How narrow can a meniscus be?

A water meniscus naturally forms in air between an atomic force microscope (AFM) tip and a substrate. This nanoscale meniscus produces a capillary force on the AFM, and also serves as a molecular transport channel in dip-pen nanolithography (DPN). A stable meniscus is a necessary condition for DPN and for the validity of the Kelvin equation commonly applied to AFM experiments. Lattice gas Monte Carlo simulations show that, due to thermal fluctuation, a stable meniscus has a lower limit in width. We find a minimum width of 5 molecular diameters (1.9 nm) when the tip becomes atomically sharp (terminated by a single atom).     

Theoretical Study on the Capillary Force between an Atomic Force Microscope Tip and a Nanoparticle

Considering that capillary force is one of the most important forces between nanoparticles and atomic force microscope （AFM） tips in ambient atmosphere, we develop an analytic approach on the capillary force between an AFM tip and a nanoparticle. The results show that the capillary forces are considerably affected by the geometry of the AFM tip, the humidity of the environment, the vertical distance between the AFM tip and the nanoparticle, as well as the contact angles of the meniscus with an AFM tip and a nanoparticle. It is found that the sharper the AFM tip, the smaller the capillary force. The analyses and results are expected to be helpful for the quantitative imaging and manipulating of nanoparticles by AFMs.     

Capillary Interactions between a Probe Tip and a Nanoparticle

To understand capillary interactions between probe tips and nanoparticles under ambient conditions, a theoretical model of capillary forces between them is developed based on the geometric relations. It is found that the contribution of surface tension force to the total capillary force attains to similar order of magnitude as the capillary pressure force in many cases. It is also shown that the tip shape and the radial distance of the meniscus have great influence on the capillary force. The capillary force decreases with the increasing separation distances, and the variance of the contact angles may change the magnitudes of capillary forces several times at large radial distances. The applicability of the symmetric meniscus approximation is discussed.     

Mechanism of contrast formation in atomic force microscopy in water

We use computer modeling to investigate the mechanism of atomic-scale corrugation in frequency-modulation atomic force microscopy imaging of inorganic surfaces in solution. Molecular dynamics simulations demonstrate that the forces acting on a microscope tip result from the direct interaction between a tip and a surface, and forces entirely due to the water structure around both tip and surface. The observed force depends on a tip structure and is a balance between largely repulsive potential energy changes as the tip approaches and the entropic gain when water is sterically prevented from occupying sites near the tip and surface.     

Nucleation time of nanoscale water bridges

Water capillaries bind together grains of sand. They also can bind an atomic force microscope tip to a substrate. The kinetics of capillary condensation at the nanoscale is studied here using friction force microscopy. At 40% relative humidity we find that the meniscus nucleation times increase from 0.7 to 4.2 ms when the temperature decreases from 332 to 299 K. The nucleation times grow exponentially with the inverse temperature 1/T obeying an Arrhenius law. We obtain a nucleation energy barrier of 7.8 x 10(-20) J and an attempt frequency ranging between 4 and 250 GHz, in excellent agreement with theoretical predictions. These results provide direct experimental evidence that capillary condensation is a thermally activated phenomenon.     

Properties of droplet formation made by cone jet using a novel capillary with an external electrode

A capillary with an external electrode for cone-jet mode of electrospray has been developed to spot a droplet accurately on a substrate surface. The external electrode is made by gold deposition around tip of a glass capillary. The electrospray was made by applying a positive pulsed dc voltage to the solution in the capillary. Using a positive bias voltage to the external electrode, the meniscus of the solution at the tip deformed to be more sharp, and center of the meniscus was prolonged. This deformation stabilized the trajectory of the jet from the Taylor cone at the tip. From the experimental result, accuracy of positioning of the droplet having 0.3 pL volume was improved with the standard deviation of 1.1 μm, from that of 2.5 μm for conventional capillary without the external electrode.     

Surface adhesion properties of graphene and graphene oxide studied by colloid-probe atomic force microscopy

Surface adhesion properties are important to various applications of graphene-based materials. Atomic force microscopy is powerful to study the adhesion properties of samples by measuring the forces on the colloidal sphere tip as it approaches and retracts from the surface. In this paper we have measured the adhesion force between the colloid probe and the surface of graphene (graphene oxide) nanosheet. The results revealed that the adhesion force on graphene and graphene oxide surface were 66.3 and 170.6 nN, respectively. It was found the adhesion force was mainly determined by the water meniscus, which was related to the surface contact angle of samples.     

