Orientation Distribution Function of Statistical Segments in Deformed Polymer Networks

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Abstract
When a crosslinked network is deformed unidimensionally, the distribution of chain displacement vectors becomes rather well oriented along the stretching direction. It is shown that the distribution function w(cosχ) pertaining to the individual statistical segments comprising the network chains may be expressed in a series of Legendre polynomials. This function should be of value in the theoretical treatment of the kinetics of formation, and of the distribution of orientations, of crystallites formed in stretched networks. Examination of the distribution function indicates that the segmental orientation remains rather poor, even for highly strained networks. An expression is derived for 〈cos2χ〉 from the present treatment, where χ is the angle between a statistical segment and the stretching direction. Finally, expressions applicable only for low relative elongations are presented which relate the distribution function w(cosχ) to the experimentally measurable retractive force or birefringence of a stretched network.