Pore morphologies and diffusion within hydrated polyelectrolyte membranes: Homogeneous vs heterogeneous and random side chain attachment

Abstract

Using dissipative particle dynamics pore morphologies within model ionomer membranes are simulated. The ionomers are composed of hydrophobic backbones and side chains that are end-linked with a hydrophilic acid containing site. The separation distance between successive branching points is bi-modal, being alternating short (distance x) and long (distance y). The dependence of morphology on ion exchange capacity and separation distance is investigated. Phase separated morphologies were calculated at a water content of 16 vol. %. An increase of side chain density results in a decreasing size of the water containing pores, distance between them and decreasing Bragg spacing. For fixed side chain density, an increase in difference between the longer and shorter separation distance (y - x) results in a larger Bragg spacing. Monte Carlo calculations demonstrate that a large majority of the water is contained within a percolating network that allows for long-range diffusion. Diffusion constants vary drastically with architecture: Diffusion is fastest for architectures for which the side chains are highly non-uniformly distributed (y ≫ x). For architectures with the same side chain density, the tracer diffusion constants increase linearly with increase of the asymmetry ratio y∕x (y > x). This is caused by the cooperative action of those terminal acidic sites that are topologically close together, allowing them to arrange pair wise along the pore walls and make the pores larger. We verified that for polymer architectures that mimick Nafion1200 similar trends are obtained, resulting in increased H(2)O, O(2), and H(2) permeation for statistical side chain distribution as compared to a uniform distribution of side chains. This trend is most pronounced for H(2)O and less pronounced for H(2).

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

“…This result is essentially the same as obtained for block polymers [40]. Also for (hypothetical) Nafion the calculated water diffusion constants at several hydration levels were found to increase with y/x [34]. Interestingly, for a realistic statistical side chain distribution better agreement with experiment was found [34] as compared with the simulation results in Ref.…”

“…Usually the volumes V represented by each type of DPD bead are chosen to be the same. In modeling fuel cell membranes they are typically in between V = 0.06 nm 3 [34,39,41,42] and V = 0.18 nm 3 [35,36]. These correspond to the volume occupied by N m = 2 and N m = 6 water molecules, respectively.…”

“…For grafted polymers for which the side chains are distributed equidistantly along the polymer backbone (uni-modal distribution) and with a single pendent hydrophilic fragment, the size of the water containing pores and water diffusion coefficients increase with side chain length [41]. When the side chains are kept at the same length but the inter-branching distance along the backbone is alternatingly long and short (y > x, bimodal distribution), the pore size and diffusion increases with increase of bimodal character, or asymmetry parameter y/x [34,42,43]. This result is essentially the same as obtained for block polymers [40].…”

“…For example, at hydration level of k = 5 water molecules per SO 3 H site, Pivovar and Pivovar [37] measured a local water mobility of $1.6 Â 10 À5 cm 2 /s, which is $70% of the pure water value of 2.3 Â 10 À5 cm 2 /s. In later works [34,[39][40][41][42][43][44] where DPD was applied in combination with MC tracer diffusion calculations it was found/predicted that among membranes of the same IEC the pore morphology and diffusion constants depend strongly on the specific architecture of the model polymers. The main obtained trends are summarized below.…”

“…Other methods that have been invoked to generate equilibrium morphologies of hydrated Nafion of size O(10 4 nm 3 ) from random starting configurations are Coarse Grained MD (CGMD) [25,26], Bond Fluctuation Model (BFM) [27], Monte Carlo in combination with the Reference Interaction Site Model (MC/RISM) [28], self-consistent approaches [29] and the dissipative particle dynamics (DPD) simulation method [30][31][32][33][34][35][36]. Yamamoto and Hyodo [30] applied DPD and calculated for system size $2.3 Â 10 4 nm 3 Nafion1200 morphologies (1200 means the equivalent weight (EW) of 1200 g polymer per one mole of sulfonic sites).…”