The capillary interaction between two vertical cylinders

Particles floating at the surface of a liquid generally deform the liquid surface. Minimizing the energetic cost of these deformations results in an inter-particle force which is usually attractive and causes floating particles to aggregate and form surface clusters. Here we present a numerical method for determining the three-dimensional meniscus around a pair of vertical circular cylinders. This involves the numerical solution of the fully nonlinear Laplace-Young equation using a mesh-free finite difference method. Inter-particle force-separation curves for pairs of vertical cylinders are then calculated for different radii and contact angles. These results are compared with previously published asymptotic and experimental results. For large inter-particle separations and conditions such that the meniscus slope remains small everywhere, good agreement is found between all three approaches (numerical, asymptotic and experimental). This is as expected since the asymptotic results were derived using the linearized Laplace-Young equation. For steeper menisci and smaller inter-particle separations, however, the numerical simulation resolves discrepancies between existing asymptotic and experimental results, demonstrating that this discrepancy was due to the nonlinearity of the Laplace-Young equation.     

Viscosity dependence of electrochemical etching for gold tip fabrication

We suggest an electrochemical etching method with viscous etchant to enhance the sharpness of tip of scanning probe microscope. The viscosity of the etchant mixed with HCl solution and glycerol was used as a control parameter in addition to the voltage applied to the tip. In order to improve the sharpness of the tip, a nano-scale meniscus formed between the end of the tip and the liquid level was used. The shapes, aspect ratios, and radii of tips were measured depending on the concentration of the etchant. It was found that the tip etched with the mixed liquid with glycerol was sharper than the tip with the pure HCl solution. This can be explained by the fact that the meniscus formed by viscous liquid is maintained with a thinner diameter and causes final etching until the meniscus bridge is ruptured.     

A new ac electrospray mechanism by Maxwell-Wagner polarization and capillary resonance

We report a new high-frequency (>10 kHz) ac electrospray that is capable of generating micron-sized electroneutral drops. Unlike its dc counterpart, the drops are not ejected continuously from a sharp Taylor cone but intermittently from a resonating meniscus at the orifice. We attribute the resonant frequency to the capillary-inertia vibration time of the meniscus and the drop ejection to the Maxwell-Wagner electric stress at the drop tip, which is observed to reverse its direction across a crossover frequency. Above this frequency, the oppositely directed Maxwell-Wagner force causes the liquid to recede up the microneedle as an apparent electrowetting effect.     

Sliding velocity dependence of adhesion in a nanometer-sized contact

The influence of sliding velocity on the adhesion force in a nanometer-sized contact was investigated with a novel atomic force microscope experimental setup that allows measuring adhesion forces while the probe is sliding at continuous and constant velocities. For hydrophobic surfaces, the adhesion forces (mainly van?der?Waals forces) remain constant, whereas for hydrophilic surfaces, adhesion forces (mainly capillary forces) decrease linearly with a logarithmic increase of the sliding velocity. The experimental data are well explained by a model based on a thermally activated growth process of a capillary meniscus.     

Experimental evidence for ice formation at room temperature

The behavior of water under extreme confinement and, in particular, the lubrication properties under such conditions are subjects of long-standing controversy. Using a dedicated, high-resolution friction force microscope, scanning a sharp tungsten tip over a graphite surface, we demonstrate that water nucleating between the tip and the surface due to capillary condensation rapidly transforms into crystalline ice at room temperature. At ultralow scan speeds and modest relative humidities, we observe that the tip exhibits stick-slip motion with a period of 0.38+/-0.03 nm, very different from the graphite lattice. We interpret this as the consequence of the repeated sequence of shear-induced fracture and healing of the crystalline condensate. This phenomenon causes a significant increase of the friction force and introduces relaxation time scales of seconds for the rearrangements after shearing.     

Understanding magnetic force microscopy

Magnetic force microscopy is a new method for imaging ferromagnetic domains with a high lateral resolution (10 nm). In this paper we give the basic tip parameters that have to be taken into account to achieve a quantitative image interpretation. For the electrochemically otched polycrystalline iron, nickel and cobalt wires, the tip-apex domain is found to be oriented along the tip axis, because of shape anisotropy. The stray field emerging from the tip apex is comparable to the size of the tip saturation field. The effective domain lengthL determines the image formation: the force due to magnetization patterns of scales which are large compared toL follow the point-dipole approximation. In the opposite case, a single-pole model is more appropriate. While a cobalt tip can be treated as an isolated domain, for nickel and iron a net polarization in the tip wire induced by the front apex-domain has to be considered. A new analytical theory provides an overall understanding of the image formation and allows the determination of the magnetic field vector and the estimation of its magnitude from measurements.     

