Spatial Coarse-Graining of Methane Adsorption in Graphene Materials

We investigate the spatial coarse-graining of interactions in host-guest systems within the framework of the recently proposed interacting pair approximation (IPA) (Pazzona et al., J. Chem. Phys. 2018, 148, 194108). Basically, the IPA method derives local effective interactions from the knowledge of the bivariate histograms of the number of adsorbate molecules (occupancy) in a pair of neighboring subvolumes taken at different values of the chemical potential. Here, we extend the IPA approach to the case in which every subvolume is surrounded by more than one class of neighbors, and we apply it on two systems, methane on a single graphene layer and methane between two graphene layers, at several temperatures and adsorbate densities. We obtain coarse-grained adsorption isotherms and reduced variances of the occupancy in a quantitative agreement with reference atomistic simulations. A quantitative matching is also obtained for the occupancy correlations between neighboring subvolumes, apart from the case of high adsorbate densities at low temperature, where the matching is refined by preprocessing the histograms through a quantized bivariate Gaussian distribution model.