Analysis of Time-Varying, Stochastic Gas Transport through Graphene Membranes

Molecular transport measurements through isolated nanopores can greatly inform our understanding of how such systems can select for molecular size and shape. In this work, we present a detailed analysis of experimental gas permeation data through single layer graphene membranes under batch depletion conditions parametric in starting pressure for He, H2, Ne, and CO2 between 100 and 670 kPa. We show mathematically that the observed intersections of the membrane deflection curves parametric in starting pressure are indicative of a time dependent membrane permeance (pressure normalized molecular flow). Analyzing these time dependent permeance data for He, Ne, H2, and CO2 shows remarkably that the latter three gases exhibit discretized permeance values that are temporally repeated. Such quantized fluctuations (called "gating" for liquid phase nanopore and ion channel systems) are a hallmark of isolated nanopores, since small, but rapid changes in the transport pathway necessarily influence a single detectable flux. We analyze the fluctuations using a Hidden Markov model to fit to discrete states and estimate the activation barrier for switching at 1.0 eV. This barrier is and the relative fluxes are consistent with a chemical bond rearrangement of an 8-10 atom vacancy pore. Furthermore, we use the relations between the states given by the Markov network for few pores to determine that three pores, each exhibiting two state switching, are responsible for the observed fluctuations; and we compare simulated control data sets with and without the Markov network for comparison and to establish confidence in our evaluation of the limited experimental data set.