# Spatial coarse-graining of methane adsorption in graphene materials

## TL;DR

This paper extends the Interacting Pair Approximation method to spatial coarse-graining of methane adsorption in graphene systems, accurately reproducing atomistic simulation results for various conditions.

## Contribution

The authors develop an extended IPA approach for complex neighbor interactions, enabling accurate coarse-grained modeling of methane adsorption in graphene materials.

## Key findings

- Coarse-grained isotherms match atomistic simulations.
- Occupancy correlations are quantitatively reproduced.
- Refinement improves accuracy at high densities and low temperatures.

## Abstract

We investigate the spatial coarse-graining of interactions in host-guest systems within the framework of the recently proposed Interacting Pair Approximation (IPA). Basically, the IPA method derives local effective interactions from the knowledge of the bivariate histograms of the number of sorbate 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 sorbate densities. We obtain coarse-grained (CG) 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 sorbate densities at low temperature, where the matching is refined by pre-processing the histograms through a quantized bivariate Gaussian distribution model.