Thermal diode utilizing asymmetric contacts to heat baths

We propose a simple thermal diode passively acting as a rectifier of heat current. The key design of the diode is the size asymmetry of the areas in contact with two distinct heat baths. The heat-conducting medium is liquid, inside of which gaslike regions are induced depending on the applied conditions. Simulating nanoscale systems of this diode, the rectification of heat current is demonstrated. If the packing density of the medium and the working regime of temperature are properly chosen, the heat current is effectively cut off when the heat bath with narrow contact is hotter, but it flows normally under opposite temperature conditions. In the former case, the gaslike region is induced in the system and it acts as a thermal insulator because it covers the entire narrow area of contact with the bath.

Figure 1

Schematics of bimetal switch. The bimetal, comprising two separate metals joined together (each metal has a different thermal expansion coefficient), is fixed to the heat bath $T_1$ at one end. (a) When the bimetal is straight, it comes into contact with the other heat bath $T_2$. Then heat current can flow between the two heat baths. (b) Under some temperature conditions, the bimetal bends owing to the difference in the thermal expansion coefficients. Then there is no pathway for heat between the baths. In this way, the bimetal switch can work as an on (a) and off (b) switch for heat currents.

Figure 2

Schematics of the system. $N$ particles are enclosed in the rectangular box $\left(L_x\times L_y\times L_z\right)$. They interact with each other through the LJ potential. Two gray rectangular regions inside the box are set up as the areas of contact with the heat baths (at temperatures $T_1$ and $T_2$). Only when particles are inside these regions, they are subjected to Langevin thermal forces. We introduce asymmetry in the sizes of the areas of contact with the heat baths: the area of contact with the bath 1 on the left side has the volume $h_x\times L_y\times L_z$, whereas that with the bath 2 on the right side has the smaller volume $b_x\times b_y\times b_z$. In most simulations, we used $L_x=24$, $L_y=L_z=48$, and $h_x=b_x=b_y=b_z=6$. The mirrored wall conditions are applied on both ends along the $x$ direction and the periodic boundary conditions are applied along the other directions $\left(y,z\right)$.

Figure 3

Performance of the rectification of thermal current. The steady heat current $J_1^{\text{st}}$ (energy per unit time) from bath 1 to the system, which is equal to $-J_2^{\text{st}}$ from bath 2, is plotted versus the temperature difference $T_1-T_2$ of the baths. (a) Close-up of (b). We used the number density $\rho =0.65$ $\left(N=35942\right)$ and the mean temperature $\left(T_1+T_2\right)/2=0.75$. For each simulation, initial conditions were prepared at $T_1=T_2=0.75$ and the nonequilibrium temperature condition was applied for $t\ge 0$. The heat current (averaged for each 100 time units) was observed during $2000<t<4000$ [three-sigma error bars are plotted in (a)].

Figure 4

Snapshot of the system in the heat conducting nonequilibrium steady states: $xy$ coordinates of particles inside the slice of thickness $b_z=6$ are plotted with dots. The solid lines show system boundaries and the broken lines show the areas of contact with the heat baths. (a) $T_1=0.6$ and $T_2=0.9$. Gaslike regions overlap the area of contact with the narrow-contact bath. (b) $T_1=0.9$ and $T_2=0.6$. No apparent gaslike regions exist.

Figure 5

Response of heat currents to switching of temperature conditions. Averaged heat currents $J_1$ from bath 1 (the wide-contact bath) to the system for each ten time units are plotted. Each graph shows a single trajectory of the system. Initially, the system was prepared at $T_1=T_2=0.75$. (a) At $t=0$, $\left(T_1,T_2\right)$ is switched to (0.9, 0.6) and then to (0.6, 0.9) at $t=1000$. (b) The reverse case of (a). At $t=0$, $\left(T_1,T_2\right)$ is switched to (0.6, 0.9) and then to (0.9, 0.6) at $t=1000$. For both directions of switching, the system exhibits smooth responses and good diode effects.

Figure 6

Steady heat currents $J_1^{\text{st}}$ for various number densities $\rho$. Almost the same setting as in the case of Fig. 3 were used. For $T_1-T_2\ge 0.7$ and $\rho \ge 0.9$, the heat currents were observed during $5000<t<6000$. For other conditions, heat currents were observed during $1000<t<2000$.

Figure 7

Local density vs local (kinetic) temperature in the heat-conducting states (plotted with open circles or triangles). Both local quantities are averages over the particles inside the rectangular cell regions with a size of $6\times 6\times 1$ (evaluated for regions located further than $3\sigma$ from the walls). The parameters are the same as the case of Fig. 4. (a) $T_1=0.6$ and $T_2=0.9$. (b) $T_1=0.9$ and $T_2=0.6$. Solid lines are liquid-gas coexistence curves obtained by equilibrium simulations $\left(T_1=T_2\right)$. Dotted line is isobar obtained by equilibrium simulations. The pressure $\left(p=0.48\right)$ on the dotted line is chosen to be the same value as that in the heat-conducting steady states of (b). Data in the heat-conducting states closely follow the equilibrium line. This implies that deviations from the local equilibrium are small at the scale of this plot.