Off-Lattice, Soft, Coarse-Grained Models

While the evaluation of the interactions in a dense system is computationally beneficial, the underlying lattice structure requires the usage of special simulation techniques to accurately calculate the contribution of the nonbonded interactions to the pressure. These difficulties can be mitigated by using a soft, coarse-grained, off-lattice model. Since forces are well defined in off-lattice models, one can use Brownian dynamics or dissipative particle dynamics methods [97-103]. Also, simulations under constant pressure or surface tension are feasible. 

One possibility to motivate such an off-lattice description is to use the pairwise interactions in Eq. (5.49) in conjunction with a linear assignment function II and average the potential v(r, r ) over a uniform distribution of grid positions keeping the particle positions, r, r, fixed. 

This procedure restores translational invariance [41,104] and results in a potential of the form 

These interactions with cubic anisotropy can be well approximated by an isotropic Gaussian form 

Such a model with a Gaussian form of the interaction, v, has been utilized by Zuckermann and coworkers [105] in order to investigate polymer brushes. The DPD-model of Groot and collaborators [100-102] also shares many features with this soft coarse-grained model. In this model, the conservative force is derived from a pairwise potential of the form 

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