Power Laws for the Thermal Slip Length of a Liquid/Solid Interface From the Structure and Frequency Response of the Contact Zone

Abstract

The newest and most powerful electronic chips for applications like artificial intelligence generate so much heat that liquid based cooling has become indispensable to prevent breakdown from thermal runaway effects. While cooling schemes like microfluidic networks or liquid immersion are proving effective for now, further progress requires tackling an age old problem, namely the intrinsic thermal impedance of the liquid/solid (L/S) interface, quantified either by the thermal boundary resistance or thermal slip length. While there exist well known models for estimating bounds on the thermal impedance of a superfluid/metal interface, no analytic models nor experimental data are available for normal liquid/solid interfaces. Researchers therefore rely on non-equilibrium molecular dynamics simulations to gain insight into phonon transfer at the L/S interface. Here we explore correlated order and motion within the L/S contact zone in an effort to extract general scaling relations for the thermal slip length in Lennard-Jones (LJ) systems. We focus on the in-plane structure factor and dominant vibrational frequency of the first solid and liquid layer for 180 systems. When scaled by the temperature of the liquid contact layer and characteristic LJ interaction distance, the data collapse onto two power law equations, one quantifying the reduction in thermal impedance from enhanced in-plane translational order and the other from enhanced frequency matching in the contact zone. More generally, these power law relations highlight the critical role of surface acoustic phonons, an area of focus which may prove more useful to development of analytic models and instrumentation for validating the relations proposed.