Force-distance Relation Research Articles

Stretchable silver electrodes adopting double stress release design directly deposited on an eco-flex substrate

In this paper, stretchable electrodes adopting a double stress release structure were fabricated and characterized on eco-flex substrates. First, the correlation between mechanical properties applying surface plasma treatment and stretching capability of stretchable silver electrodes directly deposited on eco-flex substrate was studied. The Young’s modulus values of the substrate and metal were extracted using the force-distance relation via atomic force microscopy employing Johnson–Kendall–Roberts model. It was found that, as the Young’s modulus increased with the increase of plasma treatment time, the stretching capability first improved; then, samples showed no improvement over long plasma treatment time. This indicates that there is an optimum plasma treatment time to simultaneously achieve high stretching capability and low initial resistance. Using the optimum time, stretchable silver electrodes adopting double stress release structure along lateral and vertical directions were fabricated and the high stretching capability of the silver electrodes was achieved up to tensile strain of about 160%, as was high stability of up to 1000 times the multi-cycling strain.

Force-Distance Relation for Dental Magnets - Fitted Equation.

The force-distance power law for dental magnets had been unresolved until a theoretical study found that only even inverse powers were allowed; for simple magnets inverse fourth power was the only possibility. It remained to demonstrate that this indeed did apply to real magnets, the present purpose. The force exerted by a series of real dental magnets to a large steel plate, and in a few cases to dental magnet keepers, as a function of distance was recorded. Curve-fitting of that data was explored. using the equation previously used for long dipoles, but allowing the power to be a free parameter. An index of 4 was the only feasible value. Corresponding fitted parameter values were then examined in relation to magnet design and each other. The theoretical power law index was confirmed to be 4. For a satisfactory fit, a 'polar offset' and a 'stretch power' were again required to better approximate the experimental results. Polar offset appears to be a function of apparent pole strength; stretch power less clearly so. The motivating question is settled.

Evaluations on Ceramic Fracture Toughness Measurement by Edge Chipping

Advanced ceramics, such as alumina and zirconia, are widely used in modern industries, due to their superior properties, such as high hardness and strength. Fracture toughness is a significant property that describes the capability of materials to resist crack instability and expansion to failure, and also helps when calculating the allowable working stress, and crack size, of the component. This paper comprehensively lists the current toughness-testing methods. With comparative investigations of various methods, edge chipping is found to be the simplest way of measuring the ceramic fracture-toughness, in terms of the dominant median crack, chip geometrical similarity, and force-distance relations, giving consideration to its potential application in industry. Moreover, to avoid the data variance from crack-length measurement in edge chipping, it is further proposed that the energy analyses can be used to improve the way in which the toughness expression is formulated.

Numerical modeling of the mechanics of the interaction of DNA nucleotides

The telomere plays an important role to protect chromosomes from interaction with surrounding media as well as its length can be an important factor for the age prediction of an individual. Therefore, fundamental research remains relevant. The given investigation provides a numerical experiment from the mechanics perspective. By applying the DEM, the dynamics of a simplified telomere nucleotide interaction is presented. The applied knowledge is considered from previous investigations where numerical modeling of the dynamics of the interaction of ultrafine objects was analyzed. The nucleotides interaction is modeled based on a Lennard-Jones potential, while for the force-distance relation the presented equations are integrated in time, giving values of distance and velocity in dependence on time. The work outlines the ability to consider the acting force values between nucleotides, taken from known physical experiments on forces. A comparison of different nucleotides interaction, with A/T as well as G/C is also given.

Reliability of cancer cell elasticity in force microscopy

Evaluating the mechanical properties of biological cells in their living state is of upmost importance for understanding cellular behavior in health or disease and in particular cancer cells. In recent years, force microscopy and spectroscopy have become inevitable tools to attain the elastic modulus of cells as a whole using colloidal probes or with high lateral precision by sharp tips. However, the obtained values have to be treated with due care to avoid data misinterpretation. Here, we present a comparison of elasticity between four metastatic cancer cell lines (lung, liver, skin, and breast epithelial-type cancer cells) taken by colloidal and sharp probes using force spectroscopy on cell monolayers and stress the impact of a stiff substrate, which cells are attached to, on the measured values especially in cancerous cells, which depict abnormalities in structure and cellular components. As a result of our analysis, we suggest to solely use sharp probes for the mechanical characterization of cancer cells when the force-distance relation is fit by a conventional contact mechanics model such as the Hertz model.

