Gel to glass transition in simulation of a valence-limited colloidal system

We numerically study a simple model for thermo-reversible colloidal gelation in which particles can form reversible bonds with a predefined maximum number of neighbors. We focus on three and four maximally coordinated particles, since in these two cases the low valency makes it possible to probe, in equilibrium, slow dynamics down to very low temperatures $T$. By studying a large region of $T$ and packing fraction $\phi$ we are able to estimate both the location of the liquid-gas phase separation spinodal and the locus of dynamic arrest, where the system is trapped in a disordered non-ergodic state. We find that there are two distinct arrest lines for the system: a {\it glass} line at high packing fraction, and a {\it gel} line at low $\phi$ and $T$. The former is rather vertical ($\phi$-controlled), while the latter is rather horizontal ($T$-controlled) in the $(\phi-T)$ plane. Dynamics on approaching the glass line along isotherms exhibit a power-law dependence on $\phi$, while dynamics along isochores follow an activated (Arrhenius) dependence. The gel has clearly distinct properties from those of both a repulsive and an attractive glass. A gel to glass crossover occurs in a fairly narrow range in $\phi$ along low $T$ isotherms, seen most strikingly in the behavior of the non-ergodicity factor. Interestingly, we detect the presence of anomalous dynamics, such as subdiffusive behavior for the mean squared displacement and logarithmic decay for the density correlation functions in the region where the gel dynamics interferes with the glass dynamics.