  We consider concentration dependence of rheological properties of associative
telechelic polymer solutions. Experimental results for model telechelic polymer
solutions show rather strong concentration dependence of rheological
properties. For solutions with relatively high concentrations, linear
viscoelasticity deviates from the single Maxwell behavior. The concentration
dependence of characteristic relaxation time and moduli is different in high
and low concentration cases. These results suggest that there are two different
concentration 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. We
propose single chain type transient network models to explain experimental
results. Our models incorporate the spatial correlation effect of micellar
cores and average number of elastically active chains per micellar core (the
network functionality). Our models can reproduce non-single Maxwellian
relaxation and nonlinear rheological behavior such as the shear thickening and
thinning. They are qualitatively consistent with experimental results. In our
models, the linear rheological behavior is mainly attributable to the
difference of network structures (functionalities). The nonlinear rheological
behavior is attributable to the nonlinear flow rate dependence of the spatial
correlation of micellar core positions.
