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
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.
