Twinkling Fractal Theory of the Glass Transition

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, is the main element of the Twinkling Fractal Theory (TFT) presented herein and the percolating fractal twinkles with a frequency spectrum F(omega) similar to omega(df-1) exp - vertical bar Delta E vertical bar /kT as solid and liquid clusters interchange with frequency omega. The Orbach vibrational density of states for a fractal is g(omega) similar to omega(df-1), where d(f) = 4/3 and the temperature dependent activation energy behaves as Delta E similar to (T-2 - T-g(2)). 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(w) 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) similar to t(-1/3) (short times), C(t) similar to t(-4/3) (long times) and C(t) similar to t(-2) (omega < omega(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 = 2D(o)/9k, where D-o is the interatomic bonding energy similar to 2-5 kcal/mol and is comparable to the heat of fusion Delta H-f. Because anharmonicity controls both the thermal expansion coefficient alpha(L) and T-g, the TFT uniquely predicts that alpha LxT(g) approximate to 0.03, which is found to be universal for a broad range of glassy materials from Pyrex to polymers to glycerol. Below T, the glassy structure attains a frustrated nonequilibrium state by getting constrained on the fracal structure and the thermal expansion in the glass is reduced by the percolation threshold p(c) as alpha(g) approximate to P-c alpha(L). The change in heat capacity Delta C-p = 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 = 3/D-f, where Df 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 alpha(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 = 1/[1-p(c)] approximate to 2. The TFT is universal to all glass forming liquids. (C) 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2765-2778, 2008