Deformation and adhesive contact of elastomeric membranes

We have developed a highly sensitive inflation technique for probing adhesive interactions between soft materials. In this method, an elastomeric membrane is placed across a cylindrical glass tube and is pressurized into contact with a substrate. The adhesive interaction between the membrane and the substrate is obtained from the angle of contact, which is determined indirectly from the measured contact radius and applied pressure. An analysis of the membrane profile based on the numerical solution of the axisymmetric Laplace equation is developed. In a nonadhesive situation, where the membrane contact angle is known to be zero, the analysis is used to obtain the relationship between the membrane deformation and the biaxial membrane strain. Linearization of the governing equations is used to develop an analytic solution for the contact angle and energy release rate, making a connection to existing, more restrictive analyses of this problem. Results from three different types of membranes are presented as illustrative applications of the method. The substrate in these experiments is the gold electrode surface of a quartz crystal resonator, and the effect of membrane contact on the crystal resonance is summarized briefly. Adhesive interactions between the membranes are minimized in most cases by adding a grafted polyethylene glycol brush to one or both of the contacting surfaces.