Configurational studies on amylose. II. Moments and distribution functions

Statistical mechanical averages of vectors and tensors characterizing the configuration of amylose chains have been calculated. These quantities are expressed in the reference frame affixed to the first glucose unit, the x axis being situated along the O(4)—O(1) virtual bond vector, and the Y axis in the plane of the virtual bond and the O(4)—C(4) bond. The persistence vector a as defined by the average of the end-to-end vector r converges slowly to the limiting persistence vector a _∞ with increasing chain length. Configurational averages of the Cartesian tensors formed from the displacement vector ρ = r ? a have been computed up to seventh rank according to the generator matrix method. The density distribution functions W_α (ρ) evaluated for x_u = 40 by using the three-dimensional Hermite polynomial expansion truncated at the term involving the tensor of seventh rank are approximately cylindrically symmetric about one of the principal axes of the second-moment tensor <ρ^×2. The density distribution function W_α(ρ) is slightly asymmetric even for x_u = 80.