Johnson-Kendall-Roberts Research Articles

Contact Creep Behavior of Polydimethylsiloxane and Influence of Load, Tip Size, and Crosslink Density

Time-dependent indentation creep behaviors of polydimethylsiloxane (PDMS) samples of different crosslink densities were studied through contact creep tests loaded with silica tips. Step loads from 0.1 to 10 mN were applied and held for 600 s. The data of penetration depth versus time were recorded during the holding period. A Hertz-type viscoelastic model was used to compute the creep compliance of the samples and the Johnson–Kendall–Roberts (JKR) theory was used to obtain the initial equivalent modulus, infinite equivalent modulus, and work of adhesion between the tested each pair of the PDMS and fused silica tip surfaces. The comparison between initial and infinite equivalent moduli obtained from the Hertz viscoelastic theory and the JKR theory shows that the adhesion between the tip and the sample surface plays an importance role in affecting the analysis results when the indentation strain is small. The influences of crosslink density, applied load, and tip size on the localized PDMS properties are discussed.

Adhesion Effect Model of a Single Biomimetic Fiber Based on JKR Contact Theory

Fibrillar structure adhesives can adhere strongly to surfaces as a gecko does. The adhesion and detachment of each fiber has significant effects on the adhesion enhancement. In the present study, we report the adhesion effect of a single fiber. Based on the JKR (Johnson-Kendall-Roberts) theory, nonlinear mechanical models are built to formulate the process of adhesion and detachment between a fiber and substrate. Comparisons of the experimental and simulative results reveal consistent process trend of adhesion and detachment, which suggests the potential applicability of the present model.

Adhesive Evidence for Gecko-Inspired Biomimetic Fiber: Combination of Experiments and Modeling

A gecko-inspired silicone rubber array was successfully fabricated by ICP etching strategy. Adhesion properties of this gecko-inspired structure were studied through two parallel and independent approaches: experiments and model simulations. In our former work, based on the JKR (Johnson-Kendall-Roberts) contact theory, we proposed a nonlinear mechanical model to formulate the adhesion between a fiber and substrate. Now SPM experimental results verify the maximum adhesion force; show that fiber structure has being relatively better adhesion than unstructured. Moreover, some experimental phenomena explained by our present model.

Adhesion of nanoscale asperities with power-law profiles

The behavior of single-asperity micro- and nanoscale contacts in which adhesion is present is important for the performance of many small-scale mechanical systems and processes, such as atomic force microscopy (AFM). When analyzing such problems, the bodies in contact are often assumed to have paraboloidal shapes, thus allowing the application of the familiar Johnson–Kendall–Roberts (JKR), Derjaguin–Müller–Toporov (DMT), or Maugis–Dugdale (M–D) adhesive contact models. However, in many situations the asperities do not have paraboloidal shapes and, instead, have geometries that may be better described by a power-law function. An M–D-n analytical model has recently been developed to extend the M–D model to asperities with power-law profiles. We use a combination of M–D-n analytical modeling, finite element (FE) analysis, and experimental measurements to investigate the behavior of nanoscale adhesive contacts with non-paraboloidal geometries. Specifically, we examine the relationship between pull-off force, work of adhesion, and range of adhesion for asperities with power-law-shaped geometries. FE analysis is used to validate the M–D-n model and examine the effect of the shape of the adhesive interaction potential on the pull-off force. In the experiments, the extended M–D model is applied to analyze pull-off force measurements made on nanoscale tips that are engineered via gradual wear to have power-law shapes. The experimental and modeling results demonstrate that the range of the adhesive interaction is a crucial parameter when quantifying the adhesion of non-paraboloidal tips, quite different than the familiar paraboloidal case. The application of the M–D-n model to the experimental results yields an unusually large adhesion range of 4–5nm, a finding we attribute to either the presence of long-range van der Waals forces or deviations from continuum theory due to atomic-scale roughness of the tips. Finally, an adhesion map to aid in analysis of pull-off force measurements of non-paraboloidal tips is presented. The map delineates the cases in which a simplified rigid analysis can be used to analyze experimental data.

