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Kapitza resistance in basic chain models with isolated defects

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 $β$-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.