Universal 2D Soft Nano-Scale Mosaic Structure Theory for Polymers and Colloids

Abstract

A basic concept in chain-particle cluster-motion, from

Soft matrix and fixed point of Lennard-Jones potentials for different hard-clusters in size at glass transition

“…It is interesting that the scheme of the topologically fast-slow mode-coupling is similar to that of the current Mode-Coupling. 31 However, since Berry' phase is geometric, nonintegrable, and topological in nature, and independent of dynamics, the geometric mode-coupling is fundamentally different from the current Mode-Coupling Theories.…”

“…"Thaw" here means both the "interface expansion" of molecule (chain-particle) (4 parallel transports surround its own z-axis) and the repeated structural rearrangements only appear in the local z-space. In a reference a 0 local field, z-space i-th order of 2D IE loop-flow also defines a z-axial i-th order of 2D thawing cluster V i (a 0 ) with relaxation time (i.e., regression time to form i-th order of loop-flow) τ i ; and a compacted i-th order of 3D faceted hard-sphere σ i (a 0 ) to hop along z-direction, 31 they can be called as directional (faceted) hard-cluster.…”

“…30 The physical basis of this idea has been looking for, and has recently found that is an unexplored and more fundamental concept in condensed matter physics. 31 The new concept is the parallel transport of instantaneous sync (Van der Waals) induced electron charge coupling pair moving from one end to other end on an intermolecular interface, named as interface excitation (IE) between two neighboring molecules (chain-particles) with antiparallel hop-delocalization. In physical theory, many complicated phenomena originate from the global properties of parallel transport of simple quantum systems (Berry's phase).…”

“…(a) Geometric mode-coupling shortly but clearly shows the universal geometric potential picture of boson peck and the geometric frustration -percolation transition at GT, not only suitable for small molecules, but also for macromolecules, 31 After introducing the concept of IE, GT can be defined as the localization -delocalization transition of clusters, accompanied with the appearances of boson peak, abnormal heat capacity, abnormal heat expansion, geometric frustration-percolation and "tunneling" and so on. From the viewpoint of excitation energy equilibrium between the directional regression-order potential and the directional hop-disorder kinetic, GT may also originate in the inherent potential (the nonintegrable induced potential) geometric structure in random systems.…”

“…Based on this understanding, a soft nanosize mosaic geometric structure theory of GT has been proposed. 31 The central concept is transient 2D soft matrix structures that appeared in 8 instantaneous moments of Brownian regressions in a certain direction, e.g. in local z-axial.…”