Gelation and phase coexistence in colloidal suspensions with short-range forces: Generic behavior versus specificity

The interplay between physical gelation and equilibrium phase transitions in asymmetric binary mixtures is analyzed from the effective fluid approach, in which the big particles interact via a short-range effective attraction beyond the core due to the depletion mechanism. The question of the universality of the scenario for dynamical arrest is then addressed. The comparison of the phase diagrams of the hard-sphere mixture and the Asakura-Oosawa models at various size ratios shows that strong specificity is observed for nonideal depletants. In particular, equilibrium gelation, without the competition with fluid-fluid transition is possible in mixtures of hard-sphere colloids. This is interpreted from the specificities of the effective potential, such as its oscillatory behavior and its complex variation with the physical parameters. The consequences on the dynamical arrest and the fluid-fluid transition are then investigated by considering in particular the role of the well at contact and the first repulsive barrier. This is done for the actual effective potential in the hard-sphere mixture and for a square well and shoulder model, which allows a separate discussion of the role of the different parameters, in particular on the localization length and the escape time. This study is next extended to mixtures of “hard-sphere-like” colloids with residual interactions. It confirms the trends relative to equilibrium gelation and illustrates a diversity of the phase behavior well beyond the scenarios expected from simple models.

Figure 1

(Color online) Phase diagram of the (a) Asakura-Oosawa and (b) hard-sphere mixture models for $\text{q}=12.5$ in the effective fluid representation. Solid lines: binodals; dashes: nonergodicity transition lines.

Figure 2

Phase diagram of the HS mixture for $q=10$. Solid lines: binodals; dashes: nonergodicity transition lines.

Figure 3

(Color online) Same as Fig. 1 for $q=5$ (inset: $q=4$). The dots in (b) are the nonergodicity transition line for $q=8$ (note that the FF transition is absent for $q\le 8$).

Figure 4

Nonergodicity transition lines and FF critical points in the $\left({\eta }_b,B_{2r}\right)$ plane for different effective potentials. $q=5$: ${\varphi }_{AO}$ (solid diamonds), ${\varphi }^{\ast }$ (circles), and ${\varphi }_{HS}^{eff}$ (open diamonds). $q=10$: ${\varphi }_{HS}^{eff}$ (squares). C denotes the critical point when present. The inset compares $q=5$: ${\varphi }_{AO}$ (diamonds) and $q=12.5$: ${\varphi }_{AO}$ (solid triangles) and ${\varphi }_{HS}^{eff}$ (open triangles).

Figure 5

(Color online) HS mixture effective potential for $q=5$ and ${\rho }_s^{\ast }=0.6$. Insets: variation with ${\rho }_s^{\ast }=0.6$ of the reduced widths ${\delta }_{att}^{\ast }$ and ${\delta }_{rep}^{\ast }$ (top), and energies ${\epsilon }_{att}^{\ast }$ and ${\epsilon }_{rep}^{\ast }$ (bottom) deduced form the Götzelmann, Evans and Dietrich (GED) potential.

Figure 6

(Color online) Fluid-fluid and nonergodicity transition lines for $q=5$. ${\varphi }_{HS}^{eff}$ (solid), ${\varphi }_{AO}$ (open), and ${\varphi }^{\ast }$ (half filled). The FF binodal exists only for ${\varphi }_{AO}$. Inset: ${\varphi }_{AO}$ (solid line) and ${\varphi }_{HS}^{eff}$ (dashes) for ${\rho }_s^{\ast }=0.2$ and 0.8.

Figure 7

Square well and shoulder potential.

Figure 8

Nonergodicity transition lines and FF critical point (C) for the SWS potential for (a) ${\delta }_{att}^{\ast }=0.03$ and (b) ${\delta }_{att}^{\ast }=0.1$, with ${\epsilon }_{rep}/{\epsilon }_{att}=1$. Solid line: ${\delta }_{rep}^{\ast }=0$. Dashes: ${\delta }_{rep}^{\ast }={\delta }_{att}^{\ast }$. Dots: ${\delta }_{rep}^{\ast }=2.3{\delta }_{att}^{\ast }$. For the FF critical points (C: squares), ${\epsilon }_{att}/k_B{T}_c$ increases with ${\delta }_{rep}$. Inset (a): comparison with [55] (dots) for ${\delta }_{rep}^{\ast }=0$. Inset (b): nonergodicity line for ${\delta }_{rep}^{\ast }={\delta }_{att}^{\ast }$, and ${\epsilon }_{rep}={\epsilon }_{att}/2$ (long dashes), ${\epsilon }_{rep}={\epsilon }_{att}$ (short dashes), and ${\epsilon }_{rep}=2{\epsilon }_{att}$ (dots and dashes) (the FF critical point does not vary).

Figure 9

Variation with $T^{\ast }$ of the particle localization length in the nonergodic state for SWS potentials with ${\delta }_{att}^{\ast }=1$. Dots: ${\epsilon }_{rep}=0$; dashes: (${\epsilon }_{rep}={\epsilon }_{att}$, ${\delta }_{rep}^{\ast }={\delta }_{att}^{\ast }$); long dashes: (${\epsilon }_{rep}={\epsilon }_{att}$, ${\delta }_{rep}^{\ast }=2.3{\delta }_{att}^{\ast }$); dot and dashes: (${\epsilon }_{rep}=2{\epsilon }_{att}$, ${\delta }_{rep}^{\ast }={\delta }_{att}^{\ast }$).

Figure 10

(Color online) Nonergodicity transition lines of a mixture of hard-sphere-like particles for $q=5$ and ${\xi }_{sb}={\sigma }_{sb}/100$. Dashes: pure hard spheres; dots: ${\epsilon }_{sb}=+\frac{3}{2}{k}_{B}T$ (with ${\epsilon }_{sb}$ as the contact value); solid line: ${\epsilon }_{sb}=-\frac{3}{2}{k}_{B}T$. Inset: $q=10$. Dashes: pure hard spheres; solid line: ${\epsilon }_{sb}=-\frac{3}{2}{k}_{B}T$.

Figure 11

Phase diagram of a mixture of hard-sphere-like particles for $q=10$, ${\xi }_{sb}={\sigma }_{sb}/40$, and ${\epsilon }_{sb}=-\frac{3}{2}{k}_{B}T$. Solid line: binodals; dashes: nonergodicity transition line. Inset: corresponding effective potential for ${\rho }_s^{\ast }=0.6$.