Short-range Interaction Forces Research Articles

A mathematical model-based investigation of liquid film dewetting over porous solid substrates

Thin liquid films resting on solid surfaces are susceptible to dewetting when physical inhomogeneities like surface roughness, textured patterns, and porosities are present on the substrate surface. These inhomogeneities affect liquid transport phenomena through dynamic wetting behavior and imbibition. They can render the liquid film unstable, thereby resulting in rupture and dewetting. Here, we mathematically model and simulate the dynamics of a thin liquid film with passive air above it, dewetting a porous solid substrate that bounds the liquid from below. The solid is modeled as a surface with regions of equally spaced pores, with a partial slip condition for the lateral velocity component of the liquid film, a spatially varying long-range attractive force parameter, as well as short-range repulsive interaction force parameters between the liquid–air interface and liquid–solid interface. Our results explain how the size and spacing of pore regions on the substrate, slip length of the liquid, and intermolecular force potentials influence the formation of morphological patterns and dewetting time scales of the liquid film.

A cysteine and Hg2+ detection method based on transformation supramolecular assembly of cyanine dye by AGRO100

ETC (3,3′-di(3-sulfopropyl)-4,5,4′,5′-dibenzo-9-ethylthiacarbocyanine triethylammonium salt), as a derivative of thiazole, is capable of forming various aggregates by the short-range noncovalent interaction forces under specific conditions, accompanying with significant absorbance and fluorescence characteristics. In this work, a label-free probe (ETC) for the detection of Cys (Cysteine) and Hg2+ was developed based on transformation between monomers and J-aggregations by AGRO100. AGRO100 can transform between single-stranded DNA and G-quadruplex to realize recognition of Cys and Hg2+ in dual-channel mode. These recognitional signals can be captured by UV–visible absorption spectra and fluorescence spectroscopy. ETC exhibits high sensitivity and selectivity with the detection limit of 0.197 nM in a wide range of 0–15 μM, which can apply of Cys and Hg2+ detection in human serum.

Interacting Brownian particles exhibiting enhanced rectification in an asymmetric channel

Rectification of interacting Brownian particles is investigated in a two-dimensional asymmetric channel in the presence of an external periodic driving force. The periodic driving force can break the thermodynamic equilibrium and induces rectification of particles (or finite average velocity). The spatial variation in the shape of the channel leads to entropic barriers, which indeed control the rectification of particles. We find that by simply tuning the driving frequency, driving amplitude, and shape of the asymmetric channel, the average velocity can be reversed. Moreover, a short range interaction force between the particles further enhances the rectification of particles greatly. This interaction force is modeled as the lubrication interaction. Interestingly, it is observed that there exists a characteristic critical frequency Ωc below which the rectification of particles greatly enhances in the positive direction with increasing the interaction strength; whereas, for the frequency above this critical value, it greatly enhances in the negative direction with increasing the interaction strength. Further, there exists an optimal value of the asymmetric parameter of the channel for which the rectification of interacting particles is maximum. These findings are useful in sorting out the particles and understanding the diffusive behavior of small particles or molecules in microfluidic channels, membrane pores, etc.

Adhesin Protein Interaction of Staphylococcus Aureus Bacteria with Various Biomaterial Surfaces

The primary stage of adhesion during implant infection is dominated by interactions of the surface proteins of the bacteria with the substrate atoms. In the current work, molecular dynamics (MD) simulations have been utilized to investigate the mechanics of the associated adhesion forces of bacteria on different surfaces. The unfolding of these adhesion proteins is investigated in order to map these events to earlier experiments on bacterial de-adhesion (using single cell force spectroscopy) with real-life substrates (i.e., ultrahigh molecular weight polyethylene, hydroxyapatite, Ti alloy, and stainless steel). The adhesion of Staphylococcus aureus adhesin (i.e., SpA) is observed by altering their orientation on the silica substrate through MD simulations, followed by capturing unfolding events of three adhesins (SpA, ClfA, and SraP) of variable lengths possessing different secondary structures. The output long-range and short-range interaction forces and consequent visualization of changes in the secondary structure of protein segments are presented during the de-adhesion process. Simulation results are correlated with extracted short-range forces (using Poisson regression) from real-life bacterial de-adhesion experiments. Insights into such protein-substrate interactions may allow for engineering of biomaterials and designing of nonbiofouling surfaces.

