# Overview of capillary rheometry--part 1.

Description of instrument

The capillary rheometer used in the rubber industry is a precise instrument to measure the rheology of a rubber sample under carefully controlled conditions of temperature and applied shear rate. As noted in ASTM D 5099, there are two types of capillary rheometers used to test rubber:

* Piston type capillary rheometer; and

* screw extrusion type capillary rheometer.

Today, the piston type is usually the instrument of choice for precisely measuring rheological properties. Also, the piston type imparts much less shearing energy to the rubber sample before rheological measurements are made. In this review, most of our discussions will center on the piston type (ref. 1). A basic diagram of a piston type capillary rheometer is shown in figure 1.

[FIGURE 1 OMITTED]

Basic rheological measurements

The pre-weighed rubber specimen is placed at the bottom of the barrel of the rheometer. Then the piston is mechanically moved into the barrel. Through the computer, the travel speed of the piston pushing against the rubber is pre-programmed to move at predetermined speeds. Equation 1 is used to calculate the apparent shear rate that is directly applied to the rubber specimen.

Shear rate ([sec.sup.-1]) = [32 (barrel area) * (ram rate)]/[[pi] [(die diameter).sup.3]] (1)

From this equation, it can be seen that the apparent shear rate is directly proportional to the ram rate or travel speed of the piston that is moving in the barrel against the rubber, forcing it through the orifice in the die mounted at the end of the barrel. The rest of this equation is composed of fixed geometric constants.

On the other hand, the resulting shear stress is calculated from the measured pressure from the pressure transducer mounted near the bottom of the barrel. This pressure is a result of the controlled movement of the piston against the rubber being tested. Equation 2 can be used to calculate the apparent shear stress (ref. 2).

Shear stress = barrel pressure/4(L/D) (2)

Where: L = length of the capillary (tube) in the die attached to the end of the barrel; and D = diameter of the capillary in the die attached to the end of the barrel.

One can see from equation 2 that shear stress (usually in kPa) is directly proportional to the measured barrel pressure. The rest of this equation again consists of fixed geometric constants.

The viscosity ([eta]) is a measure of the resistance of uncured rubber to flow. Equation 3 gives the calculation for viscosity.

Viscosity ([eta]) = shear stress/shear rate (3)

If we have not applied the Bagley and Rabinowitsch corrections, then dividing the apparent shear stress by the apparent shear rate will determine the apparent viscosity ([[eta].sub.app]). When using a die with a relatively high L/D, the apparent viscosity approaches the true viscosity. On the other hand, running a capillary rheometer with a low L/D die can be better for making die swell measurements (ref. 3).

Die swell (or extrudate swell) is another important measurement performed with the capillary rheometer. The die swell is directly measured by the shadow created from a laser beam hitting the extrudate. This percent die swell is calculated from equation 4.

% die swell = [(E-O)/O] x 100% (4)

Where: E = diameter of extrudate; and O = diameter of the capillary.

It is better to use dies with lower L/D values for better accuracy and test sensitivity to differences in die swell. Die swell is related to a compound's uncured elasticity or nerviness. Figure 2 is a schematic diagram showing how laser light can be used to measure die swell of the extrudate (refs. 4 and 5). Figure 3 demonstrates die swell from extrusion of a rubber compound.

[FIGURES 2-3 OMITTED]

Capillary rheometry has been used in the rubber industry for about 30 years. The first MPT (Monsanto Processability Tester) was introduced in 1976.

The old technology MPT used a special 19.05 mm (0.75 in.) diameter barrel for the relatively high viscosity rubber (compared to plastic hot melts). The MPT piston was designed to have an effective travel distance of one inch (2.54 cm) in the barrel. This travel distance was divided into four equal fractions of one-fourth inch (0.635 cm) each for four different zones for measuring viscosities at four different ram travel speeds (shear rates) (ref. 6).

With the introduction of the ARC 2020 capillary rheometer, there has been a complete redesign, with the latest state-of-the-art mechanical design, electronics and software. The ARC 2020 can use two different barrels that are interchangeable. One barrel is 0.5 inch (1.27 cm) in diameter, which is designed for use with conventional rubber compounds. The other barrel, which is 3/8 of an inch in diameter (0.9525 cm), can be substituted when testing thermoplastic elastomers (TPE) or thermoplastics. These barrels are 9" (22.86 cm) in length with a working length of 4" (10.16 cm), four times the working distance that the older MPT had. Also, with the much more flexible and fully programmable software, one can now create test configurations with as many as 10 working zones (compared to only four zones for the MPT). With the greater working length of the ARC 2020, one can create test configurations that have greater running distance at very high shear rates (ref. 7). With the older technology of the MPT, there was very little running time at very high shear rates (high ram speeds), and therefore only fair test repeatability and statistical test sensitivity. Also, the ARC 2020 calculates shear stress from the pressure transducer inserted into the barrel at a low position and from a load cell connected to the piston. The MPT only used a pressure transducer inserted into the barrel.

