Ballistic thermal rectification in asymmetric homojunctions

Ballistic thermal rectification is of significance for the management of thermal transport at the nanoscale since the size of thermal devices shrinks down to the phonon mean free path. By using the single-particle Lorentz gas model, the ballistic thermal transport in asymmetric homojunctions is investigated. The ballistic thermal rectification of the asymmetric rectangular homojunction is enhanced by the increasing structural asymmetry. A hyperbolic tangent profile is introduced to the interface to study the effect of interface steepness on thermal transport. We find that the thermal rectification ratio increases with the decreasing interface steepness, indicating that a gradual interface is of benefit to increase the thermal rectification. Moreover, the thermal rectification of the asymmetric homojunction can be improved by either increasing the temperature gradient or decreasing the average temperature of two heat sources.

Figure 1

Schematic diagram of the asymmetric rectangular homojunction in (a) forward direction and (b) backward direction. The asymmetric homojunction is composed of two rectangles having length $L_1$ and $L_2$, and width $D_1$ and $D_2$. The temperatures of heat reservoirs on the hot side and cold side are denoted by $T_h$ and $T_c$, respectively. (c) Temperature distribution along the transport direction with different width ratio for the asymmetric rectangular homojunction with $D_2$=200, $L_1=L_2=100$, $T_h$=2.0, and $T_c$=1.0 in the forward direction. (d) Thermal rectification ratio is independent with the width of asymmetric rectangular homojunction under a given width ratio.

Figure 2

Thermal rectification ratio as a function of the width ratio. Inset: The corresponding forward and backward heat flows as a function of the width ratio.

Figure 3

(a) Schematic diagram of the asymmetric homojunction with a hyperbolic tangent interface. (b) Temperature distribution along the transport direction of asymmetric homojunctions with different steepness of the interface. The parameters of the model is set to be $D_1=200$, $D_2=150$, $L_1=L_2=60$, $L_3=80$, $T_h=2.0$, and $T_c=1.0$.

Figure 4

(a) Thermal rectification ratio of asymmetric homojunctions as a function of interfacial steepness under different temperature gradients. The temperatures of the hot and cold sources are set to be $T_h=T+\mathrm{\Delta }T/2$ and $T_c=T-\mathrm{\Delta }T/2$, respectively and the average source temperature is set to be $T=100$. Inset: the corresponding forward and backward heat flows for the case of $\mathrm{\Delta }T=60$. (b) thermal rectification ratio of asymmetric homojunctions as a function of interfacial steepness under different average source temperatures. The temperature difference is set to be $\mathrm{\Delta }T=20$. Inset: schematic diagrams of asymmetric homojunction models with $a=5$ and $a=0.02$.

Figure 5

(a) Thermal rectification ratio of asymmetric homojunctions as a function of temperature difference between two heat sources under different interfacial steepness. The average source temperature is set to be $T=100$. (b) Thermal rectification ratio of asymmetric homojunctions as a function of average source temperature under different interfacial steepness. The temperature difference is set to be $\mathrm{\Delta }T=20$.

Figure 6

(a) Upper panel: the probability distribution function of $t_{f,LL}$ for a particle emitted from the left heat source and finally absorbed by the left heat source in the forward direction for the case of $a=0.02$ (red line) and $a=5$ (black line). Lower panel: the difference of the probability distribution function of $t_{f,LL}$ between the case of $a=0.02$ and $a=5$. (b) Probability distribution function of $t_{f,LR}$ for the case of $a=0.02$ (red line) and $a=5$ (black line) and their difference. (c) Probability distribution function of $t_{f,RL}$ for the case of $a=0.02$ (red line) and $a=5$ (black line) and their difference. (d) Cumulative distribution function of the total transports for the case of $a=0.02$ (red line) and $a=5$ (black line).