Giant Nonmonotonic Stretching Response of a Self-Associating Polymer in Shear Flow

Self-associating polymers are ubiquitous in synthetic and biological systems. Here, we use a combination of simulation and theory to show that these polymers exhibit a counterintuitive strong nonmonotonic stretching response in shear flow. Furthermore, we demonstrate that this behavior can be tuned by controlling the barrier for dissociation of the bonds and develop a quantitative and predictive theory based on conformational transitions to explain the observed behavior. Our results can be important in understanding previous experimental and theoretical observations and further aid in the development of novel smart materials.

Figure 1

Relevant transitions in conformational space. A coil or globule will be stretched by a shear flow $\tilde{\dot{\gamma }}$. The concurrent tumbling instability will drive the polymer back into the coil or globule; however, due to either hydrodynamic effects or association constraints the polymer may be at first resistant to stretching for some subsequent amount of time. We dub this state the “stuck-globule” (sg) state, and the traditional coil-elongational description represents the “coil-stretch” (cs) state. The arrows show the conformational trajectory of a self-associating polymer in shear flow.

Figure 2

The energy landscape for a single associating pair of binding monomers. If two spatially adjacent monomers are within the reaction radius, there is a possibility that these monomers will bind and a spring between the two will form. The energy barrier to form this bond is given by $\Delta E_B$, and the barrier to unbind from this bond is given by $\Delta E_{\mathrm{UB}}$.

Figure 3

(a) Polymer elongation $⟨L⟩/(2N)$ as a function of the shear rate $\tilde{\dot{\gamma }}$ for different values of $\Delta E_0$ and $\Delta E_{\mathrm{UB}}$. As expected, decrease in $\Delta E_0$ results in the collapse of the polymer at all values of $\tilde{\dot{\gamma }}$. Increasing values of $\Delta E_{\mathrm{UB}}$ demonstrate the presence of a marked decrease in the ability of the polymer to elongate under the influence of shear for all values of $\Delta E_0$. The response for a $\Theta$ polymer is also shown, and also demonstrates nonmonotonicity due to the same effect as that seen for the binders, only solely due to hydrodynamic effects. (b) $⟨L⟩/(2N)$ vs $\tilde{\dot{\gamma }}$ for different values of $\Delta E_{\mathrm{UB}}$ at $\Delta E_0=0$. Simulation data (points) matches well with the theoretical prediction (lines). The Lennard-Jones (LJ) response for a polymer of similar level of collapse $\tilde{u}=0.55$ is also shown (connected points), and serves as an input for the theory. Green arrows correspond to time sequences shown in (c). For (a) and (b), error bars are smaller than symbol size. (c) Polymer elongation $\tilde{L}/(2N)$ as a function of time at a number of shear rates with $\Delta E_0=0$ and $\Delta E_{\mathrm{UB}}=5.0$. Notice the suppression of stretching events as shear rate is increased.