Grained Model and Simulation Protocol

In the following, a recipe is provided of typical CGMD simulations of the PEM microstructure. In the first step, the atomistic system must be mapped onto a coarsegrained model, in which spherical beads with predefined, subnanoscopic length scale replace groups of atoms. The CGMD model uses polar, nonpolar, and charged beads to represent water, polymer backbones, anionic sidechains, and hydronium ions in a hydrated ionomer system (Marrink et al., 2007). 

In the second step, parameters of renormalized interaction energies between beads are specified, defining the force field under which the system trajectory evolves. Interactions between beads could be determined by force matching procedures from atomistic interactions (Izvekov and Violi, 2006 Izvekov et al., 2005) or by fitting of experimental structural correlation functions (Marrink et al., 2007). 

After defining the structural representation of the coarse-grained system and interaction terms, a simulation protocol has to be devised. This protocol involves an equilibration or thermalization phase, as well as production runs. In a production run, the system trajectory is simulated under well-defined thermodynamic conditions, over a specified period of time, in order to generate a statistically meaningful ensemble of uncorrelated system configurations. In the final step, these configurations are analyzed using RDF, and density maps that provide direct information on size, shape, and distribution of phase domains in the composite medium. 

Results can be compared to all-atom simulations for calibration and refinement of interaction parameters. Further analysis could involve Monte Carlo procedures in order to obtain shape and size distributions of ionomer and water clusters from the structures formed during CGMD simulations. Moreover, stable structures from CGMD studies could form the basis for mobility studies by atomistic MD simulations, using remapping procedures. 

Malek et al. (2008) employed a typical coarse-grained parameterization of hydrated Nafion. Clusters of four water molecules are represented by polar beads. Clusters of three water molecules and a hydronium ion correspond to charged beads. An ionomer sidechain is represented by a single charged bead. A four-monomeric unit of PTFE (-[-CF2-CF2-CF2-CF2-CF2-CF2-CF2-CF2-]- on the backbone, corresponds to a nonpolar bead. All beads are assigned a radius 0.43 nm and a volume of 0.333 nm  

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