Abstract
We have derived the fundamental formula of phonon transport in water for the evaluation of quantum thermal conductance by using a one-dimensional phonon model based on the nonequilibrium Green’s function method. In our model, phonons are excited as quantum waves from the left or right reservoir and propagate from left to right of HO layer or vice versa. We have assumed these reservoirs as being of periodic structures, whereas we can also model the HO sandwiched between these reservoirs as having aperiodic structures of liquid containing N water molecules. We have extracted the dispersion curves from the experimental absorption spectra of the OH stretching and intermolecular modes of water molecules, and calculated phonon transmission function and quantum thermal conductance. In addition, we have simplified the formulation of the transmission function by employing a case of one water molecule (N=1). From this calculation, we have obtained the characteristic that the transmission probability is almost unity at the frequency bands of acoustic and optical modes, and the transmission probability vanishes by the phonon attenuation reflecting the quantum tunnel effect outside the bands of these two modes. The classical limit of the thermal conductance calculated by our formula agreed with the literature value (order of W/K) in high temperature regime (>300 K). The present approach is powerful enough to be applicable to molecular systems containing proteins as well, and to evaluate their thermal conductive characteristics.
Highlights
In recent years, advances in the fabrication and characterization of nanoscale systems allow for a better understanding of the heat flow at the microscopic level [1]
Tanaka et al [10,11] studied molecular dynamics of water by microwave heating. In contrast to these classical-mechanics-based approaches, Fisher [12] showed that the Landauer transport formalism can be applied to the formulations of the quantum thermal conductance of heat flux carried by phonons between hot and cold reservoirs on the basis of nanoscale models of inorganic materials
We show detailed mathematical formulations based on equilibrium Green’s functions, non-equilibrium Green’s functions and phonon transmission function in the Appendix A, and describe simplified formulas used in the calculations of main text
Summary
Advances in the fabrication and characterization of nanoscale systems allow for a better understanding of the heat flow at the microscopic level [1]. A forthcoming challenge in the series of debates [14,15] is to establish a relevant theoretical framework for thermal conduction by setting up nanoscale models of biological cells containing liquid water and proteins. Regarding this issue, Lervik et al [20] calculated the thermal conductivity at the protein–water interface in terms of classical molecular dynamics. We have extracted the dispersion curves from experimental absorption spectrum of water and evaluated quantitatively quantum heat conduction characteristics such as the phonon transmission function and the thermal conductance.
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