(615b) Flat-Histogram Monte Carlo Simulation of Binary Adsorption in Crystalline Porous Adsorbents

Adsorption of gases by solid sorbents is considered to be a platform technology for chemical separations. In particular, adsorption is viewed as an advantageous alternative to thermal separations such as distillation due to lower process duties. Adsorption isotherms are often used to quantify the performance of an adsorbent material, but measurements (whether experimental or computational) are typically of isotherms of pure adsorbates even though separations necessarily involve multiple adsorbate species. Theoretical approaches for estimation of multicomponent isotherms from single-component isotherms are available, but direct measurement of multicomponent isotherms is often necessary.

In this work, we describe an approach to directly measure binary adsorption isotherms and associated properties using molecular simulation. The approach is based on extension of established Flat-histogram Monte Carlo (FHMC) techniques to a mobile adsorbate phase containing two species. In FHMC, a simulation samples different loading states (i.e., the number of each type of adsorbate molecule, termed macrostates) and biases transitions between the macrostates using the accumulated transition statistics. The accumulated transition statistics ultimately yield the probability distribution of the macrostates; for a binary adsorbate phase this probability distribution is two-dimensional, which is more challenging to measure than that of a single-component due to the need to numerically minimize an penalty function. To reduce the complexity of the simulation space, we adopt a directed search strategy similar to that of Shen and Errington [1] where the two-dimensional macrostate space is decomposed into trajectories of A) the pure fluid macrostates and B) macrostates with fixed total number of adsorbate molecules (diagonals). Simulations for these trajectories can be represented by single-dimensional macrostate descriptors, allowing simpler one-dimensional FHMC simulations that exploit accelerations that are only possible for such one-dimensional simulations. The macrostate distributions along the pure-species axes and the fixed-total diagonals are subsequently combined to yield the full two-dimensional macrostate probability distribution.

We implement this strategy using the FEASST simulation toolkit [2] for binary fluids composed of Nitrogen and Carbon Dioxide, both as bulk mixtures and adsorbed in crystalline MOFs and zeolites. Due to sampling challenges, we also incorporate advanced Monte Carlo trial moves that improve acceptance ratios and expedite the simulations. For both the bulk and confined fluids, we compute the properties of the fluid (density, internal energy, pressure/free-energy etc.) from the two-dimensional macrostate distributions using the binary-fluid extension of the histogram reweighting approach that was previously introduced for adsorption of single-component fluids [3]. Hence, the approach yields properties such as the adsorption isotherm, heat of adsorption, adsorption selectivity, and (possibly) the adsorbed-phase diagram from a single macrostate distribution. Additionally, our approach yields a reusable equation of state for the bulk binary gas mixture that we release in the NIST Standard Reference Simulation Website. Lastly, we discuss and evaluate options for reducing the required number of simulations.

References:

1. V. K. Shen and J. R. Errington; J Chem Phys, 2005, 122, pp 064508; DOI: https://doi.org/10.1063/1.1844372
2. H. W. Hatch, N. A. Mahynski, and V. K. Shen, J Res NIST, 2013, 123, pp123004; DOI: https://doi.org/10.6028/jres.123.004
3. D. W. Siderius and V. K. Shen; J Phys Chem C, 2013, 117, pp 5861-5872; DOI: https://doi.org/10.1021/jp400480q