Molecular heat transport across a time-periodic temperature gradient

Abstract

The time-periodic modulation of a temperature gradient can alter the heat transport properties of a physical system. Oscillating thermal gradients give rise to behaviors such as modified thermal conductivity and controllable time-delayed energy storage that are not present in a system with static temperatures. Here, we examine how the heat transport properties of a molecular lattice model are affected by an oscillating temperature gradient. We use analytical analysis and molecular dynamics simulations to investigate the vibrational heat flow in a molecular lattice system consisting of a chain of particles connected to two heat baths at different temperatures, where the temperature difference between baths is oscillating in time. We derive expressions for heat currents in this system using a stochastic energetics framework and a nonequilibrium Green’s function approach that is modified to treat the nonstationary average energy fluxes. We find that emergent energy storage, energy release, and thermal conductance mechanisms induced by the temperature oscillations can be controlled by varying the frequency, waveform, and amplitude of the oscillating gradient. The developed theoretical approach provides a general framework to describe how vibrational heat transmission through a molecular lattice is affected by temperature gradient oscillations.

The effect of temperature oscillations on energy storage rectification in harmonic systems

“…In the limit of constant bath temperatures, the system will reach a steady state in which the system energy flux vanishes, J sys = 0. But, in the systems examined here, the system energy flux does not vanish because of the temperature oscillations [14,65]. The system energy flux in the respective thermal bias state is…”

“…Because the bath temperatures are periodic in time, the model will not reach steady state defined by ∂ t ⟨E(t)⟩ = 0 and J L (t) = −J R (t). Instead, it approaches a time-dependent nonequilibrium state with an average energy that is oscillating in time and, therefore, a system energy flux J sys (t) that is not equal to zero for all t. A framework based on the NEGF approach has previously been employed by us to obtain the exact expression for J sys (t) in a system consisting of a harmonic chain connected to baths with oscillating temperatures [65]. That theoretical framework and the analytical expression used to calculate the system energy flux are given in appendix.…”

“…That theoretical framework and the analytical expression used to calculate the system energy flux are given in appendix. Details of the mathematical derivation are found in [65]. The oscillating system energy implies that the system is storing and releasing energy as the temperature gradient is oscillating.…”

“…It has recently been observed that subjecting a system to a time-periodic temperature gradient can alter the energy transport properties of the system in comparison to a static temperature gradient and give rise to novel and emergent transport phenomena [63][64][65]. Time-dependent temperatures can be used to affect system properties across various length scales [66][67][68][69] including to induce thermal rectification in macroscopic solid-state systems [70].…”

“…Here, we present results that illustrate how an oscillating temperature gradient affects energy storage rectification ratios in a harmonic molecular chain. We apply the formalism developed previously by us in [64,65] to calculate the energy fluxes and the corresponding energy storage properties in the model. This formalism uses a nonequilibrium Green's function (NEGF) approach adapted to treat the non-stationary distributions that arise when the bath temperatures are time-periodic.…”