Jump-precursor state emerges below the crossover temperature in supercooled $o$-terphenyl

In a supercooled liquid, the crossover temperature $T_c$ separates a high-temperature region of diffusive dynamics from a low-temperature region of activated dynamics. A molecular-dynamics simulation of all-atom, flexible $o$-terphenyl [Eastwood et al., J. Phys. Chem. B 117, 12898 (2013)] is analyzed with advanced statistical methods to reveal the molecular features associated with this crossover. The simulations extend to an α-relaxation time of 14 μs (272.5 K), two orders of magnitude slower than at $T_c$ (290 K). At $T_c$ and below, a distinct state emerges that immediately precedes an orientational jump. Compared to the initial, tightly caged state, this jump-precursor state has a looser cage, with solid-angular excursions of 0.054–0.0125 × 4π sr. At $T_c$ (290 K), rate heterogeneity is already the dominant cause of stretched relaxation. Exchange within the distribution of rates is faster than α relaxation at $T_c$, but becomes equal to it at the lowest temperature simulated (272.5 K). The results trend toward a recent experimental observation near the glass transition (243 K) [Kaur et al., Phys. Rev. E 98, 040603(R) (2018)], which saw exchange substantially slower than α relaxation. Overall, the dynamic crossover comprises multiple phenomena: the development of heterogeneity, an increasing jump size, an emerging jump-precursor state, and a lengthening exchange time. The crossover is neither sharp, nor a simple superposition of the high- and low-temperature regimes; it is a broad region that contains unique and complex phenomena.

Figure 1

(a), (d) 1D correlation functions $C_{\ell }\left(\tau \right)$ for $\ell =1$ to 20. (b), (e) The Green's function $G(X,\tau )$ (solid line) and fits to the three-population model (points). Slices are shown at delays τ where $C_1\left(\tau \right)$ equals the values shown in the legend. The same times are marked by vertical bars in (a), (d). (c), (f) Magnified view of the Green's function after removing a constant (c) or a straight-line (f) component. Top row: below $T_c$ (272.5 K). Bottom row: at $T_c$ (290 K).

Figure 2

(a) Occupancies of the three populations (solid curves: A black, B orange, D green) derived from fits to the Green's functions [Figs. 1 and 1] along with fits to the three-population model (A dots, B triangles, D squares) at $T_c$ (290 K, left) and below $T_c$ (272.5 K, right). (b) The 3D correlation function $C_{101}({\tau }_3,{\tau }_2,{\tau }_1)$ below $T_c$ (272.5 K) shown as 2D decay spectra ${\widehat{C}}_{101}(T_3,{\tau }_2,T_1)$ at various values of ${\tau }_2$. (c) Comparison of the domain lifetime [$f_{\mathrm{het}}\left({\tau }_2\right)$, red solid line], α relaxation [$C_1\left(\tau \right)$, blue dash-dotted line], and the precursor-state formation [$A\left(\tau \right)$, black dashed line] at $T_c$ (290 K, left), below $T_c$ (272.5 K, middle), and near $T_g$ (244.5 K, right, from Ref. [30]).