Normal contact and friction of rubber with model randomly rough surfaces.

We report on normal contact and friction measurements of model multicontact interfaces formed between smooth surfaces and substrates textured with a statistical distribution of spherical micro-asperities. Contacts are either formed between a rigid textured lens and a smooth rubber, or a flat textured rubber and a smooth rigid lens. Measurements of the real area of contact A versus normal load P are performed by imaging the light transmitted at the microcontacts. For both interfaces, A(P) is found to be sub-linear with a power law behavior. Comparison with two multi-asperity contact models, which extend the Greenwood-Williamson (J. Greenwood and J. Williamson, Proc. Royal Soc. London Ser. A, 295, 300 (1966)) model by taking into account the elastic interaction between asperities at different length scales, is performed, and allows their validation for the first time. We find that long range elastic interactions arising from the curvature of the nominal surfaces are the main source of the non-linearity of A(P). At a shorter range, and except for very low pressures, the pressure dependence of both density and area of microcontacts remains well described by Greenwood-Williamson's model, which neglects any interaction between asperities. In addition, in steady sliding, friction measurements reveal that the mean shear stress at the scale of the asperities is systematically larger than that found for a macroscopic contact between a smooth lens and a rubber. This suggests that frictional stresses measured at macroscopic length scales may not be simply transposed to microscopic multicontact interfaces.

Noise-activated dissociation of soft elastic contacts.

Adhesive forces are capable of deforming a soft elastic object when it comes in contact with a flat rigid substrate. The contact is in stable equilibrium if the total energy of the system arising from the elastic and surface forces exhibits a minimum at a zero or at a slightly negative load. However, as the system is continually unloaded, the energy barrier decreases and it eventually disappears, thus leading to a ballistic separation of the contact. While this type of contact splitting has received wide recognition, what has not been much appreciated with these types of soft adhesion problems is that rupture of a contact can also occur at any finite sub critical load in the presence of a noise. The soft contact problems are unique in that the noise can be athermal, whereas the metastable and stable states of the thermodynamic potential can arise from the competition of the elastic and the interfacial energies of the system. Analysis based on Kramers' theory and simulations based on Langevin dynamics show that the contact rupture dynamics is amenable to an Eyring's form of a force and noise-induced escape of a particle from a potential well that is generic to various types of colloidal and macromolecular processes. These ideas are useful in understanding the results of a recent experiment involving the noise-activated rolling dynamics of a rigid sphere on a surface, where it is pinned by soft micro-fibrillar contacts.

Vibration spectroscopy of a sessile drop and its contact line.

Resonance frequencies of small sessile liquid drops (1-20 µL) were estimated from the power spectra of their height fluctuations after subjecting them to white noise vibration. Various resonance modes could be identified with this method as a function of the mass of the drop. Studies with water drops on such supports as polystyrene (θ ≈ 80°) and a superhydrophobic surface of microfibrillar silicone rubber (θ ≈ 162°) demonstrated that the resonant frequency decreases with the contact angle, θ. This trend is in remarkable agreement with the current models of the resonant vibration of sessile drops. A novel aspect of this study is the analysis of the modes of a slipping contact line that indicated that its higher frequency modes are more severely damped than its lower ones. Another case is with the glycerol-water solutions, where the resonance frequency decreases with the concentration of glycerol purely due to the capillary effects. The interface fluctuation, on the other hand, is strongly correlated with the kinematic viscosity of the liquid. Thus, these experiments provide a means to measure the surface tension and the viscosity of very small droplets.

Random motion with interfacial contact: driven diffusion vis-à-vis mechanical activation.

