Detachment of stretched viscoelastic fibrils

New experimental results are presented about the final stage of failure of soft viscoelastic adhesives. A microscopic view of the detachment of the adhesive shows that after cavity growth and expansion, well adhered soft adhesives form a network of fibrils connected to expanded contacting feet which fail via a sliding mechanism, sensitive to interfacial shear stresses rather than by a fracture mechanism as sometimes suggested in earlier work. A mechanical model of this stretching and sliding failure phenomenon is presented which treats the fibril as a nonlinear elastic or viscoelastic rod and the foot as an elastic layer subject to a friction force proportional to the local displacement rate. The force on the stretched rod drives the sliding of the foot against the substrate. The main experimental parameter controlling the failure strain and stress during the sliding process is identified by the model as the normalized probe pull speed, which also depends on the magnitude of the friction and PSA modulus. In addition, the material properties, viscoelasticity and finite extensibility of the polymer chains, are shown to have an important effect on both the details of the sliding process and the ultimate failure strain and stress. Electronic supplementary material Appendix B is only available in electronic form at and are accessible for authorised users.     

Rubber friction on smooth surfaces

We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped form, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.     

摩擦导致的聚合物表层微观结构改变

应用大规模分子动力学方法, 模拟了锥形探头在非晶态聚合物薄膜表面的滑动摩擦过程, 研究了摩擦导致的聚合物薄膜表层微观结构改变, 以及探头与基体间黏着作用、滑动速度和分子链长度对基体表层微观结构改变的影响. 当探头与基体之间为黏着作用时, 摩擦导致基体表面滑痕区域的键取向沿滑动方向重新取向, 导致表层分子链回转半径沿滑动方向伸长, 并且这些表层微观结构的改变程度随滑动速度的减小而增大. 在摩擦导致结构改变的过程中, 链端单体和链中单体的贡献作用不同, 形成了不同的分子链拉伸变形机制. 当样本缠结度较大或探头滑动速度较小时, 相比于链中单体, 探头对链端单体的拖曳作用使更多分子链发生拉伸变形. 研究还发现, 在探头与聚合物薄膜系统中, 使薄膜表层微观结构发生改变是摩擦能量耗散的重要途径.     

Effect of correlated temperature fluctuations on the phase dynamics in an ultrathin lubricant film

The melting of an ultrathin lubricant film at friction between atomically smooth surfaces is studied with allowance for fluctuations of its temperature, which are described by the Ornstein-Uhlenbeck process. The behavior of the most probable types of shear stresses arising in the lubricant is considered, and phase diagrams for second-and first-order phase transformations (the melting of an amorphous lubricant and that of a crystalline lubricant, respectively) are constructed. It is shown that, in the former case, lubricant temperature fluctuations lead to the formation of a stick-slip friction domain separating the domains of dry and sliding friction, which is typical of first-order transitions. In the latter case, three domains of stick-slip friction arise, which mark the transitions between dry friction and metastable and stable sliding friction. As the time of correlation of lubricant temperature fluctuations gets longer, the temperature of rubbing surfaces rises to the point where sliding friction sets in.     

First-order phase transition between the liquidlike and solidlike structures of a boundary lubricant

A thermodynamic model for characterization of the first-order phase transition between the structural states of a boundary lubricant is suggested. It is shown that melting of the lubricant is due both to a rise in its temperature and to shear experienced by friction surfaces when elastic strains (stresses) exceed a critical value. A phase diagram with regions of dry and sliding friction is constructed. Using a mechanical analogue of the tribological system, the dependence of the friction force on the lubricant temperature and relative shear rate of the friction surfaces is analyzed. The observed conditions of stick-slip friction, which is the main reason for friction parts wear, are described. Reasons for stick-slip friction are revealed.     

