Ab Initio Molecular Dynamics and Lattice Dynamics-Based Force Field for Modeling Hexagonal Boron Nitride in Mechanical and Interfacial Applications

Hexagonal boron nitride (hBN) is an up-and-coming two-dimensional material, with applications in electronic devices, tribology, and separation membranes. Herein, we utilize density-functional-theory-based ab initio molecular dynamics (MD) simulations and lattice dynamics calculations to develop a classical force field (FF) for modeling hBN. The FF predicts the crystal structure, elastic constants, and phonon dispersion relation of hBN with good accuracy and exhibits remarkable agreement with the interlayer binding energy predicted by random phase approximation calculations. We demonstrate the importance of including Coulombic interactions but excluding 1–4 intrasheet interactions to obtain the correct phonon dispersion relation. We find that improper dihedrals do not modify the bulk mechanical properties and the extent of thermal vibrations in hBN, although they impact its flexural rigidity. Combining the FF with the accurate TIP4P/Ice water model yields excellent agreement with interaction energies predicted by quantum Monte Carlo calculations. Our FF should enable an accurate description of hBN interfaces in classical MD simulations

Generalized Mechanistic Model for the Chemical Vapor Deposition of 2D Transition Metal Dichalcogenide Monolayers

Transition metal dichalcogenides (TMDs) like molybdenum disulfide (MoS₂) and tungsten disulfide (WS₂) are layered materials capable of growth to one monolayer thickness <i>via</i> chemical vapor deposition (CVD). Such CVD methods, while powerful, are notoriously difficult to extend across different reactor types and conditions, with subtle variations often confounding reproducibility, particularly for 2D TMD growth. In this work, we formulate the first generalized TMD synthetic theory by constructing a thermodynamic and kinetic growth mechanism linked to CVD reactor parameters that is predictive of specific geometric shape, size, and aspect ratio from triangular to hexagonal growth, depending on specific CVD reactor conditions. We validate our model using experimental data from Wang <i>et al.</i> (<i>Chem. Mater.</i> <b>2014</b>, <i>26</i>, 6371−6379) that demonstrate the systemic evolution of MoS₂ morphology down the length of a flow CVD reactor where variations in gas phase concentrations can be accurately estimated using a transport model (<i>C</i>_Sulfur = 9–965 μmol/m³; <i>C</i>_MoO3 = 15–16 mmol/m³) under otherwise isothermal conditions (700 °C). A stochastic model which utilizes a site-dependent activation energy barrier based on the intrinsic TMD bond energies and a series of Evans–Polanyi relations leads to remarkable, quantitative agreement with both shape and size evolution along the reactor. The model is shown to extend to the growth of WS₂ at 800 °C and MoS₂ under varied process conditions. Finally, a simplified theory is developed to translate the model into a “kinetic phase diagram” of the growth process. The predictive capability of this model and its extension to other TMD systems promise to significantly increase the controlled synthesis of such materials

Quantitative Modeling of MoS₂–Solvent Interfaces: Predicting Contact Angles and Exfoliation Performance using Molecular Dynamics

The large-scale synthesis of molybdenum disulfide (MoS₂) using liquid-phase exfoliation, as well as several of its intended applications, including desalination membranes and biosensors, involve liquids coming into intimate contact with MoS₂ surfaces. Molecular dynamics (MD) simulations offer a robust methodology to investigate nanomaterial/liquid interactions involving weak van der Waals forces. However, MD force fields for MoS₂ currently available in the literature incorrectly describe not only the cohesive interactions between layers of MoS₂ but also the adhesive interactions of MoS₂ with liquids such as water. Here, we develop a set of force-field parameters that reproduce the properties of bulk 2H-MoS₂, with special attention to the distinction between the covalent, intralayer terms and the noncovalent, interlayer Coulombic and van der Waals interactions. The resulting force field is compatible with MD force fields for liquids and can correctly describe interactions at MoS₂–liquid interfaces, yielding excellent agreement with experimental contact angles for water (a polar solvent) and diiodomethane (a nonpolar solvent). In light of these results, previously published simulations studies on the desalination potential and biocompatibility of MoS₂ devices need to be reevaluated. Potential of mean force (PMF) calculations demonstrate that use of our new force field can explain the current selection of solvents used in experimental studies of the liquid-phase exfoliation of MoS₂ flakes, including the colloidal stability of the resulting dispersion. Our new force field enables an accurate description of MoS₂ interfaces and will hopefully pave the way for simulation-aided design in applications including membranes, microfluidic devices, and sensors

