Nanoscale-roughness influence on pull-off adhesion force in liquid and air.

The pull-off adhesion force was measured by atomic force microscopy in sphere-plate geometry in water where a capillarylike behavior develops due to nanobubbles and was compared to the corresponding capillary adhesion in air. The sphere and the plate were coated with gold, and the pull-off adhesion force was measured as a function of the evolving surface roughness of the plate, and the retraction velocity of the interacting surfaces. In absolute magnitude, the pull-off force in air is larger than that in liquid by an order of magnitude or more, but in both cases, the pull-off force follows a monotonic decrease with increasing roughness. However, the relative decrement of the adhesion force in water was approximately 300%, and significantly higher than that in air for the same change of the rms roughness in the range ∼7-14 nm. Finally, the adhesion force in water shows a relatively complex dependence on the retraction velocity of the interacting surfaces as the roughness increases due to possible deformation of the nanobubbles and the bridges they form between the surfaces.

Influence of optical property contrast on the critical distribution of electrostatic torques in double-beam torsional Casimir actuators: Non-linear actuation toward chaotic motion.

Here, we discuss how to achieve the stable actuation of a double beam torsional micro-actuator over the largest possible displacement of the moving component under the influence of Casimir and electrostatic torques, when the rotating component is constructed from different materials. The main part of this study is devoted to finding the optimal distribution of the electrostatic torque between the left and right sides of the micro-actuator to reach the maximum stable operation of the device. The latter is manifested by switching from homoclinic to heteroclinic orbits in the phase portraits. Indeed, the bifurcation curves and the phase portraits have been employed to show the sensitivity of the critical distribution of the electrostatic torque, beyond which the device does show stable performance, on the contrast of the optical properties of the moving component and the applied voltage in a conservative autonomous system. Moreover, for driven systems, the Melnikov function approach and the Poincaré portraits are used to study the presence of chaotic motion, which eventually leads to stiction. It is shown that the application of the optimal distribution of the electrostatic torque can significantly decrease the possibility of chaotic motion, and at this optimal level, the threshold curves reveal less difference between systems with different optical contrast.

Nonlinear actuation of micromechanical Casimir oscillators with topological insulator materials toward chaotic motion: Sensitivity on magnetization and dielectric properties.

We have investigated the dynamical actuation of micro-electromechanical systems under the influence of attractive and repulsive Casimir forces between topological insulator plates as a function of their dielectric function and coating magnetization. The analysis of the Casimir force in the limit of strong and weak magnetization shows that the attractive force, which is produced for plate magnetizations in the same direction, is greater than the repulsive force that is produced for opposite magnetizations. However, both forces remain comparable for intermediate magnetizations. Moreover, for weak magnetization, the attractive force becomes stronger for an increasing dielectric function, while the opposite occurs for the repulsive force. On the other hand, increasing magnetization decreases the influence of the dielectric function on both the repulsive and attractive forces. Furthermore, for conservative systems, bifurcation and phase portrait analysis revealed that increasing magnetization decreases the regime of stable operation for devices with attractive forces, while their operation remains always stable under the presence of repulsive forces. Finally, for non-conservative periodically driven systems, the Melnikov function and Poincaré portrait analysis show that for magnetizations in the same direction leading to strong attractive Casimir forces, chaotic motion toward stiction is highly likely to occur preventing the long-term prediction of actuating dynamics. A remedy for this situation is obtained by the application of any magnetization in opposite directions between the interacting surfaces since the repulsive force makes it possible to prevent stiction.

Sensitivity of actuation dynamics on normal and lateral Casimir forces: Interaction of phase change and topological insulator materials.