Direct Adhesive Measurements between Wood Biopolymer Model Surfaces

For the first time the dry adhesion was measured for an all-wood biopolymer system using Johnson-Kendall-Roberts (JKR) contact mechanics. The polydimethylsiloxane hemisphere was successfully surface-modified with a Cellulose I model surface using layer-by-layer assembly of nanofibrillated cellulose and polyethyleneimine. Flat surfaces of cellulose were equally prepared on silicon dioxide substrates, and model surfaces of glucomannan and lignin were prepared on silicon dioxide using spin-coating. The measured work of adhesion on loading and the adhesion hysteresis was found to be very similar between cellulose and all three wood polymers, suggesting that the interaction between these biopolymers do not differ greatly. Surface energy calculations from contact angle measurements indicated similar dispersive surface energy components for the model surfaces. The dispersive component was dominating the surface energy for all surfaces. The JKR work of adhesion was lower than that calculated from contact angle measurements, which partially can be ascribed to surface roughness of the model surfaces and overestimation of the surface energies from contact angle determinations.

A Model for Removal of Compact, Rough, Irregularly Shaped Particles from Surfaces in Turbulent Flows

A model for removal of compact, rough, irregularly shaped particles from surfaces in turbulent flow was developed. Following the approach of our previous bumpy particle model, irregularly shaped particles were modeled as spherical particles with a number of bumps on them. To improve the model, the effect of surface roughness was added to the bumps. Each bump was modeled with large number of asperities and the Johnson-Kendall-Roberts (JKR) adhesion theory was used to model the adhesion and detachment of each bump and asperity in contact with the surface. The total adhesion force for each bump was obtained as the summation of each asperity force in contact with the substrate. To account for the variability observed in the removal of particles, the number of bumps and roughness values of particles are assumed to be random, respectively, with Poisson and log-normal distributions. For particle separation from the surface, the theory of critical moment was used, and the orientation of bumps on the surface was considered when determining the range of shear velocity needed for removal of the irregularly, shaped particles. The effects of particle size, turbulent flow, particle irregularity, and particle surface roughness on detachment and resuspension were studied for different particles and surfaces. Model prediction for removal of rough, irregularly shaped graphite particles from steel substrate was compared with the available experimental data and earlier numerical models, and good agreement was obtained. This study may find application in adhesion and detachment of irregular particles from flooring in indoor and outdoor environments.

Asymmetric spatula heads combined with lateral forces provide a mechanism for controlling the adhesive attachment of a range of spider species

Dry adhesion is a common strategy utilized throughout nature, allowing attachment of animals to a large range of surfaces. Crucially, it enables the animal to switch rapidly and safely between attachment and detachment in order to facilitate motion. Here we investigate the magnitude and directionality of the dry adhesion systems of a number of spider species. Atomic force microscopy (AFM) was used to measure the normal adhesion strength of a single setule. Secondly, scanning electron microscopy (SEM) was used to directly observe the interaction of a spider seta with an AFM cantilever tip and then, based on the known stiffness of the cantilever and the deflection distance, to estimate the adhesion force between them. The AFM-measured values for normal adhesion of single spider setules to a surface (9–16 nN) were similar to values predicted by the Johnson–Kendall–Roberts (JKR) model. In contrast, the force of adhesion, estimated from the SEM images, between the seta and the cantilever reached values as high as 10 μN, much higher than predicted by the JKR theory alone. With spiders, as with geckos, the principle of contact splitting leads to an increase in adhesion force. In addition, it was observed that significantly higher adhesion occurred when the setules were dragged laterally across a spherical surface in the proximal direction (i.e. towards the spider's tarsus). When pushed in the opposite direction, adhesion was greatly reduced. This confirms that the spider dry adhesion system is another example of directional adhesion.

Measurement of the elastic modulus of polymeric films using an AFM with a steel micro-spherical probe tip

The elastic moduli of polystyrene (PS), polymethylmethacrylate (PMMA) and polydimethylsiloxane (PDMS) films were evaluated using an Atomic Force Microscope (AFM) with a steel micro-spherical probe tip. The elastic moduli of the polymeric films were determined with respect to indentation depth using the Hertz and Johnson-Kendall-Roberts (JKR) models. The measured elastic moduli of PS, PMMA and PDMS were determined to be 2.6 GPa, 0.74 GPa, and 4 MPa at indentation depths of 1.7 nm, 4 nm, and 120 nm, respectively. These results confirm the validity of the proposed method for effectively measuring the elastic properties of polymeric thin films.

