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

TL;DR

This work tackles the intrinsic thermal impedance at liquid/solid interfaces by performing non-equilibrium molecular dynamics on 180 Lennard-Jones S/L/S systems. It reveals two robust power-law scalings for the thermal slip length $L_T$: one controlled by the in-plane translational order in the contact layer via $S^ extparallel_{ ext{max}}$, and another by the vibrational coupling via the frequency ratio $\nu_S/\nu_L$, with data collapsing when scaled by the contact-layer temperature $T_c$ and LJ length scale $\sigma_{LS}$. The findings emphasize the role of surface phonons in mediating cross-boundary heat transfer and show that master curves can describe $L_T$ across varied interfacial chemistries within LJ-type systems. These results offer a path toward analytic models of interfacial thermal impedance and motivate experimental probes of contact-layer structure and vibrational spectra, despite the inherent measurement challenges.

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.

Figures (9)

• Figure 1: Illustration of the thermal slip length $L_T= \Delta T/|dT/dz|_{liq}$.
• Figure 2: (a) Layered geometry of entire computational cell. Scalings of variables and layer dimensions for the geometry can be found in Tables \ref{['tbl:dimlessunits']} and \ref{['tbl:slablengths']}. Coordinate origin $z=0$ was situated at the midplane of the liquid layer. (b) FCC crystal unit cell with lattice constant 1.560 (reduced units) showing [001] facet plane (red). For all runs, the surface normal to the [001] plane was oriented parallel to the thermal flux vector $J_z$.
• Figure 3: Increase in thermal flux $J_z$ with increasing $T_\textrm{source}-T_\textrm{sink}$, increasing $\varepsilon_{LS}$ and decreasing $\sigma_{LS}$. Connector lines are a guide to the eye.
• Figure 4: (a) - (c) Reduction in the temperature jump $\Delta T$ at the hotter (H) and colder (C) L/S interface for smaller differential $T_\textrm{source} - T_\textrm{sink}$, smaller $\sigma_{LS}$ or larger $\varepsilon_{LS}$. Connector lines are a guide to the eye.
• Figure 5: (a) - (c) Reduction in the thermal slip length $L_T$ at the hotter (H) and colder (C) L/S interface with increasing value $\varepsilon_{LS}$ and decreasing value $\sigma_{LS}$.