Friction temperature dependence

However, the Green s function of the bath Gb(t, t ) = 5 Z/5Q(t)5Q(t ) may have a form quite different from a single-phonon Green s function and may exhibit a strong temperature dependence. It would be interesting, for example, to see explicitly how this kernel, say, for a liquid, reduces to the phonon Green s function but with temperature-dependent parameters so that the friction coeflScient rj depends on temperature. To the authors knowledge this has not been done as yet. 

K.A. Grosch, The speed and temperature dependence of rubber friction and its bearing on the skid resistance of tires. The Physics of Tire Traction, Theory and Experiment. D.L. Hayes and A.L. Browne (eds.). Plenum Press, New York/London, 1974, 143. 

By the development of hot spots by friction. This is shown particularly by the effect of added materials of a gritty nature. For initiation to occur, the melting point of the grit must be above a limiting temperature dependent on the explosive. Initiation is favoured by a low thermal conductivity and also by a high hardness value. 

The monomeric friction factors and i have a temperature dependence given by the Williams-Landel-Ferry (WLF) relation, equation (27) ... 

Fig. 3.8 Temperature dependence of the monomeric friction coefficients for PEP and PE. The symbols present the NSE results (filled triangle PEP, filled circle PE). The solid lines display the respective rheological predictions extrapolations are shown as dashed lines (solid lines prediction [51],point dashed line prediction [34] for PEP)...

Fig. 4.35 Right-hand side Monomeric friction coefficients derived from the viscosity measurements on PB [205]. The open and solid symbols denote results obtained from different molecular weights. Solid line is the result of a power-law fit. Dashed line is the Vogel-Fulcher parametrization following [205]. Left hand side Temperature dependence of the non-ergodicity parameter. The three symbols display results from three different independent experimental runs. Solid line is the result of a fit with (Eq. 4.37) (Reprinted with permission from [204]. Copyright 1990 The American Physical Society)...

The friction factor depends upon the same features that govern the viscosity of small-molecule liquids. At low temperatures f0 depends on T — T% (Tg < T< Tg+ 4-100° C), and at higher temperatures it depends on an activation energy for flow. The value of 3 for a solution depends on the properties of both components and their concentrations, but it is independent of the large scale structure of the polymer as long as its molecular weight is large (Mn > 104 for most linear polymers). 

The temperature dependence of the friction coefficient of poly(acrylamide) gel was studied at two different concentrations of acrylamide (AAm) and N,N -methylenebisacrylamide (Bis) AAm Bis = 1.24 M 22.4 mM and AAm Bis = 693 mM 7 mM. The weight concentrations of these sample gels was about 8.8 and 5 wt.%, respectively. The composition of the latter gel is almost the same as the composition typically recommended for acrylamide gel electrophoresis. The friction coefficient of these gels was measured at a fixed pressure of 5.88 x 103 Pa, which corresponds to 60 cm of the height of the water column. The temperature was varied from about 0 to 60 °C. 

Fig. 6. The temperature dependence of the friction coefficient of the poly( acrylamide) gels. The total concentrations of acrylamide are 1.24 M (8.8% mass fraction), and 693 mM (5% mass fraction), respectively. Open symbols are used for the results obtained in the cooling process and closed symbols represent the results taken upon increasing the temperature. In the upper part of this figure, the temperature dependence of the ratio f(T)/rj T) is shown. The values of the viscosity are taken from a table. Symbols are the same as those used in the raw value of the friction coefficient...

Here, both the viscosity of water and the correlation length of the gel are a function of the temperature. Therefore, in order to discuss the temperature dependence of the correlation length of the gel, it is convenient to use the ratio f(T) /r (T) rather than the raw value of the friction coefficient f(T) since the ratio directly represents the effective size of the pores and their distribution. 

The temperature dependence of the friction coefficient of poly(acrylamide) gels are analyzed according to the above equation. In our analysis, the values of the viscosity of water is taken from the table. The results thus obtained are also shown in Fig. 6. It can be seen from this figure that the friction of the poly(acrylamide) gel normalized with the viscosity of water is independent of the temperature. It indicates that the pore size of the poly(acrylamide) gel is stable in the temperature range studied. 

The temperature dependence of the friction coefficient normalized by the viscosity of the water, f/rj, is given in Fig. 10. The solid symbols are used in the increasing of the temperature and the open symbols are used in the lowering of the temperature. The values of the viscosity of the water, tj(T), are taken from the literature. For the chemically cross-linked gels, such as the poly(acrylamide) gel, the friction, f/rj, is independent of the temperature which has been already shown in previous section. It is, however, found from this figure that the friction... 

Fig. 10. The temperature dependence of the friction coefficient f of polyfiV-isopropylacrylamide) gel normalized by the viscosity of water T - Solid circles are used in the increasing of the temperature and open circles are used for the lowering of the temperature...

In practical applications, the increase of viscous friction with speed is often lower than expected from Eq. (11.9). The explanation is that friction leads to an increased temperature of the lubricant which reduces the viscosity. For most lubricants the temperature dependence of the viscosity is given by... 

At much higher temperatures, where CDCs are able to develop, one has a temperature dependence of ocdc> which involves both oy2 and the monomeric friction coefficient, f. In systems where the activation energy of f is high enough, its temperature dependence can lead to a steeper decrease of ctcdc with increasing temperature than for ay. For such polymers, at temperatures not much lower than Ta, CDCs can be the favoured micromechanism and a SDZ-CDC transition will take place. 

A few comments on (2.27), (2.29), and (1.12) are appropriate at this point. The activation energy in the Arrhenius region is independent of 17, since friction changes only the velocity at which a classical particle crosses the barrier and thus affects only the preexponential factor. However, friction reduces both kc and Tc and thereby widens the Arrhenius region. Dissipation has a noticeable effect on the temperature dependence of... 

In view of these complexities, it is remarkable that Eq. 4.1-4 represents numerous metal-metal, dry frictional data rather well, for both the static and sliding cases. Polymers, on the other hand, exhibit an even more complex frictional behavior on metal. This is, perhaps, not surprising, since the physical situation involves a relatively soft, viscoelastic, and temperature-dependent material in contact with a hard, elastic, and much less temperature- and rate-dependent material. Empirical evidence of these complexities is the nonlinear relationship between the frictional force and the normal load... 

The value of the coefficient of friction is connected with relative motion of small portions of the macromolecule, so that its temperature dependence is similar to that found for low-molecular-weight liquids, and can be written in the following form at temperatures much higher than the glass transition point... 

Electron-hole pairs have already been treated on the Hartree-Fock level in otherwise classical high-dimensional molecular dynamics simulation using the molecular dynamics with electronic friction method [120]. In this approach, the energy transfer between nuclear degrees of freedom and the electron bath of the surface is also modelled with a position-dependent friction term, but additionally temperature-dependent fluctuating forces are included. 

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