Modeling the Chemo-mechanical Behavior of Reactive Polymer Gels
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Modeling the Chemo-mechanical Behavior of Reactive Polymer Gels Victor V. Yashin and Anna C. Balazs Department of Chemical and Petroleum Engineering, University of Pittsburgh, 1249 Benedum Hall, Pittsburgh, PA 15261, U.S.A. ABSTRACT We consider a theoretical model of a reactive polymer gel in which the reaction can proceed in an oscillatory regime and generate traveling chemical waves accompanied by waves of local swelling-deswelling. This type of gel could be used for fabricating chemo-mechanical devices with self-sustained rhythmic action, and gel-based pumps. We assume that the BelousovZhabotinsky (BZ) reaction takes place in the reactive gel. The BZ reaction generates periodic reduction-oxidation (redox) changes of a metal catalyst covalently bonded to a hydrogel that is immersed in a solution containing the rest of the BZ reagents. The redox changes in the metal affect the polymer-solvent interactions, resulting in variations in the gel volume. The selfoscillation of the gel volume, and the traveling waves of local swelling in a hydrogel with the BZ reaction have been experimentally observed by Yoshida and co-workers. To describe the system theoretically, we employ the Oregonator model of the BZ reaction, and the two-fluid model of gel dynamics. Propagation of one-dimensional wave trains through the reactive gel is simulated. The structure of the traveling swelling-deswelling waves is studied.
INTRODUCTION Polymer gels are known for their capability to undergo dramatic volume changes in their response to chemical, mechanical and electrical stimulation [1-4]. This ability to change shape or volume allows polymer gels to perform mechanical work while being supplied with energy from a chemical source, such as reagents or reactions. Until recently, gels were not known to exhibit periodic oscillations in a closed system; periodic external stimulation was needed to induce these volumetric changes. However, a significant breakthrough occurred when Yoshida and coworkers synthesized a responsive gel that underwent the Belousov-Zhabotinsky (BZ) reaction [5,6], and thereby fabricated a gel that exhibited autonomous spatial and temporal oscillations. The BZ reaction involves the oxidation of an organic substrate (such as citric or malonic acid) by a bromate ion in the presence of a metal-ion catalyst under acidic conditions. In solution, the BZ reaction exhibits the well-known reduction-oxidation (redox) reaction, which leads to temporal and spatial oscillations. These oscillations are easily observed due to the color difference between the oxidized and reduced states of the metal-ion catalyst. In the case of polymer gels, the metal catalyst is grafted onto the polymer network, and the substrate contains the rest of the BZ reagents [5,6]. The oscillatory BZ reaction generates a periodic change of the charge on the metal-ion catalyst that, in turn, drives the rhythmic swelling and deswelling of the responsive polymer gel. In other words, the gel generates periodic mechanical action from the chemical e
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