  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 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. 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 membranes. Simplified
interpretations of experimentally measured barriers can lead to incorrect
assumptions about the underlying mechanisms governing transport and miss the
mechanisms most relevant to the overall permeability.
