High frequency contact mechanics based on quartz crystal resonators: application to polymer surfaces
- PDF / 799,567 Bytes
- 8 Pages / 595 x 842 pts (A4) Page_size
- 63 Downloads / 199 Views
B2.5.1
High frequency contact mechanics based on quartz crystal resonators: application to polymer surfaces Steffen Berg and Diethelm Johannsmann*1 Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany Abstract High frequency contact mechanics experiments were carried with a quartz crystal resonator, the surface of which was coated with a polystyrene film. The experiment is based on the ring-down of the resonator after the electrical excitation has been stopped. When a tip touches the quartz surface, the shear motion of the quartz is perturbed, which can be used to study force–displacement and force–speed relations in the contact zone. A nonlinear spring constant κ1(x) and a nonlinear friction coefficient ξ1( x& ) are explicitly derived. When a ceramic sphere touches a polymer film the friction force depends more than linearly on lateral speed. This contrasts to metal-metal contacts or contacts between ceramic surfaces, where the friction force depends either linearly of sub-linearly on speed. Introduction The friction forces between macroscopic bodies still are poorly understood. In contrast to hydrodynamic (Stokes-type) friction, where the friction force is proportional to speed, sub-linear force–speed relations are often found in sliding friction between solid surfaces.1,2 Coulomb’s law even states that the friction force is independent of sliding speed. Usually, this behavior is associated with point contacts, large local stresses, and concomitant nonlinear force–speed relations on the microscopic scale. In order to investigate this microscopic friction force experimentally, an instrument with well-defined geometry and good positioning accuracy is needed. The established instruments of nanotribology3 like the AFM4 and the Surface Forces Apparatus (SFA) 5 fulfill these requirements. However, they do not allow for high speed. Quartz crystal resonators have been proposed as tools for microtribology6,7,8 because they can fill this gap. They combine high speed and accurate positioning due to their high frequency of operation. In previous work6,8 we have monitored the shifts in resonance frequency and bandwidth of the laterally oscillating quartz resonator while approaching a sphere to its surface. Both surfaces may be covered by a protective coating or a lubricant. When the two bodies are tightly locked, the shifts in frequency and bandwidth are well explained in terms of the Hertz model. 6,8 In the transition range one often observes a peak in the bandwidth which cannot be accounted for by this simple model. The additional dissipation is caused by interfacial friction.6,7,8 In previous experiments, the resonance frequency and the bandwidth were determined by impedance spectroscopy. A resonance curve was fitted to the conductance spectrum after the frequency of the impedance analyzer had been swept across the resonance. Importantly, this analysis assumes that the quartz is a simple harmonic oscillator, that is, that all forces depend linearly on displacement or speed. This assumption shoul
Data Loading...
