Chain deformation relationships between

We consider four possible relationships between sample deformation and chain deformation. 

Because this kind of reaction takes place at low temperatures, thermal oscillations do not essentially contribute to backbone stretching. In fact, Ea is zero in this case. When Ea of bond scission is less than that required to form the active particles, cracking exhibits the character of a mechanically activated chemical reaction—chain scission in active particles takes place. There is a cause-and-effect relationship between the strain processes (which are cumulative in the deformed fragment to activate the backbone) and the destruction processes. 

We again stress that this relationship has rigorous physical meaning only if the distribution of local kink orientations has cylindrical symmetry about the director nevertheless, it may provide a semi-quantitative relationship between the REV-8 lineshape and the concentration of chain deformations if the process is at least of a highly random nature. If the ratio p changes with temperature according to a Boltzmann factor, we expect the quantity... 

Fig. 35 Relationship between dendritic core deformation and mesogen type and the conformation of the side-chain liquid crystalline dendrimers...

Using this approach SANS has been used to measure the dimension of the Gaussian coil structure of a single chain in melts, solution and blends, provided an affirmation of the screened excluded volume model, and a verification of scaling laws in polymer solutions, determined the structure of diblock copolymer aggregates, and established the relationship between the micro and macroscopic deformation in rubber elasticity. 

Doi and Edwards argue for a particular relationship between stress and orientation3. They assume that the primitive path steps deform affinely (Fig. 4) and that the chain segments contained in those steps respond initially like independent Gaussian strands. 

The primary goal of a general statistical theory is to derive an equation of state for the elastomeric molecular network which will hold for any deformation including swelling. Since the major contribution to the elasticity is entropic the molecular interpretation depends on how the stress affects the conformational distribution of an assembly of chains. The successful statistical model will provide predictive relationships between the molecular structure and topology of the network and its macroscopic behavior, e.g., mechanical and swelling responses. 

The M-FJC is used to describe the extensimi of the polymer and the entropic restoring force generated. The M-FJC model treats a macromolecule as a chain of statistically independent segments of Kuhn lengths 1, and the segment can be deformed tmder stress, as shown in Scheme 30.3a. The relationship between the extension and external force acting on the polymer chain is based on the extended Lan-gevin function [13,60] ... 

The x-ray patterns of natural rubber in the relaxed and extended states led J.R. Katz and others to develop a random coil model for polymer chains. The "Katz Effect" which was repeated by H. Mark helped to establish a relationship between mechanical deformation and concomitant molecular events in all macromolecules. 

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