Contribution of internal degree of freedom of soft molecules to Soret effect

We study the Soret effect in binary dimer-monomer mixtures using nonequilibrium molecular dynamics simulations and investigate the pure contribution of the internal degree of freedom of flexible molecules to the Soret effect. We observe that the thermal diffusion factor tends to decrease and change its sign as the molecules become softer. We propose two possible mechanisms for our observations: change of the molecule structures with the temperature, causing bulkier molecules to migrate to the hotter region, and asymmetry of the restitution between rigid and flexible molecules, due to which flexible molecules show larger restitution when placed at the hotter region.

Figure 1

(a) Profiles of the local kinetic energies of the monomers ($K_{\mathrm{m}}^{\mathrm{tra}}$) and the dimers ($K_{\mathrm{d}}^{\mathrm{tra}},K_{\mathrm{d}}^{\mathrm{vib}}$, and $K_{\mathrm{d}}^{\mathrm{rot}}$) along the temperature gradient. The average packing fraction and the spring constant are $\varphi =0.073$ and $k=400\epsilon /{\sigma }^2$, respectively. The temperatures at the thermostatted regions are $T_{\mathrm{h}}=5\epsilon$ and $T_{\mathrm{c}}=\epsilon$. In the inset, the scaled kinetic energies are replotted. (b) Profiles of the local densities of the dimer ${\rho }_{\mathrm{d}}$ and the monomer ${\rho }_{\mathrm{m}}$. The parameters are the same as those in (a).

Figure 2

(a) Profiles of the concentration of the dimers $c={\rho }_{\mathrm{d}}/({\rho }_{\mathrm{d}}+{\rho }_{\mathrm{m}})$ in a dilute mixture of $\varphi =0.073$. The temperature difference $\mathrm{\Delta }T=T_{\mathrm{h}}-T_{\mathrm{c}}$ is changed. (b) Profiles of the concentration of the dimers in a dense mixture of $\varphi =0.234$.

Figure 3

(a) Plots of the thermal diffusion factor ${\alpha }_T$ against the packing fraction $\varphi$. The spring constant is changed. ${\alpha }_T$ for the mixture of the rigid dimer and monomer is also presented. (b) Plots of ${\alpha }_T$ with respect to the spring constant $k$. The packing fraction is changed.

Figure 4

The thermal diffusion factors in the mixtures of two monomers A and B are plotted against $\varphi$. Black circle: mixtures of monomers with different masses; red square: mixtures of monomers with different radii.

Figure 5

The differences of the chemical potentials between the dimers and monomers ${\tilde{\mu }}_{\mathrm{d}}$ are plotted against the temperature $\langle T\rangle$, the mixing ratio $\chi$, and the packing fraction $\varphi$ in (a), (b), and (c), respectively. In (a) and (c), the temperature is $T=3\epsilon$.

Figure 6

(a) Probability distributions $P\left(r\right)$ of the bond length $r$ in the dimer-monomer mixtures of $\varphi =0.036$ and 0.234. The spring constant is $k=10\epsilon /{\sigma }^2$. The temperature $T$ is changed. (b) Plots of the averaged bond length $\langle r\rangle$ with respect to the temperature $\mathrm{\Delta }T$ in the dimer-monomer mixtures.

Figure 7

(a) The coefficients of restitution between a dimer and a monomer are shown against the spring constant $k$, which are obtained in 1D simulations for two cases, X: $(T_{\mathrm{d}},T_{\mathrm{m}})=(5\epsilon ,\epsilon )$, Y: $(T_{\mathrm{d}},T_{\mathrm{m}})=(\epsilon ,5\epsilon )$. (b) The differences of the coefficients of restitution $\mathrm{\Delta }e=e_{\mathrm{X}}-e_{\mathrm{Y}}$ are shown with the spring constant. The exponent $n$ in the WCA potential is changed.