We report the observation of a transition in the dynamical properties of water nano-menicus which dramatically change when probed at different time scales. Using a AFM mode that we name Force Feedback Microscopy, we observe this change in the simultaneous measurements, at different frequencies, of the stiffness G'(N/m), the dissipative coefficient G"(kg/sec) together with the static force. At low frequency we observe a negative stiffness as expected for capillary forces. As the measuring time approaches the microsecond, the dynamic response exhibits a transition toward a very large positive stiffness. When evaporation and condensation gradually lose efficiency, the contact line progressively becomes immobile. This transition is essentially controlled by variations of Laplace pressure.Visco-elastic properties of water nanobridges[1] at very different time scales, have never been investigated despite ubiquitous presence of capillarity. Associated forces are among the most intense at nanoscales with important consequences in soils and granular media. Interest in dynamical properties is immediately raised if one considers interacting surfaces with roughness scales down to nanometer. Even at moderate speeds, such as v=1m/s, characteristic times of surface interaction down to microsecond appear in these conditions. Our measurements approaching these time scales, further strengthen the relevance of the dynamical properties to describe how real surfaces interact and are certainly of crucial importance in numerous AFM experiments [2]. We here report measurements of dynamical properties of a water nanobridge for a continuous range of the surface gap and a frequency bandwidth up to 0.1 MHz. We identify two regimes: one is the thermodynamical equilibrium; the second is out of equilibrium. Evaporation and condensation of water molecules between the liquid and the gas phase ensures that the nano-meniscus curvature is the one at thermodynamical equilibrium(2H=-1/r k ) where 2H is the water bridge curvature and r k is the Kelvin radius. At time short enough, molecule exchanges between the liquid and the gas phase are no longer efficient and the water nanobridge is led to acquire a constant volume. The liquid bridge relaxation time is the time needed for the bridge to adapt its shape as required by thermodynamical equilibrium, when its length h is abruptly changed by δh. This is controlled by molecular transport through diffusion mechanisms in gas phase. This relaxation time τ can be estimated as in SFA context, see Ref.[3]. τ = 2γρr 2 ln(R/ρ)/P sat r k 2 D

We present a method to tune the resonance frequency and the Q-factor of micro and nano-metric mechanical oscillators. A counteracting loop drives a capacitive force applied to the oscillator. The proportional and differential gains are used to shift the resonance frequency up to 75% and to tune the Q-factor of the oscillator, by changing its effective stiffness and damping ratio. The oscillator position is monitored in a large bandwidth with a fiber-optic based interferometer. We applied this simple operational scheme with different oscillators for modifying easily their dynamical properties. Compared to alternative methods requiring external fields, our method can either increase or decrease the resonance frequency in a frequency range much more extended. This opens up a wide range of applications, from force sensors with extremely low elastic constants but high quality factor to tunable energy harvesters or to high-frequency tuning of radio frequency filters. The control scheme can work in different media, and is then suitable to be applied to biological sensors and actuators.

In this article, we measure the viscous damping G", and the associated stiffness G', of a liquid flow in sphere-plane geometry in a large frequency range. In this regime, the lubrication approximation is expected to dominate. We first measure the static force applied to the tip. This is made possible thanks to a force feedback method. Adding a sub-nanometer oscillation of the tip, we obtain the dynamic part of the interaction with solely the knowledge of the lever properties in the experimental context using a linear transformation of the amplitude and phase change. Using a Force Feedback Microscope (FFM)we are then able to measure simultaneously the static force, the stiffness and the dissipative part of the interaction in a broad frequency range using a single AFM probe. Similar measurements have been performed by the Surface Force Apparatuswith a probe radius hundred times bigger. In this context the FFM can be called nano-SFA.In this paper, we aim to measure the hydrodynamic interaction in water between a microsphere and a hard and plane surface at different distances and at different frequencies using a single probe. In this regime, the viscous behavior is expected to be dominating. Previous experiments have been run in air with conservative forces [1]. Using an electrical coupling between an AFM tip and a metallic surface as test interaction in air, we probed the static and dynamic part of the interaction where in this case the stiffness is expected to match the minus of the derivative of the static force and the damping to be null. In liquid, from the dynamic transition from a viscous-dominated behavior at large distance to an elastic-dominated behavior at short distance, we aim to extract mechanical properties of soft thin films as SFA does [2]. The hydrodynamic pressure will gently deform the soft sample without touching it and propose an alternative to the classical hard mechanical contact. The increase in the frequency range of this mechanical testing and the decrease of the tip radius, compare to the SFA[3], allows us to probe the viscoelastic properties of soft thin films and the possibility of the frequency dependence and compare it to bulk values. Properties can dramatically change with respect to the frequency as we have demonstrated in the case of capillary bridge [? ]. Here in this test experiment, we use non-deformable surface and spherical probe, and we explore the dissipation due to the flowing liquid. Other experiments with an AFM setup have been performed [4,5] in order to measure the hydrodymanic behavior either with respect to the sphere-plane separation or for different frequencies using one lever. The dissipation is expected to follow the lubrication approximation and to be frequency dependent, f=ω/2π, if reported in N/m. The lubrication approximation holds for low Reynolds number, thus R> >z, and the dissipation follow[2]:R is the tip radius, the dynamic viscous coefficient of the water, equal to 1 mPA.s at 20°C, from IAPWS standards, and z is the tip sample distance. The linear frequ...