Rapid Probe Engagement and Withdrawal With Force Minimization in Atomic Force Microscopy: A Learning-Based Online-Searching Approach

In this article, the problem of rapid probe engagement and withdrawal in atomic force microscopy (AFM) is addressed. Probe engagement and withdrawal is needed in almost all AFM operations, ranging from imaging to nanomanipulation. However, due to the highly nonlinear force-distance relation, large probe-sample interaction force can be induced during the probe engagement and withdrawal process, resulting in sample deformation and damage and measurement errors. Rapid probe engagement and withdrawal is needed to achieve high-speed AFM operations, particularly, to capture and interrogate dynamic evolutions of the sample. We propose an online-searching-based optimization approach to minimize both the engagement (and withdrawal) time and the interaction force. The force-displacement profile of the probe is partitioned and then optimized sequentially, by immersing optimal trajectory design and iterative learning control into the Fibonacci search process. The proposed approach is illustrated through experimental implementations on two different types of polymer species, a polydimethylsiloxane sample, and a dental silicone sample, respectively.

Density functional theory of electrolyte solutions in slit-like nanopores II. Applications to forces and ion exchange

An extended reference fluid density approach/weighted correlation approximation (RFD/WCA) of density functional theory (DFT) for size-asymmetric electrolytes presented in part I is applied to calculate the forces and the ion exchange for Ca- and Na-montmorillonite systems in equilibrium with salt solutions. Our modeling shows that the DFT calculations are in excellent agreement with Monte Carlo simulations and experimental results. The results indicate that the ion size plays an important role in force-distance relation. Due to the excluded volume effect, the osmotic pressure curve predicted by DFT is shifted towards larger separation distances with increasing the diameter of counterions. Additionally, the interaction can be switched from attraction to repulsion with increasing diameter of counterions from standard to hydrated ionic size. Furthermore, the quantitative characterization of the exchange of calcium for sodium at room temperature on Wyoming bentonite is investigated with the DFT modeling in aqueous solutions at pH7.0. It is found that a significant variation of the selectivity coefficient could be observed with the surface charge density, ionic diameter and interlayer separations. This implies that ion selectivity in compacted bentonite differs from that in dilute smectite dispersions.

Adhesive contact of an elastic semi-infinite solid with a rigid rough surface: Strength of adhesion and contact instabilities

The effect of adhesion on the contact behavior of elastic rough surfaces is examined within the framework of the multi-asperity contact model of Greenwood and Williamson (1966), known as the GW model. Adhesive surface interaction is modeled by nonlinear springs with a force–displacement relation governed by the Lennard–Jones (LJ) potential. Constitutive models are presented for contact systems characterized by low and high Tabor parameters, exhibiting continuous (stable) and discontinuous (unstable) surface approach, respectively. Constitutive contact relations are obtained by integrating the force–distance relation derived from the LJ potential with a finite element analysis of single-asperity adhesive contact. These constitutive relations are then incorporated into the GW model, and the interfacial force and contact area of rough surfaces are numerically determined. The development of attractive and repulsive forces at the contact interface and the occurrence of instantaneous surface contact (jump-in instability) yield a three-stage evolution of the contact area. It is shown that the adhesion parameter introduced by Fuller and Tabor (1975) governs the strength of adhesion of contact systems with a high Tabor parameter, whereas the strength of adhesion of contact systems with a low Tabor parameter is characterized by a new adhesion parameter, defined as the ratio of the surface roughness to the equilibrium interatomic distance. Applicable ranges of aforementioned adhesion parameters are interpreted in terms of the effective surface separation, obtained as the sum of the effective distance range of the adhesion force and the elastic deformation induced by adhesion. Adhesive strength of rough surfaces in the entire range of the Tabor parameter is discussed in terms of a generalized adhesion parameter, defined as the ratio of the surface roughness to the effective surface separation.

