SCATTERED INTENSITY FROM HIGHER CONNECTED POLYMERS IN SOLUTION

The aim of this work is to compute the structure factor of any arbitrary D-dimensionally-connected polymers (1≤D<2) in dilute solution. We use the standard cut-off function method, which is successfully applied to liquid systems and to fractal aggregates. For monodisperse systems, we find that the corresponding structure factor is simply given by the Gauss hypergeometric function 2F1, the three parameters of which depend explicitly on the fractal and the Euclidean dimensions. This function reproduces the two limiting behaviors, in the Guinier and intermediate regimes. This result is applied to several systems, namely, compact and convex polymeric objects, rod-like, linear and branched polymers. We then extend this result to polydisperse branched polymers. We show that polydispersity induces a change in the structure factor, from the simple hypergeometric function 2F1 to the generalized one 2F1, with four parameters that also depend on both fractal and Euclidean dimensions.