Single-Particle and Collective Slow Dynamics of Colloids in Porous Confinement

Using molecular dynamics simulations, we study the slow dynamics of a hard sphere fluid confined in a disordered porous matrix. The presence of both discontinuous and continuous glass transitions as well as the complex interplay between single-particle and collective dynamics are well captured by a recent extension of mode-coupling theory for fluids in porous media. The degree of universality of the mode-coupling theory predictions for related models of colloids is studied by introducing size disparity between fluid and matrix particles, as well as softness in the interactions.

Figure 1

Kinetic diagram of the QA HS system: MCT transition lines (thin lines; from Ref. 7) and dynamic arrest line from simulations (thick line; see text for definition). The $A_3$ singularity predicted by MCT is indicated by a solid triangle. Open and solid circles indicate equilibrated and glassy simulated state points, respectively.

Figure 2

Upper panels: intermediate scattering functions at ${\varphi }_m=0.05$ for different values of ${\varphi }_f$: (a) connected part $F_c(k=7.0,t)$ and (b) self part $F_s(k=7.0,t)$. Solid lines are fits to the second-order expansion of the $\beta$ correlator (see text). Error bars for selected times represent 1 standard deviation on the average over matrix realizations. Lower panels: nonergodicity parameter $f(k)$ (symbols) for (c) connected and (d) self correlators at ${\varphi }_m=0.05$, ${\varphi }_f=0.50$. The corresponding nonergodicity parameters predicted by MCT at ${\varphi }_f=0.446$ are included as solid lines.

Figure 3

Intermediate scattering functions at ${\varphi }_m=0.20$ for different values of ${\varphi }_f$: (a) connected part $F_c(k=7.0,t)$ and (b) self part $F_s(k=7.0,t)$. Error bars as in Fig. 2. Inset of (b): enlarged view of the plateau of $F_s(k=7.0,t)$ at long times.

Figure 4

MSD at constant ${\varphi }_f=0.1$ for ${\varphi }_m=0.05$, 0.10, 0.15, 0.20, 0.225, 0.25, and 0.275 (from left to right). Solid lines are fits to $\delta r^2(t)\sim t^z$ in the subdiffusive regime. Error bars as in Fig. 2. Inset: $z$ as a function of ${\varphi }_f$ for selected ${\varphi }_m$ (symbols as in the main plot).

Figure 5

MCT kinetic diagram for (a) QA hard spheres with size ratio $\lambda =0.5$, 1.0, and 2.0 (from left to right) and (b) QA soft spheres with $\lambda =1.0$ and repulsive exponent $n=6$, 7, and 10 (from top to bottom). Lines as in Fig. 1. Solid triangles indicate points where type $A$ and $B$ transitions meet.