SCATTERING FUNCTIONS OF POLYMERIC CORE-SHELL STRUCTURES AND EXCLUDED-VOLUME CHAINS

General expressions for the scattering functions of polydisperse parti cles with an arbitrary number of concentric shells of lamellar, cylind rical, or spherical symmetry are derived. For shells consisting of den se polymer layers or brushes with algebraic density profiles, phi(r) s imilar to r(alpha), it is possible to obtain closed analytical express ions by taking advantage of the mathematical properties of hypergeomet ric functions. The same formalism can be employed to derive a closed e xpression for the form factor of polydisperse excluded volume chains a ssuming a des Cloizeaux-type segment distribution function.