Molecular Dynamics of Heat Transfer and Quantum Mechanics

Molecular Dynamics (MD) is used in computational heat transfer to determine the thermal response of nanostructures. Finding basis in classical statistical mechanics, MD relates the thermal energy of the atom to its momentum by the equipartition theorem. Momenta of atoms in an ensemble are determined by solving Newton’s equations with inter-atomic forces derived from Lennard-Jones potentials. Statistical mechanics always assumes the atom has thermal energy, or equivalently the capacity to absorb heat. Otherwise, the temperature of the atoms cannot be related to its thermal energy, the consequence of which is atoms in nanostructures have the same heat capacity as those at the macroscale. For bulk materials, MD heat transfer is performed for an ensemble of atoms in submicron computation boxes under periodic boundary conditions. Consistent with statistical mechanics, MD simulations of the bulk are valid because atoms having heat capacity in discrete submicron boxes under periodic boundary conditions are equivalent to those in the bulk that do indeed have heat capacity. Quantum mechanics (QM) differs. Unlike MD simulations of the bulk with atoms having heat capacity, QM precludes atoms in discrete nanostructures from having heat capacity. Nevertheless, the literature is replete with MD simulations of discrete nanostructures with atoms having heat capacity. Although consistent with statistical mechanics, MD of discrete nanostructures is invalid by QM. By QM, atoms in discrete nanostructures lacking heat capacity cannot conserve heat by an increase in temperature, and therefore the classical modes of heat transfer – convection, radiation, and conduction that depend on temperature have no meaning. Instead, conservation at the nanoscale proceeds by the creation of non-thermal QED induced EM radiation that charges the discrete nanostructures by the photoelectric effect, or is emitted to the surroundings. QED stands for quantum electrodynamics and EM for electromagnetic. Examples of MD simulations are presented that by QM are valid or invalid and recommendations made for how invalid MD heat transfer of discrete nanostructures may be consistent with QM. For interacting nanostructures, MD heat transfer simulations consistent with QM are computationally intractable, and therefore finite element (FE) simulations are proposed using estimates of QED radiation from the nanostructures in programs such as ANSYS and COMSOL