Contact mechanics and rubber friction for randomly rough surfaces with anisotropic statistical properties

In this paper we extend the theory of contact mechanics and rubber friction developed by one of us (B.N.J. Persson, J. Chem. Phys. 115, 3840 (2001)) to the case of surfaces with anisotropic surface roughness. As an application we calculate the viscoelastic contribution to the rubber friction. We show that the friction coefficient may depend significantly on the sliding direction, while the area of contact depends weakly on the sliding direction. We have carried out experiments for rubber blocks sliding on unidirectionally polished steel surfaces. The experimental data are in a good qualitative agreement with the theory.     

Effects of non-flat contact and interference on self-assembled monolayers under sliding friction

The nanotribology mechanism of alkanethiol self-assembled monolayers (SAM) chemisorbed on a gold surface under a non-flat contact by a tilt plane was studied using molecular dynamics (MD) simulations. The molecular trajectories, tilt angles, normal forces, shear forces, and frictional coefficient of the SAM were evaluated during the friction and relaxation processes for various parameters, including the tilt angle of the slider, interference magnitude, and SAM length. At the nanoscale, the magnitude of interface interactional forces is strongly dependent on the magnitude of the contact area, not on the surface geometry. The contact area and the exerted normal force of the SAM increase with decreasing the tilt angle of the slider at the same contact interference. In contrast, the periods in both normal force and shear force are gradually delayed as the tilt angle of the slider increases. Once the contact interference increases, the normal force and shear force increase together. During the sliding friction process with a smaller tilt slider angle, SAM molecules can maintain a better collective ordered structure. Short SAM molecules are more sensitive to a compressive loading and react to a larger normal force under the same contact interference due to the deformation of a larger tilt angle and decrease in chain length. The friction coefficient of SAM is significantly more dependent on the tilt angle of the slider than the contact interference.     

Molecular-dynamics simulations with explicit hydrodynamics II: On the collision of polymers with molecular obstacles

We present a study of the dynamics of single polymers colliding with molecular obstacles using Molecular-dynamics simulations. In concert with these simulations we present a generalized polymer-obstacle collision model which is applicable to a number of collision scenarios. The work focusses on three specific problems: i) a polymer driven by an external force colliding with a fixed microscopic post; ii) a polymer driven by a (plug-like) fluid flow colliding with a fixed microscopic post; and iii) a polymer driven by an external force colliding with a free polymer. In all three cases, we present a study of the length-dependent dynamics of the polymers involved. The simulation results are compared with calculations based on our generalized collision model. The generalized model yields analytical results in the first two instances (cases i) and ii)), while in the polymer-polymer collision example (case iii)) we obtain a series solution for the system dynamics. For the case of a polymer-polymer collision we find that a distinct V-shaped state exists as seen in experimental systems, though normally associated with collisions with multiple polymers. We suggest that this V-shaped state occurs due to an effective hydrodynamic counter flow generated by a net translational motion of the two-chain system.     

Non-Amontons behavior of friction in single contacts

We report on the frictional properties of a single contact between a glassy polymer lens and a flat silica substrate covered either by a disordered or by a self-assembled alkylsilane monolayer. We find that, in contrast to a widely spread belief, the Amontons proportionality between frictional and normal stresses does not hold. Besides, we observe that the velocity dependence of the sliding stress is strongly sensitive to the structure of the silane layer. Analysis of the frictional rheology observed on both disordered and self-assembled monolayers suggests that dissipation is controlled by the plasticity of a glass-like interfacial layer in the former case, and by pinning of polymer chains on the substrate in the latter one.     

Polymer confinement and bacterial gliding motility

Cyanobacteria and myxobacteria use slime secretion for gliding motility over surfaces. The slime is produced by the nozzle-like pores located on the bacteria surface. To understand the mechanism of gliding motion and its relation to slime polymerization, we have performed molecular dynamics simulations of a molecular nozzle with growing inside polymer chains. These simulations show that the compression of polymer chains inside the nozzle is a driving force for propulsion. There is a linear relationship between the average nozzle velocity and the chain polymerization rate with a proportionality coefficient dependent on the geometric characteristics of the nozzle such as its length and friction coefficient. This minimal model of the molecular engine was used to explain the gliding motion of bacteria over surfaces.     