Force spectroscopy using a quartz length-extension resonator

Frequency modulation atomic force microscopy detects the interaction force between the tip and the sample by measuring the change in the resonance frequency of an oscillating force sensor. Short-range interaction force can be selectively detected by a small oscillation amplitude. A quartz length-extension resonator (LER) offers the advantage of small-amplitude operation by virtue of its ultrahigh stiffness. Here, we demonstrate that an LER can accurately measure the short-range interaction force at cryogenic temperature even under a high magnetic field. We derive a formula for calculating the effective stiffness of an oscillating LER by using the theory of elasticity. The obtained dynamic stiffness is 1.23 times greater than the static stiffness, and this difference significantly affects the estimation of the interaction force. Using a properly calibrated LER, force curves are measured on Si(111)-(7 × 7) surfaces. The maximum attractive short-range forces above Si adatoms using several tip apex states are in the ranges of the values previously obtained by Si cantilevers.

Diffusion of interacting particles in a channel with reflection boundary conditions.

The diffusive transport of biased Brownian particles in a two-dimensional symmetric channel is investigated numerically considering both the no-flow and the reflection boundary conditions at the channel boundaries. Here, the geometrical confinement leads to entropic barriers which effectively control the transport properties of the particles. We show that compared to no-flow boundary conditions, the transport properties exhibit distinct features in a channel with reflection boundary conditions. For example, the nonlinear mobility exhibits a nonmonotonic behavior as a function of the scaling parameter f, which is a ratio of the work done to the particles to available thermal energy. Also, the effective diffusion exhibits a rapidly increasing behavior at higher f. The nature of reflection, i.e., elastic or inelastic, also influences the transport properties firmly. We find that inelastic reflections increase both the mobility and the effective diffusion for smaller f. In addition, by including the short range interaction force between the Brownian particles, the mobility decreases and the effective diffusion increases for various values of f. These findings, which are a signature of the entropic nature of the system, can be useful to understand the transport of small particles or molecules in systems such as microfluidic channels, membrane pores, and molecular sieves.

Dynamics of trapped interacting vortices in Bose–Einstein condensates: a role of breathing degree of freedom

With use of a variational principle, we investigate a role of breathing width degree of freedom in the effective theory of interacting vortices in a trapped single-component Bose–Einstein condensates in two dimensions, under strong repulsive cubic nonlinearity. For the trial function, we choose a product of two vortex functions, assuming a pair interaction, and employ the amplitude form of each vortex function in the Padé approximation, which accommodates a hallmark of the vortex core. We obtain the Lagrange equation for the interacting vortex-core coordinates coupled with the time-derivative of width and also its Hamilton formalism by having recourse to a non-standard Poisson bracket. By solving the Hamilton equation, we find rapid radial breathing oscillations superposed on the slower rotational motion of vortex cores, consistent with numerical solutions of the Gross–Pitaevskii equation. In higher-energy states of two vortex systems, the breathing width degree of freedom plays the role of a kicking in the kicked rotator, and generates chaos with a structure of sea-urchin needles. The by-products of the present variational approach include: (1) the charge-dependent logarithmic inter-vortex interaction multiplied with a pre-factor, which depends on the scalar product of a pair of core-position vectors; (2) the charge-independent short-range repulsive inter-vortex interaction and spring force.

Identifying the absolute orientation of a low-symmetry surface in real space

We present atomic-scale force interaction data acquired on an insulating low-symmetry substrate, namely the calcite$(10.4)$ surface. A pronounced asymmetry of the imaged species is apparent along the vertical axis, which will be identified as a tilted band of purely attractive short-range interaction forces. An independent determination of the absolute surface orientation by an optical method suggests that the observed asymmetry is related to the tilt of the carbonate groups within the surface, which, in turn, is linked to the surface orientation. Thus our noncontact atomic force microscopy based work presents the determination of the absolute orientation for a low-symmetry surface.

