Polymer viscous drag

Polymers crystallize when the crystalline state is more thermodynamically stable than the molten one. The system progresses towards a low energy state, but lull crystallization is hindered by chain entanglements, branches, side group interactions, and viscous drag on chains. 

In the perspective discussed in the present contribution, bundle formation occurs within the amorphous phase and in undercooled polymer solutions. It does not imply necessarily a phase separation process, which, however, may occur by bundle aggregation, typically at large undercoolings [mode (ii)]. In this case kinetic parameters relating to chain entanglements and to the viscous drag assume a paramount importance. Here again, molecular dynamics simulations can be expected to provide important parameters for theoretical developments in turn these could orient new simulations in a fruitful mutual interaction. 

We should first emphasize that viscosity is a macroscopic parameter which loses its physical meaning on a molecular scale. Therefore, the term microviscosity should be used with caution, and the term fluidity can be alternatively used to characterize, in a very general way, the effects of viscous drag and cohesion of the probed microenvironment (polymers, micelles, gels, lipid bilayers of vesicles or biological membranes, etc.). 

When dash pot and spring elements are connected in parallel they simulate the simplest mechanical representation of a viscoelastic solid. The element is referred to as a Voigt or Kelvin solid, and it is shown in Fig. 3.10(c). The strain as a function of time for an applied force for this element is shown in Fig. 3.11. After a force (or stress) elongates or compresses a Voigt solid, releasing the force causes a delay in the recovery due to the viscous drag represented by the dash pot. Due to this time-dependent response the Voigt model is often used to model recoverable creep in solid polymers. Creep is a constant stress phenomenon where the strain is monitored as a function of time. The function that is usually calculated is the creep compliance/(f) /(f) is the instantaneous time-dependent strain e(t) divided by the initial and constant stress o. ... 

It is also known that SRGs arise from surface-initiated processes.The free polymer surface can be treated as a thin, mobile layei with a viscous drag between layers dominated by the force f x,y,z). The limit superficial velocity, v, due to this force is ... 

Consideration of another major modification that has been applied to the flexible chain model seems pertinent at this point. It has long been appreciated that the velocity field of the solvent would be perturbed deep inside a coiled polymer molecule. It is clear that this effect is not considered in the above treatment because the viscous drag is given as psXi in equation (3-51) irrespective of whether Xi happens to be inside the coiled molecule or on its surface. Thus one might expect the Rouse formulation to be most applicable to polymer-solvent systems in which the elongated conformations of polymer chains predominate. For such conformations, there would be little shielding of one part of a molecule by another part of the same molecule. This is the case in... 

Pectin is a mixture of complex polymers (1-3). These are formed during primary wall formation while the cell wall is expanding in surface area. At these early stages of growth the pectin polymers contribute in a major way to the texture of the wall especially to its ability to expand and stretch. The wall is much more a fluid structure at this time and water is an extremely important constituent. The primary wall when the matrix is non-lignified can be considered as a fluid plastic structure so that any load applied to the wall is transmitted to the microfibrils by the viscous drag of the plastic deformation of the matrix. This can alter very much with the composition and physical state of the matrix materials, especially with that of the pectin complex ( 3). 

Plasma proteins organize on polymer substrates in different ways. Adsorbates are influenced by substrate physicochemical properties and by environmental factors, especially fluid shear and bulk protein distribution. Different types of binding interactions and more than one conformation for adsorbed protein are observed. In the case of albumin, the irreversibly adsorbed conformation, as measured by pulse intrinsic fluorescence, appears to be substantially altered from that of bulk albumin. Microaggregated albumin and undenatured forms are seen at the polymer interface, which are readily desorbed by viscous drag. 

Virk, P. S., and Merrill, E. W., Onset of dilute polymer solution phenomena, in Proceedings of the Symposium on Viscous Drag Reduction, Dallas, TX, Wells, C. S., Ed., Plenum Press, New York, 1969, pp. 107-130. 

The motion of the clusters is ruled by the balance between the van der Waals attraction/ repulsion forces and the resistance to flow that arises from the viscous drag. The van der Waals forces between clusters always attract. On the other hand, the van der Waals forces between clusters and aqueous phase may either attract, which brings the clusters toward the surface of the particle, or repel, which brings the clusters toward the center of the polymer particle. Figure 6.3 illustrates a case in which the clusters are attracted by the water. It is worth mentioning that the van der Waals forces are proportional to the interfacial tensions. The final morphology heavily depends on the kinetics of... 

Equation 11 is Smoluchowsky s equation including an additional friction force due to the polymer. v(x) is the fluid velocity parallel to the particle surface at location x, the first term on the left is the viscous drag, the second is the force imparted to the fluid by the monomer beads, f is a friction coefficient and r(x) is the monomer density. The right hand term is the electrical volume force which is proportional to the field E and to the net charge p(x) per unit volume. The electrophoretic mobility Ue, which is the limit of v(x)/E for x > > lc can be expressed in the following form (see Appendix) ... 

There are a number of extruders, which do not utilize an Archimedean screw for transport of the material, but still fall in the class of continuous extruders. Sometimes these machines are referred to as screwless extruders. These machines employ some kind of disk or drum to extrude the material. One can classify the disk extruders according to their conveying mechanism (see Table 2.1). Most of the disk extruders are based on viscous drag transport. One special disk extruder utilizes the elasticity of polymer melts to convey the material and to develop the necessary diehead pressure. 

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