A simple method for the simulation of steady-state diffusion through membranes: pressure-tuned, boundary-driven molecular dynamics

Abstract

We present a novel molecular dynamics-based simulation technique for investigating gas transport through membranes. In our simulations, the main control parameters are the partial pressure for the components on the input side of the membrane and the total pressure on the output side. The essential point of our scheme is that this pressure control should be realised by adjusting the particle numbers in the input and output side control cells indirectly. Although this perturbation is applied sufficiently far from the membrane, the bulk-phase properties are well controlled in a simulation cell of common size. Numerical results are given for silicalite-1 membrane with permeating CH 4 , CO 2 , H 2 and N 2 gases as well as with binary mixtures of CO 2 with the other three components. To describe interactions between particles, we used the simple shifted and cut Lennard -Jones potential with parameters available in the literature. It is expected that the proposed technique can be applied to several other types of membranes and transported fluids in order to support the development of a deeper understanding of separation processes.

Concentration gradient driven molecular dynamics: a new method for simulations of membrane permeation and separation

“…Here we note that in MD simulations of membranes creating a vacuum effect is a challenging task as also mentioned by others. 15 , 21 To create the vacuum effect, a larger outlet force constant, k O i , was used compared to the inlet force constant, k I i . The values of parameters used in eqn (1) & (2) and the locations of the force and control regions are given in Table S2.…”

“… 14 However, DCV-GCMD method doesn't work efficiently for dense fluids due to the extremely low acceptance rates for the insertion and deletion of the molecules. Moreover, according to Ható et al 15 coupling MC moves with MD can be problematic since the ratio of insertion/deletion steps vs. MD steps should be optimized in order to perform a reliable simulation.…”

“…Moreover, applying an external force all over the simulation box requires care because if the bias exceeds a critical level then thermostat or barostat algorithms can fail to do their job due to fictional increase of particle velocities. 15 To address this concern, in their study of gas permeation through slit pores, Frentrup et al 25 restricted the external force in to a considerably small region in the simulation box (boundary-driven NEMD) in attribution to the position of the small force region placed at the boundary of the simulation box. The same authors extended their method to investigate single gas permeation of CO 2 and He through a PIM-1 polymer membrane.…”

“… 26 Even though their methodology allows the circulation of fluid molecules between the permeate and feed sides to ensure a continuous simulation, it does not provide any control over the density of fluids at the inlet and outlet of the membrane. To address the shortcomings of previous methods Ható et al 15 proposed a methodology which was essentially a combination of the method of Frentrup et al 25 and of the DCV-GCMD method of Heffelfinger et al , 11 thus again requiring the coupling of MC and MD algorithms. All the methods we summarized above served to the purposes they were developed for and deserve credit; however, none of them provide a platform for running a steady state and continuous simulation for a mixture across a membrane without involving a hybrid MC and MD approach.…”

Membrane separation study for methane-hydrogen gas mixtures by molecular simulations

“…This means that while all properties calculated and monitored in the control cells predominantly stem from the movements and interactions of particles in these regions, the artificial perturbation of the system is only present in the boundary regions of the simulation cell [18]. Our earlier test clearly showed that the particles inserted into the system have no "memories" of their initial velocities before they reach the interaction range of the membrane [19].…”