SCATTERING BY LINEAR, BRANCHED, AND COPOLYMER CHAIN MOLECULES FOR LARGE SCATTERING VECTORS

If one expands the expression of the intensity scattered by polymers or copolymers in the large q range, one observes that, for Gaussian chains, this intensity follows a law of the type i(q) = Aq-2 + Bq-4. The coefficient A characterizes the length of the statistical element, and the coefficient B is easily measured using the Zimm representation. For a linear chain B gives the number-average degree of polymerization. In the case of branched polymers without loops, it depends mainly on the number of statistical elements between two cross-links or one cross-link and an end. If the polymer is sufficiently long, it gives the number-average degree of polymerization of these branches. A general formula is given and applied to classical examples: star, alternating, a comblike copolymer. The effect of polydispersity and the case of block copolymers with blocks of different chemical nature are discussed. These results are also extended to stretched polymers. This method could give new information in the interpretation of neutron scattering data.