Effect of salt on the compression of polyelectrolyte brushes in a theta solvent

Classical strong-stretching theory (SST) predicts that, as opposing polyelectrolyte brushes are compressed together in a salt-free theta solvent, they contract so as to maintain a finite polymer-free gap, which offers a potential explanation for the ultra-low frictional forces observed in experiments despite the application of large normal forces. However, the SST ignores chain fluctuations, which would tend to close the gap resulting in physical contact and in turn significant friction. In a preceding study, we examined the effect of fluctuations using self-consistent field theory (SCFT) and illustrated that high normal forces can still be applied before the gap is destroyed. We now look at the effect of adding salt. It is found to reduce the long-range interaction between the brushes but has little effect on the short-range part, provided the concentration does not enter the salted-brush regime. Consequently, the maximum normal force between two planar brushes at the point of contact is remarkably unaffected by salt. For the crossed-cylinder geometry commonly used in experiments, however, there is a gradual reduction because in this case the long-range part of the interaction contributes to the maximum normal force.     

Friction and normal forces of model friction modifier additives in simulations of boundary lubrication

ABSTRACT

Interaction forces between solid surfaces are often mitigated by adsorbed molecules that control normal and friction forces at nanoscale separations. Molecular dynamics simulations were conducted of opposing semi-ordered monolayers of united-atom chains on sliding surfaces to relate friction and normal forces to imposed sliding velocity and inter-surface separation. Practical examples include adsorbed friction-modifier molecules in automatic transmission fluids. Friction scenarios in the simulations had zero, one, or two fluid layers trapped between adsorbed monolayers. Sliding friction forces increased with sliding velocity at each stable separation. Lower normal forces were obtained than in most previous nanotribology molecular simulations and were relatively independent of sliding speed. Distinguishing average frictional force from its fluctuations showed the importance of system size. Uniform velocities were obtained in the sliding direction across each adsorbed film, with a gradient across the gap containing trapped fluid. The calculated friction stress was consistent with measurements reported using a surface forces apparatus, indicating that drag between an adsorbed layer and trapped fluid can account sufficiently for sliding friction in friction modifier systems. An example is shown in which changes in molecular organisation parallel to the surface led to a large change in normal force but no change in friction force.     

Sliding friction with polymer brushes

Using high-resolution shear force measurements, we examine in detail the frictional drag between rubbing surfaces bearing end-tethered polymeric surfactants (brushes). The drag attains a maximum on initial motion, attributed to elastic stretching of the chains, which falls by a cascade of relaxations to a value characteristic of kinetic friction. This has a very weak velocity dependence, attributed to chain moieties dragging within a self-regulating, mutual interpenetration zone. When sliding stops, the shear stress across the polymer layers decays logarithmically with time, consistent with the relaxation of a network of dangling ends.     

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.     

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.     

Departures from Amonton's law of friction

The method of transition from light friction (rolling) to heavy friction (sliding) is used for analyzing the principal departure from Amonton's law (force of sliding friction T proportional to the normal pressure force N) for several metal — nonmetal pairs when the sliding time t approaches zero. It appears that the departure mode is, under these conditions, the same for all pairs which have been tested here. Experimental and theoretical evidence is given to prove that all other modes of departure from Amonton's law represent consequences of changes in the rubbing surfaces which occur during sliding and that, therefore, such departures will appear only after a long enough period of sliding.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 94–98, November, 1974.     

载荷对壁虎刚毛束的摩擦各向异性特性影响的实验研究

用离体壁虎刚毛阵列在自制微黏附摩擦测试台上对预加载荷对刚毛摩擦与黏着的各向异性特性的影响进行了实验研究.实验结果表明,在逆壁虎刚毛自然弯曲方向卷出实现脱附时, 刚毛所受摩擦力与法向力成正比,摩擦系数为0.6;沿顺刚毛自然弯曲方向卷入实现黏附时, 随预载荷增加摩擦力增加,法向力由黏附力变为斥力.在同等预载荷下,卷入方向的摩擦力是卷出方向的2倍以上. 本文提出了摩擦各向异性特征参数,对壁虎刚毛的黏着与摩擦各向异性进行了定量表征, 这种特性是由刚毛的弯曲及多等级结构决定的. 关键词： 壁虎刚毛 黏着 摩擦 各向异性     

An integrated simulation and statistical technique for?investigating the effect of interpenetration polymer brushes in a good solvent

