Dimensionality reduction of free energy profiles of benzene in silicalite-1: calculation of diffusion coefficients using transition state theory

Abstract

ENERGIE:MATERIAUX+EPA:HJOThis study describes the development and application of a new computational methodology for calculating the self-diffusivity of sorbate molecules strongly confined within shape-selective nanoporous materials. An umbrella sampling strategy, employing repulsive walls to confine the sorbate within specific regions of the pore space, is invoked to extract free energy profiles with respect to the sorbate degrees of freedom. Based on these profiles, it is shown how the multidimensional problem of translational diffusion of benzene in flexible silicalite-1 can be reduced first to a six-dimensional problem, then to a three-dimensional (3D) problem and finally, to a 1D problem. A 3D free energy distribution is accumulated as a function of the benzene centre of mass position and ultimately reduced to a set of 1D profiles for the benzene centre of mass along the pore axes. From these profiles, the rate constants for jumps executed by benzene between sorption sites are calculated using transition state theory; from the latter rate constants, the low-occupancy self-diffusivity is obtained using the MESoRReD method [Kolokathis PD, Theodorou DN. On solving the master equation in spatially periodic systems. J Chem Phys. 2012;137:034112]. The activation energy for diffusion and preferred orientations in the various sorption states in silicalite are in very favourable agreement with available experimental measurements

KoBra: A rate constant method for prediction of the diffusion of sorbates inside nanoporous materials at different loadings

“…In all these applications, diffusion of adsorbates (benzene, p‐xylene, xenon, isobutene, methane, ethane, propane and generally hydrocarbons) inside nanoporous materials takes place, and a detailed description of this process is of a large interest. There are different methods to estimate the diffusion of adsorbates inside these materials, and a large number of experiments have been conducted for this purpose.…”

“…There are different methods to estimate the diffusion of adsorbates inside these materials, and a large number of experiments have been conducted for this purpose. The most common ones are pulse field gradient nuclear magnetic resonance (PFG NMR), quasi elastic neutron scattering (QENS), gravimetric techniques and molecular dynamics (MD) simulations . The results of all these methods do not always agree each other.…”

“…In the case of MD simulations, if the porous diameter is comparable with the kinetic diameter of the sorbate, the sorbate is trapped inside the pore, and diffusion jumps become extremely rare within the computational margins of a conventional MD simulation, which are usually of the order of nanoseconds. In these cases, MD simulation has to be used together with the transition state theory (TST) . TST is based on the calculation of transition rate constants, which describe the probability of a transition from one state to another state inside the porous network per one time unit .…”

“…In these cases, MD simulation has to be used together with the transition state theory (TST) . TST is based on the calculation of transition rate constants, which describe the probability of a transition from one state to another state inside the porous network per one time unit . We note that a “state” here is a very restricted area where the sorbate stays for a long time and does jumps to another area.…”

A study of CO2/CO separation by sub-micron b-oriented MFI membranes

“…However, the diffusion in the c-direction is signicantly slower than in the a-and b-directions. 15,16 It has been shown 14,17 that b-oriented MFI lms may allow for somewhat faster transport of molecules, especially bulky molecules (e.g. xylenes) since the straight pores will be running along the lm thickness.…”