Correlation between temperature variations of static and dynamic properties in glass-forming liquids

Detailed analysis of the static structure factor $S\left(Q\right)$ in several glass-forming liquids reveals that the temperature variations of the width of the main diffraction peak $\mathrm{\Delta }Q\left(T\right)$ correlate with the fragility of these liquids. This observation suggests a direct connection between rather subtle structural changes and sharp slowing down of structural relaxation in glass-forming liquids. We show that this observation can be rationalized using the Adam-Gibbs approach, through a connection between temperature variations of structural correlation length, $l_c\sim 2\pi /\mathrm{\Delta }Q$, and the size of cooperatively rearranging regions.

Figure 1

X-ray scattering data for polystyrene (PS) $\mathrm{MW}=500\mathrm{g}/\mathrm{mol}$, propylene carbonate (PC), and salol. Symbols present experimental data. For PS and PC the data in a glassy state at $T\sim 0.9T_g$ (blue circles) and in a liquid state at $T\sim 1.3T_g$ (red triangles). Thick solid lines correspond to the fit by a sum of two Lorentzian functions, which are shown by dashed and thin solid lines. Only the data in a glassy state and their fit by three Lorentzian functions are shown for salol.

Figure 2

Dependence of the diffraction peak width normalized by the peak position $\mathrm{\Delta }Q/Q_{max}$ vs $T/T_g$ for materials with wide variations in fragility (from $\mathrm{GeS}{\mathrm{e}}_2$ with $m=32$ to PC with $m=100$). The error bars are within the symbol size.

Figure 3

The relative change in the width of the main diffraction peak [Eq. (2)] vs fragility for several glass-forming systems. (a) $\mathrm{\Delta }{Q}_{\mathrm{liq}}$ was chosen at $T=1.3T_g$; (b) $\mathrm{\Delta }{Q}_{\mathrm{liq}}$ was chosen at temperature when ${\tau }_{\alpha }\sim {10}^{-7}-{10}^{-9}\mathrm{s}$. The error bars are within the symbol size.

Figure 4

(a) Correlation between the ratio of the CRR sizes $L\left(1.3T_g\right)/L\left(T_g\right)$ and the ratio of the structural correlation lengths $l_c\left(1.3T_g\right)/l_c\left(T_g\right)$. Materials shown and reference for ${\tau }_{\alpha }\left(T\right)$ are the following: orthotherphenyl (OTP) [40], propylene carbonate (PC) [41], sucrose benzoate (SB) [42], polystyrene (PS) oligomer with $\mathrm{MW}=0.5\mathrm{kg}/\mathrm{mol}$ [43], salol [44], glycerol [41], and propylene glycol (PG) [41]. (b) The dependence of log ${\tau }_{\alpha }\left(T\right)$ on $l_c{\left(T\right)}^3/T$ normalized to its value at $T_g$ for PS, SB, PC, and glycerol. Symbols are the same as in (a).