Polymer frictional forces

Klein J ef a/1994 Reduction of frictional forces between solid surfaces bearing polymer brushes Nature 370 634-7... 

Fig. 21 —Friction force and topography images of the L-B films of Cgo-Pst hyperbranched polymer under load 2 nN using AFM/FFM, image (a) and (b) are friction force images and image (c) is the topography.

Figure 24 is a diagram of friction versus load derived from the friction force images of the above hgures. Figure 25 is also a diagram of friction versus load done in the same monolayer L-B him of C Q-Pst polymer but in a different scan range. 

Figures 27-30 are diagrams of friction force versus load for different multilayer L-B hlms of the C5o-Pst hyperbranched polymer molecules obtained using AFM/FFM. The...

Jimenez-Castellanos et al. developed a method to measure both the adhesional and frictional forces involved in the attachment of such tablets to mucosa. These researchers found that a good correlation existed between the maximal adhesion strength and polymer content of the tablets tested [155]. 

According to these equations, for a given separation system, the main parameters involved in the separation of SDS-protein complexes are the electric force, the frictional force, and the retardation coefficient. These parameters are in turn affected by the strength of the electric field, molecular charge, analyte shape and size, polymer concentration, and temperature. 

In the case of an immobile macromolecule in solution it is possible to estimate a value of the frictional force (F) developed between the solvent and polymer molecules by assuming the macromolecule to consist of a number (n) of solid spherical entities and applying the Stokes formula in a modified form (Eq. 5.8). 

CO is the angular frequency of the applied ultrasonic wave. For an applied frequency of 500 kHz, the frictional force developed in the above polymer system, according to Eq. 4.9, may be calculated to be approximately 7.8 x 10 N. This is obviously many orders of magnitude less than that required to rupture a C-C bond. The conclusion must be that the more dilute a polymer solution, the more likely it is that the... 

Several solids conveying models were developed by Campbell and his students at Clarkson University [19, 20]. These models will be referred to as either the Clarkson University models or the Campbell models. They proposed that the movement of the screw flight was pushing the polymer bed as the screw turns rather than the frictional force at the barrel moving the polymer pellets down the screw. For these models, they assumed that the solid bed behaved more like an elastic fluid rather than a solid and removed the torque balance constraint. Campbell and Dontula [20] reasoned that because the solid polymer pellets more closely resemble an elastic particulate fluid, no torque balance in the bed would be necessary. They further assumed that the force normal to the pushing flight was due to a combination of the force due to the pressure in the channel and a force proportional to the frictional force exerted at the barrel by the solid bed. The Campbell-Dontula model was first published as ... 

The previously unresolved force, F (F in previous models) is assumed to be proportional to the frictional force between the polymer bed and the barrel. 

The failure of the Rouse theory was attributed to the pathological nature of medium motions in entangled systems, and not any special defect in the Rouse representation of the polymer chain itself. For Rouse chains in a deforming continuous medium, the frictional force depends on the systematic velocity of the bead relative to the medium. The frictional force on a bead is therefore a smootly... 

This treatment assumes that the forces between molecules in relative motion are related directly to the thermodynamic properties of the solution. The excluded volume does indeed exert an indirect effect on transport properties in dilute solutions through its influence on chain dimensions. Also, there is probably a close relationship between such thermodynamic properties as isothermal compressibility and the free volume parameters which control segmental friction. However, there is no evidence to support a direct connection between solution thermodynamics and the frictional forces associated with large scale molecular structure at any level of polymer concentration. 

Along with the frictional force on a bead, given by Eq. (9), there will be in general other forces F-, derived in part from the potential energy U that holds the polymer chain together, and in part from external sources, e.g., electric or centrifugal fields. The total force on the y th bead is thus Fj + F/. 

The extruder is used since it mixes, melts, and degases the polymer. However, as said in the previous paragraph, from an exergetic point of view, it is not an efficient apparatus, since it dissipates mechanical work into heat by frictional forces. A possible alternative to the extruder could therefore be a separate degasser, a static mixer, or a gear pump to push the polymer melt through the mixer and perforated plate (Figure 11.6). 

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