Modeling Interactions between Graphene and Heterogeneous Molecules

Abstract

The Lennard–Jones potential and a continuum approach can be used to successfully model interactions between various regular shaped molecules and nanostructures. For single atomic species molecules, the interaction can be approximated by assuming a uniform distribution of atoms over surfaces or volumes, which gives rise to a constant atomic density either over or throughout the molecule. However, for heterogeneous molecules, which comprise more than one type of atoms, the situation is more complicated. Thus far, two extended modeling approaches have been considered for heterogeneous molecules, namely a multi-surface semi-continuous model and a fully continuous model with average smearing of atomic contribution. In this paper, we propose yet another modeling approach using a single continuous surface, but replacing the atomic density and attractive and repulsive constants in the Lennard–Jones potential with functions, which depend on the heterogeneity across the molecules, and the new model is applied to study the adsorption of coronene onto a graphene sheet. Comparison of results is made between the new model and two other existing approaches as well as molecular dynamics simulations performed using the LAMMPS molecular dynamics simulator. We find that the new approach is superior to the other continuum models and provides excellent agreement with molecular dynamics simulations.

Continuum Modeling with Functional Lennard-Jones Parameters for Methane Storage inside Various Carbon Nanostructures

“…According to Stevens et al, 37 the interaction energy E between methane and a homogeneous nanostructure can be evaluated by where η i is the atomic density of a given molecule in the interaction and K n ( n = 3, 6) is the integral defined by where ρ is the Euclidean distance between two molecules, d S is the surface element of the carbon nanostructure, and d V is the volume element of the methane molecule, which has the standard Cartesian representation ( ar sin ϕ cos θ, ar sin ϕ sin θ, ar cos ϕ), where r ∈ [0, 1], θ ∈ [0, 2π], and ϕ ∈ [0, π] are three variables parametrizing the sphere. The functions f n for n = 3 and 6 are interaction functions representing the attractive and repulsive coefficients of the Lennard-Jones potential, respectively.…”

“…Using the interaction functions has the twofold benefit of accounting for the heteronuclear nature of methane and maintaining a fully continuous approximation of the molecule, allowing for a single expression to determine the potential energy between methane and the carbon nanostructure. As discussed in Stevens et al, 37 we assume that f 3 ( r ) = A ( r ) and f 6 ( r ) = B ( r ) and that they follow a sigmoidal profile, where a stronger interaction is found in the inner region, due to the carbon–carbon interaction with the nanostructure, and a weaker interaction is toward the surface of the molecule, due to the hydrogen–carbon interaction. Here, we assume that the sigmoidal function has the form α arctan( m ( r 0 – r )) + β, where α and β for A ( r ) and B ( r ) can be found, respectively, from the conditions A (0) = A C–C , A ( a ) = A C–H , B (0) = B C–C , and B ( a ) = B C–H , where the attractive and repulsive constants for carbon–carbon (C–C) and carbon–hydrogen (C–H) are given in Table 1 .…”

“…For methane–nanotube and coronene–nanotube interactions, Stevens et al 37 demonstrate that applying a homogeneous approximation to a heterogeneous molecule can lead to inaccurate results, particularly at small intermolecular distances. Furthermore, results from Stevens et al’s 36 continuous model of methane encapsulated within a carbon nanotube show better agreement with molecular dynamics simulations than that of the semicontinuous approach used by Adisa et al 39 As such, this paper applies the continuous model assuming methane as a whole sphere of varying interaction strength 36 to study the problems presented by Adisa et al., 40 − 42 which are methane encapsulated in a fullerene, methane within a nanotube bundle, and methane entering an open nanocone.…”

Continuum Modelling for Encapsulation of Anticancer Drugs inside Nanotubes

“…Moreover, the atom at point Q is assumed to have coordinates (β, 0, 0), where 0 ≤ β < c; thus, the distance ρ from a typical surface element of the nanotube surface to point Q may given by ρ 2 = (c − β) 2 + 4βc sin 2 (ω/2) + z 2 . The continuum approach assumes that the atoms are uniformly distributed throughout the volume or over the surface of the molecule, and the molecular interatomic interaction energy is determined through integration over the volume or surface of each molecule [31]. Thus, the energies interacting between the nanotube and the atom at point Q can be obtained by carrying out a surface integral equation of the Lennard-Jones function over the surface of the nanotube, namely…”

On the Consistency of the Exfoliation Free Energy of Graphenes by Molecular Simulations

“…The material is used to produce graphene-based composites or films, a key requirement for applications such as thin-film transistors, conductive transparent electrodes, photovoltaics and biomedical implants [13][14][15]. The availability of high-quality graphene samples has increased the interest for explicit molecular simulations of the exfoliation processes and relevant applications [16][17][18][19].…”