Molecular Dynamics Simulations Of Heat Transfer Research Articles

Atomistic simulations, mesoscopic modeling, and theoretical analysis of thermal conductivity of bundles composed of carbon nanotubes

The propensity of carbon nanotubes (CNTs) to self-organize into continuous networks of bundles has direct implications for thermal transport properties of CNT network materials and defines the importance of clear understanding of the mechanisms and scaling laws governing the heat transfer within the primary building blocks of the network structures—close-packed bundles of CNTs. A comprehensive study of the thermal conductivity of CNT bundles is performed with a combination of non-equilibrium molecular dynamics (MD) simulations of heat transfer between adjacent CNTs and the intrinsic conductivity of CNTs in a bundle with a theoretical analysis that reveals the connections between the structure and thermal transport properties of CNT bundles. The results of MD simulations of heat transfer in CNT bundles consisting of up to 7 CNTs suggest that, contrary to the widespread notion of strongly reduced conductivity of CNTs in bundles, van der Waals interactions between defect-free well-aligned CNTs in a bundle have negligible effect on the intrinsic conductivity of the CNTs. The simulations of inter-tube heat conduction performed for partially overlapping parallel CNTs indicate that the conductance through the overlap region is proportional to the length of the overlap for CNTs and CNT-CNT overlaps longer than several tens of nm. Based on the predictions of the MD simulations, a mesoscopic-level model is developed and applied for theoretical analysis and numerical modeling of heat transfer in bundles consisting of CNTs with infinitely large and finite intrinsic thermal conductivities. The general scaling laws predicting the quadratic dependence of the bundle conductivity on the length of individual CNTs in the case when the thermal transport is controlled by the inter-tube conductance and the independence of the CNT length in another limiting case when the intrinsic conductivity of CNTs plays the dominant role are derived. An application of the scaling laws to bundles of single-walled (10,10) CNTs reveals that the transition from inter-tube-conductance-dominated to intrinsic-conductivity-dominated thermal transport in CNT bundles occurs in a practically important range of CNT length from ∼20 nm to ∼4 μm.

Unphysical Heat Transfer by Molecular Dynamics

Molecular Dynamics (MD) simulations based on classical statistical mechanics allow the atom to have thermal heat capacity. Quantum mechanics (QM) differs in that the heat capacity of atoms in submicron nanostructures vanishes. Nevertheless, MD simulations of heat transfer in discrete nanostructures are routlinely performed and abound in the literature. Not only are discrete MD sumultions invalid by QM, but give unphysical results, e.g., thermal conducitvity in nanofluids is found to exceed standard mixing rules while in solid metal films depends on thickness. QM explains the unphysical results by negating the heat capacity of atoms in discrete nanostructures, thereby precluding the usual conservation of absorbed electromagnetic (EM) energy by an increase in temperature. Instead, the absorbed EM energy is conserved by QED inducing the creation of non-thermal EM radiation inside the nanostructure that by the photoelectric effect creates charge in the nanostructure, or is emitted to the surroundings. QED stands for quantum electrodynamics. Unphysical results occur because the QED induced radiation is not included in the nanoscale heat balance, but if included the physical results for discrete nanostructures are found. Examples of unphysical MD simulatons are presented.

An analytical model for the thermal conductivity of silicon nanostructures

A simple model of thermal conductivity, based on the harmonic theory of solids, is used to study the heat transfer in nanostructures. The thermal conductivity is obtained by summing the contribution of all the vibration modes of the system. All the vibrational properties (dispersion curves and relaxation time) that are used in the model are obtained using the data for bulk samples. The size effect is taken into account through the sampling of the Brillouin zone and the distance that a wave vector can travel between two boundaries in the structure. The model is used to predict the thermal conductivity of silicon nanowires and nanofilms, and demonstrates a good agreement with experimental results. Finally, using this model, the quality of the silicon interatomic potential, used for molecular-dynamics simulations of heat transfer, is evaluated.