We investigated here the influence of the lateral and normal Casimir force on the actuation dynamics between sinusoidal corrugated surfaces undergoing both normal and lateral displacements. The calculations were performed for topological insulators and phase change materials that are of high interest for device applications. The results show that the lateral Casimir force becomes stronger by increasing the material conductivity and the corrugations toward similar sizes producing wider normal separation changes during lateral motion. In a conservative system, bifurcation and Poincaré portrait analysis shows that larger but similar in size corrugations and/or higher material conductivity favor stable motion along the lateral direction. However, in the normal direction, the system shows higher sensitivity on the optical properties for similar in size corrugations leading to reduced stable operation for higher material conductivity. Furthermore, in non-conservative systems, the Melnikov function with the Poincaré portrait analysis was combined to probe the possible occurrence of chaotic motion. During lateral actuation, systems with more conductive materials and/or the same but high corrugations exhibit lower possibility for chaotic motion. By contrast, during normal motion, chaotic behavior leading to stiction of the moving components is more likely to occur for systems with more conductive materials and similar in magnitude corrugations.

Chaotic motion due to lateral Casimir forces during nonlinear actuation dynamics.

We investigated here the influence of the lateral Casimir force on the dynamical actuation of devices with interacting materials covering a broad range of optical properties ranging from poor to good conductors, such as, for example, nitrogen doped SiC and Au, respectively. The conservative actuating system shows a central heteroclinic orbit surrounded by a finite number of homoclinic orbits, because at higher periods, an increased lateral Casimir force will be necessary to counterbalance the restoring force. As a result, the conservative system reaches stable operation sooner for the higher conductivity materials (Au-Au), indicating the significant impact of the material optical properties on the lateral Casimir force. Furthermore, for the non-conservative driven systems, the decrement of the Melnikov parameter α leads to a faster disappearance of the satellite homoclinic orbits in the Poincaré portraits, followed by a strong shrinkage of the central heteroclinic orbit toward unstable chaotic motion. The latter is more pronounced for the lower conductivity materials since comparison shows the Au-Au system to be significantly more stable than the SiC-SiC system. Therefore, in actuating systems where the lateral Casimir force could play a significant role, the higher conductivity materials appear to be a better choice to ensure stable operation against a chaotic motion.

Sensitivity of nonequilibrium Casimir forces on low frequency optical properties toward chaotic motion of microsystems: Drude vs plasma model.

Here, we investigate the sensitivity of nonequilibrium Casimir forces to optical properties at low frequencies via the Drude and plasma models and the associated effects on the actuation of microelectromechanical systems. The stability and chaotic motion for both autonomous conservative and nonconservative driven systems were explored assuming good, e.g., Au, and poor, e.g., doped SiC, interacting conductors having large static conductivity differences. For both material systems, we used the Drude and plasma methods to model the optical properties at low frequencies, where measurements are not feasible. In fact, for the conservative actuating system, bifurcation and phase space analysis show that the system motion is strongly influenced by the thermal nonequilibrium effects depending on the modeling of the optical properties at low frequencies, where also the presence of residual electrostatic forces can also drastically alter the actuating state of the system, depending strongly on the material conductivity. For nonconservative systems, the Melnikov function approach is used to explore the presence of chaotic motion rendering predictions of stable actuation or malfunction due to stiction on a long-term time scale rather impossible. In fact, the thermal effects produce the opposite effect for the emerging chaotic behavior for the Au-Au and SiC-SiC systems if the Drude model is used to model the low optical frequencies. However, using the plasma model, only for the poor conducting SiC-SiC system, the chance of chaotic motion is enhanced, while for the good conducting Au-Au system, the chaotic behavior will remain unaffected at relatively short separations (<2 µm).

Dependence of non-equilibrium Casimir forces on material optical properties toward chaotic motion during device actuation.

The sensitivity of nonequilibrium Casimir forces on material optical properties can have strong impact on the actuation of devices. For this purpose, we considered nonequilibrium Casimir interactions between good and poor conductors, for example, gold (Au) and highly doped silicon carbide (SiC), respectively. Indeed, for autonomous conservative systems, the bifurcation and phase portrait analysis have shown that the nonequilibrium Casimir forces can have significant impact on the stable and unstable operating regimes depending on the material optical properties. At a few micrometer separations, for systems with high conductivity materials, an increasing temperature difference between the actuating components can enhance the stable operation range due to the reduction of the Casimir force, while for the poor conductive materials, the opposite takes place. For periodically driven dissipative systems, the Melnikov function and Poincare portrait analysis have shown that for poor conductive systems, the nonequilibrium Casimir forces lead to an increased possibility for chaotic behavior and stiction with an increasing temperature difference between the actuating components. However, for good conducting systems, the thermal contribution to Casimir forces reduces the possibility for chaotic behavior with increasing temperature, as comparison with systems without thermal fluctuations shows. Nevertheless, the positive benefit of good conductors toward increased actuation stability and reduced the chaotic behavior under nonequilibrium conditions can be easily compromised by any voltage application. Therefore, thermal, nonequilibrium Casimir forces can influence the actuation of devices toward unstable and chaotic behavior in strong correlation with their optical properties, and associated conduction state, as well as applied electrostatic potentials.

