Free energy landscapes for the thermodynamic understanding of adsorption-induced deformations and structural transitions in porous materials

Soft porous crystals are flexible metal-organic frameworks that respond to physical stimuli such as temperature, pressure, and gas adsorption by large changes in their structure and unit cell volume. While they have attracted a lot of interest, molecular simulation methods that directly couple adsorption and large structural deformations in an efficient manner are still lacking. We propose here a new Monte Carlo simulation method based on non-Boltzmann sampling in (guest loading, volume) space using the Wang-Landau algorithm, and show that it can be used to fully characterize the adsorption properties and the material's response to adsorption at thermodynamic equilibrium. We showcase this new method on a simple model of the MIL-53 family of breathing materials, demonstrating its potential and contrasting it with the pitfalls of direct, Boltzmann simulations. We furthermore propose an explanation for the hysteretic nature of adsorption in terms of free energy barriers between the two metastable host phases.