Electrophoretic flow of interacting polymer chains: Effects of temperature, polymer concentration, and porosity

Abstract

Using a Monte Carlo simulation in three dimensions, we studied the variation of the root-meansquare (rms) displacement (Rrms) of polymer chains with time and the rates of their mass transfer (j) as a function of biased field (B), polymer concentration (p), chain length (Lc), porosity (ps), and temperature (T). In homogeneous/annealed system, the rms displacement of the chains shows a drift-like behavior, Rrms ∼ t, in the asymptotic time regime preceded by a subdiffusive power-law (Rrms ∼ tk, with k < 1/2) at high p. The subdiffusive regime expands on increasing Lc and p but reduces on increasing T or B. In quenched porous media, the drift-like behavior of Rrms persists at low barrier concentration (pb) and high T. However, at high pb and/or low T, chains relax into a subdrift and/or subdiffusive behavior especially with high p or long Lc. Flow of chains is measured via an effective permeability (σ) using a linear response assumption. In annealed system, σ increases monotonically with B at high T and low p but varies nonmonotonically at low T, high p and high Lc. We find that σ decays with Lc, σ ∼ L, where α depends on B, p and T with a typical value a α ∼ 0.43−0.64 for p = 0.1-0.3 at B = 0.5. Further, σ decays with p, σ ∼ − Cp with a decay rate C sensitive to T and B. In quenched porous media, even at low pb and high T, σ varies nonmonotonically with bias, i.e., the increase of σ is followed by decay on increasing the bias beyond a characteristic value (Bc). This characteristic bias seems to decrease logarithmically with barrier concentration, Bc ∼ −klnpb. The prefactor k depends on the chain length, k ≈ 0.35 for shorter chains (Lc = 20, 40) and ≈ 0.15 for longer chains (Lc = 60). Scaling dependence of σ on Lc similar to that in annealed system is also observed in porous media with different values of exponent α. The current density shows a nonlinear power-law response, j ∼ Bσ, with a nonuniversal exponent δ ≈ 1.10−1.39 at high temperatures and low barrier concentrations.