Part I: Measuring reliable, dissipation-corrected steady shear viscosities through continuous shear
Almost 50 years of experience in the rheological testing of elastomer compounds have led to a new testing instrument – the RPA rotational by GOETTFERT. The Rubber Process Analyzer (RPA) is used to analyze rubber compounds in both the plastic and vulcanized states as well as to characterize crosslinking behavior. In conventional RPAs, the lower die half is driven with a sinusoidal rotational motion (oscillation), while the torque transmitted through the sample is measured at the upper die half. In addition, LAOS (large amplitude oscillatory shear), cure isotherms, temperature sweeps, relaxation, step, or ramp tests can be performed.
The new RPA rotational features a continuously rotating lower chamber equipped with an integrated gradient temperature sensor for determining the temperature buildup created by shear dissipation — a unique feature on the market. Figure 1 schematically illustrates the fundamental difference between conventional RPA designs and the RPA rotational.
In part I of the RheoInfo on the RPA rotational, we will take a closer look at the RPA rotational option of continuous rotation measurements. These allow us to directly measure steady shear viscosities, which is not possible with conventional RPAs. Furthermore, the disturbing influence of the shear dissipation temperature buildup will be demonstrated, together with a GOETTFERT-exclusive correction procedure based on the gradient temperature sensor.
Figure 1: Conventional rubber process analyzers (RPA) are rotational rheometers with limited rotation (left side). Accordingly, measurements are mostly limited to oscillatory stimuli. The RPA rotational (right side) is one of the first RPAs with a moving die that can perform rotations of unlimited amplitude. This creates the possibility for continuous rotation measurements to determine the steady shear viscosity. Thanks to the built-in gradient temperature sensor, the temperature buildup due to dissipative heating can be detected and corrected, allowing for reliable viscosity data even under fast shear conditions. The figure is reprinted from a KGK Rubberpoint article 1.
Continuous rotation measurements are performed by an sudden change in angular velocity or shear rate, also referred to as a step shear test. The tests are perfomed isothermally at a certain set temperature TSet. The response to the imposed shear rate is the measured torque, which provides the shear stress as a function of time. The shear viscosity is then calculated as the ratio of shear stress and shear rate. Figure 2 shows some exemplaric measurements with various applied shear rates performed with a polyisobuylene (PIB,Oppanol B15N).
After a certain time, the shear viscosity approaches an equilibrium plateau level, the so-called steady shear viscosity. The steady-state viscosity plateau is well-defined for slower shear rates, but for shear rates of 50 1/s and above (fast shear regime), the plateau gradually vanishes towards a sloped appearance of the curves. Here, the impact of shear dissipation becomes visible. The introduced mechanical energy is transformed into heat, leading to a rapid temperature increase in the measured material beyond the intended isotherm at TSet. Hence, the material’s temperature-dependent viscosity decreases. The effect becomes naturally more pronounced with increased shear rate. For low shear rates below 50 1/s, shear dissipation can be basically neglected, so no corrections are required. Therefore, several low shear rates can be measured with the same sample, saving time and costs. Yet, for high shear rates of 50 1/s and above, it is recommended to use a new sample for each continuous rotation measurement due to the high shear dissipation.
Figure 2: Viscosity curves determined during continuous rotation measurements for a PIB at a set temperature of 60 °C. The upper graph shows the curves of all applied shear rates. The fast shear regime is highlighted via a gray background and further zoomed onto in the lower graph. Curves with low shear rates establish a distinct steady shear plateau after some equilibration time, while fast shear measurements show a continuously decreasing course due to shear dissipation. The figure is reprinted from a KGK Rubberpoint article 1.
Figure 3 shows the actual sample temperatures TSample from the fast shear measurements on PIB, determined from the integrated gradient temperature sensor of the RPA rotational. For e.g. a shear rate of 500 1/s, an extreme temperature increase of more than 70 °C in 3 s measurement time is found. This temperature buildup has drastic influence on the measured viscosity. With the exact knowledge of the time-dependent sample temperature, it is possible to reconstruct the viscosity curve that would be expected if no dissipative temperature increase occurred.
Figure 3: The time-dependent sample temperatures of the four dissipation-affected fast shear measurements of PIB known from Figure 2. TSample is calculated from the difference signal of the gradient temperature sensor that is installed in the RPA rotational. The figure is reprinted from a KGK Rubberpoint article 1.
Figure 4 shows the PIB measurements, but with applied dissipation correction for the fast shear regime (orange curves). We see that through this correction procedure, the fast shear measurements reestablish well-defined plateaus, hence a true steady shear region becomes visible. The correction procedure basically ‘straightens’ the curves of the dissipation-affected measurements. The exact value of the steady shear viscosity of each measurement is then extracted at the respective plateau. From the ratio of corrected and uncorrected values, a correction factor for each measurement can be calculated. For the 500 1/s measurement, the correct shear viscosity is almost 50 % higher than the uncorrected curve would suggest.
