In biomimetic and biological systems, interactions between surfaces are often mediated by adhesive molecules, nanoparticles, or colloids dispersed in the surrounding solution. We present here a general, statistical-mechanical model for two surfaces that interact via adhesive particles. The effective, particle-mediated interaction potential of the surfaces is obtained by integrating over the particles' degrees of freedom in the partition function. Interestingly, the effective adhesion energy of the surfaces exhibits a maximum at intermediate particle concentrations, and is considerably smaller both at low and high concentrations. The effective adhesion energy corresponds to a minimum in the interaction potential at surface separations slightly larger than the particle diameter, while a secondary minimum at surface contact reflects depletion interactions. Our results can be generalized to surfaces with specific receptors for solute particles, and have direct implications for the adhesion of biomembranes and for phase transitions in colloidal systems.
We consider an adhesive contact between a thin soft layer on a rigid substrate and a rigid cylindrical indenter ("line contact") with account of the surface tension of the layer. First, it is shown that the boundary condition for the surface outside the contact area is given by the constant contact angle - as in the case of fluids in contact with solid surfaces. In the approximation of thin layer and under usual assumptions of small indentation and small inclination angles of the surface, the problem is solved analytically.
The dynamics of adhesion of a spherical micro-particle to a ligand-coated wall, in shear flow, is studied using a Langevin equation that accounts for thermal fluctuations, hydrodynamic interactions and adhesive interactions. Contrary to the conventional assumption that thermal fluctuations play a negligible role at high P$\acute{e}$clet numbers, we find that for particles with low surface densities of receptors, rotational diffusion caused by fluctuations about the flow and gradient directions aids in bond formation, leading to significantly greater adhesion on average, compared to simulations…
Polymer-surface interactions are crucial to many biological processes and industrial applications. Here we propose a machine-learning method to connect a model polymer's sequence with its adhesion to decorated surfaces. We simulate the adhesive free energies of $20,000$ unique coarse-grained 1D sequential polymers interacting with functionalized surfaces and build support vector regression (SVR) models that demonstrate inexpensive and reliable prediction of the adhesive free energy as a function of the sequence. Our work highlights the promising integration of coarse-grained simulation with da…
A self-consistent model is developed to investigate attachment / detachment kinetics of two soft, deformable microspheres with irregular surface and coated with flexible binding ligands. The model highlights how the microscale binding kinetics of these ligands as well as the attractive/repulsive potential of the charged surface affects the static deformed configuration of the spheres. It is shown that in the limit of smooth, neutral charged surface (i.e., the Debye length, $κ\rightarrow \infty $), interacting via elastic binders (i.e., the stiffness coefficient, $λ\rightarrow 0$) the adhesion …
The elastic and adhesive properties of a solid surface can be quantified by indenting it with a rigid sphere. Indentation tests are classically described by the JKR-law when the solid is very stiff, while recent work highlights the importance of surface tension for exceedingly soft materials. Here we show that surface tension plays a crucial role even for stiff solids: it regularizes the crack-like singularity at the edge of the contact. We find that the edge region exhibits a universal, self-similar structure that emerges from the balance of surface tension and elasticity. The similarity theo…
Surface roughness is known to easily suppress the adhesion of elastic surfaces. Here a simple model for the contact of \emph{viscoelastic} rough surfaces with significant levels of adhesion is presented. This approach is derived from our previous model [E. Barthel and G. Haiat {\em Langmuir}, 18 9362 2002] for the adhesive contact of viscoelastic spheres. For simplicity a simple loading/unloading history (infinitely fast loading and constant pull-out velocity) is assumed. The model provides approximate analytical expressions for the asperity response and exhibits the full viscoelastic adhesive…
