Viscosity Capillary rheometer

J The viscosity characteristics of a polymer melt are measured using both a capillary rheometer and a cone and plate viscometer at the same temperature. The capillary is 2.0 mm diameter and 32.0 mm long. For volumetric flow rates of 70 x 10 m /s and 200 x 10 m /s, the pressures measured just before the entry to the capillary are 3.9 MN/m and 5.7 MN/m, respectively. 

The shear viscosity, especially as measured with capillary rheometers characterized by high shear rates, is hardly sensitive to material structure since the investigator usually has to deal with the substantially destroyed structure in the molten sample. Melt stretching experiments would normally provide much more information [33]. 

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]. 

Capillary rheometers are used extensively to measure viscosity in the intermediate to high shear rate range. The rheometer has for all practical purposes a lower limit in viscosity measurement because of the plunger seals. These seals are shown on the bottom of the plunger in Fig. 3.16, and they induce a frictional resistance when they are pushed through the rheometer barrel. The piston force can be evaluated without polymer in the barrel, but it is always a source of error at low viscosities because of experimental variability. Moreover, barrel friction is one of the critical corrections that must be made when evaluating viscosity measurements... 

A new polymer was developed by the polymer scientists in a company. A sample has been provided to the process development laboratory to determine the viscosity of the polymer as a function of shear rate and temperature. The instrument available is an old capillary rheometer. The piston has a diameter of 9.525 mm, and a series of capillaries that fit the rheometer barrel have a diameter of 2.54 mm and lengths of 25.4, 50.8, 76.2, and 101.6 mm. The rheometer temperature was set at 270 °C. Shear viscosity data are needed to estimate process performance. 

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. 

PPG (at higher temperatures) behaves like a typical pseudoplastic non-Newtonian fluid. The activation energy of the viscosity in dependence of shear rate (284-2846 Hz) and Mn was detected using a capillary rheometer in the temperature range of 150-180°C at 3.0-5.5 kJ/mol (28,900 Da) and 12-13 kJ/mol (117,700 Da) [15]. The temperature-dependent viscosity for a PPG of 46 kDa between 70 and 170°G was also determined by DMA (torsion mode). A master curve was constructed using the time-temperature superposition principle [62] at a reference temperature of 150°G (Fig. 5) (Borchardt and Luinstra, unpublished data). A plateau for G was not observed for this molecular weight. The temperature-dependent shift factors ax were used to determine the Arrhenius activation energy of about 25 kJ/mol (Borchardt and Luinstra, unpublished data). 

Fig. 10. Viscosity and first normal stress difference vs. shear stress for polypropylene (at 200 °C) filled with calcium carbonate (50 wt%) with and without a titanate coupling agent (TTS ) (O, ) pure polypropylene (PP) (A,A) PP/CaC03=50 50 (by wt.) ( , ) PP/CaC03=50 50 with TTS (1 wt%). The open symbols were obtained from a cone and plate instrument and the closed symbols from a slit/capillary rheometer.

Rubber-based nanocomposites were also prepared from different nanofillers (other than nanoclays) like nanosilica etc. Bandyopadhyay et al. investigated the melt rheological behavior of ACM/silica and ENR/silica hybrid nanocomposites in a capillary rheometer [104]. TEOS was used as the precursor for silica. Both the rubbers were filled with 10, 30 and 50 wt% of tetraethoxysilane (TEOS). The shear viscosity showed marginal increment, even at higher nanosilica loading, for the rubber/silica nanocomposites. All the compositions displayed pseudoplastic behavior and obeyed the power law model within the experimental conditions. The... 

A third evaluation which can be applied to good effect to describe the processability of the polymer is a variable-load melt viscosity measurement. A precaution here is to conduct this test last, on the scraps left over from other physical testing, since the temperature in the rheometer may degrade the precious material irreversibly. A variable-load capillary rheometer simulates extrusion and may thereby provide the strand for evaluation of qualitative... 

Melt flow rheology measurements were obtained on the MBAS polymer using an Instron capillary rheometer. The data reported were obtained using an 0.056-inch capillary, 90° included angle, with an L/D of 36. In Figure 5 the maximum shear stress (lb/in2) is plotted vs. the apparent shear rate (sec 1). The apparent viscosity (lb-sec/in2) vs. tem-... 

Steady shear viscosities can be measured with two different instruments. The System IV can measure polymer viscosities from about 0.001 to 10 sec 1 while the Gottfert Capillary Rheometer is capable of obtaining viscosities from 0.1 to 100,0001/s. In steady shear, the strains are very large as opposed to the dynamic measurements that impose small strains. In the capillary rheometer, the polymer is forced through a capillary die at a continuously faster rate. The resulting stress and viscosity are measured by a transducer mounted adjacent to the die. A schematic of the system is illustrated in Figure 5. 

The raw data from the capillary rheometer measurements are subject to four important corrections to obtain true viscosity and shear rate values. These corrections, which are fully described in Kwag (1998) and Kwag et al. 

The capillary viscometer. The most common and simplest device for measuring viscosity is the capillary viscometer. Its main component is a straight tube or capillary, and it was first used to measure the viscosity of water by Hagen [28] and Poiseuille [60], A capillary rheometer has a pressure driven flow for which the velocity gradient or strain rate and also the shear rate will be maximum at the wall and zero at the center of the flow, making it a non-homogeneous 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 basic features of the capillary rheometer are shown in Fig. 2.46. A capillary tube of a specified radius, R, and length, L, is connected to the bottom of a reservoir. Pressure drop and flow rate through this tube are used to determine the viscosity. This will be covered in detail in Chapter 5. 

Many of the comments in the previous chapter about the selection of grade, additives and mixing before moulding apply equally in preparation for extrusion. It is important of course that the material should be appropriate for the purpose, uniform, dry, and free from contamination. It should be tested for flow and while many tests have been devised for this it is convenient to classify them as either for low or high rates of shear. The main terms used in such testing ( viscosity , shear rate , shear strain , etc.) are defined in words and expressed as formulae in ISO 472, and it is not necessary to repeat them here. Viscosity may be regarded as the resistance to flow or the internal friction in a polymer melt and often will be measured by means of a capillary rheometer, in which shear flow occurs with flow of this type—one of the most important with polymer melts—when shearing force is applied one layer of melt flows over another in a sense that could be described as the relationship between two variables—shear rate and shear stress.1 In the capillary rheometer the relationship between the measurements is true only if certain assumptions are made, the most important of which are ... 

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. 

A variety of laboratory instruments have been used to measure the viscosity of polymer melts and solutions. The most common types are the coaxial cylinder, cone-and-plate, and capillary viscometers. Figure 11 -28 shows a typical flow curve for a thermoplastic melt of a moderate molecular weight polymer, along with representative shear rate ranges for cone-and-plate and capillary rheometers. The last viscometer type, which bears a superficial resemblance to the orifice in an extruder or injection molder, is the most widely used and will be the only type considered in this nonspecialized text. 

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). 

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