“Contact” of Nanoscale Stiff Films

We investigated the contact behaviors of a nanoscopic stiff thin film bonded to a compliant substrate and derived an analytical solution for determining the elastic modulus of thin films. Microscopic contact deformations of the gold and polydopamine thin films (<200 nm) coated on polydimethylsiloxane elastomers were measured by indenting a soft tip and analyzed in the framework of the classical plate theory and Johnson-Kendall-Roberts (JKR) contact mechanics. The analysis of this thin film contact mechanics focused on the bending and stretching resistance of thin films and is fundamentally different from conventional indentation measurements where the focus is on the fracture and compression of the films. The analytical solution of the elastic modulus of nanoscopic thin films was validated experimentally using 50 and 100 nm gold thin films coated on polydimethylsiloxane elastomers. The technical application of this analysis was further demonstrated by measuring the elastic modulus of thin films of polydopamine, a recently discovered biomimetic universal coating material. Furthermore, the method presented here is able to quantify the contact behaviors of nanoscopic thin films, effectively providing fundamental design parameters, the elastic modulus, and the work of adhesion, crucial for transferring them effectively into practical applications.

Verification of the applicability of classical contact theories for nanoscale contact problems using multiscale simulation

Using the quasicontinuum (QC) method, multiscale simulation of nanocontact process between a Ni indenter and a Cu substrate is performed to verify the applicability of classical contact theories for nanoscale contact problems. In addition, around the comparison of the multiscale simulation results and the classical contact theories, such as the Hertz theory, the Johnson–Kendall–Roberts (JKR) theory and the Maugis–Dugale (M–D) theory, a further discussion is presented. The contact force and the contact radius of Ni indenter, as well as the contact stress distribution during the nanocontact process are investigated in detail. The multiscale model indicates that the Lomer–Cottrell locks observed during nanocontact process act as obstacles to the dislocation motion in the Cu substrate beneath the Ni indenter, which leads elastic deformation dominantly in the Cu substrate during nanocontact process. The comprehensive analysis shows that, compared with other classical contact models, the M–D model has a wider range of application, which can more precisely describe the relation between the applied force and the contact radius during nanocontact process. The stress distribution curve obtained from the M–D theory agrees well with that obtained from the QC method. Due to the adhesion effect, a small irregular tension zone adjacent to the non-local region underneath the indenter is observed in the QC simulation.

Adhesive full stick contact of a rigid cylinder with an elastic half-space

The problem of adhesive contact of a rigid cylinder with an elastic half-space is considered. The proposed adhesive contact model differs from the Johnson–Kendall–Roberts (JKR) model by preserving the influence of the contact shear stresses in the problem formulation and considering the so-called full stick contact due to the large values of the friction coefficient between contacting surfaces, as opposed to the frictionless contact assumed in the JKR model. An analytical treatment of the problem is presented, with the corresponding boundary-value problem formulated in the bipolar coordinates. A general solution in the form of Papkovich–Neuber functions and the Fourier integral transform is used to obtain an exact solution to the formulated boundary-value problem. Comparison of the results with the JKR model shows that accounting for the contact shear stresses leads to smaller contact areas as compared to those predicted by the JKR model.

Adhesion and Friction Properties of Molecularly Thin Perfluoropolyether Liquid Films on Solid Surface

The adhesion and friction properties of molecularly thin perfluoropolyether (PFPE) lubricant films dip-coated on a diamond-like carbon (DLC) overcoat of magnetic disks were studied using a pin-on-disk-type micro-tribotester that we developed. The load and friction forces were simultaneously measured on a rotating disk surface under an increasing/decreasing load cycle and slow sliding conditions. Experiments were performed using two types of PFPE lubricants: Fomblin Z-tetraol2000S with functional end-groups and Fomblin Z-03 without any end-group. The curves of the friction force as a function of the applied load agree with the curves estimated using the Johnson-Kendall-Roberts (JKR) model. The friction forces on the Z-03 films having different thicknesses were not found to decrease drastically; however, the friction forces on the Z-tetraol film were found to decrease drastically when the film thickness is more than ~1.2 nm. This drastic change in the case of the Z-tetraol film is estimated to be affected by the coverage of the lubricant film.

