Functional Frictional Forces

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

Another remarkable feature of thin film rheology to be discussed here is the quantized" property of molecularly thin films. It has been reported [8,24] that measured normal forces between two mica surfaces across molecularly thin films exhibit oscillations between attraction and repulsion with an amplitude in exponential growth and a periodicity approximately equal to the dimension of the confined molecules. Thus, the normal force is quantized, depending on the thickness of the confined films. The quantized property in normal force results from an ordering structure of the confined liquid, known as the layering, that molecules are packed in thin films layer by layer, as revealed by computer simulations (see Fig. 12 in Section 3.4). The quantized property appears also in friction measurements. Friction forces between smooth mica surfaces separated by three layers of the liquid octamethylcyclotetrasiloxane (OMCTS), for example, were measured as a function of time [24]. Results show that friction increased to higher values in a quantized way when the number of layers falls from n = 3 to n = 2 and then to M = 1. 

Fig. 17—Quantized changes in both film height and friction force, measured on an island of C12 thiols on Au(111) as a function of applied load (taken from Ref. [31]).

The L-B film studied consists of two-layer organic molecules. The first layer of the L-B film is adsorbed on silicon substrate by the polarization terminals of the molecules. During the micro friction test, the probe contacted with the polarization terminal of the second layer. As a result, there was a special attractive force between the polarization terminal of the second layer and the probe. Therefore, the L-B film does not have the function of reducing friction force under the current experimental condition. 

Rubber friction differs from that of friction between hard solids in that the friction force is a nonlinear function of the load and depends strongly on both speed and temperature, whilst in hard solids the load dependence is linear and the friction force is virtually independent of speed and temperature [1]. 

FIGURE 26.15 Friction force on ice as function of the (a) load at a constant ice temperature of —5°C and a speed of 1.5 km/h, for two compounds showing the experimental points and the fitted power function (h) showing the calculated power functions of seven compounds. Their main ingredients are shown helow. (c) Shows the relative ratings with compound 1 as reference, (d) to (f) Show similar graphs for the speed dependence at a load of 75 N. 

FIGURE 26.16 The frictional force and the relative rating of the seven compounds of figure 14 as a power function of the ice surface temperature at a load of 75 N and a speed of 1.5 km/h. 

In contrast to the frictional force, the resulting abrasion is generally a nonlinear function of the pressure p... 

In the simulations, the inner nanotube was initially displaced relative to the outer tube by a distance x. To reduce surface area, the inner nanotube was pulled into the outer tube and a potential energy minimum was found to exist when the inner tube is completely embedded. However, because of the accumulation of kinetic energy, the inner tube will move past this minimum and extend beyond the other end of the outer tube. In the absence of frictional forces, one would anticipate that this process would be repeated indefinitely, with the relative displacements of the two nanotubes oscillating between +x and —x. In the presence of frictional forces, the maximum displacement will decrease with time. This can be seen from the data shown in Figure 24, where the relative displacement of the nanotubes and frictional forces are shown as functions of time. 

Figure 24 Top Friction force between two nanotubes as a function of time. Bottom Displacement of the nanotubes as a function of time. Gray and black lines indicate incommensurate and commensurate geometries, respectively. Reproduced with permission from reference 92.

Although this treatment does not explicitly involve interactions at a solid-liquid interface, the application of Green s function to find the stochastic friction force may be an excellent opportunity for modeling interfacial friction and coupling, in the presence of liquid. An interesting note made by the authors is that the stochastic friction mechanism is proportional to the square of the frequency. This will likely be the case for interfacial friction as well. 

Figure 3. Potential functions for surface ( and friction ( forces as a function of the distance d front cellulose acetate membrane material for different solution...

Following FerrelK, the second term in Equation 2 can be expressed as a Green-Kubo integral over a flux-flux correlation function. The transport is due to a velocity perturbation caused by two driving forces, the Brownian force and frictional force. The transport coefficient due to the segment-segment interaction can be calculated from the Kubo formula(9 ... 

Chain strength = Frictional force as a function of chain length... 

Fig. 13.14. Ultrasonically induced lubricity for a SisNu cantilever on a Si surface (a) schematic of experiment (b) friction force and cantilever normal deflection as a function of ultrasonic amplitude for applied loads Fj = 0, F2 = 2 nN sliding speed 50nms-1 (Dinelli et al. 1997).

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