Tuning Colloid-Interface Interactions by Salt Partitioning

We show that the interaction of an oil-dispersed colloidal particle with an oil-water interface is highly tunable from attractive to repulsive, either by varying the sign of the colloidal charge via charge regulation or by varying the difference in hydrophilicity between the dissolved cations and anions. In addition, we investigate the yet unexplored interplay between the self-regulated colloidal surface charge distribution with the planar double layer across the oil-water interface and the spherical one around the colloid. Our findings explain recent experiments and have direct relevance for tunable Pickering emulsions.

Figure 1

(a) Geometry of a colloidal sphere with radius $a=1\mu \mathrm{m}$ and a dielectric constant ${\epsilon }_c=2.6$ in cylindrical coordinates $(r,z)$ at a distance $d$ from an oil-water interface, with the position on the particle surface indicated by the polar angle $\vartheta$. The oil and water are characterized by dielectric constants ${\epsilon }_o=7.92$ and ${\epsilon }_w=80$, respectively. The self-energies $(f_{+},f_{-})=(6,10)$ in units of $k_{B}T$ determine the degree of ion partitioning among the two solvents. In (b), we show the electrostatic potential $\varphi (r,z)/\beta e$ for a positively charged sphere at $d=a$ along the $z$ direction at fixed $r$, with the Donnan potential ${\varphi }_D$ indicated, and as a surface plot in (c). We set the charge-regulating equilibrium constant $K_{+}{a}^3=1$ ($p{K}_{+}=8.8$) and the screening length in oil ${\kappa }_o^{-1}=10\mu \mathrm{m}$.

Figure 2

Double layer destruction for a charged particle with radius $a=1\mu \mathrm{m}$, with self-energies $(f_{+},f_{-})=(6,10)$, oil screening length ${\kappa }_o^{-1}=10a$, equilibrium constant $K_{\pm }{a}^3=1$ ($p{K}_{\pm }=8.8$), and bulk salt concentrations ${\rho }_s^0=0.093\mathrm{nM}$ (oil) and ${\rho }_s^w=0.28\mu \mathrm{M}$ (water). In (a)–(c) the particle is positively charged $(Z>0)$, and in (d)–(f) negatively charged $(Z<0)$. For clarity, we introduced a cutoff for the scaled net ion density $[{\rho }_{+}(\mathbf{r})-{\rho }_{-}(\mathbf{r})]/{\rho }_s^o$. The insets show the particle charge distribution $a^2\sigma (\vartheta )$.

Figure 3

Particle-interface potential $\mathrm{\Phi }(d)$ for oil screening length ${\kappa }_o^{-1}=10a$. The full curves are the results for (a) $p{K}_{\pm }=5.8$ and (b) $p{K}_{\pm }=8.8$. The red (green) curves are for a negative (positive) particle with self-energies $(f_{+},f_{-})=(6,10)$, and the blue curves are for $f_{+}=f_{-}=0$ and are independent of the sign of $Z$. The insets show the absolute charge $|Z(d)|$. The green ($Z>0$) and red ($Z<0$) dashed curves show the approximation $\tilde{\mathrm{\Phi }}(d)$.