Role of Counter-substrate Surface Energy in Macroscale Friction of Nanofiber Arrays

The effect of counter-substrate surface energy on macroscale friction of nanofiber array is studied. Low-density polyethylene (LDPE) fibrillar array fabricated from silicon nanowire template is tested against glass substrates modified with various self-assembled monolayers, which exhibit a wide range of surface energy. A large drop in friction over a narrow range of surface energy is observed and explained in terms of drastically reduced number of fibers in actual contact, in addition to the reduced surface energy. The relationship between surface energy and fiber engagement is discussed with Johnson-Kendall-Roberts (JKR) and elastic beam models.

Application of Johnson–Kendall–Roberts model in nanomanipulation of biological cell: air and liquid environment

The application of Johnson–Kendall–Roberts (JKR) contact mechanics model in manipulation of a biological cell (DNA) using AFM will be studied in both air and liquid environments. Using JKR model in liquid environment requires adding interaction forces to its external force and applying equivalent adhesion energy to equations. These changes modify the adhesion force and the deformation in liquid environment. To discover the process of biological cell deformation owing to applied load by AFM, results will be compared with the results of a gold nanoparticle in the same condition, and theoretical and experimental data for mouse embryonic stem cell. Comparisons show that to have the same deformation for DNA and a gold nanoparticle, different forces are needed owing to different elasticity modulus. Sensitivity analysis of JKR deformation to elasticity modulus proved this claim. Although contact area for DNA is larger than a gold nanoparticle, less applied force is needed to have the same deformation.

Measuring the Adhesion Force on Natural Fibre Surface Using Scanning Probe Microscopy

This work has focused on measuring the adhesion forces on both untreated and atmospheric helium plasma treated single jute fibre surfaces using scanning probe microscopy (SPM). The measurements were conducted on three differently aged surfaces for one week, three weeks and six weeks using a standard silicon nitride tip in force-volume (f-v) mode. Up to 256 adhesion data points were collected from various locations on the surface of the studied fibres using in-house developed software and the resulting data were statistically analysed by the histogram method. Results obtained from this analysis method were found to be very consistent with a small statistical variation. The work of adhesion, W a, was calculated from measured adhesion force using the Johnson–Kendall–Roberts (JKR) and Derjaguin–Muller–Toporov (DMT) models. Increases in both adhesion force and work of adhesion were observed on jute fibre with certain levels of atmospheric plasma treatment and ageing time.

Synthesis and functionalization of poly(ethylene glycol) microparticles as soft colloidal probes for adhesion energy measurements

We report on the synthesis and operation of new soft colloidal probes (SCPs) as sensors for adhesion energy measurements. The measurements involve determination of the thermodynamic work of adhesion using the Johnson–Kendall–Roberts (JKR) approach. To maximize the sensitivity as well as the specificity of adhesion measurements in aqueous media we use highly compliant poly(ethylene glycol) (PEG) microparticles as SCPs. The chemical inertness of PEG offers advantages as probe material, but at the same time complicates the integration of functional groups. Consequently, we focus on the development of a straightforward yet variable surface modification procedure involving radical surface chemistry using benzophenone as the photoinitiator. With this highly versatile method we are able to introduce various functionalities like carboxy or amine groups directly to the PEG network. These functionalized SCPs can then be further modified with more complex structures such as dendritic oligo(amidoamines). With a first set of SCPs, adhesion energies were measured on model surfaces revealing the contributions due to acid–base, electrostatic and hydrophobic interactions in water. We successfully showed that the developed PEG probes allow for the study of contact behaviour without expensive instrumentation and with high sensitivity suitable to detect very weak (biological) interactions.

Surface energy tunable nanohairy dry adhesive by broad ion beam irradiation

We present a simple and shape-controllable method to tune the surface energy and tilting angle of nanohairy structures using broad ion beam irradiation. First, the vertical nanohair arrays made of ultraviolet (UV)-curable polyurethane acrylate (PUA) material were prepared by replica molding. Subsequently, the nanohairs were bent to a wide range of angles from 0 (vertical) to 75° (stooped hairs) by the oblique broad Ar ion beam. The surface energy was tuned with normal oxygen (O2) ion beam irradiation together with aging effect (47.1 to 71.9 mJ m−2). It was observed that the shear adhesion strength was significantly increased from 25.2 to 58.1 N cm−2 on the hydrophilic test surface and from 22.8 to 45.7 N cm−2 on the hydrophobic test surface, respectively, with the variation of surface energy from 47.1 to 71.9 mJ m−2. In addition, the shear adhesion strength was increased from 58.1 to 124.1 N cm−2 and from 45.7 to 110.6 N cm−2 on hydrophilic and hydrophobic test surfaces, respectively, as the tilting angle was varied from 0 to 75° at the highest surface energy of 71.9 mJ m−2. The measured adhesion data were compared with the theoretical adhesion forces based on Johnson–Kendall–Roberts (JKR), modified-JKR, peel zone (PZ), and Kendall peeling models, suggesting that the contact state of nanohairs is a mixture of tip and side contacts.

