Twinkling fractal theory of the glass transition

Abstract

In this paper we propose a solution to an unsolved problem in solid state physics, namely, the nature and structure of the glass transition in amorphous materials. The development of dynamic percolating fractal structures near T g is the main element of the Twinkling Fractal Theory (TFT) presented herein and the percolating fractal twinkles with a frequency spectrum F(ω) ∼ ωdf-1 exp - |ΔE|/kT as solid and liquid clusters interchange with frequency ω. The Orbach vibrational density of states for a fractal is g(ω) ∼ ωdf-1, where d f = 4/3 and the temperature dependent activation energy behaves as ΔE ∼ (T2 - Tg2). The key concept of the TFT derives from the Boltzmann population of excited states in the anharmonic intermolecular potential between atoms, coupled with percolating solid fractal structures near Tg. The twinkling fractal spectrum F(ω) at Tg predicts the correct dynamic heterogeneity behavior via the spatio-temporal thermal fluctuation autocorrelation relaxation function C(t). This function behaves as C(t) ∼ t-1/3 (short times), C(t) ∼ t-4/3 (long times) and C(t) ∼ t-2 (ω