We consider concentration dependence of rheological properties of associativetelechelic polymer solutions. Experimental results for model telechelic polymersolutions show rather strong concentration dependence of rheologicalproperties. For solutions with relatively high concentrations, linearviscoelasticity deviates from the single Maxwell behavior. The concentrationdependence of characteristic relaxation time and moduli is different in highand low concentration cases. These results suggest that there are two differentconcentration regimes. We expect that densely connected (well percolated)networks are formed in high-concentration solutions, whereas sparsely connected(weakly percolated) networks are formed in low-concentration solutions. Wepropose single chain type transient network models to explain experimentalresults. Our models incorporate the spatial correlation effect of micellarcores and average number of elastically active chains per micellar core (thenetwork functionality). Our models can reproduce non-single Maxwellianrelaxation and nonlinear rheological behavior such as the shear thickening andthinning. They are qualitatively consistent with experimental results. In ourmodels, the linear rheological behavior is mainly attributable to thedifference of network structures (functionalities). The nonlinear rheologicalbehavior is attributable to the nonlinear flow rate dependence of the spatialcorrelation of micellar core positions.
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