Molecular Simulation and Multistate Analysis for Efficient Property Estimation in Polymeric Systems: A Case Study on PIM-1

Abstract

In the present study, an application of the Multistate Bennett Acceptance Ratio (MBAR) method to analyze results from molecular simulations of polymeric systems is presented. Thermodynamic properties and gas sorption isotherms of PIM-1, a polymer of intrinsic microporosity, over a broad range of thermodynamic states were calculated using isobaric-isothermal and grand canonical ensembles through Molecular Dynamics and Monte Carlo simulations. The statistically optimal MBAR estimator was used to generate continuous properties as a function of thermodynamic state, based on the density of states and the degree of overlap between the probability distributions of individual simulations. The relationship between the statistical uncertainties of the results, conditional on the sampled ensemble, and the computational demand of the simulations was also investigated. A simple method is presented to guide computational effort toward estimating thermodynamic properties of molecular systems within a target MBAR statistical uncertainty, with systematic contributions from polymer morphology assessed separately. The proposed optimization method enables a significant reduction in the number of independent simulations required to obtain continuous estimates of volumetric thermodynamic properties and gas sorption isotherms, which provides substantial improvements in the statistical quality of the results and optimization of computational resources. Furthermore, the methodology, which was previously applied to small gases such as CO2 and CH4 and their mixtures as a generalized equation-of-state framework for predicting pVT relationships from molecular simulation data, is extended here to polymeric systems and expanded to include multistate adsorption calculations based on MBAR. These developments demonstrate the potential of the approach to be further extended to other complex systems for which experimental data are limited.