Quasi-Casimir coupling induced phonon heat transfer across a vacuum gap

Highlights

• Heat exchange between two walls separated by a vacuum gap exists and enhances exponentially by narrowing the gap distance.

• Heat transfer across a sub-nanometer vacuum gap is owing to the thermal resonance induced by the quasi-Casimir coupling.

• Local heat flux at the interfacial layers increases singularly, showing the dependence of the strong thermal resonance.

Abstract

In vacuum, thermal energy is transported by photons (thermal radiation) but not phonons. Recent studies, however, indicated that phonon heat transfer across a vacuum gap is mediated by the quantum fluctuation of electromagnetic fields. Specifically, in the heat exchange between two objects separated by a nanoscale vacuum gap, phonons carry thermal energy more efficiently than photons. However, it remains unclear if phonons can propagate without electromagnetic fields. Here, we demonstrate that phonon transmission across a sub-nanometer vacuum gap can be induced by quasi-Casimir force subjected to the Lennard–Jones atoms using classical molecular dynamics simulation. The net heat flux across the vacuum gap increases exponentially as the gap distance decreases, owing to acoustic phonon transmission. The local heat flux, evaluated using the Irving–Kirkwood method, increases singularly at the interfacial layers, while that at the inner layers agrees well with the net heat flux. These findings provide evidence of the strong thermal resonance induced by quasi-Casimir coupling between the interfacial layers. Thus, we conclude that the quasi-Casimir coupling induced by intermolecular interaction is a heat transfer mode for phonon heat transfer across a vacuum gap in nanoscale.

Introduction

Nanoscale heat transfer has been a challenging research topic since last decade [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36]. The scale of the gap distance D dominates the heat transfer between two objects at different temperatures in vacuum, from the conventional heat conduction (D = 0) to thermal radiation (D > λ_T, Wien's wavelength λ_T $\cong$ 10⁻⁵ m at room temperature) [1]. As shown in Fig. 1, when the objects are separated by a gap of D < λ_T, known as the regime of the near-field radiative heat transfer (NFRHT), the amount of heat transfer can be several orders of magnitude greater than Planck's blackbody limit [2], [3], [4], [5], [6], [7]. Therefore, the NFRHT has attracted considerable interest in advanced applications of thermal management [8,9], radiative cooling [10,11], nanogap near-field thermophotovoltaics [12], and heat-assisted magnetic recording [13,14].

The thermal energy transported by the coupling between the electromagnetic waves of the heating object and the phonons or plasmons of the cooling object in the regime of NFRHT, has been explored using the fluctuating electrodynamics theory [15] and experiments [16], [17], [18]. In the regime of D < 10⁻⁷ m, the atomic Coulomb interaction between two polar nanoparticles dominates the NFRHT in the gap distance of 8–100 nm [19], while the phonons serve as effective thermal carriers between two objects separated by a nanometer vacuum gap [20], [21], [22], [23], [24], [25], [26], [27], [28]. In particular, phonon coupling in electric fields becomes significant in the transition regime from NFRHT to heat conduction. The existence of an extra tunnel for thermal energy transfer across a gap of 0–2.8 nm between two NaCl slabs was proposed due to phonon coupling induced by long-range Coulomb forces in the electric fields [29]. The acoustic phonons theoretically dominate the heat transfer across a gap of 1–5 nm between two Au surfaces applied a bias voltage of 0.6 V [30]. Furthermore, acoustic phonon transport has been experimentally observed in gaps ranging from 0 to 10 nm between a silicon tip and a platinum nano-heater under a bias voltage of 0.8 V [31]. However, clarifying the mechanism of the electric field assisted phonon transmission across a vacumm gap in this transition regime is still a challenging work.

On the other hand, Casimir heat transfer induced by resonance in electromagnetic fields was proposed in the transition regime from NFRHT to heat conduction. The Casimir force was first introduced in 1948 as a force acting between neutral objects based on quantum fluctuations of electromagnetic fields [32]. A local model of the dielectric function was applied to explain the phonon coupling mechanism induced by the Casimir force across a vacuum gap of D < 10 nm between two dielectric solids [33]. The quantum fluctuation has been found to resonantly enhance the heat exchange between two Si₃N₄ membranes at D < 400 nm in an electromagnetic field [34].

However, the phonon heat transfer due to the thermal resonance induced by quasi-Casimir coupling has never been verified without an electromagnetic field. To this end, in this study, a quasi-Casimir coupling model is proposed for phonon heat transfer between two parallel solid walls separated by a sub-nanometer vacuum gap in the absence of an electromagnetic field. The phonon heat transfer is investigated in systems by performing a classical molecular dynamics (MD) simulation to verify the quasi-Casimir coupling model. Consequently, we evidence the phonon heat transfer induced by the intermolecular interactive force across the vacuum gap with significant interfacial resonance.