Mechanics of contact and adhesion between viscoelastic spheres: An analysis of hysteresis during loading and unloading

Detailed finite element simulations are carried out to study the adhesive contact of viscoelastic spheres. The spheres are brought into contact by a compressive force that increases at a constant rate. Upon reaching a maximum load, the spheres are unloaded until they separate. We studied in detail the effect of loading and unloading rates on hysteresis and on the pull‐off force for a standard viscoelastic solid. The surface interaction is modeled by the Dugdale–Barenblatt model. Numerical results are compared with analytical models for bonding and debonding, including a recent theory proposed by Johnson. There is excellent agreement between analytical and finite element results for the bonding phase. However, for the debonding phase, current analytical models break down unless the loading and unloading rates are slow in comparison with the material relaxation time. Based on the finite element results, a simple approximate analytical model is proposed to quantify adhesive contact in the debonding phase. We also examine the dependence of hysteresis on interfacial parameters such as the cohesive strength and the intrinsic work of adhesion. Our results show that viscoelastic adhesive contact depends on the details of the surface interaction and cannot be determined solely by the work of adhesion. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 772–793, 2002     

Electrolytic nucleation of silver on a glassy carbon electrode: Part II. Steady-state nucleation rate

The dependence of the number of nuclei on time is investigated in a wide overvoltage interval using different glassy carbon electrodes. The data for the steady-state nucleation rate are interpreted on the basis of both classical and atomistic theoretical concepts. Conclusions are drawn for the applicability of the two models of nucleation.     

Using the Dugdale approximation to match a specific interaction in the adhesive contact of elastic objects

In the Maugis-Dugdale model of the adhesive contact of elastic spheres, the step cohesive stress sigma(0) is arbitrarily chosen to be the theoretical stress sigma(th) to match that of the Lennard-Jones potential. An alternative and more reasonable model is proposed in this paper. The Maugis model is first extended to that of arbitrary axisymmetric elastic objects with an arbitrary surface adhesive interaction and then applied to the case of a power-law shape function and a step cohesive stress. A continuous transition is found in the extended Maugis-Dugdale model for an arbitrary shape index n. A three-dimensional Johnson-Greenwood adhesion map is constructed. A relation of the identical pull-off force at the rigid limit is required for the approximate and exact models. With this requirement, the stress sigma(0) is found to be k(n)Deltagamma/z(0), where k(n) is a coefficient, Deltagamma the work of adhesion, and z(0) the equilibrium separation. Hence we have sigma(0) = 0.588Deltagamma/z(0), especially for n=2. The prediction of the pull-off forces using this new value shows surprisingly better agreement with the Muller-Yushchenko-Derjaguin transition than that using sigma(th) = 1.026Deltagamma/z(0), and this is true for other values of shape index n.     

Relation between the alpha-relaxation and Johari-Goldstein beta-relaxation of a component in binary miscible mixtures of glass-formers

The coupling model was applied to describe the alpha-relaxation dynamics of each component in perfectly miscible mixtures A(1-x)B(x) of two different glass-formers A and B. An important element of the model is the change of the coupling parameter of each component with the composition, x, of the mixture. However, this change cannot be determined directly from the frequency dispersion of the alpha-relaxation of each component because of the broadening caused by concentration fluctuations in the mixture, except in the limits of low concentrations of either component, x --> 0 and x --> 1. Fortunately, the coupling model has another prediction. The coupling parameter of a component, say A, in the mixture determines tau(alpha)/tau(JG), the ratio of the alpha-relaxation time, tau(alpha), to the Johari-Goldstein (JG) secondary relaxation time, tau(JG), of the same component A. This prediction enables us to obtain the coupling parameter, n(A), of component A from the isothermal frequency spectrum of the mixture that shows both the alpha-relaxation and the JG beta-relaxation of component A. We put this extra prediction into practice by calculating n(A) of 2-picoline in binary mixtures with either tri-styrene or o-terphenyl from recently published broadband dielectric relaxation data of the alpha-relaxation and the JG beta-relaxation of 2-picoline. The results of n(A) obtained from the experimental data show its change with composition, x, follows the same pattern as assumed in previous works that address only the alpha-relaxation dynamics of a component in binary mixtures based on the coupling model. There is an alternative view of the thrust of the present work. If the change of n(A) with composition, x, in considering the alpha-relaxation of component A is justified by other means, the theoretical part of the present work gives a prediction of how the ratio tau(alpha)/tau(JG) of component A changes with composition, x. The data of tau(alpha) and tau(JG) of 2-picoline mixed with tri-styrene or o-terphenyl provide experimental support for the prediction.     

