Nonmonotonic dynamic correlations in quasi-two-dimensional confined glass-forming liquids

It has been broadly accepted that the behavior of glass-forming liquids, where their relaxation dynamics exhibit a pronounced slowdown as they are cooled toward the glass transition temperature, is caused by the increase in one or more correlation lengths. However, the role of length scales in the dynamics of glass-forming liquids is not clearly established, and past simulation work that suggests a surprising nonmonotonic temperature evolution of spatial dynamical correlations near the mode-coupling crossover temperature has been both questioned and supported by subsequent work. Here, using molecular dynamics simulation, we also show a striking maximum in the dynamic length scale ${\xi }_{\mathrm{c}}^{\mathrm{dyn}}$ at a given temperature, but the temperature of this maximum is found to shift as the size of the confined system increases. Furthermore, we find that such a maximum disappears for all geometry sizes considered when a rough wall is replaced with a smooth, hard wall, suggesting that the nature of the nonmonotonic temperature dependence of ${\xi }_{\mathrm{c}}^{\mathrm{dyn}}$ does not reflect an intrinsic property of bulk liquids, but originates from wall effects. Our results provide new insights into the dynamics of glass-forming liquids, particularly for quasi-two-dimensional systems.

Figure 1

(a) Time dependence of the overlap profile $Q_{\mathrm{c}}(t,z)$ based on Eq. (2) at $z=7.75$ for three sandwiched geometry sizes $d$ of 16.0 (black), 32.0 (red), and 64.0 (blue). The cyan curves present the bulk behavior. (b) Temperature evolution of the ratio involving the relaxation time ${\tau }_{\mathrm{c}-\mathrm{cent}}$ for particles located at the center of the sandwiched geometry and the relaxation time ${\tau }_{\mathrm{c}-\mathrm{bulk}}$ for particles in bulk liquids for the three values of $d$ applied above. The dashed-dotted vertical bars indicate the temperatures $T_{\max -\mathrm{c}}$ where the dynamic length scale is a maximum.

Figure 2

Temperature evolution of dynamic length scales ${\xi }^{\mathrm{dyn}}$. The values of ${\xi }^{\mathrm{dyn}}$ corresponding to the blue triangles, magenta diamonds, red circles, and black squares are respectively obtained from Kob et al. [26] with a semi-infinite space model employing Eq. (3), from Flenner et al. [9] in a bulk liquid, by our method employing Eq. (3), and by our method employing Eq. (5) for a sandwiched model. The dark-yellow dashed-dotted vertical bar indicates the mode-coupling transition temperature $T_{\mathrm{c}}=5.2$ [35, 36] in bulk liquids. All confined models are of equivalent size $d=34.2$.

Figure 3

Temperature dependence of the dynamic length scales ${\xi }_{\mathrm{c}}^{\mathrm{dyn}}$ in a sandwiched geometry comprising (a) two rough walls and (b) one rough wall and one smooth, hard wall for $d$ = 16.0 (black squares), $d$ = 32.0 (red circles), and $d$ = 64.0 (blue triangles). The olive dashed, dark-yellow dashed-dotted, and black short-dashed vertical bars in both (a) and (b), respectively, represent the onset temperature $T_{\mathrm{onset}}$ = 13 [35, 36], mode-coupling transition temperature $T_{\mathrm{c}}$ = 5.2 in bulk liquids [35, 36] and the peak temperature in ${\xi }_{\mathrm{c}}^{\mathrm{dyn}}$ obtained from Kob et al. [26] in a confined system. All ${\xi }_{\mathrm{c}}^{\mathrm{dyn}}$ are calculated by Eq. (5).