Progress of de Gennes soft matrix glass model in non-crystalline solids and disordered materials

Boson and two-dimensional cluster model composed of quenching disorder eigenvalues and eigenvectors in the glass transition

“…The eigenvector is the two coupled λ-λ * th orbital axial-lines of two electrons escaping the two HSMs in clustered collision, which is one of the 16 pairs of coupled anglelines between the two HSMs, and the integrity of the 16 pairs of angle-lines de nes the CI-boson of the interactions between the two HSMs. That is, the 16 sequentially occurring eigenvalues that form CIbosons are derived from 16 non-zero values of n = 0 on the two trajectory lines of synchro-non-monotonic continuous precession plane spiral electrons 14 on two adjacent orthogonal diagonal planes. Therefore, the cluster model starts from the absolute temperature and accumulates CI-bosons excited by clustered collisions to form 2D clusters at different scales.…”

“…i) The clustering model has nine-step replica symmetries from the V 0 -cluster to the V 8 -soft matrix, while RFOT uses only one-step replica symmetry 51 to form a cluster of 200 HSMs from T k temperature to T g temperature. This difference allows the cluster model to explain the dynamic percolation network transition of V 7 -V 6 -V 7 -V 6 clusters at T k temperature 14 . Below T k , there are still seven inverse-cascade "transitions" from V 0 to V 6 to generate dynamic 2D V i ordered potential structures in equilibrium with the thermally disordered kinetic energy, so that there is no Kauzmann paradox for temperatures below T k , and entropy changes above T k .…”

“…1 in ref. [14], and χ min = 3/8 = (σ i /q i, R ) 6 ; χ max = 5/8 = (σ i+1 /q i+1, L ) 6 . From q i, R = q i+1, L , we get a set of recursive Equs: q i,R = (8/3) 1/6 σ i and σ i+1 =…”

“…Δq i = q i+1, R − q i+1, L = q i +1, R − q i, R ≈ 0.10464895 σ i , and the vibration equilibrium position, χ 0 = 1/2, q 0 = 2 1/6 σ ≈ 1.12246 σ. The Lindemann ratio d L can be rede ned as an invariant value for scaling transformation between different cluster sizes 14 .…”

“…The z-direction interface excited (z-IE) states of all CEPs constituting a z-soft matrix appear sequentially, and form one to nine z-IE closed loops around the vibrational equilibrium center of each HSM, so the excluded volume of each HSM is actually a zdirection MIES in the form of a dynamic HSM cubic lattice (HSCL). In the previous paper 14 , we simply denoted the number of CEP IE states required for a z-IE closed loop around a 0 -HSM (the physical term is the globality of n = 0) as k λ (= k α + k β + k 𝛾 + k δ ), which is the number of steps that a 0 -HSM jumps along 4diagonal closed-loop of its 2Δd cubic lattice.…”