The quantitative measurement of viscoelasticity of nano-scale entities is an important goal of nanotechnology research and there is considerable progress with advent of dynamic atomic force microscopy. The hydrodynamics of cantilever, the force sensor in AFM measurements, plays a pivotal role in quantitative estimates of nano-scale viscoelasticity. The point-mass (PM) model, wherein the AFM cantilever is approximated as a point-mass with mass-less spring is widely used in dynamic AFM analysis and its validity, particularly in liquid environments, is debated. It is suggested that the cantilever must be treated as a continuous rectangular beam to obtain accurate estimates of nano-scale viscoelasticity of materials it is probing. Here, we derived equations, which relate stiffness and damping coefficient of the material under investigation to measured parameters, by approximating cantilever as a point-mass and also considering the full geometric details. These equations are derived for both tip-excited as well as base-excited cantilevers. We have performed off-resonance dynamic atomic force spectroscopy on a single protein molecule to investigate the validity of widely used PM model. We performed measurements with AFMs equipped with different cantilever excitation methods as well as detection schemes to measure cantilever response. The data was analyzed using both, continuous beam model and the PM model. We found that both models yield same results when the experiments are performed in truly off-resonance regime with small amplitudes and the cantilever stiffness is much higher than the interaction stiffness. Our findings suggest that a simple PM approximation based model is adequate to describe the dynamics, provided care is taken while performing experiments so that the approximations used in these models are valid.

We report development of a novel instrument to measure tracer diffusion in water under nano-scale confinement. A direct optical access to the confinement region, where water is confined between a tapered fiber and a flat substrate, is made possible by coating the probe with metal and opening a small aperture( 0.1 µm to 1 µm) at its end. A well-controlled cut using an ion beam ensures desired lateral confinement area as well as adequate illumination of the confinement gap. The probe is mounted on a tuning-fork based force sensor to control the separation between the probe and the substrate with nm precision. Fluctuations in fluorescence intensity due to diffusion of a dye molecule in water confined between probe and the sample are recorded using a confocal arrangement with a single photon precision. A Monte-Carlo method is developed to determine the diffusion coefficient from the measured autocorrelation of intensity fluctuations which accommodates the specific geometry of confinement and the illumination profile. The instrument allows measurement of diffusion laws under confinement. We found that the diffusion of a tracer molecule is slowed down by more than ten times for the probe-substrate separations of 5 nm and below.

Abstract. The flow of water confined to nanometer-sized pores is central to a wide range of subjects from biology to nanofluidic devices. Despite its importance, a clear picture about nanoscale fluid dynamics is yet to emerge. Here we measured dissipation in less than 25 nm thick water films and it was found to decrease for both wetting and non-wetting confining surfaces. The fitting of Carreau-Yasuda model of shear thinning to our measurements implies that flow is non-Newtonian and for wetting surfaces the no-slip boundary condition is largely valid. On the contrary, for non-wetting surfaces boundary slippage occurs with slip lengths of the order of 10 nm. The findings suggest that both, the wettability of the confining surfaces and nonlinear rheological response of water molecules under nano-confinement play a dominant role in transport properties.

Diffusion of tracer dye molecules in water confined to the nanoscale is an important subject with a direct bearing on many technological applications. It is not yet clear, however, if the dynamics of water in hydrophilic as well as hydrophobic nanochannels remains bulk-like. Here, we present diffusion measurement of a fluorescent dye molecule in water confined to the nanoscale between two hydrophilic surfaces whose separation can be controlled with a precision of less than a nm. We observe that the fluorescence intensities correlate over fast (∼30 μs) and slow (∼1000 μs) time components. The slow time scale is due to adsorption of fluorophores to the confining walls, and it disappears in the presence of 1 M salt. The fast component is attributed to diffusion of dye molecules in the gap. It is found to be bulk-like for sub-10 nm separations and indicates that the viscosity of water under confinement remains unaltered up to a confinement gap as small as ∼5 nm. Our findings contradict some of the recent measurements of diffusion under nanoconfinement; however, they are consistent with many estimates of self-diffusion using molecular dynamics simulations and measurements using neutron scattering experiments.