(520c) Stress Generation by Solvent Absorption and Wrinkling of a Cross-Linked Coating Atop a Viscous or Elastic Base

A cross-linked gel layer constrained in-plane absorbs an equilibrium amount of solvent and experiences in-plane compressive stress. The equilibrium solvent content is predicted by setting the chemical potential of the solvent inside the gel equal to that outside. The in-plane compressive stress is predicted with the neo-Hookean constitutive equation. It is found that the equilibrium solvent content falls with rising concentration of cross-links and falling affinity of the solvent for the gel. The in-plane compressive stress peaks with rising concentration of cross-links because swellability of the gel and in-plane compressive strain fall but modulus rises with rising concentration of cross-links. The in-plane compressive stress falls with falling affinity of the solvent for the gel.

Stability analysis of a cross-linked elastic gel that has absorbed the equilibrium amount of solvent and is attached to either a viscous or an elastic bottom layer atop a rigid substrate is considered. The effects of top and bottom layer moduli (E_t and E_b), bottom-to-top layer thickness ratio (H/h), and polymer solvent interaction parameter (c) 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, which is most likely to be observed when growth is arrested. As E_t rises, the bending stiffness of the elastic layer does too and so the fastest growing wavelength (l_m) rises and equilibrium amplitude (A_e) falls. As H/h rises, the constraint of the rigid substrate diminishes and so l_m and A_e rise. As c falls, l_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, there is a critical compressive stress. If the generated compressive stress (s_0,gen) is greater that the critical stress (s_0,c), the top layer wrinkles. As the top layer modulus E_t rises, s_0,c rises and s_0,gen peaks. Therefore, wrinkling is most likely at intermediate values of E_t. Moreover, as E_t rises, the equilibrium wrinkle amplitude (A_e) peaks because s_0,gen peaks, and wrinkle wavelength (l) rises because bending stiffness rises. As E_b rises, s_0,c rises but s_0,gen does not change. Therefore, wrinkling is most likely when E_b is low. As the bottom layer modulus E_b rises, A_e and l fall because the constraint of the bottom layer rises. As the bottom-to-top layer thickness ratio H/h rises, s_0,c falls but s_0,gen does not change. Therefore, wrinkling is most likely when H/h is high. As H/h rises, A_e and l both rise because the wrinkling layer is relatively further from the rigid substrate that opposes wrinkling. As the polymer solvent interaction parameter c falls, s_0,c does not change but s_0,gen rises. Therefore, wrinkling is most likely when c is low. Moreover, as c falls, A_e rises because a better solvent generates more swelling and greater compressive strain energy, which promotes wrinkling, but does not change l significantly.