When adhesive elastomeric materials slide over hard rough surfaces at low velocities, there are two primary dissipative mechanisms that control how friction changes with sliding velocity: viscoelastic dissipation and adhesive dissipation. To distinguish the contribution of these dissipative mechanisms we have measured frictional shear stresses for crosslinked polydimethylsiloxane (PDMS) on three different rough surfaces of similar surface chemistry across nearly six decades of sliding velocity. The results show that the observed friction is dominated by adhesive dissipation, rather than viscoe…
We report rheological measurements of a noncolloidal particle suspension in a Newtonian solvent at 40% solid volume fraction. An anomalous, frequency-dependent complex viscosity is found under oscillatory shear (OS) flow, whereas a constant dynamic viscosity is found under the same shear rates in steady shear (SS) flow. We show that this contradiction arises from the underlying microstructural difference between OS and SS, mediated by weak interparticle forces. Discrete element simulations of proxy particle suspensions confirm this hypothesis and reveal an adhesion-induced, shear thinning mech…
Bioinspired artificial surfaces with tailored adhesive properties have attracted significant interest. While fibrillar adhesive pads mimicking gecko feet are optimized for strong reversible adhesion, monolithic microsphere arrays mimicking the slippery zone of the pitchers of carnivorous plants of the genus Nepenthes show anti-adhesive properties even against tacky counterpart surfaces. In contrast to the influence of topography, the influence of relative humidity (RH) on adhesion has been widely neglected. Some previous works deal with the influence of RH on the adhesive performance of fibril…
We develop an analytical model of adhesive wear between two unlubricated rough surfaces, forming micro-contacts under normal load. The model is based on an energy balance and a crack initiation criteria. We apply the model to the problem of self-affine rough surfaces under normal load, which we solve using the boundary element method. We discuss how self-affinity of the surface roughness, and the complex morphology of the micro-contacts that emerge for a given contact pressure, challenge the definition of contact junctions. Indeed, in the context of adhesive wear, we show that elastic interact…
We investigate the impact of nanoparticle roughness on the phase behaviour of suspensions in models of calcium carbonate nanoparticles. We use a Derjaguin approach that incorporates roughness effects and interactions between the nanoparticles modelled with a combination of DLVO forces and hydration forces, derived using experimental data and atomistic molecular dynamics simulations, respectively. Roughness effects, such as atomic steps or terraces appearing in mineral surfaces result in very different effective inter-nanoparticle potentials. Using stochastic Langevin Dynamics computer simulati…
Recently proposed formulation of the Boundary Element Method for adhesive contacts has been generalized for contacts of functionally graded materials with and without adhesion. First, proceeding from the fundamental solution for single force acting on the surface of a half space with a power-law varying elastic modulus, the deformation produced by constant pressure acting on a rectangular element was calculated and the influence matrix was obtained for a rectangular grid. The inverse problem for the calculation of required stress in contact area from a known surface deformation was solved by u…
Monte Carlo simulation of selective adsorption in a binary hard-disk mixture on patterned adhesive surfaces
Yukhnovskii Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine（乌克兰国家科学院尤赫诺夫斯基凝聚态物理研究所）；Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University（利沃夫国立理工大学应用数学与基础科学研究所）
Elastic sheets with macroscopic dimensions are easy to deform by bending and stretching. Yet shaping nanometric sheets by mechanical manipulation is hard. Here we show that nanoparticle self-assembly could be used to this end. We demonstrate by Monte Carlo simulation that spherical nanoparticles adhering to the outer surface of an elastic nanotube can self-assemble into linear structures as a result of curvature-mediated interactions. We find that nanoparticles arrange into rings or helices on stretchable nanotubes, and as axial strings on nanotubes with high rigidity to stretching. These self…
Contact force--indentation depth measurements in contact experiments involving compliant materials, such as polymers and gels, show a hysteresis loop whose size depends on the maximum indentation depth. This depth-dependent hysteresis (DDH) is not explained by classical contact mechanics theories and was believed to be due to effects such as material viscoelasticity, plasticity, surface polymer interdigitation, and moisture, etc. It has been observed that the DDH energy loss initially increases and then decreases with roughness. A mechanics model based on the occurrence of adhesion and roughne…
