Morphology and diffusion within model membranes: Application of bond counting method to architectures with bimodal side chain length distributions

Dependence of Solvent Diffusion on Hydrophobic Block Length within Amphiphilic–Hydrophobic Block Copolymer Membranes

“…To make a conversion to physical units, the volume of each DPD bead is set at V = 0.12 nm 3 . This value is of the same order ,,, or exactly the same ,,,,− as in recent DPD work − on hydrated membranes. The actual choice for V = 0.12 nm 3 has its origin located in the parametrization of Nafion in the DPD studies by Yamamoto and Hyodo .…”

“…Various DPD studies on membranes with PFSA-like architecture − and alternative chain architectures − followed. In particular, in order to gain more insight into the dependence of pore network and water diffusion on polymeric architecture, DPD simulations were combined with Monte Carlo trajectory calculations. ,− In these studies, water diffusion is mimicked by performing lattice MC walks of tracer particles on a 3D grid through copies of the morphologies obtained from DPD. Diffusion constants derived from the combined DPD-MC studies , on Nafion membranes resemble experimental values when the local water mobility within the pores is assumed to be similar to that of pure water.…”

“…By analyzing results obtained from more than 100 model architectures, − various trends were predicted. All polymer architectures in refs − were composed of a minority of hydrophilic C beads and a majority of hydrophobic A beads, with C beads uniformly distributed on the length scale of the whole polymer backbone (each polymer contained several repeat units). The mutual Flory–Huggins interaction parameters between A, C, and water (W) beads were intentionally kept the same.…”

“…In searching and proposing alternative polymers that promote good connected pores that facilitate long-range diffusion, architectures have been considered such as those where each repeat unit contains (i) a branched (Y-shaped) side chain, , (ii) two side chains but each of them of different length, , and (iii) similar side chains but separated by alternating distances along the backbone. ,,, At a fixed water volume fraction of 16% (ϕ w = 0.16), the average distance between water containing pores or clusters, D Cl–Cl , turned out to depend considerably on the architecture. Among the architectures with side chains alternatingly distributed (type iii), the differences in D Cl–Cl between architectures ,, increase quadratically with D topol,2 – D topol,1 , where D topol,1 and D topol,2 are the number of DPD springs (covalent bonds) between a C bead and its nearest and next nearest C bead, respectively.…”

“…Reanalysis − augmented by additional studies revealed that in general D Cl–Cl increases linearly with the parameter of merit ⟨ N bond ⟩, which is the average number of bonds between hydrophobic A beads and the nearest hydrophilic C bead within the architecture. Moreover, ⟨ N bond ⟩ is also useful when interpreting MC derived diffusion coefficients and percolation thresholds, − resulting in the following trends: (1) For a fixed IEC (or | C |) and water content (ϕ w = 0.16), water diffusion increases as a function of ⟨ N bond ⟩. (2) D MC (W) increases approximately linearly with ⟨ N bond ⟩| C || A | –1 , where | C | and | A | (=|1 – C |) are the hydrophilic C and hydrophobic A bead fractions within the architecture.…”