Shear plate rheometers

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. 

There are a number of techniques that are used to measure polymer viscosity. For extrusion processes, capillary rheometers and cone and plate rheometers are the most commonly used devices. Both devices allow the rheologist to simultaneously measure the shear rate and the shear stress so that the viscosity may he calculated. These instruments and the analysis of the data are presented in the next sections. Only the minimum necessary mathematical development will he presented. The mathematical derivations are provided in Appendix A3. A more complete development of all pertinent rheological measurement functions for these rheometers are found elsewhere [9]. 

There would be a minimum of 80 data sets needed to generate this data for one temperature. Because of the time involved, usually about 10 to 15 shear rate data points are generated at each temperature. The plot of the viscosity as a function of shear rate at 270°C is presented in Fig. 3.22. The viscosity below a shear rate of 5 1/s would be best taken using a cone and plate rheometer. The wall friction for the capillary rheometer between the piston and the rheometer cylinder wall would likely cause a force on the piston of the same order as the force due to the flow stress. 

The rheometer most often used to measure viscosity at low shear rates is the cone and plate viscometer. A schematic of a cone and plate rheometer is found in Fig. 3.24. The device is constructed with a moving cone on the top surface and a stationary plate for the lower surface. The polymer sample is positioned between the surfaces. Two types of experiments can be performed the cone can be rotated at a constant angular velocity, or it can be rotated in a sinusoidal function. The motion of the cone creates a stress on the polymer between the cone and the plate. The stress transferred to the plate provides a torque that is measured using a sensor. The torque is used to determine the stress. The constant angle of the cone to the plate provides an experimental regime such that the shear rate is a constant at all radii in the device. That is, the shear rate is independent of the radial position on the cone, and thus the shear stress is also independent of the position on the cone. 

Using the cone and plate rheometer the angle Q is forced in a sinusoidal manner, leading to linear strain being introduced in the polymer. The shear strain, y, is a sinusoidal function of time t with a shear rate amplitude of % as follows ... 

Here t is the resulting shear stress, 6 is the phase shift often represented as tan(d), and (O is the frequency. The term 6 is often referred to as the loss angle. The in-phase elastic portion of the stress is To(cosd)sin(wt), and the out-of-phase viscous portion of the stress is To(sind)cos(complex modulus and viscosity, which can be used to extend the range of the data using the cone and plate rheometer [6] ... 

The flow behaviour of polymeric electrophotographic toner systems containing carbon black varying in surface area and concentration were determined using a cone and plate rheometer [51]. As the concentration of carbon black was increased, the viscosity at low shear rates become unbounded below a critical shear stress. The magnitude of this yield stress depended primarily on the concentration and surface area of the carbon black flller and was independent of the polymer (polystyrene and polybutyl methacrylate) and temperature. It was postulated that at low shear rates the carbon black formed an independent network within the polymer which prevented flow. 

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... 

The cone-plate rheometer. The cone-plate rheometer is often used when measuring the viscosity and the primary and secondary normal stress coefficient functions as a function of shear rate and temperature. The geometry of a cone-plate rheometer is shown in Fig. 2.47. Since the angle Oo is very small, typically < 5°, the shear rate can be considered constant throughout the material confined within the cone and plate. Although it is also possible to determine the secondary stress coefficient function from the normal stress distribution across the plate, it is very difficult to get accurate data. 

Measurement of the flow properties of non-Newtonian fluids is typically accomplished via rotational techniques. The rotational methods fall into two basic types, concentric cylinder and cone and plate rheometers. In a concentric cylinder rheometer, a bob is placed inside a cylinder so that the fluid to be studied may be placed into the gap between the cylinders. This arrangement helps approximate a uniform shear rate throughout a sample by shearing only a thin film of sample fluid between... 

In the cone and plate rheometer, a cone-shaped bob is placed against a flat plate so that the fluid to be studied may be placed into the gap between the lower face of the cone and the upper face of the plate. Again, in the Searle method, the cone is rotated while in the Couette method the plate turns. In each case, the torque on the cone is measured. Figure 6.5 shows a Searle-type cone and plate arrangement. For this arrangement the shear stress is given by ... 

We note that with the cone-and-plate rheometers, fracture of the polymer melt is observed at shear rates exceeding 10 2 or 10 1 s-1. Fracture is initiated at the melt-air interface at the perimeter. This has been attributed to the fact that the elastic energy becomes greater than the energy required to fracture the polymer melt at those shear rates (22). Irrespective of the origin of the fracture, it limits the operation of the cone-and-plate instrument to below the previously mentioned shear rates. 

Figure 22.9. Schematic diagram of a true shear sliding-plate rheometer. (Reproduced with permission from Gunasekaran and Ak, 2002.)...

This section will be devoted to the Newtonian viscosity i]0, that is to situations where the shear rate is proportional to the shear stress. This is the case under steady-state conditions at low shear rates. Although rj0 may be directly measured at low shear rates in a cone and plate rheometer, it is in general not measured directly but found by extrapolation of viscosity values, as measured in a capillary rheometer, as a function of shear rate ... 

