Rheological study of transient networks with junctions of limited multiplicity. II. Sol/gel transition and rheology

Viscoelastic and thermodynamic properties of transient gels formed by telechelic associating polymers are studied on the basis of the transient network theory that considers the correlation among polymer chains via network junctions. The global information of the gel is incorporated into the theory by introducing elastically effective chains defined according to the criterion of Scanlan [J. Polym. Sci. 43, 501 (1960)] and Case [J. Polym. Sci. 45, 397 (1960)]. We also consider the effects of superbridges whose backbone is formed by several chains connected in series and containing several breakable junctions. The dynamic shear moduli of this system are well described in terms of the Maxwell model characterized by a single relaxation time and high-frequency plateau modulus. Near the critical concentration at the sol/gel transition, superbridges become infinitely long along the backbone, thereby leading to a short relaxation time tau for the network. It is shown that tau is proportional to the concentration deviation Delta near the gelation point. The plateau modulus G(infinity) increases as the cube of Delta near the gelation point as a result of the mean-field treatment, and hence the zero-shear viscosity increases as eta(0) approximately G(infinity)tau approximately Delta(4). The present model can explain the concentration dependence of the dynamic moduli observed for aqueous solutions of telechelic poly(ethylene oxide).