Cooperativity in plastic crystals

A statistical mechanical model previously adopted for the analysis of the $\alpha$-relaxation in structural glass formers is rederived within a general theoretical framework originally developed for systems approaching the ideal glassy state. The interplay between nonexponentiality and cooperativity is reconsidered in the light of energy landscape concepts. The method is used to estimate the cooperativity in orientationally disordered crystals, either from the analysis of literature data on linear dielectric response or from the enthalpy relaxation function obtained by temperature-modulated calorimetry. Knowledge of the specific heat step due to the freezing of the configurational or conformational modes at the glass transition is needed in order to properly account for the extent to which the relaxing system deviates from equilibrium during the rearrangement processes. A number of plastic crystals have been analyzed, and relatively higher cooperativities are found in the presence of hydrogen bonding interaction.

Figure 1

Real and imaginary parts of $C_p$ for LG (upper panel) obtained for a cooling rate of 0.1 K/min and a modulation frequency of $0.017{\mathrm{s}}^{-1}$. The short-dashed line is a Gaussian fitting on $C_p^{\prime \prime }$ for the calculation of the cooperativity via Eq. (21); the straight dashed lines, $C_{p,\mathrm{liq}}^{\prime }$ and $C_{p,\mathrm{glass}}^{\prime }$ are the relaxed and unrelaxed contributions to $C_p^{\prime }$, respectively, extrapolated to the whole temperature interval displayed. The Havriliak-Negami expression of Eq. (16) (solid line) is adjusted to the corresponding Cole-Cole plot of $C_{p,\mathrm{norm}}$ (lower panel) in the highlighted temperature interval. Inset “a” reports the $T$ dependence of the central relaxation time (open squares) and the best fitting linear regression (solid line); inset “b” shows how the different modes contribute to $C_{p,\mathrm{norm}}^{\prime \prime }$ depending on their characteristic relaxation time.

Figure 2

Cooperativities found for the systems of Table 1 (LG excluded); the associated glass transition temperatures are also indicated by the dotted arrows. The lines are guides for the eye.