Viscosity and friction

In Fig. 6.22 the results of a viscosity scahng by f— fxT/rj (T) of the relaxation data are shown. Such a scaling is motivated by the Rouse model and should hold for the a-relaxation. The pure PPO data (right) behave according to this expectation in contrast the PP0-IiC104 curves deviate considerably. This indicates that the coupling factor between microscopic friction and viscosity depends on temperature, possibly due to transient cross-linking via Li-ions. 

XHI. Relation Between Friction and Viscosity in the Normal Liquid... 

B. Effect of the Dynamic Structure Factor on Friction and Viscosity... 

The relation between friction and viscosity goes beyond the Stokes relation. The Navier-Stokes hydrodynamics has been generalized by Zwanzig and Bixon [23] to include the viscoelastic response of the medium. This generalization provides an elegant expression for the frequency-dependent friction which depends among other things on the frequency-dependent bulk and shear viscosities and sound velocity. 

XIII. RELATION BETWEEN FRICTION AND VISCOSITY IN THE NORMAL LIQUID... 

While the hydrodynamic theory always predicts this near equivalence of the friction and the viscosity, microscopic theories seem to provide a rather different picture. In the mode coupling theory (MCT), the friction on a tagged molecule is expressed in terms of contributions from the binary, density, and transverse current modes. The latter can of course be expressed in terms of viscosity. However, in a neat liquid the friction coefficient is primarily determined not by the transverse current mode but rather by the binary collision and the density fluctuation terms [59]. Thus for neat liquids there is no a priori reason for such an intimate relation between the friction and viscosity to hold. 

The comparative study between the time-dependent friction and the viscosity at p = 0.844 and T = 0.728 is depicted in Fig. 3. In this figure both the viscosity and the friction have been normalized to unity at t = 0 by their respective initial values. This figure has several interesting features. Both friction and viscosity exhibit a pronounced ultrafast Gaussian decay which accounts for almost 90% of the total relaxation. The Gaussian time constants... 

In the previous section we have discussed the relation between the time- and frequency-dependent friction and viscosity in the normal liquid regime. The study in this section is motivated by the recent experimental (see Refs. 80-87) and computer simulation studies [13,14, 88] of diffusion of a tagged particle in the supercooled liquid where the tagged particle has nearly the same size as the solvent molecules. These studies often find that although the fric-... 

In the supercooled liquid regime it is the structural relaxation which contributes the most to the friction and viscosity. Thus we can neglect the contribution from the transverse and longitudinal current. 

Concerning properties, SFM has become a unique technique in probing local adhesion, friction and elastic response of various materials. This is based on the ability to measure forces as small as picoNewtons and probe areas well below 100 nm. The peculiar sensitivity of the force probe to different types of static and dynamic interactions provides a great number of contrast mechanisms which can map the surface structure regarding the chemical composition and physical properties. However, in most SFM measurements the interpretation of the surface maps remain to be very intricate, mostly because of the concurrent contribution of different forces into the net force. The progress in this field relies on new developments in technique which would allow to measure the properties like stiffness, adhesion, friction and viscosity, separately. 

Thus if we consider a wide U-tube containing water in which initially the water level is higher in one arm than in the other. The level in this arm falls, passes through the equilibrium position, and then rises in the other arm to nearly the same level the reverse process then occurs. If we were able to reduce friction and viscosity to zero, we should obtain in the limit a reversible change. 

The WLF equation may be derived from the Doolittle equation [46] which relates the viscosity of a liquid to the free volume, i.e. the volume available for segmental motion. The amount of free volume increases as temperature increases and thus the segmental mobility of molecular chains increases and the degree of internal friction and viscosity, 17, decreases. The value of 17 for a rubber therefore decreases as temperature increases and at T>Tg the value r) T) at any temperature may be related to that at the glass transition temperature, r Tg), by the WLF equation for simple viscoelastic materials ... 

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