Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-05-12
Physics
Condensed Matter
Statistical Mechanics
76 pages; Key words: glass transition (theory); mosaic structure (theory); solitary wave (theory); entangled polymer dynamics
Scientific paper
A universal theoretical framework has been proposed that the solid-to-liquid glass transition and macromolecular motion within the entire temperature range from Tg to Tm and the liquid flow are absolutely determined by the intrinsic 8 orders of transient 2-D mosaic geometric structures formed by exciting interfaces. Interface excitations are cross-coupled electron pairs, which attribute to the Van der Waals repulsion electron-electron pairs with 2-D self-avoiding closed loops existing in any random system at any temperature. An interface excitation state is a vector with 8 orders of additional restoring torque, 8 orders of relaxation times, quantized energies and extra volumes. Dynamics occurred by the slow inverse cascade generates the 8 orders of potential loop-flows while the fast cascade rearranges the structure. The delocalization mode is solitary wave along the 8 orders of geodesic. Solitary wave is derived from the balance between inverse cascade and cascade. Increasing temperature only increases the number of inverse cascade and cascade. This model provides a unified mechanism to interpret ripplon, reptation, Boson peak, Ising model, non-ergodic, free volume, hard-sphere, tunneling, cage, compacting cluster, jamming behaviors, breaking solid lattice, geometrical frustration, potential energy landscape, flow-percolation, thermo-disorder-induced localized energy, average energy of cooperative migration along one direction, critical entanglement chain length, and Reynolds number, solitary wave, heteroclinic orbit in hydrodynamics. This model also directly deduces the Lindemann ratio, the famous 3.4 power law of viscosity of entangled macromolecules and the well-known WLF equation and shows that the Clapeyron equation governing all first order phase transitions in thermodynamics only holds true in each subsystem, instead of the system in glass transition.
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