Rolling of a small sphere on a patterned support of an elastomer is governed by a non-linear friction. No motion occurs when the external field is weaker than the frictional resistance. However, with the intervention of an external noise, a viscous friction like behavior emerges; thus the sphere rolls with a uniform drift velocity that is proportional to the applied field. At a very low noise strength, the sphere exhibits a stick-slip behavior with motion occurring always along the bias. With the increase in the noise strength, the sphere exhibits a diffusive drift accompanied with forward and backward displacements. During this stage of driven diffusive motion, the ratio of the integrated probabilities of the negative-to-positive work fluctuations decreases monotonically with the time of observation, from which a temperature like intensive parameter can be estimated. This parameter conforms to Einstein's ratio of diffusivity and mobility that increases almost linearly, even though the diffusivity increases super-linearly, with the strength of the noise. A new barrier crossing experiment is introduced that can be performed either with a hard (e.g. a steel ball) or with a soft (e.g. a water drop) sphere in contact with a periodically undulated substrate. The frequency of barrier crossing follows a transition state equation allowing a direct estimation of the effective temperature. These experiments as well as certain numerical simulations suggest that the effective temperature of a system controlled by a non-linear friction may not have a unique value.

Stochastic rolling of a rigid sphere in weak adhesive contact with a soft substrate.

We study the rolling motion of a small solid sphere on a fibrillated rubber substrate in an external field in the presence of a Gaussian noise. From the nature of the drift and the evolution of the displacement fluctuation of the ball, it is evident that the rolling is controlled by a complex non-linear friction at a low velocity and a low noise strength (K), but by a linear kinematic friction at a high velocity and a high noise strength. This transition from a non-linear to a linear friction control of motion can be discerned from another experiment in which the ball is subjected to a periodic asymmetric vibration in conjunction with a random noise. Here, as opposed to that of a fixed external force, the rolling velocity decreases with the strength of the noise suggesting a progressive fluidization of the interface. A state (K) and rate (V) dependent friction model is able to explain both the evolution of the displacement fluctuation as well as the sigmoidal variation of the drift velocity with K. This research sets the stage for studying friction in a new way, in which it is submitted to a noise and then its dynamic response is studied using the tools of statistical mechanics. Although more works would be needed for a fuller realization of the above-stated goal, this approach has the potential to complement direct measurements of friction over several decades of velocities and other state variables. It is striking that the non-Gaussian displacement statistics as observed with the stochastic rolling is similar to that of a colloidal particle undergoing Brownian motion in contact with a soft microtubule.

Experimental investigation of the drift and diffusion of small objects on a surface subjected to a bias and an external white noise: roles of coulombic friction and hysteresis.

We study the stochastic motion of a small solid block or a small water drop on a flat solid support in the presence of an external noise and a bias. The bias is caused either by inclining the plane of the support, as is the case with the solid block, or by creating a gradient of wettability, as is the case with a water drop. Both the solid block and the water drop exhibit drifted Brownian-like motion. There are, however, differences between the motion described here and that of a classical drifted Brownian motion, in that the Coulombic friction (for solid on solid) or wetting hysteresis (for water drops on a solid) accounts for a significant resistance to motion in addition to the kinematic friction. Although the displacement distribution here is non-Gaussian, the variance of the distribution increases with time, indicating that the overall motion follows simple diffusion. The diffusivity and the mobility of the solid object are considerably lower than the values expected when the diffusion is governed by only kinematic friction. The experimental diffusivity increases with the power of the noise with an exponent of 1.61, which is close to that (1.74) of an analysis based on the Langevin equation when the Coulombic friction is taken into account in addition to the kinematic friction. The ratio of diffusivity and mobility increases slightly sublinearly with the power of the noise with an exponent of about 0.8. The experimentally observed relaxation time of the process is, however, considerably smaller than the Langevin relaxation time. When the experimental ratio of diffusivity and mobility is taken into account in the distribution function of the displacement, the later quantity becomes amenable to an analysis that is similar to the conventional fluctuation relations.

Shear-induced adhesive failure of a rigid slab in contact with a thin confined film.