Lifetime and strength of adhesive molecular bond clusters between elastic media

With a long-term objective toward a quantitative understanding of cell adhesion, we consider an idealized theoretical model of a cluster of molecular bonds between two dissimilar elastic media subjected to an applied tensile load. In this model, the distribution of interfacial traction is assumed to obey classical elastic equations whereas the rupture and rebinding of individual molecular bonds are governed by stochastic equations. Monte Carlo simulations that combine the elastic and stochastic equations are conducted to investigate the lifetime of the bond cluster as a function of the applied load. We show that the interfacial traction is generally nonuniform and for a given adhesion size the average cluster lifetime asymptotically approaches infinity as the applied load is reduced to below a critical value, defined as the strength of the cluster. The effects of elastic moduli, adhesion size, and rebinding rate on the cluster lifetime and strength are studied under strongly nonuniform distributions of interfacial traction. Although overly simplified in a number of aspects, our model seems to give predictions that are consistent with relevant experimental observations on focal adhesion dynamics.     

Atomic configuration,electronic structure,and work of adhesion of TiN(111)//B2-NiTi(110) and TiN(111)//B19′-NiTi(010) interfaces: Insights from first-principles simulations

In this paper, the atomic configuration, electronic structure, and work of adhesion for TiN(111)//B2-NiTi(110) and TiN(111)//B19′-NiTi(010) interfaces were investigated by first-principles calculations based on density functional theory (DFT), which aim to provide a theoretical guidance for analyzing the service reliability of TiN films modified NiTi alloy devices. The results of this paper indicated that a hollow-site stacking structure was formed on the interface when Ti and N were the terminal atoms on two sides. Such interfaces demonstrated a stronger bonding performance and a more stable structure than that with Ni and Ti as the terminal atoms. The work of adhesion of the TiN(111)//B19′-NiTi(010) interface was 17.47 J/m², which is greater than the work of fracture of TiN(111) (6.73 J/m²), whereas the work of adhesion of the TiN(111)//B2-NiTi(110) interface was found to reach 5.49 J/m², which is lower than the work of fracture of TiN(111). The models of the work of adhesion between the two interfaces indicate that there are significant bond strength changes in the TiN/NiTi interface, when the NiTi substrate undergoes martensitic transformation. The results of this paper contribute significantly to the service reliability analysis of TiN films coated on NiTi alloy devices.     

The nearly constant loss,Johari‐Goldstein β‐relaxation,and α‐relaxation of 1,4‐polybutadiene

From high‐resolution dielectric spectroscopy measurements on 1,4‐polybutadiene (1,4‐PB), we show that in addition to the structural α‐relaxation and higher frequency secondary relaxations in the spectra, a nearly constant loss (NCL) is observed at shorter times/lower temperatures. The properties of this NCL are compared to those of another chemically similar polymer, 1,4‐polyisoprene. The secondary relaxations in 1,4‐PB include the well‐known Johari‐Goldstein (JG) β‐relaxation and two other higher‐frequency peaks. One of these, referred to as the γ‐relaxation, falls between the JG‐relaxation and the NCL. Seen previously by others, this γ‐relaxation in 1,4‐PB is not the JG‐process and bears no relation to the glass transition. At very low temperatures (<15 K), we confirm the existence of a very fast secondary relaxation, having a weak dielectric strength and an almost temperature‐invariant relaxation time. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 342–348, 2007     

An algorithm for three-dimensional Voronoi S-network

The paper presents an algorithm for calculating the three-dimensional Voronoi-Delaunay tessellation for an ensemble of spheres of different radii (additively-weighted Voronoi diagram). Data structure and output of the algorithm is oriented toward the exploration of the voids between the spheres. The main geometric construct that we develop is the Voronoi S-network (the network of vertices and edges of the Voronoi regions determined in relation to the surfaces of the spheres). General scheme of the algorithm and the key points of its realization are discussed. The principle of the algorithm is that for each determined site of the network we find its neighbor sites. Thus, starting from a known site of the network, we sequentially find the whole network. The starting site of the network is easily determined based on certain considerations. Geometric properties of ensembles of spheres of different radii are discussed, the conditions of applicability and limitations of the algorithm are indicated. The algorithm is capable of working with a wide variety of physical models, which may be represented as sets of spheres, including computer models of complex molecular systems. Emphasis was placed on the issue of increasing the efficiency of algorithm to work with large models (tens of thousands of atoms). It was demonstrated that the experimental CPU time increases linearly with the number of atoms in the system, O(n).     