Discriminating short-range from van der Waals forces using total force data in noncontact atomic force microscopy

Noncontact atomic force microscopy (NC-AFM) features the measurement of forces with highest spatial resolution and sensitivity, resolving forces of the order of pico-Newtons with submolecular resolution. However, the measured total force is a mixture composed of various interactions. While some interactions such as electrostatic or magnetic forces can be excluded by a careful design of the experiment, the subtraction of van der Waals forces, which mainly originate from London dispersion interactions between the macroscopic tip shank and the bulk sample, remains a challenge. We present the determination of the inherently present van der Waals forces in total interaction force data from fitting a suitable model, allowing for extraction of the short-range force component. We compare the applicability of several van der Waals models based on experimental interaction data from the calcite$(1\phantom{\rule{0.59998pt}{0ex}}0\phantom{\rule{0.59998pt}{0ex}}\overline{1}\phantom{\rule{0.59998pt}{0ex}}4)$ surface. The feasibility to fit these models to experimental data is critically discussed. We furthermore introduce criteria to assess the transition point from pure long-range interaction to mixed short- and long-range forces based on the variance of lateral and vertical force data. This determination allows us to extract the short-range interaction forces, which remained a challenge so far in NC-AFM experiments.

Flocculation and particle size analysis of expansive clay sediments affected by biological, chemical, and hydrodynamic factors

Expansive clay sediments are abundant in riverine and estuarine waters and bottom beds, and their particle size distributions (PSD) are important for the analysis of sediment transport. This paper presents an experimental study to evaluate, using a laser particle size analyzer under varying flow conditions, the intrinsic PSD of two expansive clays, a Ca- and a Na-montmorillonite and the influence of biological, chemical, and hydrodynamic factors on their flocculation and PSD. The considered biological factor consists of three extracellular polymeric substances of varying polarity, including xanthan gum, guar gum, and chitosan; the chemical factor is the salinity; and the hydrodynamic factor is the types of flow indicated by the Reynolds number and shear rate. The intrinsic PSD of both clays show a multimodal lognormal distribution with sizes ranging from 0.2 to 50 μm. All three biopolymers, xanthan gum, guar gum, and chitosan, can facilitate flocculation through long-range polymer bridging and short-range ion-dipole interaction, hydrogen bonding, and Coulomb force. The influence of salinity is different for the two clays: the particle size of the Na-montmorillonite increases with salinity, which is caused by flocculation resulting from the suppressed electrical double layer, while that of the Ca-montmorillonite is slightly reduced owing to the decreased basal spacing and cation exchange. For different hydrodynamic conditions, higher shear rate promotes the flocculation of Ca-montmorillonite, but breaks the Na-montmorillonite flocs. The significance of understanding the flocculation and PSD of expansive clays is also discussed in terms of sediment transport under different aquatic environments.

Force Mapping of the NaCl(100)/Cu(111) Surface by Atomic Force Microscopy at 78 K

A new atomic force microscopy (AFM) force mapping technique has been used to investigate insulating thin (100) films of NaCl on conducting Cu(111) substrate at 78 K. This technique was able to map the interaction forces between the AFM tip and the surface ions of the sample. The site-specific force curves of the (100) surface of the NaCl thin films are presented. We observed only an attractive short-range interaction force at the Na+ and Cl- sites. We propose simple models to explain the behavior of the force curves at the different ion sites.

Force Mapping of the NaCl(100)/Cu(111) Surface by Atomic Force Microscopy at 78 K

A new atomic force microscopy (AFM) force mapping technique has been used to investigate insulating thin (100) films of NaCl on conducting Cu(111) substrate at 78 K. This technique was able to map the interaction forces between the AFM tip and the surface ions of the sample. The site-specific force curves of the (100) surface of the NaCl thin films are presented. We observed only an attractive short-range interaction force at the Na+ and Cl- sites. We propose simple models to explain the behavior of the force curves at the different ion sites.

