Understanding the transport of ions through nanoscopic pores is essential for many scientific and technological applications such as e.g. the ionic permeation of zeolites, carbon nanotubes and ion channels through cell membranes. Nonequilibrium molecular dynamics (NEMD) simulations provide a direct access to the microscopic structural changes induced by the applied field. It is therefore a valuable tool to understand how the structure and the transport properties of liquids are affected by the external field. However, conventional NEMD methods only allow to study systems subjected to very strong fields, typically of the order of 10^9 V/m, i.e. several orders of magnitude larger than the experimentally accessible rates. Therefore, these methods only provide insight into the response of the fluid under far-from-equilibrium conditions. The limitation to very strong fields directly stems from the conventional NEMD method. In conventional NEMD simulations, properties are averaged over the steady state. For weak fields, the signal-to-noise ratio is very small: the steady-state response becomes very noisy and the steady-state averages are essentially impossible to analyze. Having a large signal-to-noise ratio (and hence subjecting the fluid to very strong fields) is crucial to obtain meaningful averages in the steady state. This basically prevents accessing the nonequilibrium response for realistic values of the field. Therefore, a direct comparison between simulation and experiment still remains impossible.

In this talk, we address the inability of conventional NEMD methods to study the response of a liquid subjected to experimentally accessible fields. For this purpose, we use the transient time correlation function (TTCF) formalism. The TTCF formalism is essentially a nonlinear generalization of the Green-Kubo relations. We show how the TTCF approach can be applied to determine the conductivity of a fluid confined in a nanopore and subjected to a realistic (experimentally accessible) field [1]. Our results provide a full picture of the dependence of conductivity on the applied field and on the effective diameter of the nanopore.

[1] C. Desgranges and J. Delhommelle, Phys. Rev. E 77, 027701 (2008)