A rigid-glass prism (square or rectangular base, rectangular cross-section) is sheared off a thin film of silicone elastomer bonded to a glass plate by applying a tangential force at various distances above the prism/elastomer interface. At a given tangential force, the prism starts to slide on the elastomeric film. As the sliding velocity, thus the frictional force, is progressively increased, an elastic instability develops at the interface that results in the formation of numerous bubbles. These bubbles, the lateral dimension of which is comparable to the thickness of the film, move across the interface with speeds 1000 times faster than the overall sliding speed of the glass prism against the PDMS film. It is found that the glass prism continues to slide on the elastomeric film as long as the applied shear stress is less than a critical value. During sliding, however, a normal stress is developed at the interface that decays from the front (i.e. where the force is applied) to the rear end of the prism. When the normal stress reaches a critical value, the prism comes off the film. The critical shear stress of fracture increases with the modulus of the film, but decreases with the thickness following a square root relationship, as is the case with the removal of rigid punches from thin elastomeric films by normal pull-off forces.

Confinement-induced instability and adhesive failure between dissimilar thin elastic films.

When two thin soft elastomeric films are separated from each other, an elastic instability develops at the interface. Although similar instability develops for the case of a soft film separating from a rigid adherent, there are important differences in the two cases. For the single-film case, the wavelength of instability is independent of any material properties of the system, and it scales only with thickness of the film. For the two-film case, a co-operative instability mode develops, which is a non-linear function of the thicknesses and the elastic moduli of both films. We investigate the development of such instability by energy minimization procedures. Understanding the nature of this instability is important, as it affects the adhesive compliance of the system and thus the energy release rate in the debonding of soft interfaces.

Lateral vibration of a water drop and its motion on a vibrating surface.

The resonant modes of sessile water drops on a hydrophobic substrate subjected to a small-amplitude lateral vibration are investigated using computational fluid dynamic (CFD) modeling. As the substrate is vibrated laterally, its momentum diffuses within the Stokes layer of the drop. Above the Stokes layer, the competition between the inertial and Laplace forces causes the formation of capillary waves on the surface of the drop. In the first part of this paper, the resonant states of water drops are illustrated by investigating the velocity profile and the hydrostatic force using a 3d simulation of the Navier-Stokes equation. The simulation also allows an estimation of the contact angle variation on both sides of the drop. In the second part of the paper, we investigate the effect of vibration on a water drop in contact with a vertical plate. Here, as the plate vibrates parallel to gravity, the contact line oscillates. Each oscillation is, however, rectified by hysteresis, thus inducing a ratcheting motion to the water droplet vertically downward. Maximum rectification occurs at the resonant states of the drop. A comparison between the frequency-dependent motion of these drops and the variation of contact angles on their both sides is made. The paper ends with a discussion on the movements of the drops on a horizontal hydrophobic surface subjected to an asymmetric vibration.

Settlement behavior of swimming algal spores on gradient surfaces.

When surfaces possessing gradients of surface energy are incubated with motile spores from the green seaweed Ulva, the spores attach on the hydrophilic part of the gradient in larger numbers than they do on the hydrophobic part. This result is opposite to the behavior of the spores observed on the homogeneous hydrophobic and hydrophic surfaces. The data suggest that the gradients have a direct and active influence on the spores, which may be due to the biased migration of the spores during the initial stages of surface sensing.

The influence of surface energy on the wetting behaviour of the spore adhesive of the marine alga Ulva linza (synonym Enteromorpha linza).

The environmental scanning electron microscope has been used to image the adhesive pads secreted by zoospores of the marine alga Ulva linza as they settle on a range of self-assembled and grafted monolayers of different wettability, under natural, hydrated conditions. Results reveal that the diameter of the adhesive pad is strongly influenced by surface wettability, the adhesive spreading more (i.e. wetting the surface better) on the more hydrophilic surfaces. This is in direct contrast to previous observations on the spreading of marine bioadhesives and is in apparent contradiction to the predictions of the Young-Dupre equation for three-phase systems. In this paper, we attempt an explanation based upon thermodynamic analysis of the wetting properties of hydrophilic proteins.

Biomimetic ratcheting motion of a soft, slender, sessile gel.