Non-Newtonian behavior

For low molecular weight, non-polymeric materials, such as water or rubber extender oils, for example, the resulting shear stress is precisely proportional to the applied shear rate. These materials are considered Newtonian fluids. On the other hand, polymeric materials, such as rubber or rubber compounds, do not proportionately increase their shear stress with a given rise in applied shear rate. These materials are non-Newtonian and display pseudo-plasticity or shear thinning behavior, as shown in figure 4. When the viscosity is calculated from shear stress and shear rate, the shear thinning profile of the polymeric material can be seen, as shown in figure 5.

[FIGURES 4-5 OMITTED]

The reason that polymeric materials, such as rubber or rubber compounds, are pseudo-plastic is simply that rubber macromolecules are randomly orientated and sometimes coiled when at rest. However, when rubber is forced into a flow, these very long molecules start orientating themselves into the direction of the flow, thus reducing the internal friction and also decreasing their resistance to flow. Some different elastomers and compounds shear thin faster than other elastomers and compounds. Capillary rheometry can quantify the extent of shear thinning that occurs for different rubber compounds. This is very important information when predicting how a given new compound will behave in a factory extrusion or injection molding process (ref. 8).

One method to quantify this shear thinning quality is to use the power law fluid equation given in equation 5.

[tau] = K[([??]).sup.N] (5)

Where [tau] = apparent shear stress; [??] = apparent shear rate; K = constant (sometimes called consistency index); and N = power law index.

We can convert this equation to a log-log expression, as shown in equation 6.

log ([tau]) = log (K) + N log ([??]) (6)

When N is equal to 1.0, then the material being tested is considered a Newtonian fluid. However, usually rubber compounds test between 0.18 and 0.33 for the calculated N (refs. 9 and 10).

The fact that the viscosity of some compounds can drop faster than other compounds when exposed to higher shear rates is very important. For example, the Mooney viscometer measures viscosity at only 1.3 [s.sup.-1] of shear rate. As shown in figure 6, the Mooney viscometer would indicate that compound 1 is higher in viscosity than compound 2. However, clearly compound 2 has the higher viscosity in downstream processes, such as extrusion or injection molding, which subject these compounds to much higher shear rates.

[FIGURE 6 OMITTED]

Correction factors used in capillary rheometry

After measuring different apparent shear stress values from different applied shear rate values, one can calculate apparent viscosity values as well. For factory problem solving and quality control work, many times the apparent shear stress, apparent shear rate and apparent viscosity values are commonly used without correction. However, to calculate the "true" (or corrected) viscosity, one must apply the Bagley correction and the Rabinowitsch correction.

Figure 7 shows how the rubber specimen is forced into the die orifice and exits the capillary.

[FIGURE 7 OMITTED]

To measure the true viscosity, it is assumed that the pressure drop over the length (L) of this die is linear and the pressure is zero at the exit from the die. As can be seen from figure 8, this assumption is not always true (ref. 11).

[FIGURE 8 OMITTED]

To implement the Bagley correction, it is necessary to run a series of tests with at least two different dies, preferably three tests, using dies of the same diameter but different L/D. For example, dies with L/D values of 10, 20 and 30 could be used. Figure 9 shows a plot of pressure vs. L/D that is extrapolated towards zero.

[FIGURE 9 OMITTED]

The intercept of barrel pressure with the L/D ratio line to the left of the origin represents the Bagley L/D correction. This accounts for the energy losses at the die entrance. So by inserting this Bagley L/D correction into equation 2 gives us equation 7:

True shear stress = (barrel pressure)/[4 (L/D + Bagley L/D correction)] (7)

Obviously, here the true (or corrected) shear stress will be less than the apparent shear stress. Since the rubber specimen being tested is known to be non-Newtonian, then the apparent shear rate also has to be re-calculated and converted to the true (or corrected) shear rate.

The true shear rate can be calculated using the Rabinowitsch correction for non-Newtonian materials, as shown in equation 8.

True shear rate = [(3N + 1)/4N] apparent shear rate (8)

Where N = power law index (from equation 5).

The true (or corrected) viscosity is simply calculated from the true shear stress (from the Bagley correction) and the true shear rate (from the Rabinowitsch correction), as shown in equation 9.

