## 2 Interfacial Adhesion and Dispersion Forces  
Interfacial thermal conductance depends on the strength of interfacial adhesion. Adhesion forces can be divided into several types. Adhesion can be chemical, diffusive, and dispersive [17]. Chemical adhesion occurs when ionic, covalent, or hydrogen bonds are formed between the surface atoms of two bodies. Chemical forces act over very short sub-nanometer distances. Diffusive adhesion occurs when the materials can merge at an interface by diffusion. This very specific adhesion can take place when the molecules of the materials in contact are mobile and can diffuse into each other. Dispersive adhesion results from physical adsorption when two materials are attracted by long-range dispersion forces acting due to electromagnetic fluctuations [27; 28; 29]. Dispersion forces are known as electrodynamic or charge fluctuation forces. These forces contribute most to the overall van der Waals interaction of electrically neutral surfaces with nonpolar molecules. In fact, dispersion forces are the main cause of interfacial adhesion upon melting of metal particles on the surface of a solid. We will focus on the dispersion forces \(F(d)\) acting between parallel plates separated by a distance \(d\). Let \(p_{c}(d)=F(d)/S\) be the interfacial contact pressure associated with the dispersion force \(F(d)\), where \(S\) is the contact area. Dispersion forces are always present and play an important role both at short and long distances \(d\). It is the Lifshitz theory that provides an exhaustive description of the interfacial interaction caused by dispersion forces at an arbitrary distance \(d\) and for materials with arbitrary complex dielectric constants \(\varepsilon_{1}(\omega)\) and \(\varepsilon_{2}(\omega)\), where \(\omega\) is the angular frequency of the electromagnetic wave [27; 28; 29]. Two characteristic lengths are introduced in the theory: \(\lambda_{T}=ch/k_{B}T\)--the characteristic wavelength of thermal radiation and \(\lambda_{0}\)--the characteristic wavelength of the absorption spectra of interacting materials, where \(c=2.998\cdot 10^{8}\) m/s is the speed of light in vacuum, \(\hbar=1.055\cdot 10^{-34}\) Js is the reduced Planck constant, and \(k_{B}=1.38\cdot 10^{-23}\) J/K is the Boltzmann constant [29]. It is assumed that \(d\) is much larger than the interatomic distance \(a\). Usually, \(\lambda_{T}\gg\lambda_{0}\), where \(\lambda_{T}\) is about 8 \(\upmu\)m at room temperature. At large distances \(d\gg\lambda_{T}\), the force \(F(d)\) acting between two flat identical materials is about \(Sk_{B}T/8\pi d^{3}\)[17; 29]. However, at \(\lambda_{T}\gg d\), the force \(F(d)\) does not depend on the temperature \(T\). In the case of the interaction of two identical materials with a dielectric constant \(\varepsilon\), the interfacial contact pressure \(p_{c}(d)\) can be represented by Equations (2) and (3) at \(\lambda_{T}\gg d\gg\lambda_{0}\) and \(\lambda_{0}\gg d\gg a\), respectively. Thus,  
\[p_{c}(d)=\frac{\pi^{2}\hbar c}{240d^{4}}\bigg{(}\frac{\varepsilon-1}{ \varepsilon+1}\bigg{)}^{2}f(\varepsilon), \tag{2}\]  
where \(f(\varepsilon)\) is of the order of 1 [17; 27; 28; 29]. For example, \(p_{c}(d)=\pi^{2}\hbar c/240d^{4}\) for metal materials. This interaction is known as the Casimir force [30]. The Casimir force (perunit area) can reach approximately \(10^{4}\) Pa at \(d=20\) nm. In the case of \(\lambda_{0}\gg d\gg a\), the interfacial contact pressure \(p_{c}(d)\) is equal to  
\[p_{c}(d)=\frac{\hbar\omega_{0}}{8\pi^{2}d^{3}}, \tag{3}\]  
where \(\omega_{0}\) is the characteristic (dominant) frequency of the absorption spectra of interacting materials [27; 28; 29]. Usually, Equation (3) is represented as  
\[p_{c}(d)=\frac{A}{6\pi d^{3}}, \tag{4}\]  
where the Hamaker constant \(A\) is of the order of \(10^{-19}\) J [17; 31; 32; 33]. For example, the contact pressure \(p_{c}(d)\) is of the order of 0.1 MPa and 5 MPa at \(d=4\) nm and 1 nm, respectively.