Conformability of a Thin Elastic Membrane Laminated on a Soft Substrate With Slightly Wavy Surface

Abstract

When laminating a thin elastic membrane on a substrate with surface roughness, three scenarios can happen: fully conformed (FC), i.e., the membrane completely follows the surface morphology of the substrate without any interfacial gap, nonconformed (NC), i.e., the membrane remains flat if gravity is not concerned, and partially conformed (PC). Good conformability can enhance effective membrane-to-substrate adhesion strength and can facilitate signal/heat/mass transfer across the interface, which are of great importance to soft electronics laminated on rough bio-tissues. To reveal governing parameters in this problem and to predict conformability, energy minimization is implemented after successfully finding the substrate elastic energy under partially conformable contact. Four dimensionless governing parameters involving the substrate roughness, membrane thickness, membrane and substrate elastic moduli, and membrane-to-substrate intrinsic work of adhesion have been identified to analytically predict the conformability status and the area of contact. The analytical prediction has found excellent agreement with experimental observations. In summary, an experimentally validated quantitative guideline for the conformability of elastic membrane on soft corrugated substrate has been established in the four-parameter design space.