Soft adhesive pads are needed for many robotics applications, and one approach is based on electroadhesion. Here we present a general analytic model and numerical results for electroadhesion for soft solids with arbitrary time-dependent applied voltage, and arbitrary dielectric response of the solids, and including surface roughness. We consider the simplest coplanar-plate-capacitor model with a periodic array of conducting strips located close to the surface of the adhesive pad, and discuss the optimum geometrical arrangement to obtain the maximal electroadhesion force. For surfaces with roug…
Thermodynamics tells us to expect underwater contact between two hydrophobic surfaces to result in stronger adhesion compared to two hydrophilic surfaces. However, presence of water changes not only energetics, but also the dynamic process of reaching a final state, which couples solid deformation and liquid evacuation. These dynamics can create challenges for achieving strong underwater adhesion/friction, which affects diverse fields including soft robotics, bio-locomotion and tire traction. Closer investigation, requiring sufficiently precise resolution of film evacuation while simultaneousl…
A simple but general analysis of stability of axis-symmetric adhesive contacts is provided. Adhesion is considered in the JKR-approximation. Depending on the shape of the contacting bodies, various scenarios are possible, including vanishing adhesive force, complete contact as well as transitions between these states.
Flaps can be detached from a thin film glued on a solid substrate by tearing and peeling. For flat substrates, it has been shown that these flaps spontaneously narrow and collapse in pointy triangular shapes. Here we show that various shapes, triangular, elliptic, acuminate or spatulate, can be observed for the tears by adjusting the curvature of the substrate. From combined experiments and theoretical models, we show that the flap morphology is governed by simple geometric rules.
We characterize the mechanical recovery of compliant silicone gels following adhesive contact failure. We establish broad, stable adhesive contacts between rigid microspheres and soft gels, then stretch the gels to large deformations by pulling quasi-statically on the contact. Eventually, the adhesive contact begins to fail, and ultimately slides to a final contact point on the bottom of the sphere. Immediately after detachment, the gel recoils quickly with a self-similar surface profile that evolves as a power law in time, suggesting that the adhesive detachment point is singular. The singula…
We study experimentally and theoretically the equilibrium adhesive contact between a smooth glass lens and a rough rubber surface textured with spherical microasperities with controlled height and spatial distributions. Measurements of the real contact area $A$ versus load $P$ are performed under compression by imaging the light transmitted at the microcontacts. $A(P)$ is found to be non-linear and to strongly depend on the standard deviation of the asperity height distribution. Experimental results are discussed in the light of a discrete version of Fuller and Tabor's (FT) original model (\te…
The compression of soft elastic matter and biological tissue can lead to creasing, an instability where a surface folds sharply into periodic self-contacts. Intriguingly, the unfolding of the surface upon releasing the strain is usually not perfect: small scars remain that serve as nuclei for creases during repeated compressions. Here we present creasing experiments with sticky polymer surfaces, using confocal microscopy, which resolve the contact line region where folding and unfolding occurs. It is found that surface tension induces a second fold, at the edge of the self-contact, which leads…
We designed spongy monoliths allowing liquid delivery to their surfaces through continuous nanopore systems (mean pore diameter ca. 40 nm). These nanoporous monoliths were flat or patterned with microspherical structures a few 10 microns in diameter, and their surfaces consisted of aprotic polymer or of TiO2 coatings. Liquid may reduce adhesion forces FAd; possible reasons include screening of solid-solid interactions and poroelastic effects. Softening-induced deformation of flat polymeric monoliths upon contact formation in the presence of liquids enhanced the work of separation WSe. On flat …
The use of molecular dynamics (MD) simulations has led to promising results to unravel the atomistic origins of adhesive wear, and in particular for the onset of wear at nanoscale surface asperities. However, MD simulations come with a high computational cost and offer access to only a narrow window of time and length scales. We propose here to resort to the discrete element method (DEM) to mitigate the computational cost. Using DEM particles with contact and cohesive forces, we reproduce the key mechanisms observed with MD, while having particle diameters and system sizes an order of magnitud…
