Orientation distribution functions for uniaxially oriented polymers

Abstract

Abstract Most methods of studying molecular orientation in polymers can give only limited information about the distribution of molecular orientations, and this is particularly true of methods for studying the noncrystalline material. It is shown, however, that if the mean values P 2 and P 4 of the second‐order and fourth‐order Legendre polynomials in cosθ can be determined for the chains in a uniaxially oriented polymer, where ‐ is the angle between the chain axis and the drawing or extrusion direction, some qualitative statements about the form of the distribution can be made with complete certainty for some, but not all, sets of values of P 2 and P 4 . It is shown in addition, that if the distribution is fairly smooth a good estimate of its general form can also be obtained, and that a knowledge of P 6 and higher‐order means will not improve this estimate appreciably unless they are known with great accuracy.