The role of molecular modeling in confined systems: impact and prospects

Abstract

Molecular modeling at the electronic and atomistic levels plays an important and complementary role to experimental studies of confinement effects. Theory and atomistic simulation can provide fundamental understanding, determine the limits of well known macroscopic laws such as Kelvin's equation, provide predictions for systems that are difficult to study via experiment (e.g. adsorption of highly toxic gases), and can be used to gain detailed molecular level information that may not be accessible in the laboratory (e.g. the local structure and composition of confined phases). We describe the most important and useful methods that are based firmly on quantum mechanics and statistical mechanics, including ab intio and classical density functional theories, and Monte Carlo and molecular dynamics simulation. We discuss their strengths and limitations. We then describe examples of applications of these methods to adsorption and equilibrium properties, including testing the Kelvin equation, determination of pore size distributions and capillary phenomena. Applications to self and transport diffusion, including single-file and anomalous diffusion, and viscous flow in nanoporous materials are described. The use of these methods to understand confinement effects on chemical reactions in heterogeneous media is treated, including effects on reaction equilibria, rates and mechanism. Finally we discuss the current status of molecular modeling in this area, and the outlook and future research needs for the next few years. The treatment is suitable for the general technical reader.

Water diffusion in zeolite membranes: Molecular dynamics studies on effects of water loading and thermostat

“…Mean square displacement (MSD) measurements were performed to determine self and collective transport coefficients given by equations (3) and (4), respectively, as well as their components in each direction. Theoretically, diffusion under confinement is divided mainly into three types of behaviour [36]: one follows Fick's law in which MSD of the fluid increases linearly with time, the second is a slower mode referred as the anomalous diffusion [63] not strictly following the Fickian behaviour, and the other is the single-file diffusion [54][55][56] where the MSD is linearly proportional to the square root of time. The Fickian mechanism takes place when there are large enough pores for the guest molecules to pass each other, and when guest-guest and host-guest collisions allow movement in three-dimensions.…”

“…Transport within a pore can be quantified through the self-diffusion coefficient D s , and the collective diffusion coefficient D c which is directly related to the transport diffusion coefficient [36]. Selfdiffusion represents the spontaneous mixing of particles among themselves, as such it is an indicator of molecular mobility.…”

“…Selfdiffusion represents the spontaneous mixing of particles among themselves, as such it is an indicator of molecular mobility. Experimentally, self-diffusivity can be determined by using pulsed field gradient nuclear magnetic resonance (PFG-NMR) [23] and quasielastic neutron scattering (QENS) measurements [36,37], however from the self-diffusivity measurement, discrimination of collective motion, i.e. transport of nano-sized water droplet, is not possible.…”

“…The collective diffusivity, which is more important parameter for evaluation of a zeolite as a potential membrane. The transport diffusivity is given by the ratio of the flux of molecules in the fluid due to a concentration gradient [38], ( − ⁄ where J is the flux, D t is the transport diffusion coefficient, C is the concentration, and z is the position), and is directly related to the collective diffusion coefficient through a thermodynamic factor [36] (…”

Diffusion in quasi-one-dimensional channels: A small system n, p, T, transition state theory for hopping times

“…However, the fundamental nature of diffusion can change dramatically if the movement of the particles is restricted to a quasi-one dimensional narrow channel in which the particles cannot pass each other [1,2]. The geometric restriction, when combined with the presence of independent stochastic forces [3,4] or a Brownian background [5] acting on the particles, results in a form of anomalous diffusion known as single file diffusion (SFD), because the relative order of the particles is preserved and a particle must wait for its neighbors to move before being able to diffuse.…”