Interpreting effective energy barriers to membrane permeation in terms of a heterogeneous energy landscape

Major efforts in recent years have been directed towards understanding molecular transport in polymeric membranes, in particular reverse osmosis and nanofiltration membranes. Transition-state theory is an increasingly common approach to explore mechanisms of transmembrane permeation with molecular details, but most applications of this theory treat all free energy barriers to transport within the membrane as equal. This assumption neglects the inherent structural and chemical heterogeneity in polymeric membranes. In this work, we expand the transition-state theory framework to include distributions of membrane free energy barriers. Our mathematical framework is mechanism-agnostic, such that it generalizes to transport through any membrane for molecular separation. However, we focus our analysis on dense nanofiltration and reverse osmosis membranes. We show that the highest free energy barriers along the most permeable paths, rather than typical paths, provide the largest contributions to the experimentally-observed effective free energy barrier. We show that even moderate, random heterogeneity in molecular barriers will significantly impact how we interpret the mechanisms of transport through these membranes. Our study suggests that experimentally-measured barriers are not easily related to the underlying mechanisms governing transport, and simplified interpretations of these barriers will likely miss the mechanisms most relevant to the overall permeability.