Development of molecular orientation and stress in biaxially deformed polymers. I. Affine deformation in a solid state

Biaxial deformation of freely jointed chain molecules in a solid state is considered. Biaxial molecular orientation is directly related to the applied deformation. Segmental orientation and stress are considered using non-Gaussian inverse Langevin statistics of the chain end-to-end vectors. Padé approximation and series expansion of the inverse Langevin function are used. orientation of chain segments and stress are analyzed for affine biaxial deformation of non-Gaussian chains. Molecular anisotropy is characterized by the norm of the average orientation tensor, ‖D‖, and the global anisotropy of the stress tensor is characterized by the norm ‖P‖. Non-linear behavior of the orientation vs. stress characteristics for isochoric uniaxial deformation, calendering (λ1=1) and biaxial deformation are discussed.