External Friction

If we consider very slow motion of a macromolecular coil with constant velocity, the force of internal resistance can be neglected and the resistance-drag coefficient for the external force can be written down as 

Let us imagine, following Pokrovskii and Pyshnograi (1988), the shear motion of the system as a motion of overlapping macromolecular coils, each of which is characterised by the function (1.24) of the mean number density of Brownian particles 

If the influence function r/(r) is known, the resistance-drag coefficient of a Brownian particle can be calculated (see Appendix E) as 

To find the influence function rj(s), we shall consider shear deformation of the system at velocity gradient 7y, while two macromolecular coils, separated by a distance dj, move beside each other at velocity 7ijdj. We add to the sum the contributions of every coil, apart from the chosen one, and find the density distribution of the energy dissipation for the chosen coil. The proportionality coefficient depends only on the concentration of the Brownian particles, if an assumption is made that local dissipation is determined by relative velocities of macromolecular coils, 

When the linear in velocity gradients approach is considered, the equilibrium density distribution function (3.19) can be used. We turn the sum into the integral and, after calculating, obtain 

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Internal viscosity (Section 4) provides another possible source of shear-rate dependence. For sufficiently rapid disturbances, a spring-bead model with internal viscosity acts like a rigid body for sufficiently slow disturbances it is flexible and indefinitely extensible. The analytical difficulties for coupled, non-linear spring-bead systems are equally severe in linear spring-bead systems with internal viscosity. Even the elastic dumbbell with internal viscosity has only been solved exactly in the limit of small e (559), where e is the ratio of internal friction coefficient to molecular (external) friction coefficient Co n. For this case, the viscosity decreases with shear rate. 

The discrepancy between the theories of Cerf and of Budtov and Gotub is not yet understood. The latter authors point to the fact that Cerf omitted the contribution of hinging on the junctions. However, when is put equal to zero in eq. (5.33), the fundamental difference in the molecular weight dependencies, as given by the second terms of eqs. (5.27), (5.31) and (5.33), does not disappear. It is perhaps superfluous to remind that both types of theories are derived only for the case that the internal friction factors are small compared with the external friction factor f. 

Fig. 5.10. Schematic course of the dependence of the initial slope tana of the extinction angle curve on the solvent viscosity jj0, according to Cerf (3). Dotted straight lines Limiting behaviour for the values zero and infinity of the ratio of internal to external friction factor...

The addition of low-viscosity additives can impede the formation of the melt film that is essential for melting. On the other hand, high-viscosity or solid additives can cause increased energy dissipation due to internal and external friction, which accelerates the formation of the melt film but can also lead to overheating of the viscous phase. 

For effective solid lubrication, it is not enough to have a material with low internal or external friction. It is also necessary for it to form films with sufficient adhesion to a substrate, and internal cohesion, to withstand rubbing under high loads. Molybdenum disulphide has this ability to a very high degree. It can be made to adhere readily and firmly to a substrate, forming a strong, cohesive film. 

The purpose of the feeding section is to compact and to transfer the feed stock into the barrel of the machine. The channel depth (Fig. 2) is normally greatest in this section. The performance of the feeding section depends on the external friction coefficient of the feed stock at the surface of the screw and barrel. 

On this basis the more brittle the explosive crystal, the more sensitive it is to impact and friction high rates of shear combined with high pressures ensure that heating occurs [88, 891. When a brittle substance is impacted, high pressures are developed and transmitted without rapid attentuation. Displacements occur within the material (internal friction), in addition to the movement of, say, the striker relative to the substance (external friction). The most significant difference between friction and impact tests may well be that in the friction tests the normal and tangential forces are applied independently of each other, whereas under impact they are applied simultaneously. 

FIs. 1 3.36 Prototype pipe welding system showing external friction stir welded head and internal mandrel (inset). Courtesy of MegaStir, Inc. 

A. "A New Method of Investigation of Supermolecular Deformation at External Friction Mekhanika Polimerov,... 

Friction of solid polymer particle or pellet against metal surfaces (termed external friction). This influences feed zone conveying rate as well as hopper flow. 

The extent of lamination can, of course, vary considerably depending on the characteristics of the body, the ratio between internal and external friction, the surface quality of the dies, etc. 

An alternative way for describing Brownian motion is to study the equation of motion for the Brownian particle with the random force f t) written explicitly. This equation — the Langevin equation with the inertial term neglected (i.e. zero acceleration) — expresses the balance of the external, friction, and fluctuation forces ... 

The parameter p is called the coefficient of external friction and is a function of density as one would expect that the higher the density is, the coefficient of external friction is higher. Millikan (1923) has shown that... 

Figure 7.6-2 Deflection of molecules after hitting the surface the coefficient of external friction will become ...

Newton was the first to realize that the force corresponding to this performance of work against internal friction behaves entirely differently from that operating in external friction he assumed that the shearing force of internal friction r is proportional to the surface /, and to the relative velocity u of the liquid planes in relative motion. By conversion to the limiting value for infinitely thin planes, he was able to write... 

It is evident from the above that a certain shearing stress must prevail between the planes of a liquid in stream-line flow in order to maintain the motion. In internal friction (as well as in external friction) a work transference into heat takes place. 

The friction between the two planes is, however, not to be regarded as directly analogous to external friction, because the internal friction of liquids is practically independent of pressure, as Coulomb showed long ago. 

Minimizes internal and external friction leading to degradation... 

Another condition that promotes good hopper flow is low friction. When friction between the pellets (internal friction) is low and friction between the pellets and the hopper (external friction) is low, solids are more likely to flow freely. Factors that may increase internal and external friction include rough surfaces, poor hopper design, moisture, heat, and static electricity. 

Pipe haul-off units form a key part of the extrusion process since they have the function of exerting a steady, uniform pull back through the cooling and calibration zones to supplement the extrusion pressure at the die head. The haul-off unit effectively creates a tensile stress in the solid material that balances the hydrostatic and viscous forces in the liquid state of the extrudate and overcomes the resistance of external friction. Haul-off units may be belt driven or multi-pad caterpillar systems. Large diameter pipes require multiple caterpillar units and thin wall pipe also require more units to avoid distortion. 

The interpretation of the soft twist as a soliton might be instructive, but is, again, very much idealized. In principle, solitons wiO propagate freely only in the absence of external friction, i.e., interchain and soliton-soliton interactions. This is most likely not going to be the case in polymer crystals. 

The internal coefficient of friction is the friction between the plastic particles themselves. The external coefficient of friction is the friction between the plastic particles and another surface, such as the barrel surface. For efficient conveying in the feed hopper, it is required that both the internal and external frictions should be low. For efficient conve5ung along the extruder screw, it is required that the barrel friction to be high and the screw friction should be low this is discussed later. 

Deposition and corrosion of Cu thin layers from an aqueous sulfate-based electrolyte were studied in situ with an AFM-EQCM system by Bund et al. [66]. The shift of the resonance frequency and of the damping of the quartz crystal (EQCM), on one side, and the evolution of surface roughness (AFM), on the other side, could be thus monitored simultaneously. No disturbance of the AFM response by the oscUlating quartz or vice versa was observed in this study. The authors proved that a quantitative separation of internal (information given by EQCM) and external friction (which is the roughness contribution, obtained by AFM) of the solid materials is possible by combining AFM and EQCM techniques. 

Derjaguin, B. V. 1935. Studies on the external friction and adhesion. V. Theory of adhesion. Zh. Fizicheskoy Himii. 6 1306-1319. 

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