Polymer solutions in confining geometries

Abbreviationsa monomer size, b segment length, b, root of J,(x) = 0, B baseline in the autocorrelation function, Bi ith virial coefficient, c concentration (number density), c, concentration of cavities, ceq equilibrium concentration, ci polymer concentration in chamber i (i= 1,2), c, concentration of obstacles, cE polymer concentration exterior to a porous medium, cr polymer concentration in the interior of a porous medium, C* overlap concentration, c; overlap concentration in the interior of a porous medium, AC concentration difference, d period of the photoexcited pattern, db width of a bottleneck, d, side of a cubic cavity, & thickness of a membrane, dp pore diameter, d, spectral dimension, Dapp app arent diffusion coefficient, D, mutual diffusion coefficient, DmE mutual diffusion coefficient exterior to the pore, D,, mutual diffusion coefficient in the interior of the porous medium , D, tracer diffusion coefficient, DtE tracer diffusion coefficient exterior to the pore, D,, tracer diffusion coefficient in the interior of the porous medium, DE diffusion coefficient exterior to the pore, D, diffusion coefficient in the interior of the porous medium, DM membrane diffusion coefficient, E complete elliptic integral of the second kind, f universal function, fh fraction of a chain in the bottleneck, f, fraction of a chain in the cavity& number of arms of a star-shaped chain, fc coherence factor,fa autocorrelation function for scattering by the exterior solution,fi autocorrelation function for scattering by the interior of a porous medium, fCaSaSSa function for Casassa's partition coefficient, F free energy of confinement per chain, K' lag coefficient, E;;' drag coefficient, g, autocorrelation function of the electric field of scattered light, g, autocorrelation function of light scattering intensity, G, probability density for a Gaussian chain, h function that gives the mean square end-to-end distance of a wormlike chain, h, monomer size in the pearl necklace model, II, hindrance factor for convection, Z-Id hindrance factor for diffusion, H,, Hamiltonian of the n chain system, I interaction, i universal integer, j universal integer, J flux, J,, Bessel function of the first kind and zeroth order, k universal variable, k, magnitude of the scattering vector, kmE concentration coefficient for &E, k,, concentration coefficient for DmI, kpi concentration coefficient for the partition coefficient, ktE concentration coefficient for DtE, k,, concentration coefficient for D,,, kB Boltzmann constant, kR concentration coefficient for the retention time, K partition coefficient, I& partition coefficient in the dilute solution limit, K0 partition coefficient of component p (,0 = H,L), K complete elliptic integral of the first kind, 1 contour of a flexible chain, 1, contour of a subchain (i= 1,2), /d deflection length, L length of a rodlike molecule, L, contour length, L, persistence length, LN length of a segment of the cylindrical cavity, m universal integer, m, cutoff for m, M molecular weight, M, number-average molecular weight, h4, weight-average molecular weight, II universal integer, ~1, refractive index of the solvent, N degree of polymerization, N, degree of polymerization for a short chain, Nd number of monomers in a subchain or a blob, N,, total number of pores, N, Avogadro's number, Nfi degree of polymerization of component p (p = H,L), p probability, pa purity of component p (0 = H,L), P reduced osmotic pressure, r universal variable, r universal variable with three components, {rl} configuration of a polymer chain, R, radius of gyration, RF' radius of gyration in the dilute limit, R$ radius of gyration of component /3 in the dilute limit, Rp pore radius, R, radius of a sphere, Stokes radius, R, end-to-end distance, RH hydrodynamic radius, RI, extension of a chain along the axis of a cylindrical pore, {R,} internal configuration of a polymer chain, s average density of planes, S entropy, SE configurational entropy of a chain in the exterior solution, S, configurational entropy of a chain in the interior solution, AS entropy change, AS,, entropy change if the whole chain is contained in the bottleneck, AS, entropy change if the whole 89 90 IWAO TERAOKA chain is contained in the cavity, T absolute temperature, t time, universal variable, tb thickness of a bottleneck, td thickness of the depletion layer, tR retention time, tRO retention time for the zero concentration limit in the injected sample, u solute to pore size ratio, U, single chain potential, U,a single chain potential for the exterior solution, U,r single chain potential for the interior solution, U, binary interaction, U, potential for the chain end, u excluded volume interaction, V, solvent velocity, I' volume, V, volume of a sphere, Vj volume of chamber j (j= 1, 2) VE exterior volume, V, interior volume, w weight concentration, w! weight concentration of component p, W,,,, weight concentration of matrix polymer in the exterior solution, wa weight concentration in the exterior solution, w, weight concentration in the interior solution, WE number of configurations available to a chain in the exterior solution, WI number of configurations available to a chain in the interior solution, X reduced concentration, Xa reduced concentration in the exterior solution, Xi reduced concentration in the interior solution, x universal variable, z universal variable, z, average number of cavities that contain a part of the chain, Z, partition function of n chain system, Z, single chain partition function, Z,, partition function of a single chain in the exterior solution, Zii partition function of a single chain in the pore, o = L/2R,, a, = 3.49; numerical coefficient, p component of a bimodal mixture of polymer, I decay rate, S universal variable, E numerical, n5 solvent viscosity, 8 angle, X activity, A,, wavelength, A, half of the reciprocal of persistence length of a tube, p chemical potential, pLg chemical potential of a reference state, puE chemical potential in the exterior, pi chemical potential in the interior, 6 correlation length, Er correlation length in the pore, z grand partition function, II osmotic pressure, oefi adjustable parameter for the chain dimension, 7 reciprocal of the decay constant, 7,s effective diffusion time, p density profile, ps porosity, 4 volume fraction, lint internal filling fraction, q& volume fraction of solutes in the exterior solution, $q volume fraction of solutes in the interior solution, 4 universal function, x0 intrinsic conductivity CONTENTS 3.5.Partitioning of a polydisperse polymer 3.5.1.Theory 3.5.2.Experiments 4. Dynamics of polymer chains in confining geometries 4.1.Theory 4.1.1.Membranetransport 4.1.2.Macroscopic diffusion in a network-structured porous medium 4.2.Diffusion experiments 4.2.1.Membrane transport 4.2.2.Transient diffusion 4.2.3.Dynamic light scattering 4.2.3.1.Scattering vector dependence 4.2.3.2.Molecular weight dependence 4.2.3.3.Chain architecture dependence 4.2.3.4.Mutual diffusion in the pore 4.2.3.5.Tracer diffusion in the pore 4.2.3.6.Short-time diffusion 4.2.4.Other experimental techniques 4.2.5.Simulations 5. Concluding remarks References