The affine rubber model and frozen-in orientation

When a polymer is spun to form a fibre the molecular network in the melt is extended and subsequently frozen in the extended state. In commercial fibre production, heat setting or subsequent hot drawing above the glass-transition temperature may also be used, but for fibres that have only been spun and drawn simultaneously the distribution of orientations in the fibre should conform to the predictions of the rubber model. 

The effective draw ratio, X, of the fibre can be determined from the shrinkage, S, when the fibre is re-heated to a temperature above the glass-transition temperature Tg. S is defined by 

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