Time-dependent probability distribution functions for orientational motions of segments in polymer chains

The spatial orientation of vectors rigidly embedded in polymer chains are described in terms of time-dependent joint probability distribution functions. Serial expansion in terms of double spherical harmonics is adopted for the probability distribution functions, with the coefficients therein evaluated from Brownian dynamics simulations. Truncation of the series after the second-order harmonics accurately reproduces the results of Brownian dynamics simulations for a 50 bond polyethylene chain whose ends are held fixed at various extensions.