A systematic examination of the morphogenesis of calcium carbonate in the presence of a double-hydrophilic block copolymer

In this paper, a systematic study of the influence of various experimental parameters on the morphology and size of CaCO3 crystals after room-temperature crystallization from water in the presence of poly(ethylene glycol)-block-poly(methacrylic acid) (PEG-b-PMAA) is presented. The pH of the solution, the block copolymer concentration, and the ratio [polymer]/[CaCO3] turned out to be important parameters for the morphogenesis of CaCO3, whereas a moderate increase of the ionic strength (0.016 M) had no influence. Depending on the experimental conditions, the crystal morphologies can be tuned from calcite rhombohedra via rods, ellipsoids or dumbbells to spheres. A morphology map is presented which allows the prediction of the crystal morphology from a combination of pH, and CaCO3 and polymer concentration. Morphologies reported in literature for the same system but under different crystallization conditions agree well with the predictions from the morphology map. A closer examination of the growth of polycrystalline macroscopic CaCO3 spheres by TEM and time-resolved dynamic light scattering showed that CaCO3 macrocrystals are formed from strings of aggregated amorphous nanoparticles and then recrystallize as dumbbell-shaped or spherical calcite macrocrystal.     

Large attractive depletion interactions in soft repulsive-sphere binary mixtures

We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure, and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results, the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed.     

Isotropic–nematic phase separation and demixing in mixtures of spherical nanoparticles with length‐polydisperse nanorods

An extension of Onsager theory is developed to simulate isotropic–nematic phase separation in a mixture of spheres with length‐polydisperse system of rods. This work is motivated by recent experimental data on nanorod liquid crystals. Prior theoretical investigations indicate that both polydispersity and the presence of spheres should increase the biphasic–nematic phase transition, that is, the nematic cloud point. Results indicate that the phase diagrams undergo drastic changes depending upon both particle geometry and rod length polydispersity. The key geometric factor is the ratio between the sphere diameter and the rod diameter. In general, length fractionation is enhanced by the addition of spheres, which may be experimentally advantageous for separating short nanorods from a polydisperse population. Simulation results also indicate that the nematic cloud and shadow curves may cross one another because of the scarcity of spheres in the shadow phase. In general, these results do indicate that the nematic cloud point increases as a function of sphere loading; however, in certain areas of phase space, this relationship is nonmonotonic such that the nematic cloud point may actually decrease with the addition of spheres. This work has application to a wide range of nanoparticle systems, including mixtures of spherical nanoparticles with nanorods or nanotubes. Additionally, a number of nonspherical particles and structures may behave as spheres, including crumpled graphene and tightly coiled polymers. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

A modeling approach to describe the adhesion of rough, asymmetric particles to surfaces

A combined theoretical and experimental study of the adhesion of alumina particles and polystyrene latex spheres to silicon dioxide surfaces was performed. A boundary element technique was used to model electrostatic interactions between micron-scale particles and planar surfaces when the particles and surfaces were in contact. This method allows quantitative evaluation of the effects of particle geometry and surface roughness on the electrostatic interaction. The electrostatic interactions are combined with a previously developed model for van der Waals forces in particle adhesion. The combined model accounts for the effects of particle and substrate geometry, surface roughness and asperity deformation on the adhesion force. Predictions from the combined model are compared with experimental measurements made with an atomic force microscope. Measurements are made in aqueous solutions of varying ionic strength and solution pH. While van der Waals forces are generally dominant when particles are in contact with surfaces, results obtained here indicate that electrostatic interactions contribute to the overall adhesion force in certain cases. Specifically, alumina particles with complex geometries were found to adhere to surfaces due to both electrostatic and van der Waals interactions, while polystyrene latex spheres were not affected by electrostatic forces when in contact with various surfaces.     

