Complex Contact-Based Dynamics of Microsphere Monolayers Revealed by Resonant Attenuation of Surface Acoustic Waves

Abstract

Contact-based vibrations play an essential role in the dynamics of granular materials. Significant insights into vibrational granular dynamics have previously been obtained with reduced-dimensional systems containing macroscale particles. We study contact-based vibrations of a two-dimensional monolayer of micron-sized spheres on a solid substrate that forms a microscale granular crystal. Measurements of the resonant attenuation of laser-generated surface acoustic waves reveal three collective vibrational modes that involve displacements and rotations of the microspheres, as well as interparticle and particle-substrate interactions. To identify the modes, we tune the interparticle stiffness, which shifts the frequency of the horizontal-rotational resonances while leaving the vertical resonance unaffected. From the measured contact resonance frequencies we determine both particle-substrate and interparticle contact stiffnesses and find that the former is an order of magnitude larger than the latter. This study paves the way for investigating complex contact-based dynamics of microscale granular crystals and yields a new approach to studying micro-to nanoscale contact mechanics in multiparticle networks.

Vibrational dynamics of a two-dimensional microgranular crystal

“…The mode labeled V corresponding to the most prominent peak in the spectra, as shown in Fig. 2(e), was previously identified as the vertical contact resonance mode [7,9,10]. Figure 2(e) also shows small peaks to either side of the V-mode peak which we assigned to horizontal-rotational modes labeled HR and RH following Ref.…”

“…In these initial studies, the observed phenomena, such as an avoided crossing in the Rayleigh SAW dispersion [7] and the resonant attenuation of SAWs by microspheres [9], could be well accounted for by a simple model where microspheres did not interact with each other [7]. Refined measurements of the resonant attenuation of SAWs * avegaflick@gmail.com † maznev@mit.edu revealed horizontal-rotational modes enabled by interparticle interactions [10]. However, none of the experiments performed on self-assembled microgranular monolayers were done on a "single-crystal" sample with long-range order extending over distances comparable to the measurement spot size.…”

“…A new frontier was opened by laser-based experiments on 2D selfassembled monolayers of micron-sized particles on a solid substrate [7][8][9][10][11]. These experiments revealed the crucial role of adhesion, which is negligible for large particles but becomes an important factor in determining the contact stiffness at the microscale.…”

“…However, there is an important difference, as vibrations of a granular monolayer involve rotations of the spheres [10,12]. Spheres also have internal mechanical degrees of freedom; consequently, in addition to contact-based modes, one would expect to see collective modes originating from spheroidal vibrations of the spheres [13].…”

“…Spheres also have internal mechanical degrees of freedom; consequently, in addition to contact-based modes, one would expect to see collective modes originating from spheroidal vibrations of the spheres [13]. The presence of the substrate significantly alters the dispersion of contact-based modes [14] and adds Rayleigh SAWs in the substrate, which interact with the vibrational modes of the monolayer [10,14]. In this work, we characterize the dispersion of these three types of modes (contact based, spheroidal, and Rayleigh) and their interaction across the entire Brillouin zone (BZ) for a chosen high-symmetry direction of a 2D microgranular crystal.…”