Introducing a reduced particle stiffness in discrete element method (DEM) allows for bigger time steps and therefore fewer total iterations in a simulation. Although this approach works well for dry non-adhesive particles, it has been shown that for fine particles with adhesion, system behaviors are drastically sensitive to the particle stiffness. Besides, a simple and applicable principle to set the parameters in adhesive DEM is also lacking. To solve these two problems, we first propose a fast DEM based on scaling laws to reduce particle Young's modulus, surface energy and to modify rolling …
At the molecular scale there are strong attractive interactions between surfaces, yet few macroscopic surfaces are sticky. Extensive simulations of contact by adhesive surfaces with roughness on nanometer to micrometer scales are used to determine how roughness reduces the area where atoms contact and thus weakens adhesion. The material properties, adhesive strength and roughness parameters are varied by orders of magnitude. In all cases the area of atomic contact rises linearly with load, and the prefactor rises linearly with adhesive strength for weak interactions. Above a threshold adhesive…
We discuss how surface roughness influence the adhesion between elastic solids. We introduce a Tabor number which depends on the length scale or magnification, and which gives information about the nature of the adhesion at different length scales. We consider two limiting cases relevant for (a) elastically hard solids with weak adhesive interaction (DMT-limit) and (b) elastically soft solids or strong adhesive interaction (JKR-limit). For the former cases we study the nature of the adhesion using different adhesive force laws ($F\sim u^{-n}$, $n=1.5-4$, where $u$ is the wall-wall separation).…
Understanding interactions between microparticles and lipid membranes is of increasing importance, especially for unraveling the influence of microplastics on our health and environment. Here, we study how a short-ranged adhesive force between microparticles and model lipid membranes causes membrane-mediated particle assembly. Using confocal microscopy, we observe the initial particle attachment to the membrane, then particle wrapping, and in rare cases spontaneous membrane tubulation. In the attached state, we measure that the particle mobility decreases by 26%. If multiple particles adhere t…
Various adhesion mechanisms that have been understood in the field of synthetic adhesives are described and these are linked with situations relevant to fouling issues. The review mainly deals with mechanical aspects of adhesion phenomena, with an emphasis on the role of the elasticity of the bodies, called substrata, attached by adhesive. The consequences of thin film geometry of the adhesive material are described, such as various heterogeneous deformations upon traction. The importance of the bonding process is discussed, as well as some examples of non-wetting surfaces. As seen from a dist…
In this paper we investigate the loading and unloading behavior of soft solids in adhesive contact with randomly rough profiles. The roughness is assumed to be described by a self-affine fractal on a limited range of wave-vectors. A spectral method is exploited to generate such randomly rough surfaces. The results are statistically averaged, and the calculated contact area and applied load are shown as a function of the penetration, for loading and unloading conditions. We found that the combination of adhesion forces and roughness leads to a hysteresis loading-unloading loop. This shows that …
We report numerical simulations of membrane tubulation driven by large colloidal particles. Using Monte Carlo simulations we study how the process depends on particle size, concentration and binding strength, and present accurate free energy calculations to sort out how tube formation compares with the competing budding process. We find that tube formation is a result of the collective behavior of the particles adhering on the surface, and it occurs for binding strengths that are smaller than those required for budding. We also find that long linear aggregates of particles forming on the membr…
We have employed a numerical procedure to analyze the adhesive contact between a soft elastic layer and a rough rigid substrate. The solution of the problem is obtained by calculating the Green's function which links the pressure distribution to the normal displacements at the interface. The problem is then formulated in the form of a Fredholm integral equation of the first kind with a logarithmic kernel, and the boundaries of the contact area are calculated by requiring that the energy of the system is stationary. The methodology has been employed to study the adhesive contact between an elas…
