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 less than or equal to D < 2) in dilute solution. We use the standard cut-off function method, which is successfull y applied to liquid systems and to fractal aggregates. For monodisperse sys tems, we find that the corresponding structure factor is simply given by th e Gauss hypergeometric function F-2(1), the three parameters of which depen d explicitly on the fractal and the Euclidean dimensions. This function rep roduces the two limiting behaviors, in the Guinier and intermediate regimes . This result is applied to several systems, namely, compact and convex pol ymeric objects, rod-like, linear and branched polymers. We then extend this result to polydisperse branched polymers. We show that polydispersity indu ces a change in the structure factor, from the simple hypergeometric functi on F-2(1) to the generalized one F-2(1), with four parameters that also dep end on both fractal and Euclidean dimensions.