Birefringence and Crystallization in Elastomers

The semitheoretical expression, fc=Δn0−csFΔnc0−cs,where fc=volume fraction crystalline, Δn0=observed birefringence, c=the stress-optical coefficient, s=the stress on actual cross section, F=a known function of crystallite orientation, and Δnc0=the birefringence of a single polymer crystal, is proposed for relating birefringence, stress, and degree of crystallinity in polycrystalline elastomers under tensile stress. This expression is shown to yield results in substantial agreement with x-ray results for the degree of crystallinity of 5°C polybutadiene when Δnc0=0.157. Birefringencedensity data on natural rubber (due to L. R. G. Treloar) are shown to be a special case of the foregoing expression, yielding a value Δnc0=0.218 for natural rubber which is in good agreement with the theoretical value for this quantity.