Elastomers cross-link density calculation

As pointed out earlier, an elastomer cross-linked above its gel point will not dissolve in a solvent, but will absorb it and swell. The swelling will continue until the forces of swelling balance the retroactive forces of the extended chains of the network. The cross-link density can then be calculated from the degree of swelling using the Flory-Rehner equation ... 

The equilibrium small-strain elastic behavior of an "incompressible" rubbery network polymer can be specified by a single number—either the shear modulus or the Young s modulus (which for an incompressible elastomer is equal to 3. This modulus being known, the stress-strain behavior in uniaxial tension, biaxial tension, shear, or compression can be calculated in a simple manner. (If compressibility is taken into account, two moduli are required and the bulk modulus. ) The relation between elastic properties and molecular architecture becomes a simple relation between two numbers the shear modulus and the cross-link density (or the... 

Given an SBR rubber that has A/ = 100,000 before cross-linking, calculate the stress at 00% elongation of the cross-linked elastomer. The density of the vulcanizate (without fillers) with 23.5 mol% styrene in the polymer is 0.98 gcm. Take the temperature to be 25" C. Express your answers in units ofMN/m. Assume... 

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