High-resolution imaging of C60 molecules using tuning-fork-based non-contact atomic force microscopy

Recent advances in non-contact atomic force microscopy (nc-AFM) have led to the possibility of achieving unprecedented resolution within molecular structures, accomplished by probing short-range repulsive interaction forces. Here we investigate C60 molecules adsorbed on KBr(111) and Cu(111) by tuning-fork-based nc-AFM. First, measurements of C60 deposited on KBr(001) were conducted in cryogenic conditions revealing highly resolved nc-AFM images of the self-assembly. Using constant-frequency shift mode as well as three-dimensional spectroscopic measurements, we observe that the relatively weak molecule–substrate interaction generally leads to the disruption of molecular assembled structures when the tip is probing the short-range force regime. This particular issue hindered us in resolving the chemical structure of this molecule on the KBr surface. To obtain a better anchoring of C60 molecules, nc-AFM measurements were performed on Cu(111). Sub-molecular resolutions within the molecules was achieved which allowed a direct and unambiguous visualization of their orientations on the supporting substrate. Furthermore, three-dimensional spectroscopic measurements of simultaneous force and current have been performed above the single molecules giving information of the C60 molecular orientation as well as its local conductivity. We further discuss the different imaging modes in nc-AFM such as constant-frequency shift nc-AFM, constant-height nc-AFM and constant-current nc-AFM as well as three-dimensional spectroscopic measurement (3D-DFS) employed to achieve such resolution at the sub-molecular scale.

An accurate and efficient method for treating aerodynamic interactions of cloud droplets

Motivated by a need to improve the representation of short-range interaction forces in hybrid direct numerical simulation of interacting cloud droplets, an efficient method for treating the aerodynamic interaction of two spherical particles settling under gravity is developed. An effort is made to ensure the accuracy of our method for any inter-particle separation by considering three separation ranges. The first is the long-range interaction where a multipole method is applied. After a decomposition into six simple configurations, explicit formulae for drag forces and torques are derived from an approximate Force–Torque–Stresslet (FTS) formulation. The FTS formulation is found to be accurate when the separation distance normalized by the average radius is larger than 5. The second range concerns the short-range interaction where the interaction force could be very large. Leading-order lubrication expansions are employed for this range and are found to be accurate when the normalized separation is less than about 0.01. Finally, for the intermediate range where no simple method is available, a third-order polynomial fitting is proposed to bridge the treatments for long-range and short-range interactions. After optimizing the precise form of polynomial fitting and matching locations, the force representation is found to be highly accurate when compared with the exact solution for Stokes flows. Using this method, collision efficiencies of cloud droplets sedimenting under gravity have been calculated. It is shown that the results of collision efficiency are in excellent agreement with results based on the exact Stokes flow solution. Collision efficiency results are also compared to previous results to further illustrate the accuracy of our calculations. The effects of particle rotation and the attractive van der Waals force on the collision efficiency are also studied. The efficient force representation developed here is more general than the usual lubrication expansion and thus can serve as a better approach to correct unresolved short-range interactions in particle-resolved simulations.

Atom-ion quantum gate

Ultracold collisions of ions with neutral atoms in traps are studied. Recently, ultracold atom-ion systems have become available in experimental setups, where their quantum states can be coherently controlled. This control allows for an implementation of quantum information processing, combining the advantages of charged and neutral particles. The state-dependent dynamics that is a necessary ingredient for quantum computation schemes is provided in this case by the short-range interaction forces that depend on the hyperfine states of both particles. In this work, a theoretical description of spin-state-dependent trapped atom-ion collisions is developed in the framework of a multichannel quantum-defect theory and an effective single-channel model is formulated that reduces the complexity of the problem. Based on this description, a two-qubit phase gate between a $^{135}\mathrm{Ba}$${}^{+}$ ion and a $^{87}\mathrm{Rb}$ atom is simulated using a realistic combination of the singlet and triplet scattering lengths. The gate process is optimized and accelerated with the help of optimal control techniques. The result is a gate fidelity of $1\ensuremath{-}{10}^{\ensuremath{-}3}$ within $350$ $\ensuremath{\mu}$s.