Solvation in hydrofluoroalkanes: how can ethanol help?

The goal of this work was to evaluate the ability of ethanol mixed with hydrofluoroalkanes (HFAs) to improve solvation of moieties of relevance to pressurized metered-dose inhalers (pMDIs). Chemical force microscopy was used to measure the adhesion force (F(ad)) between alkyl-based, ether-based and ester-based moieties (C8/C8, COC/COC and COOC/COOC interactions) in 2H,3H-perfluoropentane (HPFP)/ethanol mixtures. HPFP is a liquid that mimics propellant HFAs. The F(ad) results are thus a measure of solvation in HFAs. Johnson-Kendall-Roberts (JKR) theory was used to model the results. The F(ad) normalized by the tip radius of curvature (F(ad)/R) decreased upon the addition of ethanol, suggesting its ability to enhance the solvent environment. At 15% (v/v) ethanol, the F(ad)/R was reduced 34% for the alkyl, 63% for the ether, and down 67% for the ester tails. Thus, the solvation could be ranked as: ester > ether > alkyl. JKR theory was a reasonable model for the F(ad)/R. Ethanol, within the concentration range of interest in commercial pMDIs, provided limited enhancement in solvation of alkyl moieties. On the other hand, the cosolvent significantly enhanced solvation of ether-based and ester-based moieties, thus suggesting its potential for formulations containing amphiphiles with such groups.

Molecular dynamics for lateral surface adhesion and peeling behavior of single-walled carbon nanotubes on gold surfaces

Functional gecko-inspired adhesives have attracted a lot of research attention in the last decade. In this work, the lateral surface adhesion and normal peeling-off behavior of single-walled carbon nanotubes (SWCNTs) on gold substrates are investigated by performing detailed, fully atomistic molecular dynamics (MD) simulations. The effects of the diameter and adhered length of CNTs on the adhesive properties were systematically examined. The simulation results indicate that adhesion energies between the SWCNTs and the Au surface varied from 220 to 320 mJ m −2 over the reported chirality range. The adhesion forces on the lateral surface and the tip of the nanotubes obtained from MD simulations agree very well with the predictions of Hamaker theory and Johnson–Kendall–Roberts (JKR) model. The analyses of covalent bonds indicate that the SWCNTs exhibited excellent flexibility and extensibility when adhering at low temperatures (∼100 K). This mechanism substantially increases adhesion time compared to that obtained at higher temperatures (300–700 K), which makes SWCNTs promising for biomimetic adhesives in ultra-low temperature surroundings.

Extended hard-sphere model and collisions of cohesive particles

In two earlier papers the present authors modified a standard hard-sphere particle-wall and particle-particle collision model to account for the presence of adhesive or cohesive interaction between the colliding particles: the problem is of importance for modeling particle-fluid flow using the Lagrangian approach. This technique, which involves a direct numerical simulation of such flows, is gaining increasing popularity for simulating, e.g., dust transport, flows of nanofluids and grains in planetary rings. The main objective of the previous papers was to formally extend the impulse-based hard-sphere model, while suggestions for quantifications of the adhesive or cohesive interaction were made. This present paper gives an improved quantification of the adhesive and cohesive interactions for use in the extended hard-sphere model for cases where the surfaces of the colliding bodies are "dry," e.g., there is no liquid-bridge formation between the colliding bodies. This quantification is based on the Johnson-Kendall-Roberts (JKR) analysis of collision dynamics but includes, in addition, dissipative forces using a soft-sphere modeling technique. In this way the cohesive impulse, required for the hard-sphere model, is calculated together with other parameters, namely the collision duration and the restitution coefficient. Finally a dimensional analysis technique is applied to fit an analytical expression to the results for the cohesive impulse that can be used in the extended hard-sphere model. At the end of the paper we show some simulation results in order to illustrate the model.