Effects of symmetric and asymmetric contact angles and division of menisci during separation

Meniscus and viscous forces are sources of adhesive force when two surfaces are separated with a micro-meniscus present at the interface. The adhesive force can be one of the main reliability issues when the contacting surfaces are ultra-smooth and the normal load is small, as is common for micro/nano devices. In this paper, both meniscus and viscous forces of menisci with symmetric and asymmetric contact angles are modelled. Equations for both meniscus and viscous forces in division of menisci are analytically formulated. The role of these two forces is evaluated during the separation process. The effects of the contact angles, division of menisci, as well as liquid thicknesses, surface tension and viscosity of the liquid, and separation distance and time during separation are presented. It is found that contact angles significantly affect the break point and meniscus force, and the magnitude of meniscus force can be largely reduced by choosing proper asymmetric contact angles. ‘Force scaling’ effects are found to be true for both meniscus and viscous forces when one larger meniscus is divided into large numbers of identical micro-menisci. Meniscus force increases with the number of divisions whereas viscous force decreases by an order of inverse the number of division (1/N). Optimal configurations for low adhesion are identified. This study presents a comprehensive analysis of meniscus and viscous forces during separation of menisci under different physical configurations. It provides a fundamental understanding of the physics of the process and knowledge for control of adhesion due to liquid menisci.     

Experimental study of the motion of liquid droplets in a capillary under vibration

Results of an experimental study of the motion of small droplets in a capillary are discussed. The translational velocity of small droplets is studied as a function of the level and frequency of vibration acting together with a static force on the droplet—capillary system. The results are presented in the form of a set of curves, which reveal the nonlinear mechanical features of the system under consideration. The experiments confirm the previously developed theoretical model [7] based on the hysteresis dependence of the surface tension forces on the velocity of the meniscus motion.     

Brownian pump induced by the phase difference between the potential and the entropic barrier

Transport of Brownian particles in a finite channel is investigated in the presence of asymmetric potential and an unbiased external force. It is found that the phase differencebetween the potential (energetic barriers) and the entropic barrier can break the symmetryof the system and control the transport of Brownian particles. Especially, the particlescan be pumped through the channel from a reservoir at low concentration to one at the sameor higher concentration. There exist optimized values of the parameters (the temperatureand the amplitude of the external force) at which the pumping capacity takes its maximumvalue. The pumping capacity decreases with increasing the radius at the bottleneck of thechannel.     

On the time evolution of the liquid meniscus at the end of a capillary placed in an external electric field

Using a linearized set of equations of electrodynamics, the stability of the uniformly charged meniscus of a viscous conducting incompressible liquid at the end of a capillary is investigated and analytical expressions are derived for the electric field outside the meniscus, velocity fields in the liquid flow and meniscus, and generatrix of the meniscus shape. It is found that, if an external electric field near the meniscus exceeds that at which the free liquid surface becomes unstable against the surface charge, a finite number of longest waves become unstable with their instability growth rates nonmonotonically depending on the wavenumber. Analysis of the time evolution of the meniscus shape under various initial conditions shows that cylindrical waves with the highest instability growth rates play a decisive role in this process, while the influence of the initial deformation amplitude is insignificant.     

Thiol diffusion and the role of humidity in "Dip Pen Nanolithography"

The radii of octadecanethiol spots deposited by an atomic force microscope tip onto a gold surface were studied as a function of contact time and humidity. The deposition is well described by two-dimensional diffusion from an annular source of constant concentration, with a surface diffusion coefficient of 8400 nm(2) s(-1), independent of humidity. Facile transfer is observed even after near continuous deposition for more than 24 h in a dry N2 environment, indicating that a water meniscus is not required.     

Crack propagation as a free boundary problem

A sharp interface model of crack propagation as a phase transition process is discussed. We develop a multipole expansion technique to solve this free boundary problem numerically. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic effects are taken into account. Also, we find a saturation of the steady state crack velocity below the Rayleigh speed, tip blunting with increasing driving force, and a tip splitting instability above a critical driving force.     

Debye Entropic Force and Modified Newtonian Dynamics

Verlinde has suggested that the gravity has an entropic origin, and agravitational system could be regarded as a thermodynamical system. It is well-known that the equipartition law of energy is invalid at very low temperature. Therefore, entropic force should be modified while the temperature of the holographic screen is very low. It is shown that the modified entropic force is proportional to the square of the acceleration, while the temperature of the holographic screen is much lower than the Debye temperature T_D. The modified entropic force returns to the Newton's law of gravitation while the temperature of the holographic screen is much higher than the Debye temperature. The modified entropic force is connected with modified Newtonian dynamics (MOND). The constant a₀ involved in MOND is linear in the Debye frequency ω_D, which can be regarded as the largest frequency of the bits in screen.We find that there do have a strong connection between MOND and cosmology in the framework of Verlinde's entropic force, if the holographic screen is takento be bound of the Universe. The Debye frequency is linear in the Hubble constant H₀.