit area (J K"^ m~^) spectral density as a function of co^ - co^ = H (V^ m"^ s) structure factor (-) ordering parameter of s (-) time (s) transport (or transference) number (-) temperature (K) Taylor number (-) Trouton number (-) (internal) energy per subsystem (J) (electric) mobility (m^ V~^ s"M (internal) energy, general (J) partial molar energy (J mol"M
s^ s S Sj, S^j S^ S*^ S^, S^ /A S(q,R,i3) S{q,c), S{q) S{s) t t T Ta Tr u u U LT., Uj^. U^^ U^ U^,U^ /A u V, V
molar energy (J mol~M interfacial (excess) energy (J) interfacial (excess) energy per unit area (J m"^) excluded volume parameter (polymers) {= 1-2/) velocity (m s"M
SYMBOL LIST
v^^ v^^ Ug Y v., V^^ V^ w w u;^.^ We X X X X, X y y z z z Z{N,p,T) Z^ Greek a a a a a, a fi^2 fi /3^ j3^ /3^ fl /3 Y y Y Y r 5 Sx
xxxv
electrophoretic velocity (m s~M electro-osmotic velocity (m s~M slip velocity (m s~M volume (m^) partial molar volume {m-^ mol~M molar volume (m^ mol~M work (incl. sign) (J) interaction parameter in regular mixture theory (J mol"^) interaction energy between pair of molecules or segments (landJ) (J) Weber number {-) mol fraction (-) distance from surface (m) dimensionless line charge parameter (-) generalized force in irreversible thermodynamics (varying units) activity coefficient (molar scale) (-) dimensionless potential {Fy//RT] (-) coordination number (-) distance from surface (m) valency (-) isobaric-isothermal pairtition function (-) configuration integral for N particles (-)
linear expansion coefficient (-) real potential {V) degree of dissociation (-) contact angle (-) polarizability (C V"^ m^ = C^ J-i m^) twice binary cluster integral (-) Van der Waals constant (molecular) (J m~^); Debye-Van der Waals constant (molecular) (J m"^) Keesom-Van der Waals constant (molecular) (J m~^) London-Van der Waals constant (molecular) (J m~^) Esin-Markov coefficient (-) damping coefficient (m~M interfacial or surface tension (N m~^ or J m"^) activity coefficient (molal scale) (-) shear strain (-) rate of shear (s"i) surface (excess) concentration (mol m"^) diffusion layer thickness (m) small variation of x (dim. x )
xxxvi
SYMBOL LIST
Six] A AX « APX a
« AV ^ A^y/^^Q £ e^ € £ f 0 6 K K S /I A 1 A A A A //Q ^ ju ju jU J] 77^ T/g [r]] [;;] V V ^ ^ (J TT n 77°^ /7(h)
Dirac delta function of X (dim. x~^) displacement (m) X (final)-X(initial) X (phase (3) - X (phase a) (Galvani) potential difference (V) (Volta) potential difference (V) liquid Junction potential (V) relative dielectric permittivity (dielectric constant) (-) dielectric permittivity of vacuum (C^ N"^ m"^ or C m~^ V~M porosity (-) strain (-) electrokinetic potential (V) surface coverage = F/ F (saturated monolayer) (-) angle, angle of rotation, loss angle (-) reciprocal Debye length (m~M capillary length (m) grand (canonical) partition function (-) wavelength (m) charging parameter (-) ionic (or molar) conductivity (C V~^ m^ s~^ mol"^ = S m^ mol~M reciprocal Gouy-Chapman length (m"M molar conductivity (S m^ mol~M thermal wavelength (m) penetration depth of evanescent waves (m) magnetic permeability in vacuum (V m~^ C~^ s^) magnetic dipole moment (C m^ s~M chemical potential (J mol~^ or J molecule"M kinematic viscosity (m^ s~M Poisson ratio (-) dynamic viscosity (N s m~^) interfacial shear viscosity (N m~^ s) interfacial dilational viscosity (N m"^ s) intrinsic viscosity (concentration-based) (m^ kg'M intrinsic viscosity (volume fraction-based) (-) frequency (s"^ = Hz) linear charge density (C m"M correlation length (m) coupling parameter (Kirkwood) (-) grand (canonical) partition function of subsystem (-) surface pressure (N m~^ or J m"^) osmotic pressure (N m"^) osmotic pressure (N m"^) (ch. V. 1) disjoining pressure (N m"^)
SYMBOL LIST
p
xxxvii
a^ r T r
density (kg m"^) number density [N/V) (m~^) space charge density (C m~^) hard sphere radius (m) surface density of brushes (m"^) surface charge density (C m"^) contribution of ionic species i to surface charge (C m"^) surface charge density diffuse layer (C m"^) surface charge density Stern layer (C m~^) standard deviation of X (dim. X ) characteristic time (s) interfacial stress (N m~M line tension (N)
r 7
turbidity (m'M stress tensor (N m"^)
p^ p
T^ r
(p (j) (j) 0Q X
interfacial stress tensor (N m~M flux of x-momentum in L/-direction (kg m"^ s"^) = shear stress (N m~2), one of the nine components of the stress tensor rotational correlation time (s) rotational relaxation time (reorientation time) (s) yield stress (N m"^) volume fraction (-) o s m o t i c coefficient (-) p h a s e (-) Flory-Fox c o n s t a n t (-) excess interaction energy parameter (-)
^cr' ^cr XiX^^"^ X^ X^ X^^^^ y/ 0) Q)^ 0)^ CO co[r] a)[z) CO n Q Q Q
critical values of x and (p at phase separation interfacial potential jump (between phases (3 and a ) (V) electric susceptibility (-) adsorption energy parameter (-) critical value of x^ at the adsorption/desorption point (-) electric potential (V) angular frequency (rad s~^ or s~M angular frequency of incident radiation (rad s~^ o r s~M angular frequency of scattered radiation (rad s"^ o r s~M pair interaction (J) (ch. IV.5) local g r a n d potential density ( J m"^) (ch. V.4) local g r a n d potential density ( J m~^) (ch. V. 1) degeneracy of s u b s y s t e m (-) degeneracy of a s y s t e m or n u m b e r of realizations (-) co^-co^ (rad s"^ or s~M solid angle (sr) grand potential (J)
T^ Tj. r
xxxviii
Q^ D^ Q[N,V,U)
SYMBOL LIST
inter facial (excess) grand potential (J) interfacial (excess) grand potential per unit area (J m"^) number of realizations = microcanonical partition function (-)