Sensitivity of chaotic behavior to low optical frequencies of a double-beam torsional actuator.

We investigate here how the optical properties at low frequencies affect the actuation dynamics and emerging chaotic behavior in a double-beam torsion actuator at nanoscale separations (<200nm), where the Casimir forces and torques play a major role. In fact, we take into account differences of the Casimir force due to alternative modeling of optical properties at low frequencies, where measurements are not feasible, via the Drude and plasma models, and repercussions by different material preparation conditions. For conservative autonomous actuation, bifurcation and phase portrait analysis indicate that both factors affect the stability of an actuating device in such a way that stronger Casimir forces and torques will favor increased unstable behavior. The latter will be enhanced by unbalanced application of electrostatic voltages in double-beam actuating systems. For the case of a time-periodic driving force, we use a Melnikov function and a phase plane analysis to study the emerging chaotic behavior with respect to the Drude and plasma modeling and material preparation conditions. We find indications that any factor that leads to stronger Casimir interactions will aid chaotic behavior and prevent long term prediction of the actuating dynamics. Moreover, in a double-beam actuator chaoticity will be amplified by the application of unbalanced electrostatic voltages. Therefore, the details of modeling of optical properties and the material preparations conditions must be carefully considered in the design of actuating devices at nanoscale because here Casimir forces are omnipresent and broadband type interactions.

Dependence of chaotic behavior on optical properties and electrostatic effects in double-beam torsional Casimir actuation.

We investigate the influence of Casimir and electrostatic torques on double-beam torsional microelectromechanical systems with materials covering a broad range of conductivities of more than three orders of magnitude. For the frictionless autonomous systems, bifurcation and phase space analysis shows a significant difference between stable and unstable operating regimes for equal and unequal applied voltages on both sides of the double torsional system giving rise to heteroclinic and homoclinic orbits, respectively. For equal applied voltages, only the position of a symmetric unstable saddle equilibrium point is dependent on the material optical properties and electrostatic effects, while in any other case stable and unstable equilibrium points are dependent on both factors. For the periodically driven system, a Melnikov function approach is used to show the presence of chaotic motion rendering predictions of whether stiction or stable actuation will take place over long times impossible. Chaotic behavior introduces significant risk for stiction, and it is more likely to occur for the more conductive systems that experience stronger Casimir forces and torques. Indeed, when unequal voltages are applied, the sensitive dependence of chaotic motion on electrostatics is more pronounced for the highest conductivity systems.

Capillary-force measurement on SiC surfaces.

Capillary forces have been measured by atomic force microscopy in the sphere-plate geometry, in a controlled humidity environment, between smooth silicon carbide and borosilicate glass spheres. The force measurements were performed as a function of the rms surface roughness ∼4-14 nm mainly due to sphere morphology, the relative humidity (RH) ∼0%-40%, the applied load on the cantilever, and the contact time. The pull-off force was found to decrease by nearly two orders of magnitude with increasing rms roughness from 8 to 14 nm due to formation of a few capillary menisci for the roughest surfaces, while it remained unchanged for rms roughness <8 nm implying fully wetted surface features leading to a single meniscus. The latter reached a steady state in less than 5 s for the smoothest surfaces, as force measurements versus contact time indicated for increased RH∼40%. Finally, the pull-off force increases and reaches a maximum with applied load, which is associated with plastic deformation of surface asperities, and decreases at higher loads.

