(722f) Unraveling Entanglements and Polymer Rheology: New Rules

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 Tg is the main element of the Twinkling Fractal Theory (TFT) presented herein and the percolating fractal twinkles with a frequency spectrum F(w) ~ wdf-1 exp Delta E|/kT as solid and liquid clusters interchange with frequency ù. The Orbach vibrational density of states for a fractal is g(w) ~ wdf-1, where df = 4/3 and the temperature dependent activation energy behaves as Delta E ~ (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(w) at Tg predicts that the spatio-temporal thermal fluctuation autocorrelation relaxation function C(t) behave as C(t) ~ t-1/3 (short times), C(t) ~ t-4/3 (long times) and C(t) ~ t-2 (w