(a) Soret coefficient for octadecyl coated silica particles in toluene as a function of the volume fraction ϕ for different values of the average temperature. Solid lines are a fit to Eq. (5) for low ϕ, and dashed lines a fit to Eq. (7) for high ϕ. (b) Values of the Soret coefficient at the limit of zero volume fraction, and the single particle contribution as a function of the temperature, obtained from the fit of the data to Eq. (5). (c) Temperature dependence contribution of S T at high ϕ values are obtained from a fit of the data to Eq. (7). (a) Reprinted with permission from J. Chem. Phys. 125, 204911 (2006). Copyright 2006 American Institute of Physics.
Displaced Soret coefficient as a function ϕ, corresponding to the collective contribution. Lines correspond to those in Fig. 1. The arrow indicates increasing colloid-colloid attraction. (Inset) Difference between the “zero concentration extrapolated Soret coefficients” at low concentration in Eq. (6) and high concentration in Eq. (7).
Profiles for concentrated colloids suspensions interacting with the LJ n = 6 potential. Crosses indicate the temperature profile with values in the right axis. The left axis quantifies the normalized relative density of colloids (down triangles), solvent particles (up triangles), and the normalized relative molar fraction of colloids (bullets). Lines correspond to the linear fits to determine the gradients of temperature and molar fraction. (a) ϕ c = 0.2 as example of a positive S T with colloids excess on the cold side. (b) ϕ c = 0.3 as example of a negative S T .
Temperature gradient induced phase separation of colloids in liquid-gas coexistence regime below critical point with LJ 12-6, ε = 1.0, ϕ c = 0.1, and T 0 = 1.0. The volume fraction on the cold side of the system is ϕ c ≃ 0.37 corresponding to a liquid state. On the hot side, ϕ c ≃ 0.03 corresponding to a gas phase.
Soret coefficient S T for different mean volume fractions ϕ c for colloids with rLJ potentials in Eq. (10) with n = 6 bullets, n = 12 up-triangles, and n = 24 down-triangles. The inset displays the employed potentials.
Soret coefficients S T as a function of the volume fraction ϕ c for LJ potentials in Eq. (10) with n = 6 squares, n = 12 up-triangles. The inset displays the employed potentials.
Soret coefficients S T as a function of the volume fraction ϕ c at various attraction ranges, squares r c = 1.2, up-triangles r c = 1.1, and bullets r c = 1.0365. Arrows indicate increasing attraction ranges. The attraction strength are (a) ε = 2.0, (b) ε = 1.0, and (c) ε = 0.5. The inset in (b) is an example of employed sticky potentials in Eq. (13).
Soret coefficients S T as a function of the volume fraction ϕ c at various attraction ranges, squares ε = 2.0, up-triangles ε = 1.0, and bullets ε = 0.5. Arrows indicate increasing attraction strength. The attraction strength are (a) r c = 1.2, (b) r c = 1.1, and (c) r c = 1.0365. The inset in (b) is an example of employed sticky potentials in Eq. (13).
Soret coefficient S T as a function of the volume fraction ϕ c . Symbols are simulation results with rLJ n = 6 as displayed in Fig. 5. Dashed line corresponds to Eq. (19) with β T, c in Eq. (20). Solid line includes the additional contribution .
Parameters employed for the sticky potentials in Eq. (13).
Values of the Soret coefficient for the MPC binary mixture at various concentrations, and for two potential interactions at very low concentrations.
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