Dispersion frictional coefficient

Figure 4.58 Effect of axial ratio, alb, and concentration on friction coefficient ratio for aqueous protein dispersions. Reprinted, by permission, from P. Hiemenz, Principles of Colloid and Surface Chemistry, 2nd ed., p. 88. Copyright 1986 by Marcel Dekker, Inc.

Graphitic BN (h-BN) is used as lubricant with low friction in numerous applications. Compared to graphite the h-BN can be used as lubricant in an oxidizing atmosphere up to 900 °C as well as at extremely low temperatures, e.g., in space because no water inclusions between the atomic sheet layers are present (graphite always contains small amounts of water between the layers). Due to its excellent resistance against oxidation, its extremely low friction coefficient, and its chemical inertness, h-BN can be inserted into alloys or ceramics [105]. It can be used as a solid surface lubricant [106] or added to a liquid to get dispersions with lubricating properties. 

Maximum in friction coefficient (defined as ratio of frictional force to normal reaction force) near the PZC was found for alumina [350]. Pristine PZC was used in calculations and friction experiments were performed in 0.02 mol dm" Na2S04, thus the results could be affected by specific sorption of sulfate. Resistivity of alumina dispersions is lower than that of solutions without alumina except in the closest vicinity of the lEP [351]. 

For the micellar dispersant giving a dispersion a conductivity of 10- ohm-lcm l the frictional coefficient is found to be 10 dynes cm l sec (11), which corresponds to n=4xl0l6 ionic micelles per cubic centimeter or 65 micromoles per liter. The Debye length 1/k is calculated to be 59°, using e c kT O/o... 

Such a dependence is characteristic of the dry friction, i.e. it agrees with Coulomb s friction law, Ffr = /frFN. Consequently, the model of plastic behavior of a material or disperse system may be represented by two surfaces (two plates) with a mutual friction coefficient, fx, pressed against each other with normal force, FN, causing the tangential force, Ffr, to be equal to the critical shear stress of material (Fig. IX-7). 

The presence of dispersed fillers in the polymer material in low amounts may intensify electrization, increase the residual charge and change the friction coefficient. Introduction of the filler in the electret state exerts a still stronger effect on polymer electrization on frictional interaction with metals. Depending on the direction of the field intensity vector formed by the filler particles, the field generated by triboelectrization can be attenuated or intensified. This means that the principle of the electret-triboelectrization superposition is realized [49], which can be used to regulate the parameters of frictional interactions. Thus, by the introduction of the electret filler, e.g. mechanically activated F-3 powder, it is possible to decrease the friction force (Fig. 4.9). 

The softening dispersions of entangled low-molecular-weight polymers are often modeled by the Rouse modes modified for undiluted polymers. From their very definition only involving the coordinates of a single chain, the Rouse modes are not intermolecularly coupled, and their relaxation times, t/ /, are proportional to the monomeric friction coefficient, fo that is. 

Hydrodynamic resistance to the motion of the dispersed (spherical) particles from the continuum solvent is generally taken into account through a local friction coefficient... 

Metal oxide nanopowders/nanoparticles were used in such composites for the same purpose. It was proven that the addition of potassium titanate (Liang et al. 2005), aluminum borate (Gu and Liang 2007), or zirconia (Yan et al. 2007) nanoparticles improved the wear resistance and decreased the friction coefficient of nanocomposites. When the nanoparticles were previously modified (in zirconia-based composites, with A-[2-aminoethyl]-Y-aminopropylmethyldimethoxysilane, and Si- and P-based compounds in potassium titanate containing composites), the tribological behavior of the composites was superior due to the improved dispersion of the filler. 

Multiwalled carbon nanotubes (MWCNTs) were proven to also contribute to the increase in the wear resistance and to the reduction of the friction coefficient in modified BMI resins (Liu et al. 2007a), especially when MWCNTs are functionalized with carboxylic groups. This is because they induce a change in the main wear mechanism—from adhesive wear in neat resin to abrasive attrition—by changing the self-lubricating property of the worn surface, the dispersion of filler in the matrix, and the interfacial adhesion between filler particles and matrix. 

There are other physical measurements which reflect molecular mobility and can be related to relaxation times and friction coefficients similar to those which characterize the rates of viscoelastic relaxations. Although such phenomena are outside the scope of this book, they are mentioned here because in some cases their dependence on temperature and other variables can be described by reduced variables and, by means of equation 49 or modifications of it, free volume parameters can be deduced which are closely related to those obtained from viscoelastic data. These include measurements of dispersion of the dielectric constant, nuclear magnetic resonance relaxation, diffusion of small molecules through polymers, and diffusion-controlled aspects of crystallization and polymerization. 

One-dimensional diffusion in a stationary liquid medium is described by the first Tick s law. It shows that the diffusion flux of a substance (/) or amount of substance in moles (dS) per area (A) within a certain time (dt) is proportional to the concentration gradient (dc/dx, where dc = change in concentration of a substance at a distance x) J = dS/dt = -D.A.dc/dx. The non-stationary diffusion (the concentration gradient changes with time) is described by the second Tick s law as follows dcldt = D.S.ddf-. Diffusion coefficient D (in m /s) is related to the medium shift (A) A= (2D.At), where At = time at which the dispersed particles diffuses to distance A. Diffusion coefficient D is related to the friction coefficient which counteracts the motion of particles in the dispersion medium D = kg.T//(Einstein relation), where kg = Boltzmann constant and T = absolute temperature. If the dispersed phase particles are spherical particles... 

The sedimentation rate (a) is given by the following relations u=V.glf(p-p ) = m.glf (l-p lp)=M.glNf. f (l-p lp) =2r. g 9r) (p-Po). where V = volume of sedimentation particles, p = their density, p = density of dispersion medium, /= friction coefficient, M=molar weigh of particles, = Avogadro s number, rj = dynamic viscosity of dispersion medium. 

They are very spread out and the fluctuations observed are not always linked with an increase or decrease of the friction coefficient. This dispersion corresponds with the brutal increase of the friction coefficient observed for long resting times. 

Fig. 5.7 Doppler cooUng in a standing light wave, where the atom is acted upon by two radiation forces, one from each traveling light wave. When the saturation of the atomic transition is weak, the atomic-velocity dependences of the forces have a Lorentzian form (the curves marked + and —). The average total force is described by a curve of dispersive character, whose slope at Uz = 0 determines the friction coefficient.

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