Dynamical study of a polydisperse hard-sphere system

We study the interplay between the fluid-crystal transition and the glass transition of elastic sphere system with polydispersity using nonequilibrium molecular dynamics simulations. It is found that the end point of the crystal-fluid transition line, which corresponds to the critical polydispersity above which the crystal state is unstable, is on the glass transition line. This means that crystal and fluid states at the melting point becomes less distinguishable as polydispersity increases and finally they become identical state, i.e., marginal glass state, at critical polydispersity.

Figure 1

(Color online) Phase diagram showing the polydispersity vs packing fraction (or pressure, inset) plane. There are three equilibrium phases: fluid, crystal, fluid-crystal coexistence. The boundary between the fluid and the glass indicates a dynamical transition.

Figure 2

(Color online) Time derivatives of the mean density is plotted with respect to pressure for $\Delta =0.0–0.085$. The derivative $d\varphi /dt$ is approximated by $\left[\varphi \left(2t_w\right)-\varphi \left(t_w\right)\right]/t_w$ with $t_w/0.001=2^{19}$ and $2^{20}$.

Figure 3

(Color online) Polydispersity dependence of the density gap between the fluid and crystal states on the melting line. The results for different Young’s moduli are shown together but very little difference is observed. The solid curve denotes $\delta \varphi =0.45\times {\left(0.088-\Delta \right)}^{0.73}$. (inset) Log-log plot of the relation between the density gap and the crystalline order parameter on the melting line.

Figure 4

(Color online) Pressure dependence of the diffusion constant for fixed polydispersity. The data for various waiting times are plotted together to show the aging behavior. The initial state is random packing with packing fraction 0.50. (inset) Pressure dependence of the packing fraction for fixed polydispersity. For each $\Delta$, we show the data at three times, $t/0.001=2^{20}$, $2^{21}$, and $2^{22}$ to show good convergence.

Figure 5

(Color online) Polydispersity dependence of the packing fraction at fixed pressure. The data for FCC and random initial configurations are plotted together, which coincide for large $\Delta$. In each case, we show the data at three times, $t/0.001=2^{16}$, $2^{17}$, and $2^{18}$.