The Twinkling Fractal Theory of the Glass Transition: Applications to Soft Matter

The Twinkling Fractal Theory (TFT) of the glass transition has recently been demonstrated experimentally [J.F. Stanzione et al., J. Non Cryst. Sol., (2011, 357,311]. The hard to-soft matter transition is characterized by the presence of solid fractal clusters with liquid-like pools that are dynamically interchanging via their anharmonic intermolecular potentials with Boltzmann energy populations with a characteristic temperature dependent vibrational density of states g($\omega ) \quad \sim \quad \omega ^{df}$ . The twinkling fractal frequencies $\omega $ cover a range of 10$^{12}$ Hz to 10$^{-10}$Hz and the fractal solid clusters of size R have a lifetime $\tau \quad \sim $ R$^{Df/df}$, where the fractal dimension D$_{f}$ $\approx $ 2.4 and the fracton dimension d$_{f}$ = 4/3. Here we explore its application to a number of soft matter issues. These include (a) Confinement effects on T$_{g}$ reduction in thin films of thickness h, where by virtue of large cluster exclusion, $\Delta $T$_{g} \quad \sim $ 1/h$^{Df/df}$; (b) T$_{g}$ gradients near bulk surfaces, where the smaller clusters on the surface have a faster relaxation time; (c) Effect of twinkling surfaces on cell growth, where at T $\approx $ T$_{g}$ + 20 C, there exists a twinkling fractal range that leads to bell-shaped enhancement of cell growth and chemical up-regulation via the twinkling surfaces ``communicating `` with the cells through their vibrations; and (d) adhesion above and below T$_{g}$ where topological fluctuations associated with g($\omega )$ promotes the development of nano-nails at the interface.