Structure factors for regular polymer gels and networks

Structure factors, P(q), for regular dendrimeric polymer gels and two-dimensional tetrafunctional networks are calculated. Since the low-q limit (q being the scattering wave number) region is uninteresting for these systems (the Guinier region yields gel and network overall sizes), this paper focuses on the intermediate q region, whereby the scattering radiation is probing sizes larger than single blocks but smaller than the whole macromolecule. Kratky plots [q2P(q)vs q2] are presented for starburst dendrimer gels with varying functionality and correlation range r (with respect to a reference block) and for ‘‘crumpled sheet’’ tetrafunctional networks with varying r. For regular networks, the structure factor has contributions from the various ‘‘lattice animals’’ that correspond to a chosen pair of correlated blocks. A simple method based on multivariate Gaussian distributions is used to express the mean square intermonomer distance 〈r2ij〉 for not too complicated correlation diagrams (r