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

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.

Figure 1

Overview of the experiment. (a) Microscope image of the interface between the monolayer and blank sample regions. The scale bar is $10\mu \mathrm{m}$. (b) Schematic of the laser ultrasonic experimental setup. Normalized signal measured in the (c) blank region and (d) $132\mu \mathrm{m}$ inside the monolayer region. (e) Normalized Fourier spectra of the signals in (c) and (d) using the same colors. The red spectrum corresponds to a signal measured $400\mu \mathrm{m}$ inside the monolayer region. The vertical dashed lines denote the identified contact resonance frequencies. (f) Schematic of the dynamical model.

Figure 2

(a)–(c) Transmission spectra for SAWs propagating across the interface between the blank and monolayer regions. The color bar denotes the magnitude of the transmission coefficient. The horizontal dashed lines denote the identified contact resonance frequencies for the uncoated monolayer. The short horizontal lines on the right of the panels are the fitted contact resonance frequencies. Position denotes the distance from the interface. (a) Uncoated microsphere monolayer. (b) 20 nm of aluminum coating. (c) 40 nm of aluminum coating.

Figure 3

(a) Schematic of the experiment with large spot excitation and grating interferometer detection. (b) Normalized signal measured with the interferometer. (c) Fourier spectrum of the signal in (b).

Figure 4

Surface acoustic wave dispersion in samples with (a) an uncoated monolayer and (b) a 40 nm thick aluminum coating. The color plot denotes the normalized magnitude of the calculated 2D Fourier spectra. The horizontal dashed and dotted lines correspond to the identified contact resonance frequencies for the uncoated sample and the sample with 40 nm of aluminum, respectively. The short horizontal lines on the right of the panels are the fitted contact resonance frequencies. The red dash-dotted lines are the dispersion curves calculated using the fitted resonance frequencies.