Kapitza resistance in basic chain models with isolated defects

TL;DR

This paper investigates how Kapitza thermal resistance in one-dimensional chain models varies with interface structure, temperature, and system size, revealing differences between linear and nonlinear models and the influence of simulation parameters.

Contribution

It provides a detailed analysis of Kapitza resistance in various 1D chain models, highlighting the effects of nonlinear interactions and simulation conditions on the resistance.

Findings

Kapitza resistance is size-independent in linear models but size-dependent in some nonlinear models.

In models with convergent bulk heat conductivity, boundary resistance is thermostat- and size-independent.

Temperature dependence of Kapitza resistance indicates the role of nonlinear phonon scattering.

Abstract

Kapitza thermal resistance is a common feature of material interfaces. It is defined as the ratio of the thermal drop at the interface to the heat flux flowing across the interface. One expects that this resistance will depend on the structure of the interface and on the temperature. We address the heat conduction in one-dimensional chain models with isotopic and/or coupling defects and explore the relationship between the interaction potentials and simulated properties of the Kapitza resistance. It is revealed that in linear models the Kapitza resistance is well-defined and size-independent (contrary to the bulk heat conduction coefficient), but depends on the parameters of thermostats used in the simulation. For $\beta$-FPU model one also encounters the dependence on the thermostats; in addition, the simulated boundary resistance strongly depends on the total system size. Finally, in the models characterized by convergent bulk heat conductivity (chain of rotators, Frenkel-Kontorova model) the boundary resistance is thermostat- and size-independent, as one expects. In linear chains, the Kapitza resistance is temperature-independent; thus, its temperature dependence allows one to judge on significance of the nonlinear interactions in the phonon scattering processes at the interface.