We study the thermal conductance across solid-solid interfaces as the composition of an intermediate matching layer is varied. In absence of phonon-phonon interactions, an added layer can make the interfacial conductance increase or decrease depending on the interplay between (1) an increase in phonon transmission due to better bridging between the contacts, and (2) a decrease in the number of available conduction channels that must conserve their momenta transverse to the interface.When phonon-phonon interactions are included, the added layer is seen to aid conductance when the decrease in resistances at the contact-layer boundaries compensate for the additional layer resistance. For the particular systems explored in this work, the maximum conductance happens when the layer mass is close to the geometric mean of the contact masses. The surprising result, usually associated with coherent antireflection coatings, follows from a monotonic increase in the boundary resistance with the interface mass ratio. This geometric mean condition readily extends to a compositionally graded interfacial layer with an exponentially varying mass that generates the thermal equivalent of a broadband impedance matching network. * cap3fe@virginia.edu † Carlos A. Polanco and Rouzbeh Rastgarkafshgarkolaei contributed equally to this work. ‡ ag7rq@virginia.edu

We propose a strategy to potentially best enhance interfacial thermal transport through solid–solid interfaces by adding nano-engineered, exponentially mass-graded intermediate layers.

We present the results of classical molecular dynamics simulations to assess the relative contributions to interfacial thermal conductance from inelastic phonon processes at the interface and in the adjacent bulk materials. The simulated system is the prototypical interface between argon and "heavy argon" crystals, which enables comparison with many past computational studies. We run simulations interchanging the Lennard-Jones potential with its harmonic approximation to test the effect of anharmonicity on conductance.The results confirm that the presence of anharmonicity is correlated with increasing thermal conductance with temperature, which supports conclusions from prior experimental and theoretical work. However, in the model Ar/heavy-Ar system, anharmonic effects at the interface itself contribute a surprisingly small part of the total thermal conductance. The larger fraction of the thermal conductance at high temperatures arises from anharmonic effects away from the interface. These observations are supported by comparisons of the spectral energy density, which suggest that bulk anharmonic processes increase interfacial conductance by thermalizing energy from modes with low transmission to modes with high transmission.

We argue that the relative thermal conductance between interfaces with different morphologies is controlled by crystal structure through M min /M c > 1, the ratio between the minimum mode count on either side M min , and the conserving modes M c that preserve phonon momentum transverse to the interface. Junctions with an added homogenous layer, "uniform", and "abrupt" junctions are limited to M c while junctions with interfacial disorder, "mixed", exploit the expansion of mode spectrum to M min . In our studies with cubic crystals, the largest enhancement of conductance from "abrupt" to "mixed" interfaces seems to be correlated with the emergence of voids in the conserving modes, where M c = 0. Such voids typically arise when the interlayer coupling is weakly dispersive, making the bands shift rigidly with momentum. Interfacial mixing also increases alloy scattering, which reduces conductance in opposition with the mode spectrum expansion. Thus the conductance across a "mixed" junction does not always increase relative to that at a "uniform" interface. * cap3fe@virginia.edu

Phase change materials such as n-alkanes that exhibit desirable characteristics such as high latent heat, chemical stability, and negligible supercooling are widely used in thermal energy storage applications. However, n-alkanes have the drawback of low thermal conductivity values. The low thermal conductivity of n-alkanes is linked to formation of randomly oriented nano-domains of molecules in their solid structure that is responsible for excessive phonon scattering at the grain boundaries. Thus, understanding the thermal boundary conductance at the grain boundaries can be crucial for improving the effectiveness of thermal storage systems. The concept of the ideal crystal is proposed in this paper, which describes a simplified model such that all the nano-domains of long-chain n-alkanes are artificially aligned perfectly in one direction. In order to study thermal transport of the ideal crystal of long-chain n-alkanes, four (4) systems (C20H42, C24H50, C26H54, and C30H62) are investigated by the molecular dynamics simulations. Thermal boundary conductance between the layers of ideal crystals is determined using both non-equilibrium molecular dynamics (NEMD) and equilibrium molecular dynamics (EMD) simulations. Both NEMD and EMD simulations exhibit no significant change in thermal conductance with the molecular length. However, the values obtained from the EMD simulations are less than the values from NEMD simulations with the ratio being nearly three (3) in most cases. This difference is due to the nature of EMD simulations where all the phonons are assumed to be in equilibrium at the interface. Thermal conductivity of the n-alkanes in three structures including liquid, solid, and ideal crystal is investigated utilizing NEMD simulations. Our results exhibit a very slight rise in thermal conductivity values as the number of carbon atoms of the chain increases. The key understanding is that thermal transport can be significantly altered by how the molecules and the nano-domains are oriented in the structure rather than by the length of the n-alkane molecules.