Oscillating adhesive contacts between micron-scale tips and compliant polymers

Abstract

Adhesion of micron-scale probes with model poly(dimethylsiloxane), PDMS, elastomers was studied with a depth-sensing nanoindenter under oscillatory loading conditions. For contacts between diamond indenters (radius R = 5 or 10 μm) and PDMS, force–displacement curves were highly reversible and consistent with Johnson–Kendall–Roberts (JKR) behavior. However, our experiments have revealed striking differences between the experimental measurements of tip–sample interaction stiffness and the theoretical JKR stiffness. The measured stiffness was always greater than zero, even in the reflex portion of the curve (between the maximum adhesive force and release), where the JKR stiffness is negative. This apparent paradox can be resolved by considering the effects of viscoelasticity of PDMS on an oscillating crack tip in a JKR contact. Under well described conditions determined by oscillation frequency, sample viscoelastic properties, and the Tabor parameter (with variables R, reduced elastic modulus, E ∗ , and interfacial energy, Δ γ), an oscillating crack tip will neither advance nor recede. In that case, the contact size is fixed (like that of a flat punch) at any given point on the load–displacement cycle, and the experimentally measured stiffness is equal to the equivalent punch stiffness. For a fixed oscillation frequency, a transition between JKR and punch stiffness can be brought about by an increase in radius of the probe or a decrease in PDMS modulus. Additionally, varying the oscillation frequency for a fixed E ∗ , R, and Δ γ also resulted in transition between JKR and punch stiffness in a predictable manner. Comparisons of experiments and theory for an oscillating viscoelastic JKR contact are presented. The storage modulus and surface energy from nanoscale JKR stiffness measurements were compared to calculated values and those measured with conventional nanoindentation and JKR force–displacement analyses.