碳纳米管-聚乙烯复合材料界面力学特性分析

本文采用分子动力学模拟办法对碳纳米管-聚乙烯复合材料的界面力学特性进行了模拟和分析. 通过对单壁碳纳米管从无定形聚乙烯中抽出过程进行模拟, 研究了界面剪切应力随碳管滑移速度、聚乙烯分子链长和碳纳米管管径之间的变化关系, 并对界面的滑移机理进行了讨论. 模拟结果发现, 随着聚合物分子链长的增加, 界面临界剪切应力有显著增大, 而滑移剪切应力略显增加; 界面临界剪切应力和滑移剪切应力随着碳纳米管管径的增大而明显增加. 本文同时对界面应力的变化机理进行了模拟和讨论.     

Interrupted shear of granular media

The response of a granular material during a stop-and-go shear experiment is investigated using an annular shear cell and silicagel powders of different particle sizes. The experimental results are examined on the basis of the Dieterich-Rice-Ruina model for solid friction. In addition to making this analogy with solid friction, we describe a new instability that is observed when restarting shear, where the powder bed is found to slip and compact for short hold times but only dilates for long hold times. The minimum hold time to restore a non-slip behaviour has been investigated for different size particles and normal loadings. The observed dependencies show analogies between this behaviour and the sliding rearrangements seen above the stick-slip threshold.     

Dewetting of thin polymer films

We study the dewetting of thin polymer films deposited on slippery substrate. Recent experiments on these systems have revealed many unexpected features. We develop here a model that takes into account the rheological properties of polymer melts, focussing on two dewetting geometries (the receding of a straight edge, and the opening of a hole). We show that the friction law associated with the slippage between the film and the substrate has a direct influence on the dewetting dynamic. In addition, we demonstrate that residual stresses, which can be stored in the films due to their viscoelasticity, are a source of destabilization for polymer films, and accelerate the dewetting process.     

Stochastic theory of ultrathin lubricant film melting in the stick-slip regime

Melting of an ultrathin lubricant film under friction between atomically smooth surfaces is studied in terms of the Lorentz model. Additive noise associated with shear stresses and strains, as well as with film temperature, is introduced, and a phase diagram is constructed where the noise intensity of the film temperature and the temperature of rubbing surfaces define the domains of sliding, dry, and stick-slip friction. Conditions are found under which stick-slip friction proceeds in the intermittent regime, which is characteristic of selforganized criticality. The stress self-similar distribution, which is provided by temperature fluctuations, is represented with allowance for nonlinear relaxation of stresses and fractional feedbacks in the Lorentz system. Such a fractional scheme is used to construct a phase diagram separating out different types of friction. Based on the study of the fractional Fokker-Planck equation, the conclusion is drawn that stick-slip friction corresponds to the subdiffusion process.     

Generalization of a nonlinear friction relation for a dimer sliding on a periodic substrate

An atomic cluster moving along a solid surface can undergo dissipation of its translational energy through a direct mode, involving the coupling of the center-of-mass motion to thermal excitations of the substrate, and an indirect mode, due to damping of the internal motion of the cluster, to which the center-of-mass motion can be coupled as a result of surface potential. Focussing only on the less well understood indirect mode, on the basis of numerical solutions, we present, departures from a recently reported simple relationship between the force and velocity of nonlinear friction. A generalization of the analytic considerations that earlier led to that relationship is carried out and shown to explain the departures satisfactorily. Our generalization treats for the system considered (dimer sliding over a periodic substrate) the complete dependence on several of the key parameters, specifically internal dissipation, natural frequency, substrate corrugation, and length ratio. Further predictions from our generalizations are found to agree with new simulations. The system analyzed is relevant to nanostructures moving over crystal surfaces.     