Mechanism and Prediction of Gas Permeation through Sub-Nanometer Graphene Pores: Comparison of Theory and Simulation

Due to its atomic thickness, porous graphene with sub-nanometer pore sizes constitutes a promising candidate for gas separation membranes that exhibit ultrahigh permeances. While graphene pores can greatly facilitate gas mixture separation, there is currently no validated analytical framework with which one can predict gas permeation through a given graphene pore. In this work, we simulate the permeation of adsorptive gases, such as CO₂ and CH₄, through sub-nanometer graphene pores using molecular dynamics simulations. We show that gas permeation can typically be decoupled into two steps: (1) adsorption of gas molecules to the pore mouth and (2) translocation of gas molecules from the pore mouth on one side of the graphene membrane to the pore mouth on the other side. We find that the translocation rate coefficient can be expressed using an Arrhenius-type equation, where the energy barrier and the pre-exponential factor can be theoretically predicted using the transition state theory for classical barrier crossing events. We propose a relation between the pre-exponential factor and the entropy penalty of a gas molecule crossing the pore. Furthermore, on the basis of the theory, we propose an efficient algorithm to calculate CO₂ and CH₄ permeances per pore for sub-nanometer graphene pores of any shape. For the CO₂/CH₄ mixture, the graphene nanopores exhibit a trade-off between the CO₂ permeance and the CO₂/CH₄ separation factor. This upper bound on a Robeson plot of selectivity <i>versus</i> permeance for a given pore density is predicted and described by the theory. Pores with CO₂/CH₄ separation factors higher than 10² have CO₂ permeances per pore lower than 10^–22 mol s^–1 Pa^–1, and pores with separation factors of ∼10 have CO₂ permeances per pore between 10^–22 and 10^–21 mol s^–1 Pa^–1. Finally, we show that a pore density of 10¹⁴ m^–2 is required for a porous graphene membrane to exceed the permeance-selectivity upper bound of polymeric materials. Moreover, we show that a higher pore density can potentially further boost the permeation performance of a porous graphene membrane above all existing membranes. Our findings provide insights into the potential and the limitations of porous graphene membranes for gas separation and provide an efficient methodology for screening nanopore configurations and sizes for the efficient separation of desired gas mixtures

Fabrication, Pressure Testing, and Nanopore Formation of Single-Layer Graphene Membranes

Single-layer graphene (SLG) membranes have great promise as ultrahigh flux, high selectivity membranes for gas mixture separations due to their single atom thickness. It remains a central question whether SLG membranes of a requisite area can exist under an imposed pressure drop and temperatures needed for industrial gas separation. An additional challenge is the development of techniques to perforate or otherwise control the porosity in graphene membranes to impart molecularly sized pores, the size regime predicted to produce high gas separation factors. Herein, we report fabrication, pressure testing, temperature cycling, and gas permeance measurements through free-standing, low defect density SLG membranes. Our measurements demonstrate the remarkable chemical and mechanical stability of these 5 μm diameter suspended SLG membranes, which remain intact over weeks of testing at pressure differentials of >0.5 bar, repeated temperature cycling from 25 to 200 °C, and exposure to 15 mol % ozone for up to 3 min. These membranes act as molecularly impermeable barriers, with very low or near negligible background permeance. We also demonstrate a 1077 °C temperature O₂ etching technique to create nanopores on the order of ∼1 nm diameter as imaged by scanning tunneling microscopy, although transport through such pores has not yet been successfully measured. Overall, these results represent an important advancement that will enable graphene gas separation membranes to be fabricated, tested, and modified <i>in situ</i> while maintaining remarkable mechanical and thermal stability