In order to characterize very weak adhesive surfaces, we have developed a quantitative test inspired by the Johnson, Kendall, and Roberts adhesion test for soft adhesives, which relies on the formation and then the rupture of a capillary bridge between the surface to be tested and a liquid bath. Both the shape and the kinetics of breakage of the capillary bridge for various coatings put into contact with liquids of various viscosities and surface tensions have been studied. Several pull off regimes can be distinguished. For low pull off velocities, a quasi-static regime is observed, well descr…
Recent studies demonstrated that an elastomer containing hygroscopic inclusions absorbs moisture and swell. Here we show that a thin film of such an elastomer bonded to a rigid substrate undergoes morphological instability upon absorption of water, the wavelength of which increases linearly with its thickness. As the driving force for such a morphological instability arises from the difference of the chemical potential of water between its source and that in the film, its development is slowed down as the salinity of the water increases. Nonetheless, the wavelength of the fully developed morph…
The force of adhesion of a rotationally symmetric indenter and an elastic half-space is analyzed analytically and numerically using an extension of the method of dimensionality reduction (MDR) for superimposed normal/tangential adhesive contacts. In particular, the dependency of the critical adhesion force on the simultaneously applied tangential force is obtained and the relevant dimensionless parameters of the problem are identified. The developed method is applicable straightforwardly to adhesive contacts of any bodies of revolution.
We describe the design of micropatterned surfaces for single cell studies, based on thermoresponsive polymer brushes. We show that brushes made of poly(N-isopropylacrylamide) grafted at high surface density display excellent protein and cell anti-adhesive properties. Such brushes are readily patterned at the micron scale via deep UV photolithography. A proper choice of the adhesive pattern shapes, combined with the temperature-dependent swelling properties of PNIPAM, allow us to use the polymer brush as a microactuator which induces cell detachment when the temperature is reduced below 32degC.
A mechanically-derived contact model for adhesive elastic-perfectly plastic particles. Part II: Contact under high compaction--adding a bulk elastic response
In the present note, we start by observing that in the classical JKR theory of adhesion, using the usual Hertzian approximations, the pull-off load grows unbounded when the clearance goes to zero in a conformal "ball in socket" geometry. To consider the case of the conforming geometry, we use a recent rigorous general extension of the original JKR energetic derivation proposed by the first author which necessitates only of adhesionless solutions, and an approximate adhesionless solution given in the literature. We find that depending on a single governing parameter of the problem, theta=DeltaR…
Contact mechanics-based models for the friction of nominally flat rough surfaces have not been able to adequately capture certain key experimentally observed phenomenona, such as the transition from a static friction peak to a lower level of sliding friction and the shear-induced contact area reduction that has been observed in the pre-sliding regime especially for soft materials. Here, we propose a statistical model based on physically-rooted contact mechanics laws describing the micromechanics of individual junctions. The model considers the quasi-static tangential loading, up to full slidin…
Current engineering wear models are often based on empirical parameters rather than built upon physical considerations. Here, we look for a physical description of adhesive wear at the microscale, at which the interaction between two surfaces comes down to the contact of asperities. Recent theoretical work has shown that there is a critical micro-contact size above which it becomes energetically favorable to form a wear particle. We extend this model by taking into consideration the elastic interaction of multiple closely-spaced micro-contacts in 2D, with different sizes and separation distanc…
The wrapping equilibria of one and two adsorbing cylinders are studied along a semi-flexible filament (polymer) due to the interplay between elastic rigidity and short-range adhesive energy between the cylinder and the filament. We show that statistical mechanics of the system can be solved exactly using a path integral formalism which gives access to the full effect of thermal fluctuations, going thus beyond the usual Gaussian approximations which take into account only the contributions from the minimal energy configuration and small fluctuations about this minimal energy solution. We obtain…
