Entropy springs

Each submolecule will experience a frictional drag with the solvent represented by the frictional coefficient /0. This drag is related to the frictional coefficient of the monomer unit (0- If there are x monomer units per link then the frictional coefficient of a link is x(0- If we aPply a step strain to the polymer chain it will deform and its entropy will fall. In order to attain its equilibrium conformation and maximum entropy the chain will rearrange itself by diffusion. The instantaneous elastic response can be thought of as being due to an entropic spring . The drag on each submolecule can be treated in terms of the motion of the N+ 1 ends of the submolecules. We can think of these as beads linked... 

C. What is the entropy change for the universe (spring plus surrounding thermostat) for the total process, stretching plus return collapse to initial Lq d. How much work was performed on the spring in the stretching process ... 

It should be remembered, however, that the springs connecting the beads are entropy springs, and that the network chains are flexible either because they are above their glass transition temperature, or because they are imbedded in a solvent. 

A model network can thus be schematized by an ensemble of spring-suspended beads the elastic chains act as entropy springs, and they connect beads of constant — as yet unknown — functionality. 

The early molecular theories of rubber elasticity were based on models of networks of long chains in molecules, each acting as an entropic spring. That is, because the configurational entropy of a chain increased as the distance between the atoms decreased, an external force was necessary to prevent its collapse. It was understood that collapse of the network to zero volume in the absence of an externally applied stress was prevented by repulsive excluded volume (EV) interactions. The term nonbonded interactions was applied to those between atom pairs that were not neighboring atoms along a chain and interacting via a covalent bond. 

Gels usually consist of small amount of polymer as a network and a lai amount of solvent. Therefore when we discuss the dynamics erf polymer gels, we are tempted to deal with these Is from the stand point of the dynamics of polymer solutions. However, since the polymer chains in a gel are connected to each other via chemical bonds and/or some kinds of sj cific interaction, sudi as, hydrogen bonding or hydrophobic interaction, the gel has to be treated as a continuum. In addition, gels behave as an assembly of springs due to the entropy elasticity of polymer chains between the crosslink points. Therdbre, the dynamics of polymer gels is well described in terms of the theory of elasticity... 

An ideal elastomer has Young s modulus about 10 -10 dyn/cm (10- -10 N/m ) and reversible elasticity of hundreds of percent elongation. The force required to hold this entropy spring at fixed length falls as the temperature is lowered. This implies that (9(7/9/)t = 0. 

An ideal gas and an ideal elastomer arc both entropy springs. 

Various measurements have shown that / // is about 0.1-0.2 for polybutadiene and c/5-polyisoprene elastomers. These polymers are essentially but not entirely entropy springs. 

Equation (4-46) predicts that the stress-strain properties of an elastomer that behaves like an entropy spring will depend only on the temperature, the density of the material, and the average molecular weight between cross-links. In terms of nominal strain this equation is approximately... 

The more tightly cross-linked the elastomer, the lower will be and the higher will be its modulus. That is, it will take more force to extend the polymer a given amount at fixed temperature. Also, because the elastomer is an entropy spring, the modulus will increase with temperature. 

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