Understanding the molecular origin of shear thinning in associative polymers through quantification of bond dissociation under shear

Understanding the physics of associative polymers is often limited by our inability to directly measure bond dissociation under deformation. In this work, we developed a rheo-fluorescence technique and applied it to characterize the nonlinear shear response of linear side-functionalized polymer chains cross-linked via nickel-terpyridine complexation. As the network was sheared, the fraction of dissociated bonds was quantitatively measured based upon a change in fluorescence with metal dissociation. Shear thinning of the gel was accompanied by only a small increase in the fraction of dissociated bonds. Comparison with several transient network models shows that the shear thinning within the constraint of the measured fraction of dissociated bonds cannot be explained by classical theories that include retraction of dangling chains alone; the rheological response likely involves alternative modes of stress relaxation.

Figure 1

Reaction scheme for the synthesis of the terpyridine-functionalized monomer (II) and P(DMA-co-TpyMA), where $x=148$ and $y=7$ as determined by ${}^1\mathrm{H}$ NMR.

Figure 2

(a) Schematic of the rheo-fluorescence setup showing the position of the excitation source and collection lens, relative to the transparent upper plate. (b) The photo shows the rheo-fluorescence setup, with the optical elements mounted on a raised breadboard.

Figure 3

(a) The calibration curve for calculating the fraction of dissociated bond from the measured photodetector output, obtained using standard solutions of known concentrations of terpyridine, at a gap height of 0.3 mm. (b) The fluorescence of the standard solutions was also measured on a fluorimeter, which supports the linear relation between the measured signal and the concentration.

Figure 4

(a) The proposed network structure of the gel consists of inter (bridging) and intra (loop) chain bonds, along with dissociated (dangling) bonds. Dangling chains may exist as both terminal chains or larger dangling segments between two physical junctions. The large circles denote the pervaded volume of the chains, which are overlapping, while the small gray circles indicate the pervaded volume for strand between stickers. (b) The bonds are bis complexes of terpyridine with nickel that form through a reversible reaction with rate constants, $k_d$ and $k_a$.

Figure 5

Typical result from startup to steady shear experiments showing the change in the fraction of dissociated bonds $f_d$ and dimensionless stress $\tilde{\sigma }$ as a function of strain for two shear rates: (a) $\text{Wi}=0.96$ and (b) $\text{Wi}=8.65$, where $\text{Wi}=\dot{\gamma }{\tau }_r$. The $f_d$ are smoothing spline fits applied to filter out the inherent noise from the photodetector.

Figure 6

(a)–(c) Best fits for the VM, TE, and Sing model obtained using least-squares fit by treating the parameters of the models as fitting parameters for data obtained at 70, 75, and $80{}^{\circ }\text{C}$, respectively. (d)–(f) The corresponding $\eta$ calculated for VM, TE, and Sing models, using the same fitting parameters, compared to data obtained at 70, 75, and $80{}^{\circ }\text{C}$.

Figure 7

Normalized stress relaxation following a small step strain (strain = 1%) at 70, 75, and $80{}^{\circ }\text{C}$ for the terpy-acrylamide gel. The dotted lines are fits to a phenomenological Kohlrausch-Williams-Watts (KWW) function.

Figure 8

Effect of temperature on $K_{\text{eq}}$ (red diamonds) and fit parameters $p_0$ and $q_0$ (black symbols).