With increasing interest in nanotechnology the question arises of how heat is exchanged between materials separated by only a few nanometers of vacuum. Here we present calculations of the contribution of phonons to heat transfer mediated by van der Waals forces and compare the results to other mechanisms such as coupling through near field fluctuations. Our results show a more dramatic decay with separation than previous work. PACS number(s): 44.40.+a, 78.20.Ci

Though the dependence of near-field radiative transfer on the gap between two planar objects is well understood, that between curved objects is still unclear. We show, based on the analysis of the surface polariton mediated radiative transfer between two spheres of equal radii R and minimum gap d, that the near-field radiative transfer scales as R/d as d/R → 0 and as ln (R/d) for larger values of d/R up to the far-field limit. We propose a modified form of the proximity approximation to predict near-field radiative transfer between curved objects from simulations of radiative transfer between planar surfaces.

Phonon transport across a silicon/vacuum-gap/silicon structure is modeled using lattice dynamics calculations and Landauer theory. The phonons transmit thermal energy across the vacuum gap via atomic interactions between the leads. Because the incident phonons do not encounter a classically impenetrable potential barrier, this mechanism is not a tunneling phenomenon. While some incident phonons transmit across the vacuum-gap and remain in their original mode, many are annihilated and excite different modes. We show that the heat flux due to phonon transport can be four orders of magnitude larger than that due to photon transport predicted from near-field radiation theory.

Near-field radiative transfer between two objects can be computed using Rytov's theory of fluctuational electrodynamics in which the strength of electromagnetic sources is related to temperature through the fluctuation-dissipation theorem, and the resultant energy transfer is described using the dyadic Green's function of the vector Helmholtz equation. When the two objects are spheres, the dyadic Green's function can be expanded in a series of vector spherical waves. Based on comparison with the convergence criterion for the case of radiative transfer between two parallel surfaces, we derive a relation for the number of vector spherical waves required for convergence in the case of radiative transfer between two spheres. We show that when electromagnetic surface waves are active at a frequency the number of vector spherical waves required for convergence is proportional to Rmax/d when d/Rmax → 0, where Rmax is the radius of the larger sphere, and d is the smallest gap between the two spheres. This criterion for convergence applies equally well to other near-field electromagnetic scattering problems.

We compute near-field radiative transfer between two spheres of unequal radii R1 and R2 such that R2 ≲ 40R1. For R2 = 40R1, the smallest gap to which we have been able to compute radiative transfer is d = 0.016R1. To accomplish these computations, we have had to modify existing methods for computing near-field radiative transfer between two spheres in the following ways: (1) exact calculations of coefficients of vector translation theorem are replaced by approximations valid for the limit d ≪ R1, and (2) recursion relations for a normalized form of translation coefficients are derived which enable us to replace computations of spherical Bessel and Hankel functions by computations of ratios of spherical Bessel or spherical Hankel functions. The results are then compared with the predictions of the modified proximity approximation.

Phonons (collective atomic vibrations in solids) are more effective in transporting heat than photons. This is the reason why the conduction mode of heat transport in nonmetals (mediated by phonons) is dominant compared to the radiation mode of heat transport (mediated by photons). However, since phonons are unable to traverse a vacuum gap (unlike photons), it is commonly believed that two bodies separated by a gap cannot exchange heat via phonons. Recently, a mechanism was proposed [J. B. Pendry, K. Sasihithlu, and R. V. Craster, Phys. Rev. B 94, 075414 (2016)] by which phonons can transport heat across a vacuum gap -through the Van der Waals interaction between two bodies with gap less than the wavelength of light. Such heat transfer mechanisms are highly relevant for heating (and cooling) of nanostructures; the heating of the flying heads in magnetic storage disks is a case in point. Here, the theoretical derivation for modelling phonon transmission is revisited and extended to the case of two bodies made of different materials separated by a vacuum gap. Magnitudes of phonon transmission, and hence the heat transfer, for commonly used materials in the micro-and nano-electromechanical industry are calculated and compared with the calculation of conduction heat transfer through air for small gaps as well as the heat transfer calculation due to photon exchange.

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In this theoretical study, a disordered metamaterial coating with randomly embedded TiO2 dielectric microspheres in a polydimethylsiloxane matrix has been designed for the purpose of daytime passive radiative cooling. While retaining the necessary optical properties of high reflectivity (≈94%) in the solar spectrum and high emissivity (≈96%) in the atmospheric transparency window, the coating exhibits the following additional desirable properties: (a) low volume fraction of TiO2 microspheres, ensuring minimal possibility of agglomeration of particles during fabrication; and (b) a cooling power of 81.8 W/m2, which is among the highest for similar coatings that have been developed. We also show how a modified form of Kubelka–Munk theory with empirical relations originally developed to analyze optical scattering in biological tissue layers can be used for designing radiative cooling structures. The predictions from this method have been validated using Monte Carlo simulations. It is expected that this study will motivate further similar designs in the rapidly expanding market for effective and easy-to-fabricate coatings for daytime passive radiative cooling applications.