Coarse-grained study of the effect of hydrophobic side chain length on cluster size distributions and water diffusion in (amphiphilic-hydrophobic) multi-block co-polymer membranes

Abstract

The formation of water clusters and their evolvement towards water containing percolating networks at 16 vol% water contents is studied by dissipative particle dynamics (DPD) for 7 multi-(amphiphilic-hydrophobic)-block co-polymer model membranes. The amphiphilic (A[C]) block is composed of one hydrophobic A backbone bead to which a hydrophilic (acidic) side chain, represented by one C bead, is attached. The architecture of the hydrophobic block is systematically varied and contains x = 4 or 6 A beads and is part of the Ax-p-q[Ap][Aq] family with side chain lengths (p,q)= (0,0), (2,1), (3,0) for x = 4 and (p,q)= (0,0), (3,2), (4,1), (5,0) for x = 6. Water diffusion derived from Monte Carlo trajectory simulations through 700 mapped morphologies reveal the same trends as the water bead diffusivity during the DPD simulations. For similar ion exchange capacity (or x) an increase in hydrophobic side chain length difference, p-q, results in better connected pores, increase of the percolating cluster size, less isolated clusters and enhanced diffusion. These trends are explained by assigning to each polymer A bead a number Nbond which is the number of bonds (DPD springs) between that A bead towards the nearest C bead within the same polymer. The hydrophobic (A-bead_Abead) contact matrices show that high Nbond A beads have a propensity to contact other high Nbond A beads. As a result phase separation and water diffusion become more pronounced with increase of <Nbond>. Based on these findings an alternative to Nafion and Dow membranes can be proposed for which a large fraction of hydrophobic (CF2- CF2-) fragments are distributed along hydrophobic side chains.