Spectral mapping of heat transfer mechanisms at liquid-solid interfaces

Thermal transport through liquid-solid interfaces plays an important role in many chemical and biological processes, and better understanding of liquid-solid energy transfer is expected to enable improving the efficiency of thermally driven applications. We determine the spectral distribution of thermal current at liquid-solid interfaces from nonequilibrium molecular dynamics, delivering a detailed picture of the contributions of different vibrational modes to liquid-solid energy transfer. Our results show that surface modes located at the Brillouin zone edge and polarized along the liquid-solid surface normal play a crucial role in liquid-solid energy transfer. Strong liquid-solid adhesion allows also for the coupling of in-plane polarized modes in the solid with the liquid, enhancing the heat-transfer rate and enabling efficient energy transfer up to the cutoff frequency of the solid. Our results provide fundamental understanding of the energy-transfer mechanisms in liquid-solid systems and enable detailed investigations of energy transfer between, e.g., water and organic molecules.

Figure 1

(a) Schematic illustration of the studied system: Lennard-Jones liquid sandwiched between two Lennard-Jones solids arranged in a face-centered cubic lattice. The spectral heat current $q_{\text{l}\to \text{s}}\left(\omega \right)$ is calculated at the solid-liquid interfaces by monitoring the force and velocity trajectories of the atoms located within the potential cutoff distance from the liquid. (b) Typical temperature profile in the nonequilibrium simulation. The spectral conductance is defined as $g\left(\omega \right)=|q_{\text{l}\to \text{s}}\left(\omega \right)|/\mathrm{\Delta }{T}_s$, where $\mathrm{\Delta }{T}_s$ is the temperature jump at the surface.

Figure 2

Spectral interface conductance $g\left(\omega \right)=\left|q\left(\omega \right)\right|/\mathrm{\Delta }{T}_s$ at the left and right liquid-solid interfaces versus frequency. For reference, also the spectrally decomposed bulk conductivity of the solid is shown.

Figure 3

(a) Wave-vector-decomposed spectral heat flux and (b) interfacial density of states versus wave vector and frequency at the solid-liquid interface (arbitrary units, brighter colors correspond to larger values). (c) Wave-vector-decomposed spectral heat flux and (d) interfacial density of states in the bulk solid. The surface mode labeled as A in (a) and located on the Brillouin zone boundary $\overline{\text{X}}\text{−}\overline{\text{M}}$ contributes strongly to the interfacial conductance at $f\approx 2.3$ THz. Surface mode labeled B has, on the other hand, smaller effect on energy transfer due to its in-plane polarization. Figures have been calculated for a $20\times 20$ cross-section to improve the wave-vector resolution compared to the $8\times 8$ cross-section used in other calculations.

Figure 4

Spectral conductance at the left liquid-solid interface for various liquid-solid interaction parameters ${\varepsilon }_{\mathrm{ls}}$. The shaded regions denote the contribution of forces and velocities oriented along the $x$ coordinate (normal to the liquid-solid surface) to the total conductance [Eq. (8)].

Figure 5

(a) Spectral conductance $g\left(\omega \right)$ at the left interface for various lengths of the liquid at $T=150$ K and $P=50$ MPa. (b) Spectral conductance for various numbers of unit cells in the cross-section.

Figure 6

Spectral heat current $q\left(\omega \right)$ inside the solid in the immediate vicinity of the interface, compared to the current at the solid-liquid interface. In the labeling of heat currents in the solid, the first unit cell (u.c.) refers to the two solid monolayers closest to the liquid, second unit cell refers to the third and fourth monolayers away from the interface, etc.

Figure 7

(a) Spectral conductance $g\left(\omega \right)$ at the left liquid-solid interface for different pressures $P$. (b) Vibrational spectrum in the liquid in the three cases.

Figure 8

(a) Spectral heat current $q\left(\omega \right)$ at the left liquid-solid interface for different liquid atom masses $m_{\text{liquid}}$. (b) Vibrational spectrum in the liquid in the three cases. While the calculation of vibrational density of states in the solid would require normalizing $S\left(\omega \right)$ by the atomic mass, we have not carried out this normalization for the liquid in order to highlight the effect of liquid mass on diffusion constant [proportional to $S(\omega =0)]$.