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Modulating ion transport through nanoporous membranes is critical to manyimportant chemical and biological separation processes. The correspondingtransport timescales, however, are often too long to capture accurately usingconventional molecular dynamics (\textsc{Md}). Recently, path samplingtechniques such as forward-flux sampling (\textsc{Ffs}) have emerged asattractive alternatives for efficiently and accurately estimating arbitrarilylong ionic passage times. Here, we use non-equilibrium \textsc{Md} and\textsc{Ffs} to explore how the kinetics and mechanism of pressure-drivenchloride transport through a nanoporous graphitic membrane are affected by itslateral dimensions. We not only find ionic passage times and free energybarriers to decrease dramatically upon increasing the membrane surface area,but also observe an abrupt and discontinuous change in the locus of thetransition state. These strong finite size effects arise due to the cumulativeeffect of the periodic images of the leading ion entering the pore on thedistribution of the induced excess charge at the membrane surface in the feed.By assuming that the feed is an ideal conductor, we analytically derive afinite size correction term that can be computed from the information obtainedfrom a single simulation and successfully use it to obtain corrected freeenergy profiles with no dependence on system size. We then estimate ionicpassage times in the thermodynamic limit by assuming an Eyring-type dependenceof rates on barriers with a size-independent prefactor. This approachconstitutes a universal framework for removing finite size artifacts inmolecular simulations of ion transport through nanoporous membranes andbiological channel proteins.

journal of chemical theory and computation

Ideal Conductor Model: An analytical finite-size correction for  non-equilibrium molecular dynamics simulations of ion transport through  nanoporous membranes