A Model of Inelastic Heat Transfer Mechanism for the Excess Kapitza Conductance

Abstract

Observations of thermal boundary conductance (Kapitza conductance¹) between a classical solid and quantum media (liquid and solid helium, solid H₂ and D₂ ²) show that, in addition to the elastic processes³, inelastic processes are important^4,5. We propose here a model of inelastic thermal heat transfer between a solid and liquid helium. We assume that a helium monolayer is formed between the solid filling the half-space z<0 and the bulk liquid He at z>d (see Fig 1), due to an anisotropic field

$$W\left( z \right)\, = \,{W^s}\,\left( z \right)\, + \,{W^\ell }\,\left( z \right)$$

(1)

where W^s is the Van der Waals field from the solid and ${W^\ell }$ is the sum of Lennard-Jones potential from bulk He;

$${W^\ell }\left( z \right)\, = \,\pi {n^\ell }r_0^3\,{v_0}\,\left\{ {{{\left( {{r_0}/\left( {d - z} \right)} \right)}^9}/45\, - \,{{\left( {{r_0}/\left( {d - z} \right)} \right)}^3}/3} \right\}$$

(2)

in which ${n^\ell }$ is the atom number density of He, r₀ and v₀ are Lennard-Jones parameters of He. We solve the equation

$$\left( { - {\hbar ^2}/2m\,{d^2}/d{z^2}\, + \,W\left( z \right)} \right){\phi _m}\left( z \right)\, = \,{e_m}\,{\phi _m}\left( z \right),\,m = 0,1,2 \ldots$$

(3)

University of Tokyo, Tokyo