Modeling Dynamics of Pattern Formation and Restructuring in Constrained Hydrogel Membranes

Understanding dynamics of pattern formation in hydrogels is important for designing functional surfaces and interfaces for a number of applications. Herein, we focus on dynamically controlling patterns in three-dimensional thermoresponsive poly(N-isopropylacrylamide) (PNIPAAm) gel membranes with two clamped edges. The patterns are formed due to mechanical instability, which arises due to the constrained swelling of a polymer network undergoing extensive volume changes in response to external stimuli. We use three-dimensional gel Lattice Spring Model (3D gLSM) to simulate dynamics of the confined membranes and characterize the patterns formed. We perform a linear stability analysis using Foppl-von Karman equations for this geometry to predict patterns wavelength and critical stresses during the onset of instability. We then focus on dynamic restructuring between different patterns in response to variations in external temperature. Our results demonstrate that the wavelength, amplitude, and mode of patterns formed could be controlled dynamically by simply varying the rate of changing temperature. Our results show that a confined network exhibits bistability, which in turn is controlled by the rate of changing temperature.