Local friction at a sliding interface between an elastomer and a rigid spherical probe

This paper reports on spatially resolved measurements of the shear stress distribution at a frictional interface between a flat rubber substrate and a glass lens. Silicone rubber specimens marked close to their surface by a colored pattern have been prepared in order to measure the surface displacement field induced by the steady-state friction of the spherical probe. The deconvolution of this displacement field then provides the actual shear stress distribution at the contact interface. When a smooth glass lens is used, a nearly constant shear stress is achieved within the contact. On the other hand, a bell-shaped shear stress distribution is obtained with rough lenses. These first results suggest that simple notions of real contact area and constant interface shear stress cannot account for the observed changes in local friction when roughness is varied.     

Optimization of the surface texture for silicon carbide sliding in water

Surface texturing has been recognized as an effective means to improve the tribological performances of sliding surfaces. Usually, generation additional hydrodynamic pressure to increase the load carrying capacity is regarded as the most significant effect of surface texture. In the case of silicon carbide sliding against identical material in water, the experimental results indicate that surface texture is also helpful to improve the running-in progress to smooth the contact surfaces, showing another reason to result in low friction. Based on the consideration of enhancing the generation of hydrodynamic pressure and improving running-in progress, a surface texture pattern, which was combined with large (circle, 350 μm in diameter) and small (rectangular, 40 μm in length) dimples, was designed to maximize the texture effect on the load carrying capacity of SiC surfaces sliding in water. The friction coefficient of such textured surface was evaluated and compared with that of untextured and those only with large or small dimples only. The friction reduction mechanisms of the patterns with different dimples in size are discussed.     

Ice internal friction: Standard theoretical perspectives on friction codified,adapted for the unusual rheology of ice,and unified

Sea ice contains flaws including frictional contacts. We aim to describe quantitatively the mechanics of those contacts, providing local physics for geophysical models. With a focus on the internal friction of ice, we review standard micro-mechanical models of friction. The solid's deformation under normal load may be ductile or elastic. The shear failure of the contact may be by ductile flow, brittle fracture, or melting and hydrodynamic lubrication. Combinations of these give a total of six rheological models. When the material under study is ice, several of the rheological parameters in the standard models are not constant, but depend on the temperature of the bulk, on the normal stress under which samples are pressed together, or on the sliding velocity and acceleration. This has the effect of making the shear stress required for sliding dependent on sliding velocity, acceleration, and temperature. In some cases, it also perturbs the exponent in the normal-stress dependence of that shear stress away from the value that applies to most materials.

We unify the models by a principle of maximum displacement for normal deformation, and of minimum stress for shear failure, reducing the controversy over the mechanism of internal friction in ice to the choice of values of four parameters in a single model. The four parameters represent, for a typical asperity contact, the sliding distance required to expel melt-water, the sliding distance required to break contact, the normal strain in the asperity, and the thickness of any ductile shear zone.     

Gels at interfaces

We discuss the adsorption of polymer gels on flat surfaces. Even in cases of complete wetting where the spreading power S is positive and where an equivalent liquid would spread, the elastic stresses due to the gel deformation upon adsorption oppose the spreading. The competition between elasticity characterized by the bulk shear modulus G and capillarity characterized by the spreading power S defines a typical length scale ℓ = S/G for the deformation in the gel. For loose gels ℓ can be of the order of 1 μm. Macroscopic gels larger than ℓ deform only at their edges over a region of size ℓ. Microscopic gels smaller than ℓ show a finite deformation despite the elastic stresses. The elastic stresses limit the spreading of the polymer, but solvent can be sucked out of a swollen gel by wetting the surface. The thin solvent film can extend rather far from the gel edge and carry solvent. We calculate the kinetics of the solvent film formation and of the solvent transfer from a more swollen gel to a less swollen gel. Received 16 July 2001     

Elastic properties of polymer networks with sliding junctions

This paper proposes simple models of polymer networks with sliding junctions for molecular simulation and reports the main results obtained by Brownian dynamics on the elastic properties of networks with tri-functional sliding junctions. The stress-strain relation for isotropic swelling and uniaxial deformation are obtained and compared with those of the conventional chemical gels. We find that mobility and distribution of sliding junctions along the polymer chains drastically change with deformation, and lead to new profiles of the stress. We also find that sliding junctions aggregate by deformation, resulting in the decrease in the number of elastically effective chains.