Steady-flow rheometers

The steady and dynamic drag-induced simple shear-flow rheometers, which are limited to very small shear rates for the steady flow and to very small strains for the dynamic flow, enable us to evaluate rheological properties that can be related to the macromolecular structure of polymer melts. The reason is that very small sinusoidal strains and very low shear rates do not take macromolecular polymer melt conformations far away from their equilibrium condition. Thus, whatever is measured is the result of the response of not just a portion of the macromolecule, but the contribution of the entire macromolecule. 

Fig. 3.1 Examples of simple, viscometric, shear-flow rheometer geometries, la, 2a and 3 are steady while lb and 2b are dynamic rheological property... 

Rheological Response of Polymer Melts in Steady Simple Shear-Flow Rheometers... 

The attempt to relate the nonlinear and steady flow behavior with the plasticity (the yield stress) of the solutions of styrene (S) and butadiene (B) block copolymers were carried out by using a concentric cylinder rheometer [8]. Nonsinusoidal responses of the outer cylinder found in the SB sample were analyzed to obtain G - and G J by Eq. (78). Figure 54 shows the frequency dependence of the nonlinear dynamic modulus G - and GJ (/ = 1 and 3) for the system. Typical nonlinear behavior, that is, a large contribution of the higher odd harmonics and a plateau region in the fundamental harmonics, can be seen in the data with 60 = 2 and 4, whereas in those with 1.1° the response is nearly linear and elastic. The ratio of the amplitude of the 7th harmonics to that of the fundamental harmonics, Gj/Gj, can be used as a measure of the nonlinearity of the system, where Gj = [(Gj)+(GJ)]. Figure 55 shows the frequency dependence of Gj/G for the SB system with various... 

The polymer solution used for the production of the PAN I filaments discussed in this chapter was a 15% w/ w DMPU/PANI spin dope having a viscosity of 2l,0(K) cP at a shear rate of 1.5 s at a temperature of 25°C. A Brookfield cone-and-plate rheometer was used for the viscosity determination. The polymer solution is placed in the spin dope tank and pressurized with N2, providing a steady flow of the spin dope to the gear pump. The solution is then pumped through a 0.1 mm circular spinnerette (L/D = 2.0) into a coagulation bath consisting of NMP and water. The fiber is continuously taken up... 

To study the elastic response in the near-quiescent state we used a constant stress cone and plate rheometer to measure the recoverable shear strain after steady flow had been achieved. For an experimental liquid crystal polyester the elastic response at low stress is very large suggesting an elastic modulus of the order 400 N m —at least two orders of magnitude lower than a chemically similar polyester melt which does not exhibit liquid crystal phenomena (Fig. 3). However, at a shear stress of about 10 N —at which the conventional polyester is just starting to demonstrate significant elastic response—the high elasticity of the liquid crystal polyester collapses. 

Rheological properties of the gels were performed with a constant stress rheometer (Rheolyst ARIOOO N, TA Instruments) with a cone and plate geometry (cone diameter 40 mm and 2° angle). Rheological experiments were cmied out in steady flow, creep and dynamic oscillation modes over a wide range of shear rates, frequencies, temperatures and time. To prevent evaporation of the hydrocarbon a solvent trap (as supplied by TA Instruments) was installed for all experimrats. 

The Weissenbeig Rheogoniometer (49) is a complex dynamic viscometer that can measure elastic behavior as well as viscosity. It was the first rheometer designed to measure both shear and normal stresses and can be used for complete characterization of viscoelastic materials. Its capabilities include measurement of steady-state rotational shear within a viscosity range of 10-1 —13 mPa-s at shear rates of 10-4 — 104 s-1, of normal forces (elastic effect) exhibited by the material being sheared, and of an oscillatory shear range of 5 x 10-6 to 50 Hz, from which the elastic modulus and dynamic viscosity can be determined. A unique feature is its ability to superimpose oscillation on steady shear to provide dynamic measurements under flow conditions all measurements can be made over a wide range of temperatures (—50 to 400°C). 

Basic Protocol 2 is for time-dependent non-Newtonian fluids. This type of test is typically only compatible with rheometers that have steady-state conditions built into the control software. This test is known as an equilibrium flow test and may be performed as a function of shear rate or shear stress. If controlled shear stress is used, the zero-shear viscosity may be seen as a clear plateau in the data. If controlled shear rate is used, this zone may not be clearly delineated. Logarithmic plots of viscosity versus shear rate are typically presented, and the Cross or Carreau-Yasuda models are used to fit the data. If a partial flow curve is generated, then subset models such as the Williamson, Sisko, or Power Law models are used (unithi.i). 

To reach steady state, the residence time of the fluid in a constant stretch rate needs to be sufficiently long. For some polymer melts, this has been attained however, for polymer solutions this has proved to be a real challenge. It was not until the results of a world wide round robin test using the same polymer solution, code named Ml, became available that the difficulties in attaining steady state in most extensional rheometers became clearer. The fluid Ml consisted of a 0.244% polyisobutylene in a mixed solvent consisting of 7% kerosene in polybutene. The viscosity varied over a couple of decades on a logarithmic scale depending on the instrument used. The data analysis showed the cause to be different residence times in the extensional flow field... 

Since pressure driven viscometers employ non-homogeneous flows, they can only measure steady shear functions such as viscosity, 77(7). However, they are widely used because they are relatively inexpensive to build and simple to operate. Despite their simplicity, long capillary viscometers give the most accurate viscosity data available. Another major advantage is that the capillary rheometer has no free surfaces in the test region, unlike other types of rheometers such as the cone and plate rheometers, which we will discuss in the next section. When the strain rate dependent viscosity of polymer melts is measured, capillary rheometers may provide the only satisfactory method of obtaining such data at shear rates... 

Thus, in order to create a steady simple uniaxial extensional flow, the rheometer must cause the thin filament length to increase exponentially in time. 

This recoverable shear strain shows up when the flow of a polymer melt in a capillary rheometer is suddenly stopped. The material that has just left the capillary rheometer will clearly recover to a certain extent, in principle equal to 1/2xi>i.o/(qVo)- Fig. 15.11 the various strains are shown after starting a steady shear flow at time f = 0 and stopping it at time fi. 

The steady-state flow properties of block copolymers are often hard to measure. In steady shear, the shear stress often does not reach a clear steady-state value (Lyngaae-Jorgensen 1985). In cone-and-plate rheometers, steady shearing of an ordered block copolymer can result in edge fracture and flow irregularities, as might be expected when one forces a quasi-solid structure to flow (Winey et al. 1993a). 

Both strain- and stress-controlled rotational rheometers are widely employed to study the flow properties of non-Newtonian fluids. Different measuring geometries can be used, but coaxial cylinder, cone-plate and plate-plate are the most common choices. Using rotational rheometers, two experimental modes are mostly used to study the behavior of semi-dilute pectin solutions steady shear measurements and dynamic measurements. In the former, samples are sheared at a constant direction of shear, whereas in the latter, an oscillatory shear is used. 

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