Contact-to-connectivity crossover in the vibrational dynamics of nanoparticle assemblies

Classical contact mechanics is widely used to describe mechanical coupling in nanoparticle assemblies, yet its validity at the nanoscale remains experimentally unresolved. Here, we investigate size-dependent collective vibrational dynamics in self-assembled polystyrene nanoparticle films with particle diameters from 20 to 200 nm using VIPA-based Brillouin spectroscopy. A low-frequency band is assigned to an interaction-induced translational mode from its wavelength dependence, its separation from the intrinsic Lamb mode where both are accessible, and its persistence across the investigated size range. For particle diameters above approximately 100-150 nm, the mode frequency is consistent with Johnson-Kendall-Roberts (JKR) contact-mechanics scaling, f ∝ d^-7/6. Below ∼100 nm, the response follows a weaker power-law dependence, f ∝ d^γ with γ = -0.38 ± 0.12, indicating a deviation from homogeneous adhesive-contact scaling. Structural characterization over the same diameter range reveals reduced positional correlations and packing coherence, coincident with the change in vibrational scaling. Expressing the fitted branch as a contact-network velocity further shows that the sub-100 nm response reflects collective motion transmitted through a heterogeneous load-bearing network, rather than a bulk acoustic velocity. The measured scaling is consistent with an effective elastic-backbone description. These results establish a nanoscale crossover in the limits of applicability of classical contact mechanics and highlight mechanical connectivity as a key parameter governing collective vibrational dynamics in nanoparticle assemblies.