Stress generation by solvent absorption and wrinkling of a cross-linked coating atop a viscous or elastic base

An in-plane constrained cross-linked gel layer absorbs an equilibrium amount of solvent and experiences in-plane compressive stress. A stability analysis of such an elastic gel layer that is attached to either a viscous or an elastic bottom layer atop a rigid substrate is considered. The effects of the top and bottom layer moduli (E(t) and E(b)), the bottom-to-top layer thickness ratio (H/h), and the polymer solvent interaction parameter (chi) on the critical condition of wrinkling, wrinkle wavelength, and amplitude are examined. When the bottom layer is viscous, the compressed top layer is always unstable, and wrinkling is rate-controlled. The viscous flow of the bottom layer governs the rate and determines the fastest growing wavelength. As E(t) rises, the bending stiffness of the elastic layer does as well, and so the fastest growing wavelength (lambda(m)) rises and the equilibrium amplitude (A(e)) falls. As H/h rises, the constraint of the rigid substrate diminishes, and so lambda(m) and A(e) rise. As chi falls or as the solvent has higher affinity for the polymeric gel, lambda(m) falls and A(e) rises because better solvents create higher compressive strain that promote low-wavelength, high-amplitude wrinkles. When the bottom layer is elastic, a critical compressive stress exists. If the generated compressive stress by solvent absorption is greater than the critical stress, the top layer wrinkles. It was found that wrinkling is most likely at intermediate E(t), low E(b), high H/h, and low chi. Further, lower chi, higher H/h, and lower E(b) were found to promote higher equilibrium amplitude and higher wavelength wrinkles.