FIG. 15.13 Non-Newtonian shear viscosity r/(q) at 170 °C vs. shear rate, q, for the polystyrene mentioned in Fig. 15.12, measured in a cone and plate rheometer (O) and in a capillary rheometer ( and ) and the dynamic and complex viscosities, rj (w) (dotted line), rj (w) (dashed line) and i (< ) (full line), respectively, as functions of angular frequency, as calculated from Fig. 15.12. From Gortemaker (1976) and Gortemaker et al. (1976). Courtesy Springer Verlag. 

FIG. 15.46 Viscosity, 77, and first normal stress difference, Nh of Vectra 900 at 310 °C as functions of shear rate, according to Langelaan and Gotsis (1996). The first normal stress coefficient, Yi, is estimated from N, by the present author. ( ) Capillary rheometer ( ) and ( ) cone and plate rheometer ( ) complex viscosity rj (A) non-steady state values of the cone and plate rheometer. Courtesy Society of Rheology. 

Cone and plate rheometers solve one problem, by providing constant shear rate. They can also be designed to measure torque, dynamic properties, normal stresses, and forces in other directions. A disadvantage is that they are limited to low shear rates. 

Procedure Use a suitable cone and plate rheometer [Con-traves Rheomat 115A (cone CP-6), Physica Rheolab MC 100 (cone MK23), or equivalent] maintained at 37.8° and capable of measuring the non-Newtonian flow curve hysteresis for ascending and descending shear rates programmed from 0 to 800 s-1. Hold the rheometer at 0 s-1 for 120 s, raise it to 800 s-1 in 7.5 min, hold for 1 s, then decrease to 0 s-1 in 7.5 min to measure the thixotropic area. Check the accuracy of the rheometer with viscosity standards (Cannon ASTM Certified Viscosity Standards, S-2000 and N-350, or equivalent). The measured viscosity must be within 0.20% of the stated viscosity at 37.8°, or the rheometer s cone factor must be recalculated. 

The experimental device constructed to orient uniformly thick samples in simple shear is schematically represented in Fig. 3. It is basically a sliding-plate rheometer, the polymer sample being sheared between two temperature-controlled parallel plates. The upper plate is fixed whereas the lower plate can be displaced both horizontally and vertically with two pneumatic jacks. 

Specimens were sheared by using the above described sliding plate rheometer at two different shear stresses Oxyi 0.05 and 0.2 MPa. For axy=O.05 MPa, the behaviour of the melt was found to be nearly Newtonian. One sample was sheared at the highest shear stress up to a final shear strain of y=2.4. For the lowest shear stress, two samples with different shear strains were prepared y=2.8 and y=4. These samples are referenced in Table 7. 

As will be shown below, the experiment in the sliding plate rheometer does not allow one to determine Nl, since the normal force is in fact related to the second normal stress difference. For this reason, we studied the stress-optical law in shear by assuming that the principal directions of shear and refractive index are close to each other in the x-y plane. It is then straightforward to express the difference of principal stresses in the x-y plane... 

A plot of yapp against 1 / h will then be a straight line with slope 2Vs. This method has been used to measure the slip velocity for polyethylene melts in a sliding plate (plane Couette) rheometer by Hatzikiriakos and Dealy (1991). Analogous methods have been applied to shearing flows of melts in capillaries and in plate-and-plate rheometers (Mooney 1931 Henson and Mackay 1995 Wang and Drda 1996). 

Thus, the shear stress in the cone-and-plate rheometer varies by only 1% throughout the gap, if the cone angle is 0.1 radian (i.e., 5.7°). 

Figure 10.15 Damping of shear stress and reversal of damping as a function of time after startup of shearing in a cone-and-plate rheometer at y = 8 seer for a tumbling nematic, 8CB. In (a) the shearing direction is reversed after imposition of 170 strain units the damping of the stress nscillatinns is rp.vp.rsed. In (h), shear reversal occurs after imposition of 480 strain iiniK fhp damping is not reversed. (From Gu et al. 1993, with permission from the Journal of Rheology.)...

Figure 10.26 Viscosity versus shear rate of cholesteryl myristate in a cone-and-plate rheometer as a function of shear rate. At high temperatures, T > 83 C, the sample is a low-viscosity, Newtonian isotropic liquid. At intermediate temperatures, 83 > T > 78°C, the sample is a shear-thinning cholesteric. At low temperatures the sample is a shear-thinning smectic. (From Sakamoto et al., reprinted with permission from Mol. Cryst. Liq. Cryst. 8 443, Copyright 1969, Gordon and reach Publishers.)...

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). 

Fiber orientation can be induced by simultaneous shearing and application of electric fields. Such conditions were simulated in a plate rheometer in which the plates were also inducing an electric field. Dielectric particles of filler were oriented in the same direction as that of the electric field. The time to reach an equili-... 

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