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Register a new userSpatial coarse-graining of methane adsorption in graphene materials
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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.
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We investigate the coarse-graining of host-guest systems under the perspective of the local distribution of pore occupancies, along with the physical meaning and actual computability of the coarse-interaction terms. We show that the widely accepted approach, in which the contributions to the free energy given by the molecules located in two neighboring pores are estimated through Monte Carlo simulations where the two pores are kept separated from the rest of the system, leads to inaccurate results at high sorbate densities. In the coarse-graining strategy that we propose, which is based on the Bethe-Peierls approximation, density-independent interaction terms are instead computed according to local effective potentials that take into account the correlations between the pore pair and its surroundings by means of mean-field correction terms, without the need of simulating the pore pair separately. Use of the interaction parameters obtained this way allows the coarse-grained system to reproduce more closely the equilibrium properties of the original one. Results are shown for lattice-gases where the local free energy can be computed exactly, and for a system of Lennard-Jones particles under the effect of a static confining field.
A fundamental challenge in materials science pertains to elucidating the relationship between stoichiometry, stability, structure, and property. Recent advances have shown that machine learning can be used to learn such relationships, allowing the stability and functional properties of materials to be accurately predicted. However, most of these approaches use atomic coordinates as input and are thus bottlenecked by crystal structure identification when investigating novel materials. Our approach solves this bottleneck by coarse-graining the infinite search space of atomic coordinates into a combinatorially enumerable search space. The key idea is to use Wyckoff representations -- coordinate-free sets of symmetry-related positions in a crystal -- as the input to a machine learning model. Our model demonstrates exceptionally high precision in discovering new stable materials, identifying 1,558 materials that lie below the known convex hull of previously calculated materials from just 5,675 ab-initio calculations. Our approach opens up fundamental advances in computational materials discovery.
We consider the application of fluctuation relations to the dynamics of coarse-grained systems, as might arise in a hypothetical experiment in which a system is monitored with a low-resolution measuring apparatus. We analyze a stochastic, Markovian jump process with a specific structure that lends itself naturally to coarse-graining. A perturbative analysis yields a reduced stochastic jump process that approximates the coarse-grained dynamics of the original system. This leads to a non-trivial fluctuation relation that is approximately satisfied by the coarse-grained dynamics. We illustrate our results by computing the large deviations of a particular stochastic jump process. Our results highlight the possibility that observed deviations from fluctuation relations might be due to the presence of unobserved degrees of freedom.
We study numerically the adsorption of a mixture of CO$_2$ and CH$_4$ on a graphite substrate covered by graphene nanoribbons (NRs). The NRs are flat and parallel to the graphite surface, at a variable distance ranging from 6 r{A} to 14 r{A}. We show that the NRs-graphite substrate acts as an effective filter for CO$_2$. Our study is based on Molecular Dynamics (MD) simulations. Methane is considered a spherical molecule, and carbon dioxide is represented as a linear rigid body. Graphite is modeled as a continuous material, while the NRs are approached atomistically. We observe that when the NRs are placed 6 r{A} above the graphite surface, methane is blocked out, while CO$_2$ molecules can diffuse and be collected in between the NRs and the graphite surface. Consequently, the selectivity of CO$_2$ is extremely high. We also observe that the initial rate of adsorption of CO$_2$ is much higher than CH$_4$. Overall we show that the filter can be optimized by controlling the gap between NRs and the NRs-graphite separation.
We study the coarse-graining approach to derive a generator for the evolution of an open quantum system over a finite time interval. The approach does not require a secular approximation but nevertheless generally leads to a Lindblad-Gorini-Kossakowski-Sudarshan generator. By combining the formalism with Full Counting Statistics, we can demonstrate a consistent thermodynamic framework, once the switching work required for the coupling and decoupling with the reservoir is included. Particularly, we can write the second law in standard form, with the only difference that heat currents must be defined with respect to the reservoir. We exemplify our findings with simple but pedagogical examples.
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