Concentration dependence of rheological properties of telechelic associative polymer solutions

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 nonsingle 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.

Figure 1

Master curves of storage and loss moduli for the 1 wt% HEUR aqueous solution. The reference temperature is $T_r={25}^{\circ }\mathrm{C}$ and the superposition is performed for the slow (low-frequency) mode.

Figure 2

Master curves of storage and loss moduli for the 1 wt% HEUR aqueous solution. Data are the same as in Fig. 1 but shifted with $a_{T,1}$ determined for the $1\mathrm{wt}\%$ PEO solution. The reference temperature is $T_r={25}^{\circ }\mathrm{C}$. For comparison, the loss modulus for the 1 wt% PEO solution at $T={25}^{\circ }\mathrm{C}$ is also plotted.

Figure 3

Horizontal shift factors of the slow mode of the HEUR solution and the fast mode of the PEO solution, $a_{T,0}$ and $a_{T,1}$. The reference temperature is $T_r={25}^{\circ }\mathrm{C}$.

Figure 4

Concentration dependence of storage and loss moduli for the HEUR aqueous solutions at $T={25}^{\circ }\mathrm{C}$. The concentrations are $c=1\mathrm{wt}\%,2\mathrm{wt}\%,5\mathrm{wt}\%,$ and $10\mathrm{wt}\%$.

Figure 5

Storage and loss moduli for the HEUR aqueous solutions with various concentrations at $T={25}^{\circ }\mathrm{C}$. Angular frequency and moduli are rescaled by the inverse characteristic time $1/\tau$ and the characteristic modulus $G_0$ for the slow mode, respectively.

Figure 6

Concentration dependence of (a) the characteristic time $\tau$ and (b) the characteristic modulus $G_0$ at $T={25}^{\circ }\mathrm{C}$ obtained for the HEUR aqueous solutions. Broken and solid lines represent the fitting results for low and high concentrations, respectively.

Figure 7

A schematic image of the mean field single chain model for a dense network (the dense network model). (a) A dense network formed by elastically active chains (solid black curves) and micellar cores (circles). (b) A local structure in a dense network. Solid and dotted curves represent elastically active and inactive polymer chains, respectively. Circles represent micellar cores. The dense network model is formulated for a single tagged chain in the system. There is the effective interaction between micelles, which is expressed by the potential $v\left(\mathit{r}\right)$. A bridge chain feels the elastic potential $u\left(\mathit{r}\right)$.

Figure 8

A schematic image of the mean field single chain model for a sparse network (the sparse network model). (a) A sparse network formed by elastically active chains (solid black curves) and micellar cores (circles). (b) A local structure in a sparse network. Solid and dotted curves represent elastically active and inactive polymer chains, respectively. Circles represent micellar cores. The sparse network model is formulated for a single tagged superbridge in the system. $v\left(\mathit{r}\right)$ and $\overline{u}\left(\mathit{r}\right)$ are the effective interaction potential between micelles and the elastic potential of a superbridge.

Figure 9

Storage and loss moduli [$G^{\prime }\left(\omega \right)$ and $G^{\prime \prime }\left(\omega \right)$] deduced from a dense network model for $\tilde{\tau }=\tilde{\tau }\left(0\right)=\tilde{\tau }\left(1\right)$ calculated under some approximations. For comparison, $G^{\prime }\left(\omega \right)$ and $G^{\prime \prime }\left(\omega \right)$ of a single Maxwellian model ($G_1/G_0=0$) are also shown.