Particle capture via discrete binding elements: systematic variations in binding energy for randomly distributed nanoscale surface features

This work examines how the binding strength of surface-immobilized "stickers" (representative of receptors or, in nonbiological systems, chemical heterogeneities) influences the adhesion between surfaces that are otherwise repulsive. The study focuses on a series of surfaces designed with fixed average adhesive energy per unit area and demonstrates quantitatively how a redistribution of the adhesive functionality into progressively larger clusters (stronger stickers) increases the probability of adhesive events. The work employs an electrostatic model system: relatively uniform, negative 1 μm silica spheres flow gently over negative silica flats. The flats contain small amounts of randomly positioned nanoscale cationic patches. The silica-silica interaction is repulsive; however, the cationic patches (present at sufficiently low levels that the overall surface charge remains substantially negative) produce local attractions. In this study, the attractions are relatively weak so that multiple patches engage to capture flowing particles. Experiments reveal an adhesion signature characteristic of a renormalized random distribution when the sticker strength is increased at an overall fixed binding strength per unit area of surface. The form of the particle capture curves are in good quantitative agreement with a simple model that assumes only a fixed adhesion energy needed for particle capture. Aside from the quantitative details that provide a simple formalism for anticipating particle adhesion, this work demonstrates how increasing the heterogeneities in the surface functionality can cause a system to go from being nonadhesive to becoming strongly adhesive. Indeed, systems containing small amounts of discretized adhesive functionality are always more adhesive than systems in which the same functionality is distributed uniformly over the surface (the mean field scenario).     

Current trends and future challenges in the experimental, theoretical and computational analysis of intervalence charge transfer (IVCT) transitions

Mixed-valence chemistry has a long and rich history which is characterised by a strong interplay of experimental, theoretical and computational studies. The intervalence charge transfer (IVCT) transitions generated in dinuclear mixed-valence species (particularly of ruthenium and osmium) have received considerable attention in this context, as they provide a powerful and sensitive probe of the factors which govern electronic delocalisation and the activation barrier to intramolecular electron transfer. This tutorial review discusses classical, semi-classical and quantum mechanical theoretical treatments which have been developed over the past 35 years for the analysis of IVCT absorption bands. Particular attention is drawn to the applicability of these models for the analysis of mixed-valence complexes which lie between the fully localised (Class II) and delocalised (Class III) limits in the "localised-to-delocalised" (Class II-III) regime. A clear understanding of the complex interplay of inter- and intramolecular factors which influence the IVCT process is crucial for the design of experimental studies to probe the localised-to-delocalised regime and in guidance of the development of appropriate theoretical models.     

Sedimentation of spheres at small Reynolds number

The effect of fluid inertia on the settling of spheres in a viscous incompressible fluid is studied in the limit of small Reynolds number. The kinetic energy of flow depends on the positions of the spheres, and gives rise to forces on the spheres. In the dilute limit it suffices to study the corresponding pair interaction. The interaction is calculated from the Stokes flow for two spheres settling between plane walls in the point particle limit. The dissipative interaction between a pair of spheres is calculated from the Proudman-Pearson [I. Proudman and J. R. A. Pearson, J. Fluid Mech. 2, 237 (1957)] solution of the Navier-Stokes equations for flow about a sphere in unbounded geometry. The combination of kinetic and dissipative interaction gives rise to a repulsive force of range of the order of the sphere diameter divided by the Reynolds number.     

Traction force microscopy on-chip: shear deformation of fibroblast cells

We develop here a microfabrication compatible force measurement technique termed as ultrasoft polydimethylsiloxane-based traction force microscopy (UPTFM). This technique is devised for mapping the cellular traction forces imparted on the adhering substrate, so as to depict the physiological state of the cells surviving in the micro-confinement. We subsequently integrate the technique with a microfluidic platform for evaluating different states of stress in adherent mouse skin fibroblast L929 cells. Utilizing this technique, we monitor the spatio-temporal evolution of cellular traction forces for static incubation periods with no media replenishment as well as for dynamic flow conditions that inherently induce cell deformation and detachment. While the studies conducted on a quiescent fluid medium enable us to obtain an optimal static cell incubation period, those executed under dynamic flow conditions provide us with the minuscule details of the cellular response, deformation and detachment processes. We elucidate the correlation between shear activated cytosolic calcium ion release profile and the local traction forces as an attempt to apply UPTFM in the domain of functional biological purposes. Pertinently, we map the centroidal displacement and the maximum traction stress in characterizing the critical shear rate conditions for the onset of the cell peeling-off process, and demonstrate their contrasting features in comparison to the vesicle lift off processes in a shear flow. Theoretically, these deviations can only be explained by taking physiologically relevant cell adhesion models into consideration, which, while retaining the intrinsic simplicity, are able to reproduce the key experimental outcomes at least with qualitative agreement. We execute further theoretical investigations with variable magnitudes of membrane stiffness, viscosity and adhesion strength, so as to come up with interesting biophysical confluences.     