Figure 4: Viscosity curves of PIB known from Figure 2, but with additionally displayed dissipation-corrected viscosity curves for the fast shear regime. The corrected curves are able to equilibrate on a typical steady state plateau level. The lower graph illustrates the determination of the steady shear viscosities at the plateau of the corrected fast shear curves. The given correction factors quantify the ratio between corrected and unc The figure is reprinted from a KGK Rubberpoint article 1.
The viscosity-shear rate plot is an essential tool for industrial needs, since it directly illustrates the process-relevant shear thinning behavior of polymer materials. Figure 5 compares the uncorrected and dissipation-corrected steady shear viscosities of PIB isothermally measured at set temperatures of 60, 80, and 100 °C. In this fast shear regime, the uncorrected isothermal viscosity curves show a very steep decrease with rising shear rate due to the shear dissipation temperature buildup. The consequence is a rather untypical, disproportionally curved appearance that will be termed ‘pseudo-shear thinning’ in the following.
Figure 5: Steady shear viscosities over shear rate for PIB measured at 60, 80, and 100 °C. The left upper graph shows the uncorrected curves, the right upper graph the curves with dissipation-corrected fast shear regime (gray background). The three lower graphs illustrate the fast shear regimes of the three different temperatures in detail. In the uncorrected curves the pseudo-shear thinning effect is observed. The correction procedure addresses the issue. The figure is reprinted from a KGK Rubberpoint article 1.
The dissipation correction procedure shifts the fast shear viscosities towards higher values, with corrected steady shear viscosities that are up to 1.61 times higher than their uncorrected counterparts. Ultimately, the correction erases the pseudo-shear thinning appearance and creates a less steep and more natural course of the three corrected curves, as seen in the upper right graph.
Figure 6 shows the viscosity-shear rate plots for an EPDM (ethylene propylene diene monomer) compound and an AEM (ethylene acrylic elastomer) compound respectively measured at three different temperatures.
Figure 6: Uncorrected and corrected steady shear viscosities as a function of shear rate of an EPDM compound (left graphs) and an AEM compound (right graphs) determined at three different temperatures each. Again, the issue of pseudo-shear thinning is solved through dissipation correction. The figure is reprinted from a KGK Rubberpoint article 1.
We see here that the impact of dissipative heating is material-dependent. While the EPDM compound shows a moderate pseudo-shear thinning effect, with correction factors of up to 1.35, the AEM compound shows striking pseudo-shear thinning, with correction factors as high as 2.29. Such material-specific differences can stem from various factors, like the overall level of viscosity or differences in their viscosity-temperature-dependency.
These examples demonstrate the strong impact of dissipative heating on the rheological properties of rubber materials at high shear rates. Yet, precise and reliable viscosity data, especially in the high shear regime, play a crucial role in various industrial applications. For example, extrusion features by design the most intense shear processes in the metering zone of the screw and especially in the die region, where the extrudate quality is ultimately defined. Here, machine and parameter layout based on reliable rheological data can make the difference between a flawless product and scrap. Similar considerations apply for e.g. injection molding processes. The RPA rotational is the first and only RPA on the market that can provide dissipation-corrected steady shear viscosities for these fast shear applications.
The RPA rotational establishes the next evolutionary step of rubber process analyzers through its combination of a freely rotating die with advanced temperature measurement capabilities. The freely rotating die allows for continuous rotation measurements to determine the process-relevant steady shear viscosity over a large shear rate range. This property adequately reflects the large-scale shear flows that take place in industrial processes. The inevitable temperature buildup through shear dissipation can reach large scales and would normally delegitimate shear viscosity measurements at high shear rates. Yet, the built-in gradient temperature sensor allows to correct the effect to obtain reliable, dissipation-corrected steady shear viscosities even in the high shear regime, which is the unique feature of the RPA rotational.
Conventional RPA devices usually do not measure the steady shear viscosity directly but use oscillatory measurements and the Cox-Merz relation to estimate it. Part II of the RheoInfo on the RPA rotational will demonstrate why this conventional approach is failure-prone and why steady shear viscosity determined via continuous rotation appears as the better, more reliable alternative for industrial needs.
RPA rotational - Part 1
How continuous rotational measurements can be performed easily and corrected for dissipation
RPA rotational - Part 3
How the RPA rotational uses its dissipation correction to characterize scorch problems, among other effects, and enable new solution concepts?
1. Frey M, Sunder J. Temperature buildup in sheared rubber - Measuring reliable viscosity data and predicting scorch with the RPA rotational. KGK Rubberpoint. 2026;6.
