Polymer rheology normal stress differences

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 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). 

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). 

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 ... 

The experimental studies of the influence of fillers on the rheological properties of polymer melts by White et al. [29] best illustrate the effect of filler type. The steady shear elastic data were generated in terms of the first normal stress difference using the cone and plate arrangement of the Rheometrics Mechanical Spectrometer at a fixed temperature of 180°C. 

It is important to make plots of normal stress difference Nj vs. shear stress Ti2 rather than vs. shear rate y if correct data interpretation is intended. The former plots are independent of temperature and molecular weight of the polymer matrix (though not its distribution) and the rheological behavior is correctly interpretable by analogous comparison with the steady state compliance J. ... 

Particular examples of the first normal-stress difference Ni or its coefficient are shown in figures 12 - 29, where a comprehensive collection of examples is given for polymer solutions and melts, as well as an emulsion. These are compared with either the equivalent shear stress or the viscosity. All the different possible combinations of shear and normal-stress difference, and viscosity and normal-stress coefficient are displayed to show the way that results are presented in the rheological literature. The figures are set out to illustrate overall behaviour, with especial emphasis on low shear-rate and mid-range (i.e. power-law) behaviour. 

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