The authors model wave propagation in swollen, chemoresponsive polymer gels that are undergoing the oscillatory Belousov-Zhabotinsky (BZ) reaction. To carry out this study, they first modify the Oregonator model for BZ reactions in simple solutions to include the effect of the polymer on the reaction kinetics. They then describe the gel dynamics through the framework of the two-fluid model. The polymer-solvent interactions that are introduced through the BZ reaction are captured through a coupling term, which is added to the Flory-Huggins model for polymer-solvent mixtures. The resulting theoretical model is then used to develop the gel lattice spring model (gLSM), which is a computationally efficient approach for simulating large-scale, two-dimensional (2D) deformations and chemical reactions within a swollen polymer network. The 2D calculations allow the authors to probe not only volume changes but also changes in the sample's shape. Using the gLSM, they determine the pattern formation and shape changes in 2D rectangular BZ gels that are anchored to a solid wall. They demonstrate that the dynamic patterns depend on whether the gel is expanded or contracted near the wall, and on the sample's dimensions. Finally, they isolate a scenario where the detachment of the gel from the wall leads to macroscopic motion of the entire sample.

We develop a computational model to capture the complex, three-dimensional behavior of chemoresponsive polymer gels undergoing the Belousov-Zhabotinsky reaction. The model combines components of the finite difference and finite element techniques and is an extension of the two-dimensional gel lattice spring model recently developed by two of us [V. V. Yashin and A. C. Balazs, J. Chem. Phys. 126, 124707 (2007)]. Using this model, we undertake the first three-dimensional (3D) computational studies of the dynamical behavior of chemoresponsive BZ gels. For sufficiently large sample sizes and a finite range of reaction parameters, we observe regular and nonregular oscillations in both the size and shape of the sample that are coupled to the chemical oscillations. Additionally, we determine the critical values of these reaction parameters at the transition points between the different types of observed behavior. We also show that the dynamics of the chemoresponsive gels drastically depends on the boundary conditions at the surface of the sample. This 3D computational model could provide an effective tool for designing gel-based, responsive systems.

We developed an efficient model for responsive gels that captures large-scale, two-dimensional (2D) deformations and chemical reactions within a swollen polymer network. The 2D calculations allowed us to probe not only volume changes but also changes in sample shape. By focusing on gels undergoing the oscillatory Belousov-Zhabotinsky reaction, we observed traveling waves of local swelling that form a rich variety of dynamic patterns and give rise to distinctive oscillations in the gel's shape. The observed patterns depend critically on the gel's dimensions. The approach provides a useful computational tool for probing the dynamics of chemomechanical processes and uncovering morphological transformations in responsive gels.

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We review advances in a new area of interdisciplinary research that concerns phenomena arising from inherent coupling between non-linear chemical dynamics and mechanics. This coupling provides a route for chemical-to-mechanical energy transduction, which enables materials to exhibit self-sustained oscillations and/or waves in both concentration and deformation fields. We focus on synthetic polymer gels, where the chemo-mechanical behavior can be engineered into the material. We provide a brief review of experimental observations on several types of chemo-mechanical oscillations in gels. Then, we discuss methods used to theoretically and computationally model self-oscillating polymer gels. The rest of the paper is devoted to describing results of theoretical and computational modeling of gels that undergo the oscillatory Belousov-Zhabotinsky (BZ) reaction. We discuss a remarkable form of mechano-chemical transduction in these materials, where the application of an applied force or mechanical contact can drive the system to switch between different dynamical behavior, or alter the mechanical properties of the material. Finally, we discuss ways in which photosensitive BZ gels could be used to fabricate biomimetic self-propelled objects. In particular, we describe how non-uniform illumination can be used to direct the movement of BZ gel 'worms' along complex paths, guiding them to bend, reorient and turn.

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