Dependence of percolation threshold on side chain distribution within amphiphilic polyelectrolyte membranes

Dissipative particle dynamics (DPD) in combination with Monte Carlo (MC) tracer diffusion simulations are employed to predict percolation thresholds for diffusion within hydrated model polymer electrolyte membranes. The polymers are composed of hydrophobic backbones to which hydrophobic side chains are attached with a pending hydrophilic acidic site. In total 15 polymer architectures are considered that differ in the way the side chains are distributed along the backbones. For each architecture, phase separated morphologies are generated for a range of water contents by DPD. This paper assesses the results obtained from exhaustive simulations involving more than 130 morphologies. By mapping each morphology onto a high density grid MC trajectory, calculations are performed in which particle movement is restricted to the water containing pore networks. The following results are obtained: (1) for polymers for which the side chain density (or ion exchange capacity) is the same, those architectures for which the distance between successive branching points is alternating short and long, reveal lower percolation thresholds than architectures for which the side chain distribution is uniform; (2) increase of the side chain density (ion exchange capacity) results in a lower percolation threshold. The results are explained by differences in the topological distance between nearby hydrophilic beads within the architectures: acidic sites that are topologically close together within a polymer architecture can arrange themselves pair-wise along the pore walls. At similar water contents this results in increased pore sizes and larger diffusion constants for architectures involving the non-uniform side chain attachments.