Observing the Twinkling Fractal Nature of the Glass Transition

The main idea underlying the Twinkling Fractal Theory (TFT) of the glass transition is the development of dynamic percolating solid fractal structures near $T_{g}$, which are in dynamic equilibrium with the surrounding liquid. Solid and liquid clusters interchange at a frequency \textit{$\omega $}$_{TF}$, which is controlled by the population of intermolecular oscillators in excited energy levels in accord with the Orbach vibrational density of states for a particular fractal cluster \textit{g($\omega )$} $\sim $ \textit{$\omega $}$^{df-1}$, where the fracton dimension $d_{f}$ = 4/3. To an observer, these clusters would appear to be ``\textit{twinkling}.'' A time-lapse tapping-mode atomic force microscopy (AFM) technique has been developed in order to experimentally confirm such phenomena. The \textit{twinkling} behavior of amorphous, atactic polystyrene with $M_{W}$ = 194,000 g/mol, PDI = 1.07 (GPC) and $T_{g}$ = 375 K (DSC-heating rate of 3 K/min) has been captured above (383 K), below (358 K), and well below (298 K) its $T_{g}$. Two-dimensional space images reveal fractal dimensions consistent with the TFT. The \textit{twinkling} behavior was analyzed using a statistical autocorrelation function in conjunction with the apparent stretched exponential Kohlrausch-Williams-Watts relaxation function.