Longitudinal eigenvibration of multilayer colloidal crystals and the effect of nanoscale contact bridges

Longitudinal contact-based vibrations of colloidal crystals with a controlled layer thickness are studied. These crystals consist of 390 nm diameter polystyrene spheres arranged into close packed, ordered lattices with a thickness of one to twelve layers. Using laser ultrasonics, eigenmodes of the crystals that have out-of-plane motion are excited. The particle-substrate and effective interlayer contact stiffnesses in the colloidal crystals are extracted using a discrete, coupled oscillator model. Extracted stiffnesses are correlated with scanning electron microscope images of the contacts and atomic force microscope characterization of the substrate surface topography after removal of the spheres. Solid bridges of nanometric thickness are found to drastically alter the stiffness of the contacts, and their presence is found to be dependent on the self-assembly process. Measurements of the eigenmode quality factors suggest that energy leakage into the substrate plays a role for low frequency modes but is overcome by disorder- or material-induced losses at higher frequencies. These findings help further the understanding of the contact mechanics, and the effects of disorder in three-dimensional micro- and nano-particulate systems, and open new avenues to engineer new types of micro- and nanostructured materials with wave tailoring functionalities via control of the adhesive contact properties.