Numerical Investigation of Glassy Dynamics in Low-Density Systems

Vitrification in colloidal systems typically occurs at high densities driven by sharply varying, short-ranged interactions. The possibility of glassy behavior arising from smoothly varying, long-ranged particle interactions has received relatively little attention. Here we investigate the behavior of screened charged particles, and explicitly demonstrate that these systems exhibit glassy properties in the regime of low temperature and low density. Properties close to this low-density (Wigner) glass transition share many features with their hard-sphere counterparts, but differ in quantitative aspects that may be accounted for via microscopic theoretical considerations.

Figure 1

Evolution in the supercooled regime, upon decreasing $T$, of: (a) partial radial distribution functions $g_{11}(r)$, $g_{12}(r)$ and $g_{22}(r)$. The perfect agreement between two different simulation sizes, i.e., $N={10}^3$ (lines) and $N={10}^4$ (symbols), provides evidence that results are equilibrated, reproducible and not phase separating; (b) partial static structure factors $S_{ij}(q)$, as well as $S_{\mathrm{cc}}(q)$ [35] which rules out the presence of a demixing transition. Symbols are results for simulations with $N={10}^4$ particles, lines are splined curves.

Figure 2

Self autocorrelation function for the density of type-1 particles ${\varphi }_1^s(q,t)$ at $q\xi \simeq 1.09$: (a) $T$ dependence (from left to right: $T^{*}=10$, 5, 3, 2.5, 2.25, 2, 1.9, 1.7, 1.5, 1.3) and (b) TTS scaling only in the temperature range $1.7\lesssim T^{*}\lesssim 3$. The dashed line is a stretched exponential fit of the master curve with stretching exponent $\beta \sim 0.65$. In (a) data for the larger simulation size (symbols) are also reported. Below $T_c^{*}=1.7$ the system shows a clear aging behavior, as well as a breakdown of TTS due to the increase in the plateau height. For type-2 particles, a similar, albeit slower dynamics (due to the larger repulsion amplitude), occurs.

Figure 3

$⟨r_1^2(t)⟩$ for type-1 particles with decreasing $T^{*}$. Lines and symbols refer, respectively, to simulations with $N={10}^3$ and $N={10}^4$ particles. Inset: Power-law fit to the diffusion coefficient $D$, with exponent ${\gamma }_D=1.45$ and $T_c^{*}\simeq 1.67$.

Figure 4

Debye-Waller factors from simulations extracted from stretched exponential fits (symbols) and from MCT calculations (lines) for type-1 (left) and type-2 (right) particles, respectively. The simulation temperature is $T^{*}=2.0$, while for MCT calculations we report results at the critical temperature $T_{\mathrm{MCT}}^{*}=2.81$.