Surface adhesion and hardening effects on elastic–plastic deformation, shakedown and ratcheting behavior of half-spaces subjected to repeated sliding contact

Deformation of homogeneous elastic-perfectly plastic (EPP) and elastic-linear kinematic hardening plastic (ELKP) half-spaces due to repeated adhesive sliding contact is examined with a two-dimensional finite element model. Interfacial adhesion is modeled by nonlinear springs with a force-distance constitutive relation derived from the Lennard–Jones potential. Deformation behavior is interpreted in terms of dimensionless parameters, such as the Maugis parameter, interaction distance (interfacial gap), and plasticity parameter. Numerical results provide insight into the stress–strain response and the evolution of subsurface plasticity. The effects of the interaction distance, plasticity parameter, interfacial adhesion, and Maugis parameter on the friction and normal forces and the accumulation of plastic strain are analyzed in terms of the number of sliding cycles. Deformation maps providing information about the steady-state mode of deformation are presented for both EPP and ELKP material behaviors. Results of this study illustrate the importance of elastic–plastic material behavior and interfacial adhesion in contact deformation due to repeated surface sliding.

Computer Simulation of Water-Mediated Adhesion Between Phospholipid Bilayer and Solid Support Functionalized with Self-Assembled Monolayers

An attempt is made to estimate, via computer simulation of the force-distance relation, the free energy of adhesion between a phosphatidylethanolamine bilayer and an alkanethiolate self-assembled monolayer (SAM) in aqueous medium. The simulations are performed using the grand canonical Monte Carlo technique and atomistic force fields. The bilayer adhesion free energy is predicted to be -22 ± 3 mJ/m(2) (-1.4 ± 0.2 kcal/mol) on a hydrophilic carboxyl-terminated SAM and -1 ± 1 mJ/m(2) (-0.06 ± 0.06 kcal/mol) on a hydrophobic methyl-terminated SAM.

Computer simulation of adhesion between hydrophilic and hydrophobic self-assembled monolayers in water

The grand canonical Monte Carlo technique and atomistic force fields are used to calculate the force-distance relations and free energies of adhesion between carboxyl and methyl terminated alkanethiolate self-assembled monolayers (SAMs) in water. Both symmetric and asymmetric confinements are considered, as formed by like and unlike SAMs, respectively. As the confinement is increased, water confined by the hydrophobic methyl terminated SAMs experiences capillary evaporation. As a consequence, the adhesion energy is determined by the direct interaction between bare SAMs. In the asymmetric system, an incomplete capillary evaporation is observed, with the number of water molecules dropped by more than an order of magnitude. The remaining water molecules are all adsorbed on the hydrophilic SAM, while the hydrophobic SAM is separated from the rest of the system by a thin vapor layer. The calculated free energies of adhesion are in acceptable agreement with experiment.

Intermittent contact interaction between an atomic force microscope cantilever and a nanowire

We investigate in theory and experiment the intermittent contact interaction between an atomic force microscope (AFM) cantilever and a nanowire under ambient conditions. The nanowire is modeled as a spring reacting instantaneously to any change of the force between the wire and the cantilever. This implies that the cantilever is subject to an “effective” force-distance relation, containing not only the surface forces but also the deflection of the nanowire. Experimentally, CVD-grown tin oxide nanowires and lithographically structured silicon nanowire arrays were investigated by intermittent contact AFM. By comparison of experimental and simulated distance-dependent resonance curves it is found that the nanowires behave like “fast nanosprings” and that the adhesion force is one of the key factors determining distance-dependent resonance curves. The results are fully applicable to a scenario in which a cantilever equipped by a nanowire interacts with a surface.

