Percolation thresholds in hydrated amphiphilic polymer membranes

Abstract

Percolation thresholds for diffusion within the pores of hydrated grafted model polymer membranes are estimated by employing dissipative particle dynamics (DPD) in combination with Monte Carlo (MC) tracer diffusion calculations. The polymer backbones are composed of hydrophobic A beads to which side chains composed of y consecutively connected A beads are attached which are end linked with a hydrophilic acidic site (C bead). The side chains are distributed equidistant along the backbones for every x A backbone bead. For ten chain architectures the phase separated morphologies were calculated by DPD as a function of water volume fraction ϕw. Several trends are predicted. For fixed side chain lengths (given by y) the percolation thresholds increase with a decrease in C bead fraction within the polymer sequence (i.e., increase with equivalent weight (EW)). Among the sequences with the same C bead fraction (i.e., x + y = constant) the percolation thresholds are significantly lower for those sequences that contain the longer side chains. This is because the topological distance, defined as Dtopol. = x + 2(y + 1), between C beads is largest for the longer side chain architectures. When expressing the percolation thresholds in terms of number of water molecules λ associated with each C bead, the percolation threshold dependence can be described as function of only one single variable which is given by X = (x + y + 1)α/Dtopol. with α ∼ 2.8.