Nuclear magnetic resonance line shape from strained Gaussian networks

Elastomers when strained become anisotropic, as seen by birefringence and NMR line splitting. Brereton has shown that the fundamental model of high polymers, the ideal Gaussian chain, does not yield a split but merely a broadened line on straining. This underpinning analytic result directs one to consider richer models for chains in elastomers. We correct an error in Brereton's Gaussian analysis. The nonsplit result is retained, but the lines show some qualitative changes in shape from the results he presented. We use a method similar to his but taylored to future calculations for NMR of nematic and paranematic networks with rigid rods. We present an analytic formula for the second moment of the line shape as a function of extension lambda.