Field-induced clearing in sphere-sphere and rod-sphere binary mixtures of charged colloidal particles

Binary mixtures of larger and smaller colloids having charges of equal sign display unusual response to low-frequency electric fields. We show here that the previously reported negative torque acting on rodlike particles when in presence of a sea of smaller particles is accompanied by a field-induced clearing of the suspension. Measurements of transmitted intensity performed on mixtures of large (dilute) and small (semidilute) spherical particles indicate that such a clearing effect is universal and due to an anisotropic $E^2$-dependent redistribution of the small spheres around the large ones. We interpret this behavior as resulting from $O\left(E^2\right)$ electro-osmotic flows whose magnitude is greatly enhanced by the presence of the small particles.

Figure 1

(a) Kerr coefficient $B$ vs electric field frequency $\nu$. Full dots: PTFE. Empty dots: $\text{PTFE}+\text{P}20$ mixture. (b) Electric-field-induced turbidity variations $\Delta \tau /E^2$ vs $\nu$ in a $\text{PTFE}+\text{P}20$ mixture, measured for perpendicular polarization (${\tau }_{\perp }$, squares) and for parallel polarization (${\tau }_{\parallel }$, triangles). Diamonds: $\Delta \overline{\tau }/E^2$. Dots: $\Delta \overline{\tau }/E^2$ magnified seven times. For all data ${\varphi }_{\text{PTFE}}={10}^{-3}$, ${\varphi }_{\text{SP}}={10}^{-2}$, and ionic strength 0.5 mM KCl.

Figure 2

[(a) and (b)] Field-induced clearing coefficient (a) $\Delta \tau /E^2$ and (b) $\Delta \tau /\left(E^2{\varphi }_{\text{P}200}\right)$ vs electric field frequency $\nu$ in mixtures of large and small spheres. Full (empty) symbols indicate perpendicular (parallel) polarization. In (a) $\text{P}200+\text{P}20$ (diamonds), $\text{P}200+\text{P}30$ (squares), and ${\varphi }_{\text{P}200}=2\times {10}^{-4}$. In (b) $\text{P}200+\text{P}30$ mixtures with various ${\varphi }_{\text{P}200}$. ${\varphi }_{\text{P}200}=3\times {10}^{-4}$ (dots), ${\varphi }_{\text{P}200}=2\times {10}^{-4}$ (squares), and ${\varphi }_{\text{P}200}={10}^{-4}$ (triangles). (c) Turbidity variation $\Delta \tau$ vs $E^2$ for a $\text{P}200+\text{P}30$ mixture. (d) Relative variation in the transmitted intensity $I$ for a mixture of $\text{P}200+\text{P}30$. $\overline{I}$ indicates the value of $I$ when no field is applied. $E=24\text{V}{\text{mm}}^{-1}$ for $t<0$, while $E=0$ for $t>0$. In (c) and (d) $\nu =100\text{Hz}$ and ${\varphi }_{\text{P}200}=2\times {10}^{-4}$. In all panels ${\varphi }_{\text{SP}}={10}^{-2}$.

Figure 3

$O\left(E^2\right)$ perturbations around a P200: (a) diagram of $\delta {\varphi }_2$ used to quantitatively match the scattering data in Fig. 2b for $\nu =100\text{Hz}$ and $E=15\text{V}{\text{mm}}^{-1}$. $\delta {\varphi }_2$ is positive within two spherical volumes of radius 100 nm symmetric along $E$ and negative within an equatorial toroidal region having section equal to that of the P200. Gray levels indicate the resulting refractive index $n$: toroid $\left(n=1.335\right)$, background $\left(n=1.336\right)$, enhanced spherical volumes $\left(n=1.337\right)$, and P200 $\left(n=1.59\right)$. (b) $O\left(E^2\right)$ solvent flows around the P200 drawn according to the equations in Refs. [13, 14]. The dashed line qualitatively indicates the SP exclusion shell.