Adhesive contact: from atomistic model to continuum model

Two types of Lennard-Jones potential are widely used in modeling adhesive contacts. However, the relationships between the parameters of the two types of Lennard-Jones potential are not well defined. This paper employs a self-consistent method to derive the Lennard-Jones surface force law from the interatomic Lennard-Jones potential with emphasis on the relationships between the parameters. The effect of using correct parameters in the adhesion models is demonstrated in single sphere-flat contact via continuum models and an atomistic model. Furthermore, the adhesion hysteresis behaviour is investigated, and the S-shaped force-distance relation is revealed by the atomistic model. It shows that the adhesion hysteresis loop is generated by the jump-to-contact and jump-off-contact, which are illustrated by the S-shaped force-distance curve.

Characterization of Hydrophobic Forces for in Liquid Self-Assembly of Micron-Sized Functional Building Blocks

ABSTRACTThis paper presents the experimental and numerical study of hydrophobic interaction forces at nanometer scale in the scope of engineering micron-sized building blocks for self-assembly in liquid. The hydrophobic force distance relation of carbon, Teflon and dodeca-thiols immersed in degassed and deionized water has been measured by atomic force microscopy. Carbon and dodeca-thiols showed comparable attractive and binding forces in the rage of pN/nm2. Teflon showed the weakest binding and no attractive force. Molecular dynamic simulations were performed to correlate the molecular arrangement of water molecules and the hydrophobic interactions measured by atomic force microscopy. The simulations showed a depletion zone of 2Å followed by a layered region of 8Å in the axis perpendicular to the hydrophobic surface.

Polyelectrolyte-Compression Forces between Spherical DNA Brushes

Optical tweezers are employed to measure the forces of interaction within a single pair of DNA-grafted colloids, dependent on the molecular weight of the DNA chains, and the concentration and valence of the surrounding ionic medium. The resulting forces are short range and set in as the surface-to-surface distance between the colloidal cores reaches the value of the brush height. The measured force-distance relation is analyzed by means of a theoretical treatment that quantitatively describes the effects of compression of the chains on the surface of the opposite-lying colloid. Quantitative agreement with the experiment is obtained for all parameter combinations.

Measurement of polyamide and polystyrene adhesion with coated-tip atomic force microscopy

This work presents atomic force microscopy (AFM) measurements of adhesion forces between polyamides, polystyrene and AFM tips coated with the same materials. The polymers employed were polyamide 6 (PA6), PA66, PA12 and polystyrene (PS). All adhesion forces between the various unmodified or modified AFM tips and the polymer surfaces were in the range −1.5 to − 8 nN . The weakest force was observed for an unmodified AFM tip with a PS surface and the strongest was between a PS-coated tip and PS surface. The results point to both the benefits and drawbacks of coated-tip AFM force–distance measurements. Adhesion forces between the two most dissimilar (PA6–PS and PA66–PS) materials were significantly asymmetric, e.g., the forces were different depending on the relative placement of each polymer on the AFM tip or substrate. Materials with similar chemistry and intermolecular interactions yielded forces in close agreement regardless of placement on tip or substrate. Using experimental forces, we calculated the contact radii via four models: Derjaguin, Muller, and Toporov; Johnson, Kendall, and Roberts; parametric tip–force–distance relation; and a square pyramid–flat surface (SPFS) model developed herein. The SPFS model gave the most reasonable contact tip radius estimate. Hamaker constants calculated from the SPFS model using this radius agreed in both magnitude and trends with experiment and Lifshitz theory.

Interface-mediated interactions between particles: A geometrical approach

Particles bound to an interface interact because they deform its shape. The stresses that result are fully encoded in the geometry and described by a divergence-free surface stress tensor. This stress tensor can be used to express the force on a particle as a line integral along any conveniently chosen closed contour that surrounds the particle. The resulting expression is exact (i.e., free of any "smallness" assumptions) and independent of the chosen surface parametrization. Additional surface degrees of freedom, such as vector fields describing lipid tilt, are readily included in this formalism. As an illustration, we derive the exact force for several important surface Hamiltonians in various symmetric two-particle configurations in terms of the midplane geometry; its sign is evident in certain interesting limits. Specializing to the linear regime, where the shape can be analytically determined, these general expressions yield force-distance relations, several of which have originally been derived by using an energy-based approach.