We introduce a minimal model of solid-forming anisotropic molecules that displays, in thermal equilibrium, surface orientational order without bulk orientational order. The model reproduces the nonequilibrium behavior of recent experiments in that a bulk nonequilibrium structure grown by deposition contains regions of orientational order characteristic of the surface equilibrium. This order is deposited in general in a nonuniform way, because of the emergence of a growth-poisoning mechanism that causes equilibrated surfaces to grow slower than non-equilibrated surfaces. We use evolutionary met…
Recently, tribologists have shown increasing interest in rate-dependent phenomena occurring in viscoelastic fractures. However, in some cases, conflicting results are obtained despite the use of similar theoretical models. For this reason, we try to shed light on the effects that long and short-range adhesion has on the pull-off force in the contact of viscoelastic media by exploiting a recently developed numerical model. We find that, in the limit of long-range adhesion, the unloading velocity has little effect on the pull-off force, which is close to the value predicted by Bradley for rigid …
Tribological phenomena are governed by combined effects of material properties, topology and surface-chemistry. We study the interplay of multiscale surface structures with molecular-scale interactions towards interpreting static frictional interactions at fractal interfaces. By spline-assisted-discretization we analyse asperity interactions in pairs of contacting fractal surface-profiles. For elastically deforming asperities, force analysis reveals greater friction at surfaces exhibiting higher fractality, with increasing molecular-scale friction amplifying this trend. Increasing adhesive str…
The adhesive and frictional response of an AFM tip connected to a substrate through supramolecular host-guest complexes is investigated by dynamic Monte Carlo simulations. The variation of the pull-off force with the unloading rate recently observed in experiments is here unraveled by evidencing a simultaneous (progressive) break of the bonds at fast (slow) rates. The model reveals the origin of the observed plateaus in the retraction force as a function of tip-surface distance, showing that they ensue from the tip geometrical features. In lateral sliding, the model exhibits a wide range of dy…
Recently, there has been some debate over the effect of adhesion on the contact of rough surfaces. Classical asperity theories predict, in agreement with experimental observations, that adhesion is always destroyed by roughness except if the amplitude of the same is extremely small, and the materials are particularly soft. This happens for all fractal dimensions. However, these theories are limited due to the geometrical simplification, which may be particularly strong in conditions near full contact. We introduce therefore a simple model for adhesion, which aims at being rigorous near full co…
Adhesive [e.g. van der Waals] forces were not generally taken into account in contact mechanics until 1971, when Johnson, Kendall and Roberts (JKR) generalized Hertz' solution for an elastic sphere using an energetic argument which we now recognize to be analogous to that used in linear elastic fracture mechanics. A significant result is that the load-displacement relation exhibits instabilities in which approaching bodies `jump in' to contact, whereas separated bodies `jump out' at a tensile `pull-off force'. The JKR approach has since been widely used in other geometries, but at small length…
We study frictionless and non-adhesive contact between elastic half-spaces with self-affine surfaces. Using a recently suggested corrective technique, we ensure an unprecedented accuracy in computation of the true contact area evolution under increasing pressure. This accuracy enables us to draw conclusions on the role of the surface's spectrum breadth (Nayak parameter) in the contact area evolution. We show that for a given normalized pressure, the contact area decreases logarithmically with the Nayak parameter. By linking the Nayak parameter with the Hurst exponent (or fractal dimension), we…
Small scale contact between a soft, liquid-coated layer and a stiff surface is common in many situations, from synovial fluid on articular cartilage to adhesives in humid environments. Moreover, many model studies on soft adhesive contacts are conducted with soft silicone elastomers, which possess uncrosslinked liquid molecules (i.e. silicone oil) when the modulus is low. We investigate how the thickness of a silicone oil layer on a soft substrate relates to the indentation depth of glass microspheres in contact with crosslinked PDMS, which have a modulus of <10 kPa. The particles indent into …