This study presents a novel approach for analyzing the interaction between two parallel surfaces grafted with polymer brushes in a good solvent. In the proposed approach, MD simulations are performed to establish the mean brush height and the standard deviation of the brush height distribution for a given value of the surface separation. The corresponding probability density function (PDF) of the brush height is then determined both with and without the assumption of a brush interpenetration effect, respectively, and a statistical technique is applied to compute the corresponding interaction free energy per unit area of the grafted substrates. Finally, the Derjaguin approximation is employed to determine the corresponding value of the interaction force between the two surfaces. The results obtained for the interaction free energy and interaction force are compared with those derived using the Alexander and de Gennes (AdG) model and the Milner, Witten and Cates (MWC) model, respectively. The value of the normalized interaction free energy computed using the present method is higher than that obtained from the AdG and MWC models at larger surface separations when the brush interpenetration effect is ignored. However, the results obtained by the current method for the interaction force are found to be in better agreement with the experimental data than those obtained using the AdG or MWC models. The enhanced performance of the proposed method is attributed primarily to the use of an adaptive non-Gaussian PDF of the brush height to model the effects of brush interpenetration and fluctuations in the brush conformation at different distances from the grafting plane.     

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.     

Casimir force in dense confined electrolytes

ABSTRACT

Understanding the force between charged surfaces immersed in an electrolyte solution is a classic problem in soft matter and liquid-state theory. Recent experiments showed that the force decays exponentially but the characteristic decay length in a concentrated electrolyte is significantly larger than what liquid-state theories predict based on analysing correlation functions in the bulk electrolyte. Inspired by the classical Casimir effect, we consider an additional mechanism for force generation, namely the confinement of density fluctuations in the electrolyte by the walls. We show analytically within the random phase approximation, which assumes the ions to be point charges, that this fluctuation-induced force is attractive and also decays exponentially, albeit with a decay length that is half of the bulk correlation length. These predictions change dramatically when excluded volume effects are accounted for within the mean spherical approximation. At high ion concentrations the Casimir force is found to be exponentially damped oscillatory as a function of the distance between the confining surfaces. Our analysis does not resolve the riddle of the anomalously long screening length observed in experiments, but suggests that the Casimir force due to mode restriction in density fluctuations could be an hitherto under-appreciated source of surface–surface interaction.     

What does friction really depend on? Robust governing parameters in contact mechanics and friction

It is known that the coefficient of friction generally depends on a large number of system and loading parameters. Already Coulomb presented experimental evidence that the static coefficient of friction may depend on time, on normal force, on the contact size, on the nature of contacting materials, and on the presence of intermediate lubricant layers. For the sliding coefficient of friction, he observed the dependence on the sliding velocity as well as the force and size dependencies. Later research has shown that the friction coefficient is very sensitive to the presence of oscillations (including self-excited vibrations). In spite of the practical importance of the problem, no generalized laws of friction or empirical procedures for measuring and representing the law of friction have been developed so far, which included at least the following four parameters: contacting body velocity, normal force, shape (and thus implicitly size), and time. In the present paper, we discuss the question of how the dimension of space of governing parameters can be reduced and if a small set of “robust governing parameters” of friction can be identified. We argue that one of such robust governing parameters is the indentation depth (or relative approach) of contacting bodies and discuss further candidates for the role of robust governing parameters.     

Texture-induced modulations of friction force: the fingerprint effect

Modulations of the friction force in dry solid friction are usually attributed to macroscopic stick-slip instabilities. Here we show that a distinct, quasistatic mechanism can also lead to nearly periodic force oscillations during sliding contact between an elastomer patterned with parallel grooves, and abraded glass slides. The dominant oscillation frequency is set by the ratio between the sliding velocity and the grooves period. A model is derived which quantitatively captures the dependence of the force modulations amplitude with the normal load, the grooves period, and the slides roughness characteristics. The model's main ingredient is the nonlinearity of the friction law. Since such nonlinearity is ubiquitous for soft solids, this "fingerprint effect" should be relevant to a large class of frictional configurations and have important consequences in human digital touch.     

Dynamic analysis of a rectangular plate subjected to multiple forces moving along a circular path

A multi-degree-of-freedom (m.d.o.f.) system excited by a rough moving surface has been developed to study friction-induced oscillations. The normal degrees of freedom allow for oscillatory normal forces, while the normal-tangential coupling of friction produces parametric excitation in the slipping equations of motion. After a modal change of variables, first order averaging has been used to produce a set of autonomous equations of motion. Eigenvalue analysis of the averaged equations has produced stability predictions for the steady sliding position. Numerical integration of the original system of equations has verified the existence of locally unstable oscillations for a system excited by a rough surface input. The combination of velocity-dependent friction and a harmonically varying normal force have been shown to produce large-amplitude oscillations, in some cases leading to stick-slip responses.     

Tribological properties of silicate materials on nano and microscale

We studied the friction properties of four model silicate materials at the nanoscale and microscale. From nanotribology, we characterized the tribological properties at single asperity contact scale and from microtribology, we characterized the tribological properties at multi asperity contact scale. First, for each material we measured chemical composition by XPS, Young's modulus by acoustical microscopy and roughness σ by atomic force microscopy (AFM). Second, we measured the nanofriction coefficients with an AFM and the microfriction coefficients with a ball probe tribometer, for three hardnesses of the ball probe. We identified one friction mechanism at the nanoscale (sliding friction) and two friction mechanisms at the microscale (sliding friction and yielding friction). Comparison of the nano and microfriction coefficients at the same sliding friction regime shown, that the tribological properties of these materials didn’t depend on roughness.     

