Linear and Nonlinear Normal Interface Stiffness in Dry Rough Surface Contact Measured Using Longitudinal Ultrasonic Waves

When two rough surfaces are loaded together contact occurs at asperity peaks. An interface of solid contact regions and air gaps is formed that is less stiff than the bulk material. The stiffness of a structure thus depends on the interface conditions; this is particularly critical when high stiffness is required, for example in precision systems such as machine tool spindles. The rough surface interface can be modelled as a distributed spring. For small deformation, the spring can be assumed to be linear; whilst for large deformations the spring gets stiffer as the amount of solid contact increases. One method to measure the spring stiffness, both the linear and nonlinear aspect, is by the reflection of ultrasound. An ultrasonic wave causes a perturbation of the contact and the reflection depends on the stiffness of the interface. In most conventional applications, the ultrasonic wave is low power, deformation is small and entirely elastic, and the linear stiffness is measured. However, if a high-powered ultrasonic wave is used, this changes the geometry of the contact and induces nonlinear response. In previous studies through transmission methods were used to measure the nonlinear interfacial stiffness. This approach is inconvenient for the study of machine elements where only one side of the interface is accessible. In this study a reflection method is undertaken, and the results are compared to existing experimental work with through transmission. The variation of both linear and nonlinear interfacial stiffnesses was measured as the nominal contact pressure was increased. In both cases interfacial stiffness was expressed as nonlinear differential equations and solved to deduce the contact pressure-relative surface approach relationships. The relationships derived from linear and nonlinear measurements were similar, indicating the validity of the presented methods.

Imaging how thermal capillary waves and anisotropic interfacial stiffness shape nanoparticle supracrystals

Development of the surface morphology and shape of crystalline nanostructures governs the functionality of various materials, ranging from phonon transport to biocompatibility. However, the kinetic pathways, following which such development occurs, have been largely unexplored due to the lack of real-space imaging at single particle resolution. Here, we use colloidal nanoparticles assembling into supracrystals as a model system, and pinpoint the key role of surface fluctuation in shaping supracrystals. Utilizing liquid-phase transmission electron microscopy, we map the spatiotemporal surface profiles of supracrystals, which follow a capillary wave theory. Based on this theory, we measure otherwise elusive interfacial properties such as interfacial stiffness and mobility, the former of which demonstrates a remarkable dependence on the exposed facet of the supracrystal. The facet of lower surface energy is favored, consistent with the Wulff construction rule. Our imaging–analysis framework can be applicable to other phenomena, such as electrodeposition, nucleation, and membrane deformation.