Crystallization and reentrant melting of charged colloids in nonpolar solvents

We explore the crystallization of charged colloidal particles in a nonpolar solvent mixture. We simultaneously charge the particles and add counterions to the solution with aerosol-OT (AOT) reverse micelles. At low AOT concentrations, the charged particles crystallize into body-centered-cubic (bcc) or face-centered-cubic (fcc) Wigner crystals; at high AOT concentrations, the increased screening drives a thus far unobserved reentrant melting transition. We observe an unexpected scaling of the data with particle size, and account for all behavior with a model that quantitatively predicts both the reentrant melting and the data collapse.

Figure 1

$1/{\kappa }_0$ as a function of $C_{\mathrm{AOT}}$, determined from conductivity and viscosity measurements.

Figure 2

Confocal microscopy images of PMMA particles at $\varphi =0.23$ and (a) $C_{\mathrm{AOT}}=1$ mM, fluid; (b) $C_{\mathrm{AOT}}=5$ mM, bcc crystal; (c) $C_{\mathrm{AOT}}=50$ mM, fcc crystal; (d) $C_{\mathrm{AOT}}=200$ mM, fluid. (e) $g\left(r\right)$ for fluid samples in (a) and (d) shown with dotted purple and solid blue curves, respectively. (f) $g\left(r\right)$ for bcc crystal in (b), with major peaks (red lines) corresponding to indices (left to right) $\left\{\frac{2}{3}\frac{2}{3}\frac{2}{3}\right\}$, $\left\{100\right\}$, $\left\{\frac{1}{2}\frac{1}{2}0\right\}$, $\left\{\frac{6}{11}\frac{2}{11}\frac{2}{11}\right\}$, $\left\{\frac{1}{3}\frac{1}{3}\frac{1}{3}\right\}$, $\left\{\frac{1}{2}00\right\}$, and $\left\{\frac{6}{19}\frac{6}{19}\frac{2}{19}\right\}$. (g) $g\left(r\right)$ for fcc crystal in (c), with peaks corresponding to $\left\{110\right\}$, $\left\{100\right\}$, $\left\{\frac{2}{3}\frac{1}{3}\frac{1}{3}\right\}$, $\left\{\frac{1}{2}\frac{1}{2}0\right\}$, $\left\{\frac{3}{5}\frac{1}{5}0\right\}$, $\left\{\frac{1}{3}\frac{1}{3}\frac{1}{3}\right\}$, and $\left\{\frac{3}{7}\frac{2}{7}\frac{1}{7}\right\}$.

Figure 3

Phase diagrams for charged crystallization and reentrance as a function of $\varphi$ and $C_{\mathrm{AOT}}$ for particles with (a) $a=0.46$ $\mu \mathrm{m}$ (blue), (b) $0.70$ $\mu \mathrm{m}$ (black), and (c) $0.96$ $\mu \mathrm{m}$ (red). Experimentally determined phases marked with symbols: filled circles (fluid), open squares (bcc), open diamonds (fcc), and semifilled symbols (fluid-bcc coexistence). Solid curves denote experimental fluid-crystal boundary; solid-solid transition between bcc and fcc marked with dashed curves. (d)–(f) Phase diagrams of the same samples as a function of $\varphi$ and $1/{\kappa }_{0}a$, using the mapping from $C_{\mathrm{AOT}}$ to $1/{\kappa }_0$ in Fig. 1. Solid curves indicate numerical predictions, which closely follow the experimental data. Analytic predictions for the phase boundaries at low and high $C_{\mathrm{AOT}}$ are marked with dotted and dashed lines, respectively.

Figure 4

(a) Illustration of charged particles (blue), their double layers (red), and the OCP background (yellow). (b) Typical ion concentration profiles ${\rho }_{\pm }\left(r\right)$ around a negatively charged colloidal sphere of radius $a$ in a cell of radius $R$ in the weak-screening regime ${\kappa }_{0}R\lesssim 1$, such that the OCP-like ionic background charge ${\rho }_{+}\left(R\right)-{\rho }_{-}\left(R\right)={\rho }_{\mathrm{bg}}$ (see text) is nonvanishing. By charge neutrality the effective colloidal charge equals $(4\pi /3)(R^3-a^3){\rho }_{\mathrm{bg}}$, and the corresponding OCP point charge is $Z_{\mathrm{OCP}}=(4\pi /3)R^3{\rho }_{\mathrm{bg}}$.

Figure 5

Phase diagram for all particle radii, with $a=0.46$ $\mu \mathrm{m}$ (blue), 0.70 $\mu \mathrm{m}$ (black), and 0.96 $\mu \mathrm{m}$ (red), with experimental data and numerical calculations as in Fig. 2, shown as functions of dimensional parameters $\varphi a$ and $1/\left({\kappa }_0{a}^2\right)$. All experimental data collapse onto a single behavior (symbols), which is closely modeled by theoretical predictions (curves). Symbols are as in Fig. 3.