Mechanical model analysis for resonance shear measurement

Resonance shear measurement (RSM), which we developed based on a surface force apparatus, can investigate the structuring, and rheological and tribological properties of confined liquids as a function of the surface separation distance (D) from several μm to zero with a nanometer resolution. Using RSM, we reported that the nanoconfined liquids, including commercial lubricants, exhibited properties quite different from the bulk phase. Mechanical modeling of the resonance system is necessary to quantitatively evaluate the properties of confined liquids and/or sheared interfaces. In this study, we improved the model for RSM as follows: (1) We directly measured the movements of the upper and lower surfaces in addition to the measurement on the movement of the vertical spring to confirm the model, which could be used to estimate the parameters used in the model; (2) we proposed a modified mechanical model which considers the effect of additional motion. This model could fit the resonance curves using a identical apparatus constant for the entire measurement range, while the characteristic values of the confined liquids are the same as those obtained using our previous model, and (3) we calculated the friction (shear) force using the improved model and obtained the characteristic values (viscous and elastic parameters) of the confined liquids. This study afforded the simplicity and reliability of a mechanical model analysis of resonance curves, and the friction force calculation employing the viscous and elastic terms can be useful for studying the mechanism of friction force.