Entropy chain configurational

Curro and Mark 38) have proposed a new non-Gaussian theory of rubber elasticity based on rotational isomeric state simulations of network chain configurations. Specifically, Monte Carlo calculations were used to determine the distribution functions for end-to-end dimensions of the network chains. The utilization of these distribution functions instead of the Gaussian function yields a large decreases in the entropy of the network chains. 

Fig. 6.9 Schematic showing the effect of addition of low-molecular-weight homopolymer on block copolymer chain configuration (Hasegawa and Hashimoto 1996). (a) A symmetric diblock forms a lamellar phase, (b) On addition of homopolymer, swelling induced by solubilized homopolymer causes stretching of the corresponding block chain/and or contraction of the other block, resulting in a decrease in conformational entropy, (c) Alternatively, a curved interface is formed to attain a uniform packing density.

When polymers self-assemble to give periodic ordered phases, only a fraction of chain configurations that are available in homogeneous phases are permissible. SCFT provides a convenient framework for computing the reduction in entropy due to this effect. In this theory, individual chains are assumed to be affected by the presence of a spatially varying external field w iz). For convenience, we restrict our attention to one-dimensional phases. The partition function of a chain of s monomers of type i constrained so that the sth monomer is held fixed at z, qi, is given by... 

When a rubber is deformed, its entropy S changes. The long chains tend to adopt a most probable configuration this is a highly coiled configuration. When the material is stretched, the chains uncoil, resulting in a less probable chain configuration. When the force is removed, the system wants to return to the more probable coiled-... 

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