Flow, diffusion and crystallization of supercooled liquids: Revisited

Abstract

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, 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′(T), exhibited a weaker temperature dependence than the shear viscosity, η(T). Where the expression G(T)=f(T)/η(T) is often substituted for the more basic growth rate relationship G(T)=D(T)f(T). We showed that this practice (often used) is invalid. Here, 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 TA, and a further “crossover” to another Vogel–Fulcher–Tammann–Hesse form at a lower temperature, TB. Below TB 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.

Growth and form of spherulites

“…This assumption is plausible because these coarse-grained mobilities are functions of their molecular counterparts. Moreover, recent experiment has shown that the rate of crystallization in highly supercooled liquids is proportional to D tr , even under decoupling conditions [34,40,41]. In our model, the growth velocity scales linearly with M φ , so consistency requires M φ ∝ D tr .…”

“…These heterogeneities are associated with the formation of regions within the fluid that have either a much higher or much lower mobility relative to a simple fluid in which particles exhibit Brownian motion [1,[34][35][36]. These nanoscale heterogeneities persist on timescales of the order of the stress relaxation time, which can be minutes near the glass transition and eons at lower temperatures.…”

The violation of the Stokes–Einstein relation in supercooled water

“…The self-diffusion coefficient shows, as far as water in the present experiment is concerned, an enhancement of orders of magnitude from what expected from SER (19-21, 23, 24). These decouplings of the transport coefficients, observed as a SER violation, have been attributed to the occurrence of dynamical heterogeneities in structural glass formers (19,21,25,26). Thus, in supercooled liquids there exist regions of varying dynamics, i.e., fluctuations that dominate their transport properties near the GT.…”

Do Theories of the Glass Transition, in which the Structural Relaxation Time Does Not Define the Dispersion of the Structural Relaxation, Need Revision?

“…64,69 (iii) The separation, [log(τ R ) -log(τ JG )], of τ R from the Johari-Goldstein relaxation time τ JG at a fixed value of τ R is proportional to n. 42,62,63,70 (iV) The observed crossover at some temperature T B above T g of the temperature dependence of τ R from one VFTH equation to another, [70][71][72][73] the apparent onset of bifurcation of τ JG from τ R , 39 and the decoupling of translational diffusion from viscosity 75 are all related to the small size of n at temperatures above T B and the more rapid increase of n across T B on decreasing the temperature.…”