Example calculations rubber elasticity

An Example of Rubber Elasticity Calculations Suppose that an elastomer of 0.1 cm x 0.1 cm x 10 cm is stretched to 25 cm length at 35°C, a stress of 2 X10 dynes/cm being required. What is the concentration of active network chain segments ... 

I have included an introduction to rubber elasticity in Chapter 4 because it follows logically from considerations of conformational changes in polymers. This material need not be taught in the sequence presented, however, and this topic, or all of Chapter 4, can be introduced at any point that seems best to the instructor. Chapters 5 through 7 are quite orthodox in their plans. 1 have, however, taken the opportunity to present alkyd calculations as an example of practice in the coatings industry and formulating thermosetting materials. 

FIGURE 6.2 Example of a projection of a calculated random coil of 250 segments, r is the end-to-end distance. (Adapted from L. R. G. Treloar. The Physics of Rubber Elasticity. Clarendon, Oxford, 1975.)... 

The quantity RllM Y is Rg in A, a measure of chain stiffness. For example, polycarbonate, with (RpM y = 0.457, is stiffer than polystyrene, which has a value of 0.275. The importance of these quantities lies in their relation to physical and mechanical behavior. Both melt and solution viscosities depend directly on the radius of gyration of the polymer and on the chain s capability of being deformed. The theory of the random coU (Section 5.3), strongly supported by these measurements, is used in rubber elasticity theory (Chapter 9) and many mechanical and relaxation calculations. 

The quantities E and t] of the models shown above are not, of course, simple values of modulus and viscosity. However, as shown below, they can be used in numerous calculations to provide excellent predictions or understanding of viscoelastic creep and stress relaxation. It must be emphasized that E and rj themselves can be governed by theoretical equations. For example, if the polymer is above T, the theory of rubber elasticity can be used. Likewise the WLF equation can be used to represent that portion of the deformation due to viscous flow, or for the viscous portion of the Kelvin element. 

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