An investigation of nanoscale tribological characteristics under different interaction forces

The present study employs a Finite Element Method (FEM) atomic approach to investigate the nanoscale mechanisms of sliding friction. The current investigation chooses diamond-like carbon as the hard material, and copper as the soft material. The atomic configurations following sliding under non-interactive, attractive, and repulsive interaction forces are observed for soft-to-soft, hard-to-soft, and hard-to-hard sliding systems. The relationships between the normal force, the friction force, and the sliding distance are discussed. The current simulation results exhibit a similar trend with the findings of previous studies using molecular dynamics approach.     

Observed transition from linear to non-linear friction-load behavior using a lateral force microscope

The most commonly observed friction behavior for sliding systems is that described by Amontons laws of friction. In this case, sliding friction is independent of the gross or apparent area of contact between the materials and a linear function of the applied normal load, where the constant of proportionality is called the friction coefficient. However, for dry sliding solids in contact via a single-asperity junction, Amontons (linear) friction-load behavior is not strictly relevant. In experiments measuring sliding friction between a silicon tip and a quartz surface using an atomic force microscope (AFM), a transition from linear to non-linear friction-load behavior has been observed. This is proposed to result from a nanoscale ‘conditioning’ of a multiple-contact tip-surface interface to form a single-asperity contact.     

Prediction of dynamic friction forces in spur gears using alternate sliding friction formulations

In this communication, several sliding friction formulations used in spur gear dynamics are examined and compared in terms of the predictions of interfacial friction forces and off-line-of-action motions. Competing friction formulations include Coulomb models with time-varying friction coefficients and empirical expressions based on elasto-hydrodynamic and/or boundary lubrication regime principles. Predicted results compare well with friction force measurements.     

Polymer-brush lubrication in the limit of strong compression

By means of molecular dynamics simulations we demonstrate power laws for macroscopic transport properties of strongly compressed polymer-brush bilayers to stationary shear motion beyond the Newtonian response. The corresponding exponents are derived from a recently developed scaling theory, where the interpenetration between the brushes is taken as the relevant length scale. This allows to predict the dependence of the critical shear rate, which separates linear and non-linear behavior, on compression and molecular parameters of the bilayer. We present scaling plots for chain extension (R , viscosity (h \eta , and shear force (F over a wide range of Weissenberg numbers, W . In agreement with our theory, the simulation reveals simple power laws, R ∼ W ^0.53 , h \eta ∼ W ^-0.46 , and F ∼ W ^0.54 , for the non-Newtonian regime.     

Nature of soft vibrational modes in metallic glasses

A general theory of vibrational excitations in metallic glasses is presented, based on the disclination model of the structure of solids with local icosahedral symmetry. The representation of nonorthogonal plane waves is used, which allows one to separate the diagonal terms in the Hamiltonian, and also the terms describing scattering of these waves by fluctuations of the density and the force constants, and by topological structure fluctuations. We have derived and solved the Dyson equation for the Green’s function. We have obtained an analytical expression for the density of vibrational states of the glass. The nature of the soft vibrational modes is discussed. It is shown that these modes are resonant modes, whose presence is due to the fluctuations of the density and the force constants. Special attention is given to the role of forward scattering and the nature of the spatial variation in the amplitude of the given modes. Fiz. Tverd. Tela (St. Petersburg) 41, 372–379 (March 1999)     

Two-dimensional friction oscillator: group-preserving scheme and handy formulae

With vibration isolation of buildings and turbomachinery blades in mind, we study the dynamic behaviour of a single-mass two-degree-of-freedom oscillator with dry friction damper, viscous damper and elastic spring connected in parallel. The mass is mounted on an elastic supporting plate allowing movement in two directions on a plane. We formulate a multi-dimensional friction model, from which the sliding conditions and the sticking conditions of the mass are derived. For calculations we develop a group-preserving scheme, which preserves the projective proper orthochronous Lorentz group PSO_o(2,1) symmetry of the model in the sliding phase so as to satisfy automatically the sliding conditions at each time step without iteration at all. The oscillator is then subjected to simple harmonic excitations, and the responses are displayed. According to the simple harmonic balance method together with a circular orbit assumption on displacements, we derive closed-form formulae for handily estimating the steady state responses, which are then compared with the results calculated by the group-preserving scheme to confirm the applicability of the formulae. We also derive formulae specifically for a two-dimensional friction oscillator with rigid base support, which include an exact formula of the magnification factor and a simple formula for estimating the minimum driving force amplitude (or the maximum friction force bound) to avoid sticking.