Advanced computer simulations of nafion / water systems

Perfluorinated membranes are used in particular in polymer electrolyte fuel cells (PEFC). The well-known ionomer Nafion® (Dupont) is, due to its high proton mobility, a reference material for fuel cell applications. In water or other hydrophilic solvents the membrane segregates into a hydrophobic backbone matrix and a hydrophilic sub-phase containing clusters of both water and ions, where the cluster sizes and connectivity increase with increasing water content [1].

What is the Nafion morphology and the structure of the solvent in such systems? It has been shown recently [2] on large simulated systems that several morphological models fit the experimental scattering data, suggesting the inability of scattering experiments alone to elucidate the true structure of Nafion. However, a ’random’ model described in [2], i.e. the only explored model that did not assume a particular initial structure, could not reproduce the experimental data.

It remains a real computational challenge to generate in molecular simulations system configurations which are really decorrelated from the initial one. The time scales that can be achieved simply do not allow to obtain significant motions of the polymer (e.g. conformational changes, folding, etc.). We thus propose in this work a new random model of Nafion. A newly developped algorithm is used to generate Nafion chains with random growth paths and random starting points. A significant difference with the random model in [2] is that we do not build our systems at a density close to the final one. In order not to start with too much entangled chains, the systems are initially built at a density below the experimental one. The density after equilibration is again close to the experimental one.

Even though further improvements of the new algorithms can easily be envisaged, we demonstrate here that with the present version several sets of configurations that are compatible with the available scattering data can be generated and equilibrated. Twelve large random Nafion systems are built with different initial positions of the atoms as well as different water contents and side chain lengths (Nafion/Hyflon). They are equilibrated and then simulated for several ten nanoseconds. After equilibration, the structures are, as mentioned, compatible with the experimental scattering data. In addition we study a model similar to the one by Schmidt-Rohr and Chen [3], i.e. the newest morphological model of Nafion. The experimental scattering data are also satisfactorily reproduced with this model, hence, the prolonged debate over the structure of Nafion.

This agreement gives confidence that a more detailed analysis of the so-obtained configurations is scientifically warranted. We characterize and analyze the local, intermediate and large-scale structures by various structural parameters and domain size distributions. We therefore compute, for example, radial distribution functions (rdf), total and partial structure factors (S(q)) as well as numbers and sizes of hydrophilic clusters (depending on the definition of a cluster). The dynamics of various species in the system is also investigated, e.g. via the computation of the mean square displacements (msd) and the self-diffusion coefficients. These simulations are probably at the limit of what can today be achieved with all-atom molecular simulations of the MD type. We hope that this work will advance the ongoing debate on the structure and dynamics of these important materials.



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