Segmental Orientation

Abstract

Segmental or molecular orientation refers to the anisotropic distribution of chain-segment orientations in space, due to the orienting effect of some external agent. In the case of uniaxially stretched rubbery networks, which will be the focus of this chapter, segmental orientation results from the distortion of the configurations of network chains when the network is macroscopically deformed. In the undistorted state, the orientations of chain segments are random, and hence the network is isotropic because the chain may undertake all possible configurations, without any bias. In the other hypothetically extreme case of infinite degree of stretching of the network, segments align exclusively along the direction of stretch. The mathematical description of segmental orientation at all levels of macroscopic deformation is the focus of this chapter. Segmental orientation in rubbery networks differs distinctly from that in crystalline or glassy polymers. Whereas the chains in glassy or crystalline solids are fully or partly frozen, those in an elastomeric network have the full freedom to go from one configuration to another, subject to the constraints imposed by the network connectivity. The orientation at the segmental level in glassy or crystalline networks is mostly induced by intermolecular coupling between closely packed neighboring molecules, while in the rubbery network intramolecular conformational distributions predominantly determine the degree of segmental orientation. The first section of this chapter describes the state of molecular deformation. In section 11.2, the simple theory of segmental orientation is outlined, followed by the more detailed treatment of Nagai and Flory. The chapter concludes with a discussion of infrared spectroscopy and the birefringence technique for measuring segmental orientation. For uniaxial deformation, the deformation tensor λ takes the form λ = diag(λ, λ-1/2, λ-1/2), where diag represents the diagonal of a square matrix, and λ is the ratio of the stretched length of the rubbery sample to its undeformed reference length. The first element along the diagonal of the matrix represents the extension ratio along the direction of stretch, which may be conveniently identified as the X axis of a laboratory-fixed frame XYZ. The other two elements refer to the deformation along two lateral directions, Y and Z.