Scaling of ionic conductance in a fluctuating single-layer nanoporous membrane

Single-layer membranes have emerged as promising candidates for applications requiring high transport rates due to their low resistance to molecular transport. Owing to their atomically thin structure, these membranes experience significant microscopic fluctuations, emphasizing the need to explore their impact on ion transport processes. In this study, we investigate the effects of membrane fluctuations on the elementary scaling behavior of ion conductance G as a function of ion concentration c(0), represented as G = beta c(0)(alpha), using molecular dynamics simulations. Our findings reveal that membrane fluctuations not only alter the conductance coefficient beta but also the power-law exponent alpha. We identify two distinct frequency regimes of membrane fluctuations, GHz-scale and THz-scale fluctuations, and examine their roles in conductance scaling. Furthermore, we demonstrate that the alteration of conductance scaling arises from the non-linearity between ion conductance and membrane shape. This work provides a fundamental understanding of ion transport in fluctuating membranes.