Extensional Measurement

A sliding plate rheometer (simple shear) can be used to study the response of polymeric Hquids to extension-like deformations involving larger strains and strain rates than can be employed in most uniaxial extensional measurements (56,200—204). The technique requires knowledge of both shear stress and the first normal stress difference, N- (7), but has considerable potential for characteri2ing extensional behavior under conditions closely related to those in industrial processes. 

Extensional measurements involve a simple loading process, but with compression and torsion measurements simplifying assumptions and/or corrections need to be applied to experimental data. In compression it is necessary to assume plane strain," and Poisson s ratio measurements may be performed either at constant strain or constant stress. For a non-linear viscoelastic polymer these two methods are not equivalent. 

With fibres the possible modes of deformation are longitudinal extension, transverse compression and axial torsion, but sheet materials permit more varied experiments extensional measurements on samples cut at several angles to the stretch direction allow combinations of compliances to be obtained. For example. Young s moduli of strips cut at 0°, 45° and 90° to this direction in an orthorhombic sheet are related to compliances by"... 

More recent approaches to extensional measurements on melts are in... 

Comparisons of results from rheometers and indexers are essential in evaluating what material function dominates the indexer s response. Such comparisons can help us to determine when an indexer may give us useful rheological data, as in the case of squeezing flow. Figure 6.4.8. This ability becomes even more important in the next chapter, where we shall see that indexers are the only choice for extensional measurements on low viscosity fluids. 

Although the importance of extensional measurements is well recognized, there are relatively few data available because it is so difficult to generate homogeneous extensional flow, especially for... 

For lower viscosity fluids, an alternate to rod pulling is to use a buoyancy fluid to squeeze the sample radially. Hsu and Flummer-felt (1975) have adapted the spinning drop tensiometer (Joseph et al., 1992) shown in Figure 7.2.9 to extensional measurements. If the surrounding fluid is more dense, P2 > Pi > then the test fluid will move to the center when rotation starts. It will elongate until interfacial tension balances the inertial forces. 

The ratio of uniaxial extensional viscosity to shear viscosity by rod pulling (o) compared to apparent extensional measurements by bubble collapse (A) for a low density polyethylene. Uniaxial data shifted from 150°C to the bubble test temperature of 200 C. From Munstedt and Middleman (1981). 

The other important commercial design for extensional measurements on low viscosity fluids is the opposed nozzle device shown in Figure 8.5.2 (Fuller et al., 1987 Mikkelsen et al., 1988). In addition to the opposed-nozzle configuration, if the arm G is turned 90°, the device can also be operated as fiber spinning and tubeless siphon rheometers (Cai et al., 1992). 

Institute of the National Research Council of Canada (IMI/NRC) was made [3]. This software uses a K-BKZ [4] constitutive equation to describe the nonlinear viscoelastic behavior of the resins coupled with the WLF equation describing the temperature dependence of the resins. The K-BKZ parameters, the moduli, and corresponding relaxation times were obtained by fitting the constitutive equation to the dynamic mechanical and extensional measurements obtained for the three resins. 

Unlike shear viscosity, extensional viscosity has no meaning unless the type of deformation is specified. The three types of extensional viscosity identified and measured are uniaxial or simple, biaxial, and pure shear. Uniaxial viscosity is the only one used to characterize fluids. It has been employed mainly in the study of polymer melts, but also for other fluids. For a Newtonian fluid, the uniaxial extensional viscosity is three times the shear viscosity ... 

Extensional Viscosity. AH three types of extensional viscosity can be measured (101,103) uniaxial, biaxial, and pure shear. Only a few commercial instmments are available, however, and most measurements are made with improvised equipment. Extensional viscosity of polymer melts can be estimated from converging flow (entrance pressure) or from a melt strength drawdown test (208). 

Another type of experiment involves a fluid filament being drawn upward against gravity from a reservoir of the fluid (101,213,214), a phenomenon often called the tubeless siphon. The maximum height of the siphon is a measure of the spinnabiUty and extensional viscosity of the fluid. Mote quantitative measures of stress, strain, and strain rate can be determined from the pressure difference and filament diameter. A more recent filament stretching device ia which the specimen is held between two disks that move apart allows measurements ia low viscosity Hquids (215). AH of these methods are limited to spinnable fluids under small total strains and strain rates. High strain rates tend to break the column or filament. 

A method for measuring the uniaxial extensional viscosity of polymer soHds and melts uses a tensile tester in a Hquid oil bath to remove effects of gravity and provide temperature control cylindrical rods are used as specimens (218,219). The rod extmder may be part of the apparatus and may be combined with a device for clamping the extmded material (220). However, most of the mote recent versions use prepared rods, which are placed in the apparatus and heated to soften or melt the polymer (103,111,221—223). A constant stress or a constant strain rate is appHed, and the resultant extensional strain rate or stress, respectively, is measured. Similar techniques are used to study biaxial extension (101). 