Phase noise induced due to amplitude fluctuations in dynamic force microscopy

In dynamic force microscopy, the force sensor is driven on its resonance frequency and the amplitude of the cantilever is sustained at a constant value. The amplitude typically ranges between 0.1 and 30 nm. If a large amplitude is set, the cantilever tip senses both long-range and short-range interaction forces provided that the tip is close to the sample surface. The short-range interactions are decisive for the atomic contrast in atomic force microscopy (AFM) images. They can be separated from the long-range interactions by setting an amplitude which encompasses the typical range of the interaction force, i.e., the subangstrom regime for van der Waals contribution. It is distinctive for cantilevers operated at small driving amplitudes that the cantilever deflection can be considered as a sinusoidal signal superimposed with a quasimonochromatic random signal originating from fluctuations. If one measures experimentally the standard deviation of the phase ${\ensuremath{\sigma}}_{\ensuremath{\varphi}}$ of the signal with respect to a monochromatic reference signal, a universal relationship between the standard deviation of the phase ${\ensuremath{\sigma}}_{\ensuremath{\varphi}}$ and the cantilever amplitude ${x}_{0}$ is found. The smaller the ratio of rms amplitude of the sinusoidal signal and the rms value of random signal is, the larger the phase fluctuations are. Phase fluctuations are of importance for measurements at small amplitudes, since they determine the limit of phase-sensitive measurements or the lateral imaging resolution in the so-called pendulum mode of AFM operation. In this paper we develop a heuristic model, which provides an analytical formula for the probability density of phase noise of a sinusoidal signal superimposed by a quasimonochromatic one with respect to a reference oscillator. The variance of the phase noise can be deduced from the distribution functions. The suggested model is verified experimentally and is compared with theoretical predictions. The amplitude-dependent phase fluctuations are a powerful tool to determine the spring constant of the beam or to calibrate its oscillation amplitude.

Particle – Wafer Interactions in Semiaqueous Silicon Cleaning Systems

Interfacial interaction forces between particulate contaminants and semiconductor wafer surfaces play a key role in the understanding of post-CMP and post-lapping cleaning processes. In order to facilitate removal and prevent re-deposition of submicron particles on wafer surface, understanding, measurement, and manipulation of these forces is required. The theory of interaction forces in liquids that includes DLVO forces (van der Waals, electrical double layer) and non-DLVO (solvation, hydration, hydrophobic, steric and bridging forces) is well established and is studied elsewhere.1-4 Short range interaction forces between silica surfaces in alcohols have been successfully measured before using AFM.5-7

Flying height adjustment technologies for high-density magnetic recording

The flying height adjustment technology becomes important to achieve the stable ultra low flying height for recording density 1 Tb/in² in hard disk drive. The possible approaches towards flying height adjustment, advantages and disadvantages of different adjusting methods are discussed. Finally, the flying stability of thermal actuated slider is studied taking into account the short-range interaction forces. It is noticed that the flying height of thermal actuated slider is less sensitive to the short-range interactions than the normal slider and can sustain larger shocks. The thermal actuated flying height adjusting technology is more suitable for ultra-low flying height applications.

Air-Bearing Design Towards Highly Stable Head–Disk Interface at Ultralow Flying Height

Pushing recording density towards tera-bit per square inch and beyond requires reducing flying height to 2.5-3 nm or below. One critical challenge at such ultralow flying height is the possible head-disk crash or unstable head-disk spacing due to short-range interaction forces, such as electrostatic force, intermolecular forces, lubricant interaction force, and so on. Slider design and design strategy are investigated in this work aiming at significantly increased stability of the head-disk spacing at ultralow flying height. Nonzero surface roughness leads to a roughness-limited possible minimum flying height. A stable head-disk interface requires a full air-bearing domination even at a roughness-imposed minimum flying height. Here, the air-bearing domination means that both air-bearing force and air-bearing stiffness are larger than the combination of various short-range forces and the corresponding stiffness. Investigations presented in this paper indicate that high pressure and high-pressure concentration technology are effective approaches to extending the domination of air-bearing force towards such a roughness-limited possible minimum flying height. Slider designs, proposed by authors, exhibit satisfying flying height stability even at the roughness-limited minimum flying height

Asymptotic Completeness for Relativistic Kinetic Equations with Short-range Interaction Forces

We present an $L^1$-asymptotic completeness results for relativistic kinetic equations with short range interaction forces. We show that the uniform phase space-time bound for nonlinear terms to the relativistic nonlinear kinetic equations yields the asymptotic completeness of the relativistic kinetic equations. For this space-time bound, we employ dispersive estimates and explicit construction of a Lyapunov functional.