Abstract
The twinkling fractal theory (TFT) of the glass transition temperature T~g~ provides a new method of analyzing rate effects and time–temperature superposition in amorphous materials. The rate dependence of T~g~ was examined in the light of new experimental and theoretical evidence for the nature of the dynamic heterogeneity near T~g~. As T~g~ is approached from above, dynamic solid fractal clusters begin to form and eventually percolate rigidity at T~g~. The percolation cluster is a solid fractal and to the observer, appears to “twinkle” as solid and liquid clusters interchange in dynamic equilibrium with a vibrational density of states g(ω) ∼ ω. The solid‐to‐liquid twinkling frequencies ω~TF~ are controlled by the Boltzmann population of intermolecular oscillators in excited energy levels of their anharmonic potential energy functions U(x) such that ω~TF~ = ω exp −B(T*^2^ − T^2^)/kT in which T* ≈ 1.2__T__~g~. An oscillator changes from a solid to a liquid when a thermal fluctuation causes it to expand beyond its inflection point in the anharmonic potential. This leads to a continuous solid fraction P~s~ near T~g~ given by P~S~ ≈ 1−[(1 − p~c~) T/T~g~] where p~c~ ≈ 1/2 is the rigidity percolation threshold. Since g(ω) is continuous from very low to very high frequencies, the complex twinkling dynamics existing near T~g~ produces a continuous relaxation spectrum with many different length scales and times associated with the fractal clusters. The twinkling frequencies control the kinetics of T~g~ such that for a given observation time t when the rate γ > 1/t, only those parts of the twinkling spectrum with ω > γ can contribute to relaxation or percolation upto time t. The most important results in this article are as follows: The TFT describes the rate dependence of T~g~, both for DSC thermal heating/cooling rates and DMA frequencies as the classic T~g~ − lnγ law as T~g~(γ) = T~go~ + (k/2__B__) ln γ/γ~o~ in which the constant B = 0.3 cal/mol K^2^. The constant B appears quite universal for the 17 thermoset polymers investigated in this study and 18 linear polymers investigated by others. Many other amorphous metal and ceramic glass materials exhibited the same rate law but required a new B value approximately half that for polymers. The same B = 0.3 value was also used to successfully describe the TTS shift factors using the twinkling fractal frequencies ω~TF~ = ωexp −B(T*^2^ − T^2^)/kT, as ln a~T~(TFT) = exp B(T~R~^2^ − T^2^)/kT, which gave comparable results with the classical WLF equation, log a~T~ = [−C~1~(T − T~R~)]/[C~2~ + (T − T~R~)]. The advantage of the TFT over the WLF is that C~1~ and C~2~ are not universal constants and must be determined for every material, whereas the TFT uses one known constant B which appears to be the same for all polymers. The TFT has also been found to describe the strong and fragile nature of the viscosity behavior of liquids and the rate and temperature dependence of the yield stress in polymers. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2578–2590, 2009