Conformation and dynamics of interacting polymer chains in a porous medium

Monte Carlo simulations are performed to study the conformational and dynamical properties of interacting polymer chains with counterion solvent background in porous media generated by a random distribution of quenched barriers of concentration p(b), We study the dependence of the radius of gyration (R-g) of chains and variation of their rms displacement (R-rms) with time, on the polymer concentration (p) chain length (L-c), temperature (T) and porosity (p(s) = 1 - p(b)) as these parameters cooperate and compete. In homogensous/annealed systems (p(b) = 0), the power-law exponent gamma for the radius of gyration of the chains shows a crossover from SAW-conformation with gamma similar to 0.61 at low polymer concentrations (dilute regime p = 0.001-0.01) to an ideal chain conformation with gamma similar to 0.52 for chain concentrations p = 0.1-0.3 in three dimensions at high temperatures. In porous media, we observe a crossover from an SAW-like conformation with gamma similar to 0.64 at high porosities (p(s) greater than or equal to 0.8) to a collapse conformation with gamma similar to 0.35 at low porosities (p(s) less than or equal to 0.5 at temperature T = 1.0. The rms displacement of the chains is generally diffusive, R-rms = At-0.5, at low p and high T while it is subdiffusive R-rms = At-k, with k < 0.5 at high p and low T, For example, k similar or equal to 0.2 at p = 0.3 and T = 1.0 in three dimension in annealed systems. In quenched porous media, the motion is generally subdiffusive (at p(b) greater than or equal to 0.2 in three dimension, but becomes ultra-subdiffusive with R-rms = At-k, where k < 0.1 at low temperatures, The prefactor A shows a power-law dependence on the chain length, A similar to L-c(-u), except at high polymer concentrations and low temperature, with the exponent mu similar to 0.45-0.57 in annealed systems and similar to 0.53-0.64 in porous media at p = 0.3.