Polymer rheology normal stresses

These normal stresses are more pronounced for polymers with a very broad molecular weight distribution. Viscosities and viscoelastic behavior decrease with increasing temperature. In some cases a marked viscosity decrease with time is observed in solutions stored at constant temperature and 2ero shear. The decrease may be due to changes in polymer conformation. The rheological behavior of pure polyacrylamides over wide concentration ranges has been reviewed (5). 

Various investigations have considered the effects of titanate treatments on melt rheology of filled thermoplastics [17,41]. Figure 10, for example, shows that with polypropylene filled with 50% by weight of calcium carbonate, the inclusion of isopropyl triisostearoyl titanate dispersion aid decreases melt viscosity but increases first normal stress difference. This suggests that the shear flow of the polymer is promoted by the presence of titanate treatment, and is consistent with the view that these additives provide ineffective coupling between filler particles and polymer matrix [42]. 

The Entanglement Concept in Polymer Rheology 8.4. Second Normal Stress Function... 

The principal quantities determining the rheological behaviour of polymer melts are the viscosity and normal stress coefficients in shear and extensional... 

The reality, however, is not as simple as that. There are several possibilities to describe viscosity, 77, and first normal stress difference coefficient, P1. The first one originates from Lodge s rheological constitutive equation (Lodge 1964) for polymer melts and the second one from substitution of a sum of N Maxwell elements, the so-called Maxwell-Wiechert model (see Chap. 13), in this equation (see General references Te Nijenhuis, 2005). 

It is well known in polymer rheology that a torsional parallel-plate flow cell develops certain secondary flow and meniscus distortion beyond some stress level [ 14]. For viscoelastic melts, this can happen at an embarrassingly low stress. The critical condition for these instabilities has not been clearly identified in terms of the shear stress, normal stress, and surface tension. It is very plausible that the boundary discontinuity and stress intensification discussed in Sect. 4 is the primary source for the meniscus instability. On the other hand, it is well documented that the first indication of an unstable flow in parallel plates is not a visually observable meniscus distortion or edge fracture, but a measurable decay of stress at a given shear rate [40]. The decay of the average stress can occur in both steady shear and frequency-dependent dynamic shear. 

The rheological behaviour of the two polymers was determined using classical techniques of rheometry, already described in Chapter II. 1 (rotational and capillary rheometers for shear viscosity and first normal stress difference measurements CogsweU method for the elongational viscosity). 

Doi and Edwards (1978) and Kuzuu and Doi (1980) have solved the Smoluchowski equation (6-47)-(6-48) for simple shearing and elongational flows, and they obtained predictions of rheological behavior that are similar to those of the reptation theory for concentrated flexible polymers discussed in Section 3.7.5.1. Figure 6-19, for example, shows the shear-rate-dependence of the shear viscosity and first and second normal stress coefficients predicted by the Doi-Edwards theory for semidilute rods these results are similar to those predicted by the Doi-Edwards theory for entangled flexible molecules. At... 

The stress in viscoelastic liquids at steady-state conditions is defined, in simple shear flow, by the shear rate and two normal stress differences. Chapter 13 reviews the evolution of both the normal stress differences and the viscosity with increasing shear rate for different geometries. Semiquantitative approaches are used in which the critical shear rate at which the viscosity starts to drop in non-Newtonian fluids is estimated. The effects of shear rate, concentration, and temperature on die swell are qualitatively analyzed, and some basic aspects of the elongational flow are discussed. This process is useful to understand, at least qualitatively, the rheological fundamentals of polymer processing. 

Thermotropic LCPs have high melt elasticity, but exhibit little extrudate swell. The latter has been attributed to a yield stress and to long relaxation times (60). The relaxation times for LCPs are normally much longer than for conventional polymers. Anomalous behavior such as negative first normal stress differences, shear-thickening behavior and time-dependent effects have also been observed in the. rheology of LCPs (56). Several of these phenomena are discussed for poly(benzylglutamate) solutions in the chapter by Moldenaers et al. 

Steady shear flow measnrements, however, can measure only viscosity and the first normal stress difference, and it is difficult to derive information abont fluid structure from such measurements. Instead, dynamic oscillatory rheological measurements are nsed to characterize both enhanced oil recovery polymer solutions and polymer crosslinker gel systems (Prud Homme et al., 1983 Knoll and Pmd Homme, 1987). Dynamic oscillatory measurements differ from steady shear viscosity measnrements in that a sinusoidal movement is imposed on the fluid system rather than a continnons, nnidirectional movement. In other words, the following displacement is imposed ... 

Steady-state shear rheology typically involves characterizing the polymer s response to steady shearing flows in terms of the steady shear viscosity (tj), which is defined by the ratio of shear stress (a) to shearing rate y ). The steady shear viscosity is thus a measure of resistance to steady shearing deformation. Other characteristics such as normal stresses (Ai and N2) and yield stresses (ffy) are discussed in further detail in Chapter 3. 

Malkin (1990) reviews the rheology of filled polymers and highlights the importance of yield stresses, non-Newtonian flow, wall slip and normal stresses in filled polymer flow. Details of the effects of particle shape, concentration and adsorption on these phenomena are discussed. 

Utracki and Fisa (1982) and Metzner (1985) review the rheology of (asymmetric) fibre-and flake-filled plastics, noting the importance of the filler-polymer interface, filler-filler interactions, filler concentration and filler-particle properties in determining rheological phenomena such as yield-stress, normal-stress and viscosity profiles (thixotropy and rheo-pexy, dilatancy and shear thinning). 

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