Charles Augustin Coulomb and the fundamental law of electrostatics

In his famous experiment on the inverse square law of electrostatics, Coulomb neither defined electric charge nor gave reliable measurements of the force–distance relation. Yet the experiment has often been viewed as the basis of the fundamental law of electrostatics. This paper discusses Coulomb's life, showing the context within which he was working, how he arrived at the experiment, and the use he made of it. Physics in France in the late 18th century was undergoing a transformation from a science of holistic observation and explanations to one of universal laws and exact measurement. Coulomb was both a subject of, and an important contributor to, this change, and these two aspects are evident in his approach to the experiment and to the later uptake of his results. The reaction in the rest of Europe was initially less favourable, and the ultimate fame of Coulomb's experiment was dependent on the triumph of French mathematical physics in the 19th century.

Study on the interaction between a dislocation and impurities in KCl:Sr2+single crystals by the Blaha effect Part III Influence of heat treatment on various characteristics

Strain-rate cycling tests associated with ultrasonic oscillation were conducted at 80–239 K for two kinds of KCl:Sr2+ (0.05 mol% in the melt) single crystals: quenched and annealed specimens. Examining the relationship of temperature and dislocation velocity-effective stress exponent, m*, estimated from the data obtained in this series, we could find the suitable force-distance relation between a dislocation and the impurity. The force-distance relation for the quenched specimen approached to the Fleischer's model taking account of the Friedel relation rather than the Fleischer's model. As for the annealed specimen, the SQ was the most appropriate of the three models: the SQ, the PA, and the TR indicate a square, a parabolic, and a triangular force-distance profile respectively. The three force-distance relations are taken account of the Friedel relation. By annealing the quenched specimen, m* became low at a given temperature. This may have been caused by the following two phenomena. First, the concentration of weak obstacles to dislocation motion decreased after the heat treatment. Secondly, the resistance to movement of a dislocation in the quenched specimen was weakened by annealing it, e.g., F0 was reduced to about one-third and ϕ0 increased from 154 to 172 degrees. F0 and ϕ0 are the force acted on the dislocation and the bending angle of dislocation by the weak obstacle such as the impurity. Therefore, it may be deduced that the dislocation velocity in the quenched specimen is more sensitive to the effective stress due to the impurities than that in the annealed specimen at the temperature.

Simple test system for single molecule recognition force microscopy

We have established an easy-to-use test system for detecting receptor–ligand interactions on the single molecule level using atomic force microscopy (AFM). For this, avidin–biotin, probably the best characterized receptor–ligand pair, was chosen. AFM sensors were prepared containing tethered biotin molecules at sufficiently low surface concentrations appropriate for single molecule studies. A biotin tether, consisting of a 6 nm poly(ethylene glycol) (PEG) chain and a functional succinimide group at the other end, was newly synthesized and covalently coupled to amine-functionalized AFM tips. In particular, PEG 800 diamine was glutarylated, the mono-adduct NH 2–PEG–COOH was isolated by ion exchange chromatography and reacted with biotin succinimidylester to give biotin–PEG–COOH which was then activated as N-hydroxysuccinimide (NHS) ester to give the biotin–PEG–NHS conjugate which was coupled to the aminofunctionalized AFM tip. The motional freedom provided by PEG allows for free rotation of the biotin molecule on the AFM sensor and for specific binding to avidin which had been adsorbed to mica surfaces via electrostatic interactions. Specific avidin–biotin recognition events were discriminated from nonspecific tip–mica adhesion by their typical unbinding force (∼40 pN at 1.4 nN/s loading rate), unbinding length (<13 nm), the characteristic nonlinear force–distance relation of the PEG linker, and by specific block with excess of free d-biotin. The convenience of the test system allowed to evaluate, and compare, different methods and conditions of tip aminofunctionalization with respect to specific binding and nonspecific adhesion. It is concluded that this system is well suited as calibration or start-up kit for single molecule recognition force microscopy.