Friction coefficient short chains

As the rubbing continues, the polyphosphate layer comes into closer contact with water in oil and is hydrolyzed to give a short-chain polyphosphate, e.g., Zn2P207 (Fuller et al., 1998). During the mechanically activated processes (friction coefficient, p > 0.4), a nascent surface is generated, and in the presence of oxygen, an iron oxide is formed. The acid - base reaction between polyphosphate glasses (hard Lewis bases) and the oxides (hard Lewis acids) is... 

The tribochemical reactions based on the hard and soft acids and bases (HSAB) principle linked to the friction coefficient (p) are summarized above. The effect of tribological processes consists of the formation of mixed short-chain phosphate glasses containing sulfide precipitates. 

In other words, it is assumed here that the particles are surrounded by a isotropic viscous (not viscoelastic) liquid, and is a friction coefficient of the particle in viscous liquid. The second term represents the elastic force due to the nearest Brownian particles along the chain, and the third term is the direct short-ranged interaction (excluded volume effects, see Section 1.5) between all the Brownian particles. The last term represents the random thermal force defined through multiple interparticle interactions. The hydrodynamic interaction and intramolecular friction forces (internal viscosity or kinetic stiffness), which arise when the macromolecular coil is deformed (see Sections 2.2 and 2.4), are omitted here. 

The first relaxation process (designated A hereafter) corresponds to a Rouse-like relaxation of chain segments between entanglement points. It is assumed that the entanglement points remain fixed during the time-scale of this relaxation and that no diffusion of monomers through the slip-links is allowed in such short times. The associated relaxation time,, is related to a monomeric friction coefficient, to thie number of monomers between... 

The results have indicated that the monomeric friction coefficient is sensitive to the presence of the short chains, and is smaller, at a given temperature, than the homopolymer. This observed reduction in has been shown to be only attributed to an increase in the fractional free volume. Indeed, the temperature dependence of the monomeric friction coefficient is described by a WLF-type equation ... 

K above their glass transitions. All linear polymer melts have viscosity proportional to molar mass (ry M) for sufficiently short chains, when the data are determined at a constant friction coefficient as opposed to isothermal data. Longer chains have entanglement effects (discussed in Chapter 9) and have The full chain length dependence of... 

Understanding molecular-scale adhesion, friction, lubrication, and wear is crucial to modern technologies, such as microelectromechanical systems (MEMS) and hard disk drives.With atomic force/friction force microscopy (AFM/FFM),several studies have shown the correlation of frictional properties of self-assembled monolayers (SAMs) of alkanethiols with their chain lengths and terminal groups. The long chain monolayers (more than 12 carbon units) have lower friction coefficients compared with their short chain counterparts. Recently, Kim et al investigated the effect of the size of chain termination on frictional properties and found that the difference in friction arises predominantly from the difference in the size of the terminal groups. The AFM/FFM has also been applied to study frictional... 

T is the shortest Rouse relaxation time, which is related to the local friction coefficient experienced by short chain segments. N, is the number of bonds per chain, and Ne is the number of bonds per entanglement. 

In summary, for short times the self-dynamics of PEO follows the Rouse expectation, however, with a significant larger friction coefficient compared to pure PEO. The collective chain dynamics at longer times are further retarded and... 

In Figure 20, the effective friction coefficient/ieff is plotted against the volume fraction of the compressed, sheared polymers. All polymer surfactants show very low effective friction coefficients at volume fractions 0.3. But while the neutral bmshes and the adsorbed charged chains show a rapid increase in fi s at higher volume fractions, friction mediated by short end-attached PE bmshes remains very low up to the point of brash removal J (by which point the volume... 

In general, the coefficient of friction is not sensitive to molecular weight provided that the chains are not very short. This coefficient decreases for... 

---