Thermoplastic composites based on flax fibres and polypropylene: Influence of fibre length and fibre volume fraction on mechanical properties

Natural-fibre-mat-reinforced thermoplastic (NMT) composites based on flax fibre mats and a Polypropylene (PP) matrix were manufactured using (i) a film-stacking method and (ii) a paper making process. The influence of fibre length and fibre content on stiffness and strength is reported and compared with data for glass-mat-reinforced thermoplastic (GMT) composites, including the influence of using maleic-anhydride grafted PP. The data is also compared with existing micromechanical models like Kelly-Tyson and Cox-Krenchel for strength and stiffness, respectively. A good agreement was found between theory and experiment in case of stiffness while in case of strength the experimental values fall well below the theoretical predictions. Results indicated that NMTs are of interest for low-cost engineering applications and can compete with commercial GMTs, especially when a high stiffness per unit weight is desirable. Results also indicated that the key area for future development lies not only in improved adhesion but mainly in improving the fibre strength.     

Streptococcus mutans and Streptococcus intermedius adhesion to fibronectin films are oppositely influenced by ionic strength

Bacterial adhesion to protein-coated surfaces is mediated by an interplay of specific and nonspecific interactions. Although nonspecific interactions are ubiquitously present, little is known about the physicochemical mechanisms of specific interactions. The aim of this paper is to determine the influence of ionic strength on the adhesion of two streptococcal strains to fibronectin films. Streptococcus mutans LT11 and Streptococcus intermedius NCTC11324 both possess antigen I/II with the ability to bind fibronectin from solution, but S. intermedius binds approximately 20x less fibronectin than does the S. mutans strain under identical conditions. Both strains as well as fibronectin films are negatively charged in low ionic strength phosphate buffered saline (PBS, 10x diluted), but bacteria appear uncharged in high ionic strength PBS. Physicochemical modeling on the basis of overall cell surface properties (cell surface hydrophobicity and zeta potentials) demonstrates that both strains should favor adhesion to fibronectin films in a high ionic strength environment as compared to in a low ionic strength environment, where electrostatic repulsion between equally charged surfaces is dominant. Adhesion of S. intermedius to fibronectin films in a parallel plate flow chamber was completely in line with this modeling, while in addition atomic force microscopy (AFM) indicated stronger adhesion forces upon retraction between fibronectin-coated tips and the cell surfaces in high ionic strength PBS than in low ionic strength PBS. Thus, the dependence of the interaction on ionic strength is dominated by the overall negative charge on the interacting surfaces. Adhesion of S. mutans to fibronectin films, however, was completely at odds with theoretical modeling, and the strain adhered best in low ionic strength PBS. Moreover, AFM indicated weaker repulsive forces upon approach between fibronectin-coated tips and the cell surfaces in low ionic strength PBS than in high ionic strength PBS. This indicated that the dependence of the interaction on ionic strength is dominated by electrostatic attraction between oppositely charged, localized domains on the interacting surfaces, despite their overall negative charge. In summary, this study shows that physicochemical modeling of bacterial adhesion to protein-coated surfaces is only valid provided the number of specific interaction sites on the cell surfaces is low, such as on S. intermedius NCTC11324. Nonspecific interactions are dominated by specific interactions if the number of specific interaction sites is large, such as on S. mutans LT11. Its ionic strength dependence indicates that the specific interaction is electrostatic in nature and operative between oppositely charged domains on the interacting surfaces, despite the generally overall negatively charged character of the surfaces.     

Chemical and structural changes at the ABS polymer-copper metal interface

Creating oxygen containing moieties (hydroxyl or carbonyl) on polymer substrate surfaces is known to increase the adhesion strength of polymers to metals. However, we noticed adhesion increase with time even though no pre- or post-treatment of the polymer substrate was done. In the case of sputtered and galvanically strengthened copper coatings on acrylonitrile-butadiene-styrene polymer (ABS) substrate, the adhesion strength increased from approximately 6 J/m² to 53 J/m² during a 1008-h period. During this period structural and chemical changes of the polymer near the interface take place. Carbonyl functionalities developed on the ABS surface are most likely responsible for the large increase in the adhesion strength. Chemical changes of the polymer are probably a consequence of the galvanic deposition and a close contact of ABS with copper which is known to facilitate the oxidation of ABS.