Extensional viscosity that results purely from shear deformation seems to be of less interest, but has been measured (108). The theology of several different polymer melts in terms of shear viscosity and uniaxial and biaxial extensional viscosity has been compared (231). Additional information on the measurement of extensional viscosity are also available (105,238—240). 

Additional complications can occur if the mode of deformation of the material in the process differs from that of the measurement method. Most fluid rheology measurements are made under shear. If the material is extended, broken into droplets, or drawn into filaments, the extensional viscosity may be a more appropriate quantity for correlation with performance. This is the case in the parting nip of a roUer in which filamenting paint can cause roUer spatter if the extensional viscosity exceeds certain limits (109). In a number of cases shear stress is the key factor rather than shear rate, and controlled stress measurements are necessary. 

However, in most experiments, the loads are applied, and the resulting deformations are measured, i.e., the deformations are the dependent variables, not the loads. Thus, the expressions for the middle-surface extensional strains and curvatures in terms of the force and moment resultants would be convenient. 

Two simple invariants, U, and U5, were shown in the previous subsubsection to be the basic indicators of average laminate stiffnesses. For isotropic materials, these invariants reduce to U. =Qi. and U5 = Qqq, the extensional stiffness and shear stiffness. Accordingly, Tsai and Pagano suggested the orthotopic invariants U., and U5 be called the isotropic stiffness and isotropic shear rigidity, respectively [7-16 and 7-17]. They observed that these isotropic properties are a realistic measure of the minimum stiffness capability of composite laminates. These isotropic properties can be compared directly to properties of isotropic materials as well as to properties of other orthotropic laminates. Obviously, the comparison criterion is more complex than for isotropic materials because now we have two measures, and U5, instead of the usual isotropic stiffness or E. Comparison of values of U., alone is not fair because of the degrading influence of the usually low values of U5 for composite materials. 

Fig. 22. Schematic diagram of the opposite jets device with some of the associated streamlines (the x marks the location of the stagnation point). It has been determined that a ratio of d/(2 r0) w 1 — 1.4 constitutes the optimum geometry for extensional viscosity measurements [104]...

Any rheometric technique involves the simultaneous assessment of force, and deformation and/or rate as a function of temperature. Through the appropriate rheometrical equations, such basic measurements are converted into quantities of rheological interest, for instance, shear or extensional stress and rate in isothermal condition. The rheometrical equations are established by considering the test geometry and type of flow involved, with respect to several hypotheses dealing with the nature of the fluid and the boundary conditions the fluid is generally assumed to be homogeneous and incompressible, and ideal boundaries are considered, for instance, no wall slip. 

Flow is generally classified as shear flow and extensional flow [2]. Simple shear flow is further divided into two categories Steady and unsteady shear flow. Extensional flow also could be steady and unsteady however, it is very difficult to measure steady extensional flow. Unsteady flow conditions are quite often measured. Extensional flow differs from both steady and unsteady simple shear flows in that it is a shear free flow. In extensional flow, the volume of a fluid element must remain constant. Extensional flow can be visualized as occurring when a material is longitudinally stretched as, for example, in fibre spinning. When extension occurs in a single direction, the related flow is termed uniaxial extensional flow. Extension of polymers or fibers can occur in two directions simultaneously, and hence the flow is referred as biaxial extensional or planar extensional flow. 

It is well known that LCB has a pronounced effect on the flow behavior of polymers under shear and extensional flow. Increasing LCB will increase elasticity and the shear rate sensitivity of the melt viscosity ( ). Environmental stress cracking and low-temperature brittleness can be strongly influenced by the LCB. Thus, the ability to measure long chain branching and its molecular weight distribution is critical in order to tailor product performance. 

In summary, we have commented briefly on the microscopic applications of NMR velocity imaging in complex polymer flows in complex geometries, where these applications have been termed Rheo-NMR [23]. As some of these complex geometries can be easily established in small scales, NMR velocimetry and visc-ometry at microscopic resolution can provide an effective means to image the entire Eulerian velocity field experimentally and to measure extensional properties in elastic liquids non-invasively. 

Electrostatic repulsion of the anionic carboxylate groups elongates the polymer chain of partially hydrolyzed polyacrylamides increasing the hydrodynamic volume and solution viscosity. The extensional viscosity is responsible for increased resistance to flow at rapid flow rates in high permeability zones (313). The screen factor is primarily a measure of the extensional (elonga-tional) viscosity (314). The solution properties of polyacrylamides have been studied as a function of NaCl concentra-tion and the parameters of the Mark-Houwink-Sakaruda equation calculated... 

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