Permeation of hydrogen across graphdiyne: molecular dynamics vs. quantum simulations and role of membrane motion

Abstract

Previous research based on electronic structure calculations and molecular dynamics (MD) simulations have demonstrated that graphdiyne (GDY) is a very suitable two-dimensional membrane for the separation of small molecules in a gas mixture of different species. However, quantum effects may play a role in the dynamics of these permeation processes when light molecules are the ones involved in the crossing of the GDY subnanometric pores. In this work we report rigorous quantum-mechanical calculations together with equivalent MD simulations of the transport of H2 molecules through a static GDY membrane, as a case study for the validity of the application to these problems of classical dynamics. The force fields employed are based on an improved Lennard-Jones formulation, with parameters optimized by means of accurate ab initio calculations. It is found that, although quantum effects are still significant at the temperatures of interest (between 250 and 350 K), MD simulations are able to reasonably reproduce the dependence of the quantum permeances with the temperature. Moreover, MD permeances computed with quantum corrections through Feynman-Hibbs effective potentials provide a lower bound to quantum permeances, while the pure classical counterpart gives an upper bound, thus leading to a well delimited range of confidence of the permeation results. Furthermore, within MD simulations it is possible to incorporate the thermal motion of the GDY layer and in this situation it is observed an enhancement of the permeances with respect to the fixed membrane case, due to a significant reduction of the permeation barriers when the GDY atoms are allowed to vibrate. It seems apparent therefore, that modeling the membrane motion is crucial to provide reliable simulations of the gas transport features.

Figures (8)

• Figure 1: (a) Simulation box for MD simulations, with H$_2$ molecules represented as point particles. Note that, to save space, its height and number of molecules is half of the box actually used in the MD calculations. (b) and (c) Lateral view of the GDY membrane for fixed- and deformable-membrane simulations, respectively.
• Figure 2: Upper panel: H$_2$-C pair potential (meV) vs. intermolecular distance (Å). The ILJ potential (Eq. \ref{['EqILJ']}) is shown in black line, while red lines and red open circles are used for the ILJFH at 250 K (Eq. \ref{['EqFH2']}) and its fit to a ILJ formula, respectively. The inset presents a zoom of the region below 3 Å. Lower panel: Profile of the H$_2$-GDY interaction potential (meV) along $z$ (Å), the direction perpendicular to the membrane plane, crossing the center of a pore. In black line, bare ILJ force field, whereas the ILJFH potentials are shown in red and green lines, for 250 and 350 K, respectively. The inset shows the GDY unit cell, with the center of a pore at $(x,y,z)=(0,0,0)$.
• Figure 3: Quantum probabilities for the transmission of H$_2$ across GDY, as functions of the total incident energy (meV) and for different incident parallel velocities, $(v_{l_x},v_{l_y})$ (Eq. \ref{['Eq-parvel']}), labeled by $(l_x,l_y)$ in the legend.
• Figure 4: Hydrogen molecules distribution at T = 300 K for MD simulations considering ILJ+AIREBO interactions and both fixed and deformable membranes.
• Figure 5: Average number of crossings through fixed GDY as a function of time for each of the simulated temperatures, considering ILJFH interactions.