Scattering from solutions of star polymers

Abstract:

We study the scattering intensity of dilute and semi-dilute solutions of star polymers. The star conformation is described by a model introduced by Daoud and Cotton. In this model, a single star is regarded as a spherical region of a semi-dilute polymer solution with a local, position dependent screening length. For high enough concentrations, the outer sections of the arms overlap and build a semi-dilute solution (a sea of blobs) where the inner parts of the actual stars are embedded. The scattering function is evaluated following a method introduced by Auvray and de Gennes. In the dilute regime there are three regions in the scattering function: the Guinier region (low wave vectors, $qR \ll 1$) from where the radius of the star can be extracted; the intermediate region ($1 \ll qR \ll {f^{2/5}}$) that carries the signature of the form factor of a star with f arms: $I(q) \sim {q^{ - 10/3}}$; and a high wavevector zone ($qR \gg {f^{2/5}}$) where the local swollen structure of the polymers gives rise to the usual q ^-5/3 decay. In the semi-dilute regime the different stars interact strongly, and the scattered intensity acquires two new features: a liquid peak that develops at a reciprocal position corresponding to the star-star distances; and a new large wavevector contribution of the form q ^-5/3 originating from the sea of blobs.