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 pb. We study the dependence of the radius of gyration (Rg) of chains and variation of their rms displacement (Rrms) with time, on the polymer concentration (p), chain length (Lc), temperature (T), and porosity (ps = 1 − pb) as these parameters cooperate and compete. In homogeneous/annealed systems (pb = 0), the power-law exponent γ for the radius of gyration of the chains shows a crossover from SAW-conformation with γ ∼ 0.61 at low polymer concentrations (dilute regime p = 0.001−0.01) to an ideal chain conformation with γ ∼ 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 γ ∼ 0.64 at high porosities (ps ⩾ 0.8) to a collapse conformation with γ ∼ 0.35 at low porosities (ps ⩽ 0.5) at temperature T = 1.0. The rms displacement of the chains is generally diffusive, Rrms = At0.5, at low p and high T while it is subdiffusive Rrms = Atk, with k < 0.5 at high p and low T. For example, k ⋍ 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 pb ⩾ 0.2 in three dimension) but becomes ultra-subdiffusive with Rrms = Atk, where k < 0.1 at low temperatures. The prefactor A shows a power-law dependence on the chain length, A ∼ Lc−μ, except at high polymer concentrations and low temperature, with the exponent μ ∼ 0.45−0.57 in annealed systems and ∼0.53−0.64 in porous media at p = 0.3.