Eight orders of dynamical clusters and hard-spheres in the glass   transition
  The nature may be disclosed that the glass transition is only determined by the intrinsic 8 orders of instant 2-D mosaic geometric structures, without any presupposition and relevant parameter. An interface excited state on the geometric structures comes from the additional Lindemann distance increment, which is a vector with 8 orders of relaxation times, 8 orders of additional restoring force moment (ARFM), quantized energy and extra volume. Each order of anharmonic ARFM gives rise to an additional position-asymmetry on a 2-D projection plane of a reference particle, thus, in removing additional position-asymmetry, the 8 orders of 2-D clusters and hard-spheres accompanied with the 4 excited interface relaxations of the reference particle have been illustrated. Dynamical behavior comes of the slow inverse energy cascade to generate 8 orders of clusters, to thaw a solid-domain, and the fast cascade to relax tension and rearrange structure. This model provides a unified mechanism to interpret hard-sphere, compacting cluster, free volume, cage, jamming behaviors, geometrical frustration, reptation, Ising model, breaking solid lattice, percolation, cooperative migration and orientation, critical entanglement chain length and structure rearrangements. It also directly deduces a series of quantitative values for the average energy of cooperative migration in one direction, localized energy independent of temperature and the activation energy to break solid lattice. In a flexible polymer system, there are all 320 different interface excited states that have the same quantized excited energy but different interaction times, relaxation times and phases. The quantized excited energy is about 6.4 k = 0.55meV. 
Jialin Wu