Effect of Collisions on Properties of Nonequilibrium Steady State of Harmonic Chains with Alternating Masses

Abstract

AbstractLow dimensional nonequilibrium steady-state (NESS) systems are essential in understanding the microscopic origins of macroscopic laws. A one-dimensional chain, thermostatted either end to a different temperature, allows the study of heat flow in small scale systems. It is essential in understanding the origins of Fourier’s laws. In recent decades, many such systems have been studied in detail. The model of alternating masses connected through harmonic springs is one of them. With temperature gradient enforced and the chain in steady state, the particles’ kinetic temperatures take two values alternatingly. The higher massed particles can have lower or higher temperatures depending on whether there are even or odd numbers of particles in the chain. This model can provide us with insights into the heat flow in many nanomaterials, especially those with different masses along their lengths. The objective of this study is to understand how the temperature profile and the thermal conductivity change when the particles of a chain have a finite size and can collide with each other. Unlike the pedagogical models studied previously, our model is more realistic as two adjacent particles can never cross each other. Incorporating collisions reduce the alternating temperatures of the particles. Furthermore, collisions make the temperature profile more linear and reduce the boundary jumps at the same time. We have also computed the conductivity of the different chains by time-averaging the heat current. The thermal conductivity of the modified harmonic chains approaches length independence asymptotically, indicating a substantial modal energy redistribution in the chains with collisions, which is unlike that observed when the collisions are absent.KeywordsNESSOne-dimensional chainFourier’s lawsAlternating massCollisions