Spatial Coarse-Graining of Methane Adsorption in Graphene Materials

Abstract

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 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.

Scaling-Up Simulations of Diffusion in Microporous Materials

“…The methodology is described in detail in our previous works. 35,36 Finally, we use mass transfer statistics obtained from MD to model the dynamical evolution of the CG lattice model as a Markov process based on a local operator (Section 2.3), which we further refine in order to take into account dynamical correlations and non-Markovian effects that are observed in MD simulations (Section 2.4).…”

“…Thermodynamics. Following the Interacting-Pair-Approximation (IPA) approach, 35,36 we associate the occupancy configurations of the lattice models with a CG potential function Ω, which in the grand-canonical ensemble reads…”

“…Second, we use static properties drawn from atomistic GCMC to define occupancy-dependent effective interactions inside every cell and among neighboring cells of the lattice (Section ). The methodology is described in detail in our previous works. , …”

“…Following the Interacting-Pair-Approximation (IPA) approach, , we associate the occupancy configurations of the lattice models with a CG potential function Ω, which in the grand-canonical ensemble reads where μ is the chemical potential, H n i is the single-cell free-energy contribution of a cell with occupancy n i , K n i , n j represents the free-energy contribution of the mutual interactions between neighboring cells with occupancies n i and n j , and ⟨ ij ⟩ indicates a summation over nearest-neighboring cells. More specifically, the self-interaction term H n i represents the contribution to the free energy of the system provided by (i) the interactions among the n i guest molecules located in the i -th cavity and by (ii) the interaction between the same n i molecules and the whole framework (which, we remark, is kept rigid in our simulations).…”

“…30 The methane-carbon and methane-zeolite LJ interactions were parametrized according to our previous works. 35,36 In all the simulations, the host materials were represented as rigid frameworks. The ZTC crystalline structure, in its unrelaxed version, was downloaded from materialscloud.org, 41 while the ITQ-29 structure was taken from RASPA2's repository on github.com.…”