Velocity dependence of friction

An example of the velocity dependence of friction is given in Figure 5 for a boundary lubricant confined between two incommensurate surfaces.25 For the given choice of normal pressure and temperature, one finds four decades in sliding velocity for which Eq. [7] provides a reasonably accurate description. 

Fig. 13 Velocity dependence of frictional stress for a soft gel sliding on a smooth adhesive solid substrate. The result is based on the molecular picture in Fig. 12, which considers the thermal fluctuation of adsorption and desorption of the polymer chain, (a) The elastic term of the frictional stress of a gel. See text for a description of parameter u. (b) Summation of the elastic term and the viscous term. When v -C Vf, the characteristic polymer adsorption velocity, the elastic term is dominant. At v 2> the viscose term is dominant. Therefore, transition from elastic friction to lubrication occurs at the sliding velocity characterized by the polymer chain dynamics. (Modified from figure 1 in [65])...

I feel that surface free energy is not a good parameter to correlate with surface friction. Surface free energy may be related to cohesive energy density. There is too much data which contradicts this, e.g. (1) static/dynamic friction, (2) spin effects, (3) temperature and velocity dependence of friction. 

Friction force microscopy (FFM) Velocity dependence of frictional (g)... 

Figure 4. Scan velocity dependence of friction at discrete humidities on amorphous...

Figure 8. Time-temperature superposition analysis of frictional data collected on thin PMMA. (a) Temperature dependence offriction at four scan velocities (b) same data inverted, i.e. scan-velocity dependence of friction at multiple temperatures (c) master curve of same data sets as in (b), but shifted by variable multiplicative factors af, (d) plot of shift factors ar versus inverse temperature, with linear fit.

Figure 57 AFM height (a) and friction (b) images on a semicrystalline PVA surface, (c) Comparison of RH dependence of friction on predominantiy amorphous (1) versus highly crystalline (2) surface regions in (b). (d) Scan velocity dependence of friction versus RH on (1). Reprinted with permission from Haugstad, G. Hammerschmidt, J.A. Gladfelter, W. L. In Interfacial Properties on the Submicron Scale, Frommer, J. Ovemey, R. M. Eds. ACS Books Washington, DC, 200f Vol. 781, p 230. Copyright 2005 American Chemical Society.

The dependence of friction on sliding velocity is more complicated. Apparent stick-slip motions between SAM covered mica surfaces were observed at the low velocity region, which would disappear when the sliding velocity excesses a certain threshold [35]. In AFM experiments when the tip scanned over the monolayers at low speeds, friction force was reported to increase with the logarithm of the velocity, which is similar to that observed when the tip scans on smooth substrates. This is interpreted in terms of thermal activation that results in depinning of interfacial atoms in case that the potential barrier becomes small [36]. 

The discussion begins below with an overview of proposed energy dissipation mechanisms that lead to friction. This is followed by brief discussions of phenomenological friction laws that describe the dependence of friction upon normal load and sliding velocity. The dependence of friction on the symmetry of the surfaces that are in contact is discussed later. 

Figure 5 Typical velocity relationship of kinetic friction for a sliding contact in which friction is from adsorbed layers confined between two incommensurate walls. The kinetic friction F is normalized by the static friction Fs. At extremely small velocities v, the confined layer is close to thermal equilibrium and, consequently, F is linear in v, as to be expected from linear response theory. In an intermediate velocity regime, the velocity dependence of F is logarithmic. Instabilities or pops of the atoms can be thermally activated. At large velocities, the surface moves too quickly for thermal effects to play a role. Time-temperature superposition could be applied. All data were scaled to one reference temperature. Reprinted with permission from Ref. 25. 

To avoid stick-slip, one should try to make the spring constant high enough (using stiff materials and stable constructions). It can be shown, that stick-slip may also arise from the velocity dependence of the friction coefficient [460], When the friction coefficient decreases with sliding velocity, stick-slip is amplified. When the friction coefficient increases with velocity, stick-slip is damped out. The former is usually the case at low speeds, certainly for the transition from static to dynamic friction, whereas the latter prevails usually at high velocity. 

The validity of Coulomb s law has been verified also on the nanoscale Zworner et al. [484] showed that, for different carbon compound surfaces, friction does not depend on sliding velocity in the range between 0.1 /xm/s and up to 24 /xm/s. At low speeds, a weak (logarithmic) dependence of friction on speed was observed by Gnecco et al. [485] on a NaCl(lOO) surface and by Bennewitz et al. [486] on a Cu (111) surface. This can be modeled when taking into account thermal activation of the irreversible jumps in atomic stick-slip [487],... 

Because of the complex nature of the temperature and velocity dependence of the kinetic ice friction coefficient, it is important to measure ice friction under conditions that are as close as possible to those where the data will be applied. It is inadvisable to apply or extrapolate measurements and inferences made at low velocities to skating at much higher velocities. 

Fig. 15 Angular velocity dependence of the frictional force for PNaAMPS gel rotated on a piece of glass surface in pure water at 25 °C at different normal strains. Values of the normal compressive strains (%) and normal stresses (kPa) applied during the measurement are shown. Sample thickness 3 mm degree of swelling 27. (Reproduced, with permission, from [53])...

Taylor and Pollet [30] reported the results of a study of friction between fabrics used for clothes, including cotton, wool, polyester fibre and acrylic fibre, and aluminium, Formica and rubber under zero or low applied normal forces. The effects of various factors, such as surface roughness, directionality, nature of table surface, pressure and velocity, on frictional force are discussed and an empirical law proposed to model the dependence of friction on velocity. 

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