Picosecond Dynamic Heterogeneity, Hopping, and Johari-Goldstein Relaxation in Glass-Forming Liquids

We show that incoherent quasielastic neutron scattering from molecular liquids reveals a two-state dynamic heterogeneity on a 1 ps time scale, where molecules are either highly confined or are free to undergo relatively large excursions. Data ranging from deep in the glassy state to well above the melting point allows us to observe temperature-dependent population levels and exchange between these two states. A simple physical picture emerges from this data, combined with published work, that provides a mechanism for hopping and for the Johari-Goldstein (${\beta }_{\text{JG}}$) relaxation, and allows us to accurately calculate the diffusion coefficient, $D_T$, and characteristic times for $\alpha$, and ${\beta }_{\text{JG}}$ relaxations from ps time scale neutron data.

Figure 1

ISF at 1 ps for PG at $T=60$, 90, 120, 150, 180, 210, 240, 265, 290, 307, 320, 350, 375, 400, and 425 K (circles, top to bottom), with fits to Eq (1) (dashed lines). Inset: van Hove function with abscissa normalized by PG hydrodynamic radius corresponding to fits at $T=60$, 120, 180, 240, 290, 320, 375, and 425 K (bottom to top). Data were collected at the NIST neutron center on NG4 [8] with an energy resolution of $200\mu \mathrm{eV}$ and $\lambda =4.0\AA$.

Figure 2

Confinement length scales for LC (a)–(e) and TC (f) molecules in the two-state model at 1 ps (solid symbols) and 10 ps (hollow symbols). Solid lines are best fits. Arrows indicate $T_c$ for each material. Error bars indicate uncertainties in parameters at one standard deviation.

Figure 3

$\mathrm{\Phi }$ at 1 ps (solid symbols), and $\mathrm{\Phi }$ at 10 ps (hollow symbols). Symbols have same association as in Fig. 2. Solid and dashed lines are guides to the eye. The insets are described in the text.

Figure 4

Calculated relaxation times: ${\tau }_{\beta ,\text{JG}}$ (solid symbols), ${\tau }_{\alpha }$ (hollow symbols), ${\tau }_0={\tau }_{\beta ,\text{fast}}$ (dashed lines). Measured relaxation times: ${\tau }_{\alpha }$ (solid lines) [32, 34, 35], ${\tau }_{\beta ,\text{JG}}$ (dashed-dotted lines) [32, 34]. The upper inset shows $D_T$ values for PC [14], glycerol [33] and sorbitol [17] (symbols), and fits to Eq. (4) (solid lines). The arrows indicate $T_c$ for these liquids. Symbols have the same association with samples as in previous figures. The lower inset shows the correlation between $\gamma$ and fragility.