Viscoelastic Properties of Stimuli-Responsive Transient Polymer Networks

Chemical reactions in cross-linked polymer networks have long been a focus of polymer science because of their strong coupling to the network rheology. In particular, reversible reactions responding to various stimuli such as with thermal, pH, light, salt, and mechanical triggers promise broad applications to the development of new concepts and materials functions. Herein, rheological properties of cross-linked polymer networks made up of polymer chains, each undergoing reversible first-order chemical reaction A ⇄ B in response to such stimuli, are studied on the basis of the theoretical framework of the transient network model. We show that in general there are two fundamental relaxation times: one characterizing the rate of the reaction (chemical relaxation time) and the other the lifetime of the cross-links (rheological relaxation time). To see their interplay specifically, we focus on the formation of globules, flower micelles, loops, helices, etc., treated as first-order chemical reactions and calculate the dynamic mechanical moduli as functions of the rate constants of the reactions and the dissociation rate of the cross-links. In the limit of the permanent cross-links (reactive rubbers), we find a finite loss modulus that shows a peak at the frequency corresponding to the chemical relaxation time. The storage modulus is reduced but remains finite in the angular frequency range below this peak. The equilibrium storage modulus in the limit of ω = 0 is found as a function of the rate constants of the reaction. For the transient polymer networks with reversible cross-links of finite lifetime, competition of the two independent modes occurs: slow mode (rheological mode) and fast mode (chemical mode), corresponding to the two eigenvalues of the rate equation. Thus, we see that the complex modulus takes the form of the phenomenological Burgers model. Their relaxation times and plateau moduli are found in terms of molecular parameters. Viscoelastic properties of such reactive Burgersian fluids are studied in detail.