Lennard-Jones potential fluctuations

Dispersion forces are attractive forces between atoms at close distances. Even molecules with no permanent dipole moment have, due to the movement of their electrons, local dipole moments which induce dipoles in the opposite molecule, leading to fluctuating electrostatic attractions. At a closer distance repulsive forces develop due to an unfavorable overlap of the van der Waals spheres of both molecules. These relationships are typically described by the Lennard Jones potential, with an r attractive term and an r repulsive term (Figure 2) [59, 116]. Dipole-dipole interactions and dispersion forces are much weaker than other electrostatic interactions. Nevertheless, if there is a close contact between both molecules over a relatively large surface area, they may sum up to large values of overall interaction energies. 

The Lennard-Jones potential includes a strongly repelling term proportional to which represents the excluded volume by an atom, and a long attractive tail of the form — l/rif, which models the effect of attractive interactions between induced dipoles due to fluctuating charge distributions. This potential provides reasonable simulation results for the properties of liquid argon. The parameters dij and Sij, the effective diameter and the depth of the potential well between different atoms, can be calculated by using the combination rules since... 

In this case the first two sums contain contributions describing pairwise additive atom-atom interactions due to repulsion at short distances and dispersion attraction at large distances. The latter follows from a perturbative treatment of the fluctuations 1). The Lennard-Jones potential is... 

Nonbonded interactions are typically modeled as electrostatic interactions between partial charges on the atoms, London dispersion forces due to correlated fluctuations of the electronic clouds of the atoms, and exclusion forces at short distances. They depend on the distance between the atoms / y = r, — tj, and are represented as a sum of Coulomb and Lennard-Jones potentials. 

Particles can be assigned partial charges or integer values in the case of ions. The second type of non-honded interactions corresponds to dispersion or van der Waals forces. These are the interactions between atoms that arise from (quantum) fluctuations of the electronic charge densities. Both these interactions are represented in a second term for non-bonded interactions, for which the use of the Lennard-Jones potential has become a standard procedure in MD simulations. 

Physisorption or physical adsorption is the mechanism by which hydrogen is stored in the molecular form, that is, without dissociating, on the surface of a solid material. Responsible for the molecular adsorption of H2 are weak dispersive forces, called van der Waals forces, between the gas molecules and the atoms on the surface of the solid. These intermolecular forces derive from the interaction between temporary dipoles which are formed due to the fluctuations in the charge distribution in molecules and atoms. The combination of attractive van der Waals forces and short range repulsive interactions between a gas molecule and an atom on the surface of the adsorbent results in a potential energy curve which can be well described by the Lennard-Jones Eq. (2.1). 

Molecular dynamics simulations entail integrating Newton s second law of motion for an ensemble of atoms in order to derive the thermodynamic and transport properties of the ensemble. The two most common approaches to predict thermal conductivities by means of molecular dynamics include the direct and the Green-Kubo methods. The direct method is a non-equilibrium molecular dynamics approach that simulates the experimental setup by imposing a temperature gradient across the simulation cell. The Green-Kubo method is an equilibrium molecular dynamics approach, in which the thermal conductivity is obtained from the heat current fluctuations by means of the fluctuation-dissipation theorem. Comparisons of both methods show that results obtained by either method are consistent with each other [55]. Studies have shown that molecular dynamics can predict the thermal conductivity of crystalline materials [24, 55-60], superlattices [10-12], silicon nanowires [7] and amorphous materials [61, 62]. Recently, non-equilibrium molecular dynamics was used to study the thermal conductivity of argon thin films, using a pair-wise Lennard-Jones interatomic potential [56]. 

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