Joseph Stanzione - Observing the Twinkling Fractal Nature of the Glass Transition

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      Publication Details (including relevant citation   information):

      Accepted in the Journal of Non-Crystalline   Solids.     

      Abstract:

      A fundamental understanding of the nature and structure of the   glass transition in amorphous materials is currently seen as a   major unsolved problem in solid-state physics.  A new   conceptual approach to understanding the glass transition   temperature (Tg) of glass forming liquids   called the Twinkling Fractal Theory (TFT) has been proposed in   order to solve this problem.  The main idea underlying the   TFT is the development of dynamic rigid percolating solid fractal   structures near Tg, which are said to be in   dynamic equilibrium with the surrounding liquid.  This idea   is coupled with the concept of the Boltzmann population of   excited vibrational states in the anharmonic intermolecular   potential between atoms in the energy landscape.  Solid and   liquid clusters interchange or “twinkle” at a cluster size   dependent frequency ωTF, which is controlled   by the population of intermolecular oscillators in excited energy   levels.  The solid-to-liquid cluster transitions are in   accord with the Orbach vibrational density of states for a   particular fractal cluster g(ω) ~   ωdf-1, where the fracton dimension   df  = 4/3.  To an observer, these   clusters would appear to be “twinkling.”  In this   paper, experimental evidence supporting the TFT is   presented.  The twinkling fractal characteristics of   amorphous, atactic polystyrene have been captured via atomic   force microscopy (AFM).  Successive two-dimensional height   AFM images reveal that the percolated solid fractal clusters   exist for longer time scales at lower temperatures and have   lifetimes that are cluster size dependent. The computed fractal   dimensions, ≈ 1.88, are shown to be in excellent agreement with   the theory of the fractal nature of percolating clusters in   accord with  the TFT .  The twinkling dynamics of   polystyrene within its glass transition region are captured with   time-lapse one-dimensional AFM phase images.  The   autocorrelation cluster relaxation function was found to behave   as C(t) ~ t -4/3 and the cluster lifetimes t   versus width R were found to be in excellent agreement   with the TFT via t ~ R1.42. This paper   provides compelling new experimental evidence for the twinkling   fractal nature of the glass transition.

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