Binary colloidal mixtures in near-critical binary solvents

Abstract

The phase behavior of a single type of colloid C suspended in near-critical solvents is known to be very rich. Motivated in part by recent experiments we consider a mixture of two colloidal types C1 and C2 in a binary solvent close to its demixing critical point. We extend a mean-field description of a lattice model, previously used to investigate systems with a single type of colloid in two dimensions, to the binary colloid case in three dimensions. The model treats the system as a full four-component mixture. For simplicity we choose C1 and C2 to be hard spheres with the same radius but with different affinities for one species, B, of the AB binary solvent. We show that intricate interplay between couplings of C1 and solvent, C2 and solvent as well as solvent-solvent interactions and hard sphere packing drive significant changes in the topology of the colloidal phase diagram when the relative volume fractions of the two different colloid types change. The behavior of the two lines of triple points is particularly interesting. Our results can provide some insight into the control of the self-assembly process for colloidal 'alloys' mediated by a near-critical solvent and therefore controlled by temperature in a reversible manner

Figures (11)

• Figure 1: (a) Demixing curve of a colloid free solvent (black curve) and loci of critical points of the ternary mixture where only type 1 colloids are added. The critical lines for both choices of $\alpha$ run into the solvent critical point at reservoir composition $x_r$ = 0.5. (b) Values of $\eta$ along the critical lines in panel (a); the color code is the same. These lines are solutions to eqs. (\ref{['eq:crit_line']}). For larger values of $\eta$ the critical points become metastable with respect to the GS coexistence.
• Figure 2: Phase diagrams of a ternary mixture consisting of only type 1 colloids and a binary solvent for different temperatures as listed in the panels. G, L, and S denote the gas, liquid, and solid phases, respectively. In all cases, $R = 5$ and $\alpha = 0.29$. Panel (a) displays only FS coexistence. New phase boundaries emerge as the temperature is lowered. In panels (b) and (c) a distinct GL coexistence is manifest with upper and lower critical points (cp red dots). The emergence of SS coexistence is signaled by the blue curve with a corresponding critical point (cp blue dots). The triple GSS point between the G and two S phases is denoted by orange dots.
• Figure 3: Phase diagram of ternary mixture for $\Delta T/T_\mathrm{c}^\mathrm{s}$=0.02733 for $R=5$ and $\alpha=0.29$ in various representations. The color code is the same in all panels. The red lines denote GL coexistence terminating in a (stable) upper critical (red) point. The thin red lines display the corresponding metastable branches ending in the lower (metastable) critical point. There are two sets of triple points: tp green dots denote the upper GLS coexistence whereas tp orange dots denote the lower GSS coexistence. cp blue denotes the (lower) critical point of SS coexistence. As explained in the text, the red asterisks label GS coexistence.
• Figure 4: Phase diagram in the $(\eta, \Delta T/T_\mathrm{c}^{\mathrm{s}})$ representation at different values of the solvent reservoir concentration $x_r$ for radius $R=5$ and adsorption strength $\alpha=0.29$, (a) and (b), and for $R=6.5$ and $\alpha=0.32$ (c). In panel (a) GL coexistence is well separated from LS. In panel (b) GL phase separation becomes metastable -see dashed line and the stable L region is small. The dots denote the triple GLS line. In panel (c) there is an upper and a lower triple GLS line marked by dots.
• Figure 5: Demixing curve of the colloid free solvent (black line) and the critical lines for various fixed values of $\eta$ (a) and $\eta_2/\eta$ (b) and parameters $R=5$, $\alpha_1=0.29$, and $\alpha_2=0.7\alpha_1$. The dashed line in (a) corresponds to $\eta_2/\eta=0.5$. The dashed curves in (b) show the limiting case of a ternary mixture with colloids of type 1 ( $\alpha=\alpha_1=0.29$) and of type 2 ($\alpha=\alpha_2=0.203$). Recall that $x_\mathrm{r}$ is the reservoir composition.