Correlation functions in gel phase via mesoscopic cyclization theory of weak gels

Abstract

The theory of classic sol-gel transition (SGT) in weak gels upon which the labile infinite cluster of particles bonded via weak chemical bonds (the gel fraction) appears on the background of a set of finite clusters (the sol fraction), is revisited. The basic approaches to describe the SGT (Flory approach, Stockmayer approach and the mesoscopic cyclization (MC) theory elaborated earlier by the author) are shortly outlined. The MC theory is revisited and generalized to provide description of spatially inhomogeneous weak gels, which is exemplified by calculation of the correlation function G (q) of monomer units in the gel-phase. A reduced choice of the network structural elements leads to reproducing the results obtained earlier within the Flory approach. On the contrary, an extended selection of such elements enables us to evaluate contribution to G (q) of closed trails of bonds comprised in the infinite cluster. This contribution leads to a pronounced small-angle scattering enhancement, which is especially noticeable near the sol-gel threshold.