Computing Effective Non-Equilibrium Free Energies

The global economy requires energy-efficient separations for diverse applications in chemical production, water treatment, recovery of high-value metals, and plastics recycling. In many cases, membrane-based processes can provide efficient separations with high throughput. However, current materials typically exhibit a tradeoff between permeability and selectivity that limits the chemical species that can be separated. Nevertheless, careful engineering of existing and emerging membrane materials should push back this tradeoff to enable the widespread use of membrane separation processes. Enhancing membrane separations requires significant theoretical advancements in understanding transport processes. The synthesis of functionalized membranes has advanced considerably over the last few decades, but the theoretical understanding of the molecular mechanisms underpinning membrane separations has not. One reason for this is that separations are inherently a non-equilibrium processes, and our understanding of the driving forces for separation (and the related concept of effective free energies) is underdeveloped.



We propose here a method to capture the effective free energies of non-equilibrium steady states so that they may be used to improve the dynamic separation properties of materials. We explore a method, Non-Equilibrium Trajectory-based Sampling (NETS) designed to construct free energy curves of equilibrium and non-equilibrium systems with no prior knowledge of the free energy landscape. We demonstrate how this data-driven approach non-equilibrium molecular simulations, in models informed by experiments, can be used to determine the influence of molecular interactions on the non-equilibrium steady states that govern separation rates and selectivities. Importantly, we discuss methods for obtaining the uncertainty of these effective free energy curves. Preliminary investigations have shown that the method accurately captures effective free energies utilizing only a few hundred short trajectories originating from each interface, thereby codifying non-equilibrium steady states with sparse sampling, which can be performed in a high throughput fashion.