Dissipative particle dynamics (DPD) provides superb computational efficiency in prediction the mesoscale structure of self-assembled systems. This work is an attempt to extend DPD to systems with chemical equilibria. In such systems, the chemical structure of functional groups depends on the local environment. For example, in proton-exchange polyelectrolyte membranes dissociation of an acid group is influenced by the hydration of that particular group. We suggest a simulation framework that allows incorporation of reversible chemical reactions into soft-core DPD simulations. The reactivity is mimicked through formation and dissociation of breakable bonds implemented using a short-range attractive potential between specific bead types.
We demonstrate our approach on systems with protonation reactions and proton transfer. To model protonation equilibria, we introduce proton as a separate bead type which interacts with bases (such as water and acid anions) via cut-and-shifted Morse potential. First, we consider aqueous solutions of benzenesulfonic acid. The Morse parameters are determined from the experimental ratio of proton self-diffusion coefficient in a large water bath to the self-diffusion coefficient of water and from the experimental acid dissociation constant. We achieve a very good agreement between DPD simulations and theoretical calculations of the acid degree of dissociation. The model of benzenesulfonic acid dissociation is incorporated into DPD simulations of sulfonated polystyrene of different sulfonation degrees and water content. The system segregates into hydrophobic organic and hydrophilic aqueous subphases. We calculate the self-diffusion of water in the segregated structure and estimate proton conductivity using Nernst equation. The calculated water diffusion is in a quantitative agreement and calculated proton conductivity is in a semi-quantitative agreement with the experiment.
Left: Coarse-grained representation of benzenesulfonic acid with the coarse-graining level of three water molecules per bead. Colored blocks on the atomistic model denote the components for the respective DPD beads. C-S dimer represents the deprotonated acid ion, where the equilibrium distance and the cutoff of the associative harmonic potential between beads. Right: mesoscale structure of hydrates sulfonated polystyrene at 25% sulfonation level and hydration level of 8 water molecules per sulfonic group. Water is drawn in green, sulfonate groups in yellow, hydrated protons in black and the hydrophobic parts in red.
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