(342aq) Estimation of the Binary Interaction Parameters of the Anrtl Model Using Molecular Simulations

Process simulations play an important role in the design and optimization of an adsorption process for a given application. The mathematical expressions relating the various thermodynamic variables form the backbone of a process simulator. One such thermodynamic model for mixed-gas adsorption equilibria is the aNRTL model [1]. The model takes into account non-idealities in the adsorbed phase due to interactions of the adsorbate molecules of a binary gas mixture with an adsorbent. The arguments leading to the derivation of the molar excess Gibbs free energy and the subsequent calculations of the component activity coefficients are analogous to the NRTL model [2]. Thus, the physical significance of the aNRTL model is justified because it is based on the local composition concept [3]. The model uses one adjustable parameter called the binary interaction parameter which gives the difference in the Gibbs free energy of interaction of the adsorbate molecules with an adsorption site relative to thermal energy. The binary interaction parameter can be regressed from experimental adsorption data of binary gas mixtures. It can also be predicted from the experimental pure component adsorption data using framework of the Thermodynamic Langmuir Model [4].

Unavailability or unreliability of experimental datasets in terms of missing uncertainties and fewer data points affect the regression process, thus impacting model predictions. Therefore, it is extremely important to develop a methodology to estimate such parameters that does not make use of experimental adsorption data. Such an approach has been developed for the estimation of binary interaction parameters of the NRTL model using molecular dynamics simulations [5]. In this study, we follow a similar approach to estimate the binary interaction parameters for a pair of adsorbate molecules in MOFs such as Cu-BTC and UiO-66. We have determined the amounts adsorbed in the MOFs using Monte Carlo simulations in the Grand canonical ensemble at various conditions of pressure and temperature. This allowed us to validate the various force fields used by comparing the predicted equilibrium amounts adsorbed with experimental data. Distinct adsorption sites for a given binary pair were identified from the computed trajectories of the molecules using molecular dynamics simulations in the isothermal, isobaric ensemble. Following arguments similar to the ones used by Ravichandran et al. (2018) [5] and Brandini and Prausnitz (1982) [6], we have derived equations relating the binary interaction parameters to the molecular parameters of the adsorbate-adsorbent interactions in the first coordination shell of each distinct site. The effective molecular diameters and radius of the first coordination shells were computed from the radial distribution functions of the adsorbate-site pair. The effective interaction strength parameters for adsorbate-site pairs were determined from the potential of mean force calculations. The binary interaction parameters computed from molecular simulation gave an accurate prediction of the binary adsorption equilibria for the systems studied.

References:

1. Kaur, Harnoor, Hla Tun, Michael Sees, and Chau-Chyun Chen. "Local composition activity coefficient model for mixed-gas adsorption equilibria." Adsorption25, no. 5 (2019): 951-964.
2. Renon, Henri, and John M. Prausnitz. "Local compositions in thermodynamic excess functions for liquid mixtures." AIChE journal14, no. 1 (1968): 135-144.
3. Wilson, Grant M. "Vapor-liquid equilibrium. XI. A new expression for the excess free energy of mixing." Journal of the American Chemical Society86, no. 2 (1964): 127-130..
4. Chang, Chun-Kai, Hla Tun, and Chau-Chyun Chen. "An activity-based formulation for Langmuir adsorption isotherm." Adsorption(2019): 1-12.
5. Ravichandran, Ashwin, Rajesh Khare, and Chau‐Chyun Chen. "Predicting NRTL binary interaction parameters from molecular simulations." AIChE Journal64, no. 7 (2018): 2758-2769.
6. Brandani, V., and J. M. Prausnitz. "Two-fluid theory and thermodynamic properties of liquid mixtures: General theory." Proceedings of the National Academy of Sciences79, no. 14 (1982): 4506-4509.