Locally preferred structures and many-body static correlations in viscous liquids

The influence of static correlations beyond the pair level on the dynamics of selected model glass formers is investigated. The pair structure, angular distribution functions, and statistics of Voronoi polyhedra of two well-known Lennard-Jones mixtures as well as of the corresponding Weeks-Chandler-Andersen variants, in which the attractive part of the potential is truncated, are compared. By means of the Voronoi construction, the atomic arrangements corresponding to the locally preferred structures of the models are identified. It is found that the growth of domains formed by interconnected locally preferred structures signals the onset of the slow-dynamics regime and allows the rationalization of the different dynamic behaviors of the models. At low temperature, the spatial extension of the structurally correlated domains, evaluated at fixed relaxation time, increases with the fragility of the models and is systematically reduced by truncating the attractions. In view of these results, proper inclusion of many-body static correlations in theories of the glass transition appears crucial for the description of the dynamics of fragile glass formers.

Figure 1

Pair potentials between particles of species 1 used in this study: LJ quadratic cut and shifted (dashed line), WCAS with cubic interpolation (solid line), and WCA cut and shifted (dotted line). Inset: Force between particles of species 1 for the WCAS (solid line) and the WCA (dotted line) potentials. In both panels, the dotted vertical line marks the distance $r=2^{1/6}$ corresponding to the minimum of the LJ potential.

Figure 2

Radial distribution functions $g_{12}(r)$ for (a) the Kob-Andersen mixture and (b) the Wahnström mixtures. The state points considered are (a) $\rho =1.2$, $T=0.5$ and (b) $\rho =1.297$, $T=0.6$. In both panels, solid, dashed, and dotted lines indicate results for the LJ, WCAS, and WCA models, respectively. Error bars are smaller than the widths of the lines.

Figure 3

Angular distribution functions $D_{121}(r)$ for (a) Kob-Andersen mixtures and (b) Wahnström mixtures. State points and lines are the same as in Fig. 2. Error bars are smaller than the widths of the lines.

Figure 4

(a) Structural relaxation time $\tau$ as a function of $1/T$ for Kob-Andersen mixtures for the LJ (filled circles), WCAS (open circles), and WCA (open triangles) models. The wave vector considered for the calculation of $\tau$ is $k=7.0$. Fits to the modified Vogel-Fulcher-Tammann equation [Eq. (3)] are shown as solid lines. (b) Average number $N_{\mathrm{LPS}}$ of particles in locally preferred structure (LPS) domains formed by (0,2,8) polyhedra. Symbols have the same meaning as in (a). (c) Average fraction of particles of species 2 at the center of (0,2,8) polyhedra as a function of $1/T$. Symbols have the same meaning as in (a).

Figure 5

Same as Fig. 4 but for Wahnström mixtures. For these systems, the LPS corresponds to (0,0,12) polyhedra.

Figure 6

Average fraction $f_{\mathrm{LPS}}^m$ of LPSs in local minima (open circles, left axis) and average potential energy $u_m$ of local minima (filled circles, right axis) as a function of $T$ for Kob-Andersen mixtures for (a) the LJ model and (b) the WCAS model. The dynamic crossover temperatures $T^{*}$ obtained from fits to Eq. (3) are indicated as vertical dotted lines.

Figure 7

Same as Fig. 6 but for Wahnström mixtures. The vertical axes are analogous to those in Fig. 6.

Figure 8

Relaxation time $\tau$ as a function of the average number $N_{\mathrm{LPS}}$ of particles in the LPS domains. The corresponding fragility indices $K$ of the models, obtained from fits to the modified VFT equation [Eq. (3)], are also indicated.