Dynamical arrest and replica symmetry breaking in attractive colloids

Within the replica symmetry breaking framework developed by Mézard and Parisi we investigate the occurrence of structural glass transitions in a model of fluid characterized by hard sphere repulsion together with short-range attraction. This model is appropriate for the description of a class of colloidal suspensions. The transition line in the density-temperature plane displays a reentrant behavior, in agreement with mode coupling theory and recent molecular dynamics simulations. Quantitative differences are found, together with the absence of the predicted glass-glass transition at high density. We also perform a systematic study of the pure hard-sphere fluid in order to ascertain the accuracy of the adopted method and the convergence of the numerical procedure.

Figure 1

Replica symmetric (left) and one-step replica symmetry breaking (center) form of the correlation matrix for a replicated system. The black squares represent single elements $\left(g_{*}\right)$, while the dimension of the $n\times n$ matrix (light gray for $g_0$) and of the $m\times m$ blocks (dark gray for $g_1$) is, in general, not fixed. In the figure, $n=6$ and $m=3$. Since in the physical case of zero replica coupling the correlators corresponding to the light-gray area vanish, the numerical computations can be simplified by considering only one of the blocks (right).

Figure 2

An example of correlation functions for sticky spheres close to the dynamical glass transition. The thermodynamic state is $\rho =1.1878$ and $T=0.6$, and the data refer to the system with $\Delta =1∕64$.

Figure 3

Dependence of the critical density on the grid: the dots represent the data in the last column of the table; the dashed line is the best fit using Eq. (8).

Figure 4

Phase diagram for the square well fluid for different well widths $\Delta$. The dashed line represents the hard sphere transition density computed with the same discretization parameters.

Figure 5

$P\left(r\right)$ for the same density $(\rho =1.19)$ and $\Delta =1∕128$ but different temperatures.

Figure 6

Detailed structure of $P\left(r\right)$ at short distance for the data of Fig. 5. As the temperature decreases at constant density $\rho =1.19$ no singular behavior of $P\left(r\right)$ is observed.