Towards a statistical theory of associating telechelics: Equilibrium molecular structural distribution and one-cluster static scattering

A rigorous statistical treatment of the system of associating telechelics with due regard for formation of complicated many-chains clusters is presented for the case when the active telechelic ends associate only in two (A(2)) and threefold (A(3)) aggregates. A diagram technique to describe the structure of these clusters and find the corresponding equilibrium molecular structural distribution is introduced and a regular procedure to calculate the average structural and scattering properties of the system is elaborated. A competition between forming of the tree- and looplike fragments and its influence on the critical concentration c(g) of gelation and structural characteristics of the system are analyzed in detail. The dependences of c(g) as well as the number- and weight-averaged degrees of associations both for the tree- and looplike fragments and the clusters as a whole are plotted as functions of the properly reduced number density of telechelics and the reduced equilibrium constant of the chemical reaction 3A(2) <-> 2A(3). (C) 1999 American Institute of Physics. [S0021-9606(99)53201-7].