Polymer dependent acoustic mode coupling and Hooke's law spring constants in stacked gold nanoplates

Metal nanoparticles are excellent acoustic resonators and their vibrational spectroscopy has been widely investigated. However, the coupling between vibrational modes of different nanoparticles is less explored. For example, how the intervening medium affects the coupling strength is not known. Here, we investigate how different polymers affect coupling in Au nanoplate-polymer-Au nanoplate sandwich structures. The coupling between the breathing modes of the Au nanoplates was measured using single-particle pump-probe spectroscopy, and the polymer dependent coupling strength was determined experimentally. Analysis of the acoustic mode coupling gives the effective spring constant for the polymers. A relative motion mode was also observed for the stacked Au nanoplates. The frequency of this mode is strongly correlated with the coupling constant for the breathing modes. The breathing mode coupling and relative motion mode were analyzed using a coupled oscillator model. This model shows that both these effects can be described using the same spring constant for the polymer. Finally, we present a new type of mass balance using the strongly coupled resonators. We show that the resonators have a mass detection limit of a few femtograms. We envision that further understanding of the vibrational coupling in acoustic resonators will improve the coupling strength and expand their potential applications.