Influence of materials' optical response on actuation dynamics by Casimir forces.

The dependence of the Casimir force on the frequency-dependent dielectric functions of interacting materials makes it possible to tailor the actuation dynamics of microactuators. The Casimir force is largest for metallic interacting systems due to the high absorption of conduction electrons in the far-infrared range. For less conductive systems, such as phase change materials or conductive silicon carbide, the reduced force offers the advantage of increased stable operation of MEMS devices against pull-in instabilities that lead to unwanted stiction. Bifurcation analysis with phase portraits has been used to compare the sensitivity of a model actuator when the optical properties are altered.

Influence of surface roughness on dispersion forces.

Surface roughness occurs in a wide variety of processes where it is both difficult to avoid and control. When two bodies are separated by a small distance the roughness starts to play an important role in the interaction between the bodies, their adhesion, and friction. Control of this short-distance interaction is crucial for micro and nanoelectromechanical devices, microfluidics, and for micro and nanotechnology. An important short-distance interaction is the dispersion forces, which are omnipresent due to their quantum origin. These forces between flat bodies can be described by the Lifshitz theory that takes into account the actual optical properties of interacting materials. However, this theory cannot describe rough bodies. The problem is complicated by the nonadditivity of the dispersion forces. Evaluation of the roughness effect becomes extremely difficult when roughness is comparable with the distance between bodies. In this paper we review the current state of the problem. Introduction for non-experts to physical origin of the dispersion forces is given in the paper. Critical experiments demonstrating the nonadditivity of the forces and strong influence of roughness on the interaction between bodies are reviewed. We also describe existing theoretical approaches to the problem. Recent advances in understanding the role of high asperities on the forces at distances close to contact are emphasized. Finally, some opinions about currently unsolved problems are also presented.

Note: spring constant calibration of nanosurface-engineered atomic force microscopy cantilevers.

The determination of the dynamic spring constant (kd) of atomic force microscopy cantilevers is of crucial importance for converting cantilever deflection to accurate force data. Indeed, the non-destructive, fast, and accurate measurement method of the cantilever dynamic spring constant by Sader et al. [Rev. Sci. Instrum. 83, 103705 (2012)] is confirmed here for plane geometry but surface modified cantilevers. It is found that the measured spring constants (keff, the dynamic one kd), and the calculated (kd,1) are in good agreement within less than 10% error.

Formation and stability of hollow MgO nanoshells.

High temperature annealing of gas phase synthesized Mg nanoparticles surrounded by an MgO shell leads to formation of hollow MgO nanoshells due to the evaporation assisted Kirkendall effect. Under electron beam exposure in TEM, the (220) MgO facets reduce their high surface energy by forming cube facets, which is followed by nanoshell size reduction and collapse within a few minutes. However, in ambient conditions the nanoshells remain stable for significant periods of time and further degrade by becoming filled with carbon while lossing any MgO identity. Finally, in moderate low vacuum they remained stable for months indicating promise for applications.

Weak dispersive forces between glass and gold macroscopic surfaces in alcohols.

In this work we concentrate on an experimental validation of the Lifshitz theory for the van der Waals and the Casimir forces in gold-alcohol-glass systems. From this theory weak dispersive forces are predicted when the dielectric properties of the intervening medium become comparable to one of the interacting surfaces. Using inverse colloid probe atomic force microscopy dispersive forces were measured occasionally and under controlled conditions by addition of salt to screen the electrostatic double layer force if present. The dispersive force was found to be attractive and an order of magnitude weaker than that in air. Although the theoretical description of the forces becomes less precise for these systems even with full knowledge of the dielectric properties, we find still our results in reasonable agreement with the Lifshitz theory.

Influence of roughness on capillary forces between hydrophilic surfaces.

