Simultaneous viscosity and density measurement of small volumes of liquids using a vibrating microcantilever

Many industrial and technological applications require precise determination of the viscosity and density of liquids. Such measurements can be time consuming and often require sampling substantial amounts of the liquid. These problems can partly be overcome with the use of microcantilevers but most existing methods depend on the specific geometry and properties of the cantilever, which renders simple, accurate measurement difficult. Here we present a new approach able to simultaneously quantify both the density and the viscosity of microliters of liquids. The method, based solely on the measurement of two characteristic frequencies of an immersed microcantilever, is completely independent of the choice of cantilever. We derive analytical expressions for the liquid’s density and viscosity and validate our approach with several simple liquids and different cantilevers. Application of our model to non-Newtonian fluids shows that the calculated viscosities are remarkably robust when compared to measurements obtained from a standard rheometer. However, the results become increasingly dependant on cantilever geometry as the frequency-dependent nature of the liquid’s viscosity becomes more significant

Determining the spring constant of arbitrarily shaped cantilevers in viscous environments

Accurate calibration of the flexural spring constant of microcantilevers is crucial for sensing devices, microactuators, and atomic force microscopy (AFM). Existing methods rely on precise knowledge of cantilever geometry, make significant simplifications, or require potentially damaging contact with the sample. Here, we develop a simple equation to calculate the flexural spring constants of arbitrarily shaped cantilevers in fluid. Our approach, verified here with AFM, only requires the measurement of two resonance frequencies of the cantilever in air and in a liquid, with no need for additional input or knowledge about the system. We validate the method with cantilevers of different shapes and compare its predictions with existing models. We also show how the method’s accuracy can be considerably improved, especially in more viscous liquids, if the effective width of the cantilever is known. Significantly, the developed equations can be extended to calculate the spring constants of the cantilever’s higher eigenmodes

Development of a flexure-based nano-actuator for high-frequency in-plane directional sensing with atomic force microscopy

Scanning probe microscopies typically rely on the high-precision positioning of a nanoscale probe in order to gain local information about the properties of a sample. At a given location, the probe is used to interrogate a minute region of the sample, often relying on dynamical sensing for improved accuracy. This is the case for most force-based measurements in atomic force microscopy (AFM) where sensing occurs with a tip oscillating vertically, typically in the kHz to MHz frequency regime. While this approach is ideal for many applications, restricting dynamical sensing to only one direction (vertical) can become a serious limitation when aiming to quantify the properties of inherently three-dimensional systems, such as a liquid near a wall. Here, we present the design, fabrication, and calibration of a miniature high-speed scanner able to apply controlled fast and directional in-plane vibrations with sub-nanometer precision. The scanner has a resonance frequency of ∼35 kHz and is used in conjunction with a traditional AFM to augment the measurement capabilities. We illustrate its capabilities at a solid–liquid interface where we use it to quantify the preferred lateral flow direction of the liquid around every sample location. The AFM can simultaneously acquire high-resolution images of the interface, which can be superimposed with the directional measurements. Examples of sub-nanometer measurements conducted with the new scanner are also presented

A non-destructive method to calibrate the torsional spring constant of atomic force microscope cantilevers in viscous environments

Calibration of the torsional spring constant of atomic force microscopy cantilevers is fundamental to a range of applications, from nanoscale friction and lubrication measurements to the characterization of micro-electromechanical systems and the response of biomolecules to external stimuli. Existing calibration methods are either time consuming and destructive (ex situ static approaches), or rely on models using the frequency and quality factor (Q-factor) of the cantilever torsional resonance as input parameters (in situ dynamical approaches). While in situ approaches are usually preferred for their easy implementation and preservation of the cantilever, their dependence on the torsional resonance Q-factor renders calibration in highly viscous environments challenging. This is problematic, for example, in many nanoscale tribological applications. Here, we propose a calibration method that does not depend on the cantilever torsional Q-factor and show how the cantilever deflection can be converted into a lateral force. The method is tested with six cantilevers of different shapes and material composition and in six fluid media. The derived spring constants are compared with predictions from existing methods, demonstrating a higher precision, in particular, for highly viscous liquids

Nanoscale mapping of the directional flow patterns at liquid-solid interfaces

The nanoscale behavior of liquid molecules and solutes along the interface with solids controls many processes such as molecular exchanges, wetting, electrochemistry, nanofluidics, biomolecular function, and lubrication. Experimentally, several techniques can explore the equilibrium molecular arrangement of liquids near the surface of immersed solids but quantifying the nanoscale flow patterns naturally adopted by this interfacial liquid remains a considerable challenge. Here we describe an approach based on atomic force microscopy, and able to quantify the flow direction preferentially adopted by liquids along interfaces with nanoscale precision. The approach, called vortex dissipation microscopy (VDM), uses high-frequency directional oscillations to derive local flow information around each location of the interface probed. VDM effectively derives nanoscale flow charts of the interfacial liquid parallel to a solid and can operate over a broad range of soft and hard interfaces. To illustrate its capabilities, we quantify the dynamics of aqueous solutions containing KCl or MgCl2 along the surface of a same graphene oxide flake. We show that dissolved K+ ions can move evenly in all directions along the interface whereas Mg2+ ions tend to move in registry with the underlying lattice due to enthalpic effects. The results provide in situ nanoscale insights into the ion-specific sieving properties of graphene oxide membranes