Flow, diffusion and crystallization of supercooled liquids: Revisited

Within the last five years, investigators using NMR and forced Raleigh scattering techniques have found that the Stokes–Einstein (S–E) relation breaks down in supercooled liquids. It has been pointed out that the shear viscosity has a significantly stronger temperature dependence than either the self-diffusion coefficient, $\mathrm{D(T),}$ or the translational diffusion coefficient of tracer molecules of comparable size (not shape) to the host liquid. These observations confirm our results on trinaphthylbenzene (TNB) and 1,2 diphenylbenzene (OTP), published in a series of papers more than 30 years ago. An analysis of crystal growth rate measurements on these materials demonstrated that the transport-dominated crystal growth rate, $G^{\prime }\mathrm{(T),}$ exhibited a weaker temperature dependence than the shear viscosity, $\mathrm{\eta (T).}$ Where the expression $\mathrm{G(T)=f(T)/\eta (T)}$ is often substituted for the more basic growth rate relationship $\mathrm{G(T)=D(T)f(T).}$ We showed that this practice (often used) is invalid. Here, $\mathrm{f(T)}$ is a nucleation/growth free energy term. Reexamination of our earlier work has shown that the extent of the S–E “breakdown,” as revealed by crystal growth rate data, is consistent with the answers that are now provided by modern NMR and forced Rayleigh scattering techniques. Employing the derivative procedure of Stickel and co-workers to fit our TNB viscosity data over more than 15 orders of magnitude, requires an Arrhenius temperature dependence at high temperatures, a “crossover” to a Vogel–Fulcher–Tammann–Hesse dependence at some temperature $T_A,$ and a further “crossover” to another Vogel–Fulcher–Tammann–Hesse form at a lower temperature, $T_B.$ Below $T_B$ a disparity occurs between the temperature dependences of the transport-dominated crystal growth rate and viscosity. Where our old and the recent results coincide, the techniques represent or measure similar parameters.