In this paper, the model of inverse cascade fractal super-blocks along one direction (in the positive or negative) in the 3-dimensional space is developed to describe the self-similar motion in macromolecular system. ...In this paper, the model of inverse cascade fractal super-blocks along one direction (in the positive or negative) in the 3-dimensional space is developed to describe the self-similar motion in macromolecular system. Microscopically the cohesive and dispersed states of the motion blocks are co-existent states with vastly different probability of occurrence.Experimental results and theoretical analysis show that the microscopic cohesive state energy and dispersed state energy of each motion block are respectively equal to the macroscopic glassy state energy kT8 and molten state energy kTm of the system. This singularity unveils topologically the nonintegrability, mathematically the anholonomy, and macroscopically the emergent property. This singularity also reveals that the glass, viscoelastic and melt states are three distinct emergent properties of macromolecular motion from a macroscopic viewpoint. The fractal concept of excluded volume is introduced to depict the random motion at various scales in the system. The Hausdorff dimensions of the excluded volune and the motion blocks are both found equal to 3/2.展开更多
A basic concept in chain-particle cluster-motion, from frozen glassy state to melt state, is the 2D soft nano-scale mosaic structure formed by 8 orders of 2D interface excitation (IE) loop-flows, from small to large i...A basic concept in chain-particle cluster-motion, from frozen glassy state to melt state, is the 2D soft nano-scale mosaic structure formed by 8 orders of 2D interface excitation (IE) loop-flows, from small to large in inverse cascade and rearrangement structure in cascade along local one direction. IE has additional repulsive energy and extra vacancy volume. IE results from that the instantaneous synchronal polarized electron charge coupling pair is able to parallel transport on the interface between two neighboring chain-particles with antiparallel delocalization. This structure accords with de Gennes’ mosaic structure picture, from which we can directly deduce glass transition temperature, melt temperature, free volume fraction, critical entangled chain length, and activation energy to break solid lattice. This is also the inherency maximum order-potential structure in random systems.展开更多
文摘In this paper, the model of inverse cascade fractal super-blocks along one direction (in the positive or negative) in the 3-dimensional space is developed to describe the self-similar motion in macromolecular system. Microscopically the cohesive and dispersed states of the motion blocks are co-existent states with vastly different probability of occurrence.Experimental results and theoretical analysis show that the microscopic cohesive state energy and dispersed state energy of each motion block are respectively equal to the macroscopic glassy state energy kT8 and molten state energy kTm of the system. This singularity unveils topologically the nonintegrability, mathematically the anholonomy, and macroscopically the emergent property. This singularity also reveals that the glass, viscoelastic and melt states are three distinct emergent properties of macromolecular motion from a macroscopic viewpoint. The fractal concept of excluded volume is introduced to depict the random motion at various scales in the system. The Hausdorff dimensions of the excluded volune and the motion blocks are both found equal to 3/2.
文摘A basic concept in chain-particle cluster-motion, from frozen glassy state to melt state, is the 2D soft nano-scale mosaic structure formed by 8 orders of 2D interface excitation (IE) loop-flows, from small to large in inverse cascade and rearrangement structure in cascade along local one direction. IE has additional repulsive energy and extra vacancy volume. IE results from that the instantaneous synchronal polarized electron charge coupling pair is able to parallel transport on the interface between two neighboring chain-particles with antiparallel delocalization. This structure accords with de Gennes’ mosaic structure picture, from which we can directly deduce glass transition temperature, melt temperature, free volume fraction, critical entangled chain length, and activation energy to break solid lattice. This is also the inherency maximum order-potential structure in random systems.