Inspired by the locomotion of terrestrial limbless animals, we study the motion of a lubricated rod of a hydrogel on a soft substrate. We show that it is possible to mimic observed biological gaits by vibrating the substrate and by using a variety of mechanisms to break longitudinal and lateral symmetry. Our simple theory and experiments provide a unified view of the creeping, undulating, and inchworming gaits observed in limbless locomotion on land, all of which originate as symmetry-breaking bifurcations of a simple base state associated with periodic longitudinal oscillations of a slender gel. These ideas are therefore also applicable to technological situations that involve moving small, soft solids on substrates.

Fast drop movements resulting from the phase change on a gradient surface.

The movement of liquid drops on a surface with a radial surface tension gradient is described here. When saturated steam passes over a colder hydrophobic substrate, numerous water droplets nucleate and grow by coalescence with the surrounding drops. The merging droplets exhibit two-dimensional random motion somewhat like the Brownian movements of colloidal particles. When a surface tension gradient is designed into the substrate surface, the random movements of droplets are biased toward the more wettable side of the surface. Powered by the energies of coalescence and collimated by the forces of the chemical gradient, small drops (0.1 to 0.3 millimeter) display speeds that are hundreds to thousands of times faster than those of typical Marangoni flows. This effect has implications for passively enhancing heat transfer in heat exchangers and heat pipes.

Surface properties and hemocompatibility of alkyl-siloxane monolayers supported on silicone rubber: effect of alkyl chain length and ionic functionality.

Self-assembled monolayers of alkylsiloxanes supported on poly(dimethylsiloxane) (PDMS) rubber were used as model systems to study the relation between blood compatibility and surface composition. The inner lumen of PDMS tubes were first treated with an oxygen plasma. The resultant oxidized surfaces were post-derivatized by reaction with alkyltrichlorosilanes to form the monolayer films. The alkyl chain lengths used were slightly longer than in a previous study, and this may alter the phase-state of the monolayer from liquid-like to crystalline. The chemical properties of the monolayer were controlled by varying the chemical composition of the alkyltrichlorosilanes used. Terminal functionalities included -CH3, -CF3, -COOH, -SO3H and -(CH2CH2O)4OH. Surface derivatization was verified with static contact angle measurements and X-ray photoelectron spectroscopy. Blood compatibility was evaluated using a canine ex vivo arterio-venous series shunt model. Surfaces grafted with hydrophobic head groups such as -CH3 and -CF3 were significantly less thrombogenic than the surfaces composed of ionic head groups such as -COOH and -SO3H. Surfaces enriched in -(CH2CH2O)4OH had an intermediate thrombogenicity. Silastic pump grade tubing and polyethylene tubing, used as controls, were found to be the least thrombogenic of all the surfaces tested.

Effect of saline exposure on the surface and bulk properties of medical grade silicone elastomers.

Medical-grade silicone elastomers were subjected to accelerated aging in saline to verify the hydrolytic stability of the elastomer. Tensile strength, elongation at break, and the elastomer stress measured at 100% or 200% elongation did not change significantly for peroxide-cured sheeting aged in 37 degrees C or 100 degrees C saline for 45 h. Under similar condition, hydrosilylation cured sheeting behaved similarly; however, increases in stresses measured at 100% and 200% elongation were observed after the first hour of treatment. After the first hour, the physical properties remained relatively constant. On either elastomer, initial liquid drop advancing contact angles for water ranged from 110 degrees to 115 degrees, and in no case was a change of > 6 degrees observed as a result of aging in saline for 45 h at temperatures up to 97 degrees C. The high advancing angles indicated that the surface remained largely hydrophobic. Initial liquid drop receding contact angles ranged from 48 degrees to 64 degrees, with receding contact angles being more sensitive to accelerated aging, in one case decreasing to 14 degrees. Similar decreases in receding contact angle were observed on polyethylene subjected to the same accelerated aging conditions. Decreases in receding contact angle were not considered to be indicative of extensive hydrolysis. The observed contact angle phenomena are consistent with current views of contact angle hysteresis being caused by surface heterogeneity. There was no evidence of significant surface or bulk siloxane hydrolysis under these accelerated aging conditions.

