Observing the twinkling fractal nature of the glass transition

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 ( T g ) 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 T g , 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 ω TF , 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) ~ ω df − 1 , where the fracton dimension d f = 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 τ versus width R were found to be in excellent agreement with the TFT via τ ~ R 1.42. This paper provides compelling new experimental evidence for the twinkling fractal nature of the glass transition.