(a) The interaction potential U(D) between two colloids at a distance D at different temperatures τ ≡ T/T c − 1 > 0 immersed in a mixture at a critical composition (ϕ0 = ϕ c ). U(D) becomes attractive as τ decreases. Here n 0 = 10 mM and Δγ R, L = 0.1T/a 2, corresponding to about 3.4 mN/m. For the solid curves, Δu ± = 4 and the surfaces have the same charge σ L, R = −σ sat . Dashed-dotted curve: the same as the solid curve for τ = 0.008 except that σ L = 3σ R = −1.5σ sat . Dashed curve: the same as for τ = 0.008 except that Δu − = 8. (b) The corresponding excess surface adsorption Γ. In this and in other figures, as an approximation of a water–2,6-lutidine mixture we used T c = 307.2 K, v 0 = 3.9 × 10−29m3, C = χ/a,27 ɛ2, 6-lutidine = 6.9, and ɛwater = 79.5, and the surface area is taken to be S = 0.01μm2.
The effect of removing preferential solvation or short-range chemical interactions on the potential U(D) between the colloids at temperatures given by (a) τ = 0.009 and (b) τ = 0.005. The dashed and dashed-dotted curves show U(D) when either the surface chemical affinity or preferential solvation parameters are zero, respectively. In the solid curves both short-range chemical preference and solvation are included. These two interactions are clearly nonadditive as the solid curve is not the sum of the dashed and dashed-dotted lines.
Interaction potentials at different temperatures τ, (a) for ϕ0 = 0.48 < ϕ c with Δγ R, L = 0.1T/a 2 and (b) for ϕ0 = 0.52 > ϕ c with Δγ R, L = 0.4T/a 2. The onset temperature for attraction is higher for ϕ0 < ϕ c due to preferential solvation. In (a), at intermediate temperatures the potential has metastable states. Here we used Δu + = 4, Δu − = 8, and σ L = 3σ R = −1.5σ sat . We took the average ion density to be n 0 = 10 mM leading to κ values of κ ≃ 2.69 nm.
Solid curves show the dependence of U(D) on the mixture salt concentration n 0 with Δu + = 4 and Δu − = 8; colloidal attraction increases with the addition of salt. The attraction is weak for a salt concentration of n 0 = 0.01 M but with Δu ± = 0 (dashed curve). Here ϕ0 = ϕ c , τ = 0.008, Δγ L, R = 0.1T/a 2, and σ L = 3σ R = −1.5σ sat .
Inter colloid potentials U(D) for hydrophilic and hydrophobic colloids (antisymmetric boundary conditions). For the surface on the right we used Δγ R = 0.1T/a 2 and σ R = −σ sat . For the surface on the left we used Δγ L = −0.4T/a 2 and σ L = −0.01σ sat ≪ σ sat . (a) The interaction potential U(D) at different temperatures τ showing that U becomes attractive when τ decreases, but repulsive close to T c . Here we took for the ions Δu + = 4 and Δu − = 8. (b) U(D) at τ = 0.048 and different values of Δu ±. The interaction is purely repulsive for Δu d = Δu + − Δu − = 0 (dashed-dotted curve) and weakly attractive for Δu d = 2 (dashed curve). The attraction is much stronger in the solid curves, all having different values of Δu ± but the same difference Δu d = −4. Among these curves, the attraction is strongest for the antagonistic salt (Δu − = −Δu + = 2).
(a) The effect of the sign of the colloids’ charge on the inter-colloid potential U(D). The interaction is attractive for two positively charged surfaces and is repulsive for two negatively charged surfaces; compare the dashed-dotted and dashed curves. We used Δu + = 2, Δu − = 4, Δγ R, L = 0.1T/a 2, and τ = 0.008. In the solid curve the surfaces are both hydrophilic (Δγ R, L = 0.1T/a 2) but oppositely charged. For an antagonistic salt with Δu − = −Δu + = 6 there is a repulsive regime at an intermediate range. (b) The effect of the hydrophilicity or hydrophobicity of the colloid's surface. In the absence of preferential solvation (Δu ± = 0) two hydrophobic (and hydrophilic, not shown) surfaces weakly attract (dashed-dotted curve). For a hydrophilic salt (Δu ± = 4), hydrophobic surfaces repel (solid curve) whereas hydrophilic surfaces attract (dashed curve). We used τ = 0.003 and σ L, R = −σ sat .
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