Capillary forces have been measured by atomic force microscopy in the plate-sphere setup between gold, borosilicate glass, GeSbTe, titanium, and UV-irradiated amorphous titanium-dioxide surfaces. The force measurements were performed as a function contact time and surface roughness in the range 0.2-15 nm rms and relative humidity ranging between 2% and 40%. It is found that even for the lowest attainable relative humidity ( approximately 2%+/-1%) very large capillary forces are still present. The latter suggests the persistence of a nanometers-thick adsorbed water layer that acts as a capillary bridge between contacting surfaces. Moreover, we found a significantly different scaling behavior of the force with rms roughness for materials with different hydrophilicity as compared to gold-gold surfaces.

Roughness of microspheres for force measurements.

We have investigated the morphology and surface roughness of several commercially available microspheres to determine their suitability for force measurements using the atomic force microscope. The roughness varies considerably, depending on sphere size and material, ranging from nearly ideally flat up to micrometer-sized features. Because surface roughness significantly influences the magnitude and accuracy of measurement of surface forces, the results presented here should be helpful for colloid physicists and in particular for those performing force measurements.

Light on the moth-eye corneal nipple array of butterflies.

The outer surface of the facet lenses in the compound eyes of moths consists of an array of excessive cuticular protuberances, termed corneal nipples. We have investigated the moth-eye corneal nipple array of the facet lenses of 19 diurnal butterfly species by scanning electron microscopy, transmission electron microscopy and atomic force microscope, as well as by optical modelling. The nipples appeared to be arranged in domains with almost crystalline, hexagonal packing. The nipple distances were found to vary only slightly, ranging from about 180 to 240 nm, but the nipple heights varied between 0 (papilionids) and 230 nm (a nymphalid), in good agreement with previous work. The nipples create an interface with a gradient refractive index between that of air and the facet lens material, because their distance is distinctly smaller than the wavelength of light. The gradient in the refractive index was deduced from effective medium theory. By dividing the height of the nipple layer into 100 thin slices, an optical multilayer model could be applied to calculate the reflectance of the facet lenses as a function of height, polarization and angle of incidence. The reflectance progressively diminished with increased nipple height. Nipples with a paraboloid shape and height 250 nm, touching each other at the base, virtually completely reduced the reflectance for normally incident light. The calculated dependence of the reflectance on polarization and angle of incidence agreed well with experimental data, underscoring the validity of the modelling. The corneal nipples presumably mainly function to reduce the eye glare of moths that are inactive during the day, so to make them less visible for predators. Moths are probably ancestral to the diurnal butterflies, suggesting that the reduced size of the nipples of most butterfly species indicates a vanishing trait. This effect is extreme in papilionids, which have virtually absent nipples, in line with their highly developed status. A similar evolutionary development can be noticed for the tapetum of the ommatidia of lepidopteran eyes. It is most elaborate in moth-eyes, but strongly reduced in most diurnal butterflies and absent in papilionids.

Influence of self-affine roughness on Parsons-Zobel plots for electrical double layers.

In this paper we investigate the dependence of Parsons-Zobel plots on characteristic self-affine roughness parameters of the metal electrode in electrical double layers. Among the roughness amplitude w, the correlation length xi, and roughness exponent H, the latter appears to have the most prominent effect especially for values in the range H<0.5. In addition, with decreasing compact layer thickness the influence of roughness leads to stronger nonlinear behavior of the plots for relatively large electrode potentials. Finally, it is shown that dynamic changes of the electrode roughness (for example by growth on metal films) should be carefully quantified with respect to their influence on the Parson-Zobel plots and related double-layer systems.

Influence of surface roughness on the adhesion of elastic films.

It is shown that a self-affine roughness at the junction of an elastic film and a hard solid substrate influences considerably the adhesion of the elastic film, especially for small roughness exponents H (H<0.5) and/or large long wavelength roughness ratios w/xi with w being the rms roughness amplitude and xi being the in-plane roughness correlation length. Analytical calculations of the local surface slope allows an estimate of the roughness effects on the adhesion energy more precisely than those presented in earlier works (especially for roughness exponents H<0.5). For weak surface roughness the elastic energy contribution is significant on the film effective surface energy deltagamma(eff) and on pull-off force for elastic modulus E in the range of GPa. Moreover, in the case of partial contact an estimation of the pull-off force shows that it strongly decreases with reducing contact area due to surface.