Macroscopic evidence of the effect of interfacial slippage on adhesion.

The adhesion strengths of a viscoelastic adhesive were measured on various substrates that were prepared by grafting silanes bearing organic functional groups to silicon wafers. Conventional theories predict that adhesion should be proportional to the surface free energy of the substrate; but adhesion on a fluorocarbon surface was significantly greater than on some of the hydrocarbon surfaces, although the fluorocarbon surface has the lowest surface free energy. This result could be explained by invoking a model of adhesion based on the slippage of the adhesive at the interface.

Surface and blood-contacting properties of alkylsiloxane monolayers supported on silicone rubber.

Self-assembled monolayers of alkylsiloxanes supported on polydimethyl siloxane (PDMS) rubber were used as model systems to study the relation between blood compatibility and surface chemistry. The inner lumen of PDMS tubes was first treated with an oxygen plasma. The resultant oxidized surfaces were postderivatized by reacting them with alkyltrichlorosilanes to form the monolayer films. The chemical properties of the monolayers were controlled by varying the head-group chemical compositions. Surface derivatization was verified using variable-angle X-ray photoelectron spectroscopy (XPS or ESCA). Blood compatibility was evaluated using a canine ex vivo arteriovenous series shunt model. Surfaces grafted with hydrophobic head-groups as -CH3 and -CF3 had significantly lower platelet and fibrinogen deposition than the surfaces composed of hydrophilic groups such as -CO2CH3, -(CH2CH2O)3COCH3, and -(OCH2CH2)3OH.

How to make water run uphill.

A surface having a spatial gradient in its surface free energy was capable of causing drops of water placed on it to move uphill. This motion was the result of an imbalance in the forces due to surface tension acting on the liquid-solid contact line on the two opposite sides ("uphill" or "downhill") of the drop. The required gradient in surface free energy was generated on the surface of a polished silicon wafer by exposing it to the diffusing front of a vapor of decyltrichlorosilane, Cl(3)Si(CH(2))(9)CH(3). The resulting surface displayed a gradient of hydrophobicity (with the contact angle of water changing from 97 degrees to 25 degrees ) over a distance of 1 centimeter. When the wafer was tilted from the horizontal plane by 15 degrees , with the hydrophobic end lower than the hydrophilic, and a drop of water (1 to 2 microliters) was placed at the hydrophobic end, the drop moved toward the hydrophilic end with an average velocity of approximately 1 to 2 millimeters per second. In order for the drop to move, the hysteresis in contact angle on the surface had to be low (

Correlation between surface free energy and surface constitution.

Self-assembled monolayers (SAMs) of alkylsiloxanes on elastomeric PDMS (polydimethylsiloxane) were used as model systems to study interactions between surfaces. Surface free energies (gammasv) of these chemically modified surfaces were estimated by measuring the deformations that resulted from the contact between small semispherical lenses and flat sheets of the elastomer under controlled loads. The measured surface free energies correlated with the surface chemical compositions of the SAMs and were commensurate with the values estimated from the measurements of contact angles. This study provides direct experimental evidence for the validity of estimates of the surface free energies of low-energy solids obtained from contact angles.

Contact adhesion of thin gold films on elastomeric supports: cold welding under ambient conditions.

Thin gold films placed in contact on compliant elastomeric poly(dimethylsiloxane) supports weld together. This ;;cold welding'' is remarkable both for the low loads required and for the fact that it occurs under ambient laboratory conditions, conditions in which the gold surfaces are covered with films of weakly adsorbed organic impurities. These impurities are probably displaced laterally during the welding. Welding can be prevented by the presence of a self-assembled gold(I) alkylthiolate monolayer on the gold surfaces. The welded contacts have low electrical resistivity and can be made thin enough to transmit light. This system is a promising one with which to study interaction between interfaces.