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(x) $ x df-1 exp À|DE|/kT as solid and liquid clusters interchange with frequency x. The Orbach vibrational density of states for a fractal is g(x) $ x df-1 , where d f ¼ 4/3 and the temperature dependent activation energy behaves as DE $ (T 2 À T 2 g ). 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 T g . The twinkling fractal spectrum F(x) at T g predicts the correct dynamic heterogeneity behavior via the spatio-temporal thermal fluctuation autocorrelation relaxation function C(t). This function behaves as C(t) $ t À1/3 (short times), C(t) $ t À4/3 (long times) and C(t) $ t À2 (x \ x c ), which were found to be in excellent agreement with published nanoscale AFM dielectric force fluctuation experiments on a glassy polymer near T g . Using the Morse potential, the TFT predicts that T g ¼ 2D o /9k, where D o is the interatomic bonding energy $ 2-5 kcal/mol and is comparable to the heat of fusion DH f . Because anharmonicity controls both the thermal expansion coefficient a L and T g , the TFT uniquely predicts that a L ÂT g % 0.03, which is found to be universal for a broad range of glassy materials from Pyrex to polymers to glycerol. Below T g , the glassy structure attains a frustrated nonequilibrium state by getting constrained on the fractal structure and the thermal expansion in the glass is reduced by the percolation threshold p c as a g % p c a L . The change in heat capacity DC p ¼ C pL -C pg at T g was found to be related to the change in dimensionality from D f to 3 in the Debye approximation as the ratio C pL /C pg ¼ 3/D f , where D f is the fractal dimension of the glass. For polymers, the TFT describes the molecular weight dependence of T g , the role of crosslinks on T g , the Flory-Fox rule of mixtures and the WLF relation for the time-temperature shift factor a T , which are traditionally viewed in terms of Free-Volume theory. The TFT offers new insight into the behavior of nano-confined glassy materials and the dynamics of physical aging. It also predicts the relation between the melting point T m and T g as T m /T g ¼ 1/[1Àp c ] % 2. The TFT is universal to all glass forming liquids.

Properties of Thermosets Derived from Chemically Modified Triglycerides and Bio-Based Comonomers

“…However, in all cases the observed T g values are slightly higher than those seen for the AESO-DBI blends, suggesting that the aromatic content of the copolymer provides some rigidity. The experimental results are in good agreement with the Twinkling Fractal Theory of the glass transition, which has been extensively used to model the properties of polymers based on acrylated oils [26,27].…”

4He glass phase: A model for liquid elements

“…Therefore it is timeconsuming to attain the thermodynamic equilibrium from the glass phase by relaxation. Various microscopic models prove the existence of a phase transition at T g [31][32][33][34][35][36][37][38][39][40]. Here, we only use thermodynamic relations without considering the microscopic aspects of the liquid-glass transformation.…”

Free Volume in Molten and Glassy Polymers and Nanocomposites

“…Thus, in the vicinity of the glass transition in amorphous polymers and their CPNCs there is a large transitory zone of variable structure and properties where with decreasing T and/or increasing P there is formation of dynamic fractal solid structures; the true liquid behavior may be expected only at higher temperatures, T > T T [Wool, 2008a].…”