Kapitza resistance at a domain boundary in linear and nonlinear chains

TL;DR

This paper investigates the Kapitza thermal resistance at domain boundaries in various chain models, deriving exact expressions and analyzing temperature dependence, revealing different behaviors in linear, nonlinear, and rotator chains.

Contribution

It provides exact formulas for Kapitza resistance in linear chains and analyzes its dependence on temperature and chain type in nonlinear models, highlighting novel scaling laws.

Findings

Kapitza resistance depends on thermostat properties in linear chains.

In elastically colliding particles, resistance scales with inverse square root of temperature.

Resistance vanishes in the thermodynamic limit for Fermi-Pasta-Ulam chains.

Abstract

We explore Kapitza thermal resistance on the boundary between two homogeneous chain fragments with different characteristics. For a linear model, an exact expression for the resistance is derived, and well-defined in the thermodynamic limit. However, the resistance in this case depends on the thermostat properties and therefore is not a local property of the considered domain boundary. If the domains are nonlinear, but integrable - Toda lattice, elastically colliding particles - the anomalies are similar to the case of the linear chain, besides well-articulated thermal dependence of the resistance. For the case of elastically colliding particles, this dependence follows a simple scaling law - the resistance is proportional to the inverse square root of the temperature. For Fermi-Pasta-Ulam domains, both the temperature drop and the heat flux decrease with the chain length, but with different exponents, so the resistance vanishes in the thermodynamic limit. For the domains comprised of rotators, the thermal resistance exhibits the expected normal behavior.