Swelling-Induced Instability of Substrate-Attached Hydrogel Lines

Micro- and nano-scale hydrogel lines can be fabricated on substrates by top-down approaches such as lithography and micro/nano-imprint. When in contact with a solvent, the hydrogel lines swell under the constraint of the substrate, often resulting in distorted shapes or instability patterns. In this paper, using a nonlinear finite element method, the effects of material and geometry on swell-induced instability of substrate-attached hydrogel lines are studied. Firstly, with a two-dimensional plane-strain model, we show that crease-like surface instability occurs in hydrogel lines with the width-to-height aspect ratio greater than a critical value. Next, for relative low aspect ratios, we show that a global buckling instability occurs. In both cases, the critical conditions depend on the material parameters that characterize the elastic stiffness of the polymer network and the chemical interaction between solvent and polymer in the hydrogel.