The ability of semipermeable membranes to selectively impede the transport of undesirable ions and molecules is key to many applications, from desalination and gas separation to biological membrane transport. For instance, membranes that are only permeable to water and reject most other ions and molecules are used in water desalination. Designing more selective membranes requires characterizing the kinetics and mechanism of the transport of the species rejected by the membrane. The timescales associated with such processes, however, can be too long to be accessible to conventional MD simulations. Moreover, the driven nature of the underlying separation processes excludes the utilization of advanced sampling techniques that require microscopic reversibility. Finally, the separation of timescales between the transport of desirable species (such as water) and undesirable species (such as salts) will result in considerable changes in reservoir concentration throughout an MD trajectory, which can skew the kinetics and mechanism of transport in ways that are difficult to quantify and correct. Recently, we utilized [1] jumpy forward flux sampling (jFFS) [2], a path sampling technique developed in my group, and non-equilibrium MD to study pressure-driven ion transport through nanoporous graphitic membranes. Our approach addresses all these challenges. It not only allows us to accurately and efficiently estimate arbitrarily long mean first passage times in pressure- and field-driven filtration processes, but also to compute fluxes and permeabilities within a pseudo-equilibrium ensemble in which both reservoirs are at different- but almost constant- chemical potentials.
In this presentation, I will discuss several technical aspects of this new approach, particularly a new model that we have developed to correct for the rather strong finite size artifacts in simulations of non-equilibrium ion transport [3]. What is remarkable about this model is that it corrects for finite size effects âon the spotâ, i.e., from the information obtained from a single finite simulation. Therefore, the behavior of the system in the thermodynamic limit can be inferred without a need to conduct multiple simulations of systems with different sizes (as is the common practice in the computational chemistry community). I will also discuss some of our more recent findings on how pore topology impacts the fidelity of order parameters and how pore arrangement within a membrane can impact transport resistance and selectivity in nontrivial ways.
[1] Malmir H, Epsztein R, Elimelech M, Haji-Akbari A, Induced charge anisotropy: a hidden variable affecting ion transport through membranes, Matter, 2: 735 (2020).
[2] Haji-Akbari A, Forward-flux sampling with jumpy order parameters, J. Chem. Phys., 149: 072303 (2018).
[3] Shoemaker BA, Domingues TS, Haji-Akbari A, Ideal conductor model: An analytical finite-size correction for nonequilibrium molecular dynamics simulations of ion transport through nanoporous membranes, J. Chem. Theory Comput., 18: 7142 (2022).
