Chain shearing

Khachigian LM, Resnick N, Gimbrone MA Jr, Collins T. Nuclear factor-KB interacts functionally with the platelet-derived growth factor B-chain shear-stress response element in vascular endothelial cells exposed to fluid shear stress. / Clin Invest. 1995 96 1169-1175. 

Operator in glassy and hyperelastic states of cross-linked polymers is equal to from 0 to 1, respectively, and in transition region between these conditions from 0 to 1. Therefore Equations (1) and (2) reproduce change of concerned cross-linked polymers hyperelastic properties in all their physical states in hyperelastic, where is being momentary a-process, shear pliability s relaxation operator is equal to equilibrium shear pliability in glassy, where is only local conformational mobility of polymeric mesh s cross-site chains, shear phabihty s relaxation operator is equal to shear pliability of glassy state in transition region between these states, where both... 

UPt2 (Villars and Calvert 1985) and LaCo5P3 (Davydov and Kuz ma 1981) are the structural examples of infinite zigzag chains (shear after one unit) (fig. 82) ... 

Figure 21 Illustrating the different factors believed responsible for the lubricity of charged brushes at lower pressures, the weak interpenetration of the opposing brushes, which arises even for neutral chains and is of entropic origin (discussed eariier and in Reference 15), and results in an osmotic pressure due to configurational entropy effects this is augmented by the osmotic pressure of the counterions within the brushes (green) and at higher pressures (prior to chain shear off), the hydrated ionized monomers provide hydration lubrication.

Shearing causes polymer chains to break, therefore a decrease in molecular weight and, consequently, in thickening power. It has been shown that the higher its molecular weight, the more the polymer is sensitive to mechanical shearing (Brlant et al., 1985). 

In amoriDhous poiymers, tiiis reiation is vaiid for processes tiiat extend over very different iengtii scaies. Modes which invoived a few monomer units as weii as tenninai reiaxation processes, in which tire chains move as a whoie, obey tire superjDosition reiaxation. On tire basis of tiiis finding an empiricai expression for tire temperature dependence of viscosity at a zero shear rate and tiiat of tire mean reiaxation time of a. modes were derived ... 

Cp is tire number of elasticity active chains per volume unit. The comparison between experimental data and tire prediction by (C2.1.20) shows a reasonable agreement up to large defonnation (figure C2.1.16). For large values of X, strain hardening arises because of tire limited extensibility of tire chains or because of shear-induced crystallization. 

Flow behaviour of polymer melts is still difficult to predict in detail. Here, we only mention two aspects. The viscosity of a polymer melt decreases with increasing shear rate. This phenomenon is called shear thinning [48]. Another particularity of the flow of non-Newtonian liquids is the appearance of stress nonnal to the shear direction [48]. This type of stress is responsible for the expansion of a polymer melt at the exit of a tube that it was forced tlirough. Shear thinning and nonnal stress are both due to the change of the chain confonnation under large shear. On the one hand, the compressed coil cross section leads to a smaller viscosity. On the other hand, when the stress is released, as for example at the exit of a tube, the coils fold back to their isotropic confonnation and, thus, give rise to the lateral expansion of the melt. 

Under compression or shear most polymers show qualitatively similar behaviour. However, under the application of tensile stress, two different defonnation processes after the yield point are known. Ductile polymers elongate in an irreversible process similar to flow, while brittle systems whiten due the fonnation of microvoids. These voids rapidly grow and lead to sample failure [50, 51]- The reason for these conspicuously different defonnation mechanisms are thought to be related to the local dynamics of the polymer chains and to the entanglement network density. 

Material parameters defined by Equations (1.11) and (1.12) arise from anisotropy (i.e. direction dependency) of the microstructure of long-chain polymers subjected to liigh shear deformations. Generalized Newtonian constitutive equations cannot predict any normal stress acting along the direction perpendicular to the shearing surface in a viscometric flow. Thus the primary and secondary normal stress coefficients are only used in conjunction with viscoelastic constitutive models. 

A basic theme throughout this book is that the long-chain character of polymers is what makes them different from their low molecular weight counterparts. Although this notion was implied in several aspects of the discussion of the shear dependence of viscosity, it never emerged explicitly as a variable to be investi-tated. It makes sense to us intuitively that longer chains should experience higher resistance to flow. Our next task is to examine this expectation quantitatively, first from an empirical viewpoint and then in terms of a model for molecular motion. 

The enthalpy of the copolymerization of trioxane is such that bulk polymerization is feasible. For production, molten trioxane, initiator, and comonomer are fed to the reactor a chain-transfer agent is in eluded if desired. Polymerization proceeds in bulk with precipitation of polymer and the reactor must supply enough shearing to continually break up the polymer bed, reduce particle size, and provide good heat transfer. The mixing requirements for the bulk polymerization of trioxane have been reviewed (22). Raw copolymer is obtained as fine emmb or flake containing imbibed formaldehyde and trioxane which are substantially removed in subsequent treatments which may be combined with removal of unstable end groups. 

Flow processes iaside the spinneret are governed by shear viscosity and shear rate. PET is a non-Newtonian elastic fluid. Spinning filament tension and molecular orientation depend on polymer temperature and viscosity, spinneret capillary diameter and length, spin speed, rate of filament cooling, inertia, and air drag (69,70). These variables combine to attenuate the fiber and orient and sometimes crystallize the molecular chains (71). 

Polymer solutions are often characterized by their high viscosities compared to solutions of nonpolymeric solutes at similar mass concentrations. This is due to the mechanical entanglements formed between polymer chains. In fact, where entanglements dominate flow, the (zero-shear) viscosity of polymer melts and solutions varies with the 3.4 power of weight-average molecular weight. 

When an electric field is appHed to an ER fluid, it responds by forming fibrous or chain stmctures parallel to the appHed field. These stmctures greatly increase the viscosity of the fluid, by a factor of 10 in some cases. At low shear stress the material behaves like a soHd. The material has a yield stress, above which it will flow, but with a high viscosity. The force necessary to shear the fluid is proportional to the square of the electric field (116). 

Initiation. Free-radical initiators are produced by several processes. The high temperatures and shearing stresses required for compounding, extmsion, and molding of polymeric materials can produce alkyl radicals by homolytic chain cleavage. Oxidatively sensitive substrates can react directly with oxygen, particularly at elevated temperatures, to yield radicals. 

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