Vector length distributions and polarizabilities of effective polymer chains: a statistical segment approach

The freely orienting model of a polymer chain is generalized by considering the distribution of vector lengths and polarizabilities of the statistical segments in the chain with a constant number of skeletal bonds in each of the segments The bonds in the segments are assumed to exist in their RIS (Rotational Isomeric States) conformations. The segment is characterized, i.e., its end-to-end length and polarizability distributions are computed. Bond polarizabilities, as determined by Denbigh, have been used for polyethylene and poly(cis-isoprene), and are assumed to be independent of the environment. Two methods are used to compute the chain length distribution from the length distribution of statistical segments: (i) an exact method, using a modified version of Chandrasekhar’s approach, originally formulated for chains of segments having constant length; and (ii) an alternative approach, which considers the series expansion of the Helmholtz Free Energy of an isolated chain, making the analysis computationally more viable without significant loss in accuracy. The averages of the chain end-to-end length distributions have been computed at 373 K for poly(cis-isoprene) and at 403 and 413 K for polyethylene. Also, chain polarizability is determined from the distribution of statistical segment lengths and polarizabilities. The results are in a form that can be used to obtain stress-deformation and optical anisotropy-deformation relationships of assemblies of chains, such as crosslinked networks.