True viscosity = true shear stress/true shear rate (9)

These corrections that we have just discussed can be automatically calculated with modern software at the end of the testing (refs. 12-14).

Appearance of extrudate

The visual appearance of the extrudate from a capillary rheometer can give valuable information concerning the quality of the rubber compound. This is particularly true for extrudates produced at very high shear rates such as 1,000 [s.sup.-1]. One important quality that a capillary rheometer can detect is melt fracture. Not all rubber compounds experience melt fracture at higher shear rates. Sometimes roughness of the extrudate is called "snakeskin."

There are other causes of rough surface appearance of the extrudate besides melt fracture. For example, a poor quality of mix can cause extrudate appearance problems. The extrudate comparison in figure 10 shows a rough surface for a batch that did not receive sufficient work history vs. the smooth extrudates, which represent batches of the same compound with better mixing. Of course, premature scorch can also explain extrudate surface roughness. This cause is discussed next under capillary scorch test (ref. 15).

[FIGURE 10 OMITTED]

Capillary scorch testing

The capillary rheometer can be used as a scorch test at either low shear rate (just as the Mooney scorch is performed at low shear rate), or at a high shear rate similar to that applied in factory extrusion or injection molding. Sometimes, the capillary scorch test might be performed at the same temperature as the Mooney scorch test itself or, alternately, at a temperature relevant to the factory process. The capillary scorch condition (the onset of vulcanization) is first detected by the die swell detector, as illustrated in figure 11. Scorch will cause a rougher extrudate appearance. Lastly, scorch will cause the barrel pressure to increase. The increased variation in die swell provides a more sensitive method for investigating potential quality problems. The compound tested in figure 11 tested satisfactory with the Mooney scorch test; however, the capillary scorch test did detect a problem. This problem was later solved by using less re-worked stock (refs. 16 and 17).

[FIGURE 11 OMITTED]

Wall slippage

A typical velocity profile of the flow of a rubber polymer or rubber compound in the capillary of the die is shown in figure 12. The actual shear rate is greatest at the wall, but approaches zero toward the center of the capillary tube. The true viscosity calculation in equation 9 is actually calculating the viscosity at the wall (refs. 18 and 19).

[FIGURE 12 OMITTED]

If the rubber compound has a very high viscosity or has a chemical composition that imparts poor rubber-to-metal stickiness to the metallic wall of the capillary, then wall slip might occur, which introduces an error into the viscosity measurement. Sometimes, the test temperature might be a poor choice for this compound and wall slip might result. If there is a suspicion that wall slip is occurring, one can check by running tests with different die diameters but the same L/D, and plotting apparent viscosity vs. shear rate (see figure 13) (ref. 20).

[FIGURE 13 OMITTED]

Part 2 will appear in the February issue.

References (Part 1)

(1.) ASTM D5099, Vol. 9.01 of ASTM International Book of Standards, 2006.

(2.) J. Dick, RPA Training Course Manual, 1993.

(3.) J. Dick, Chapter 2, Rubber Technology, Compounding and Testing for Performance, Hanser, 2001.

(4.) J. Sezna, MPT Training Manual, 1990.

(5.) H. Pawlowski, "A brief qualitative introduction to rheology," slide presentation, 2006.

(6.) Monsanto MPT Brochure, 1987.

(7.) Alpha Technologies ARC 2020 Brochure, 2006.

(8.) J. Dick and M. Gale, "Processing tests," Chapter 8 in Handbook of Polymer Testing, pp. 171-223, Marcel Dekker, Inc., New York, NY, 1999, edited by R. Brown.

(9.) ibid ref. 1.

(10.) H. Kramer, "Simulation of the injection molding process with a special capillary rheometer," paper no. 29, Rubber Div. ACS Meeting, Fall, 1993.

(11.) ibid ref 5.

(12.) J. Sezna, MPT Training Manual, 1988.

(13.) ibid ref. 5.

(14.) G. Colbert and K. Ziegel, "Estimation of end corrections in capillary flow," paper at Society of Rheology, Nov. 1, 1979.

(15.) ibid ref 6.

(16.) ibid ref 14.

(17.) Monsanto MPT Manual, 1987.

(18.) C.W. Macosko, Chapter 6, "Shear rheometry: Pressure driven flows," Rheology Principles, Measurements and Applications, VCH Publishers, Inc., 1994, pp. 244-252.

(19.) ibid ref. 5.

(20.) ibid ref. 18.

by John S. Dick, Alpha Technologies (jdick@dynisco.com)
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