Introducing DHR/AR Test Geometries

Choosing the correct test geometry is an important part of the sample testing procedure. Use this section as a reference when choosing geometries

See Also
Available Test Geometries

General Recommendations

Although the physical properties (such as state and shape) of the sample generally dictate the appropriate sample geometry, it may be possible to test a sample using more than one geometry. Theoretically, the test results should be identical for the different geometries. However, experimental limitations may influence the data and may make testing with one geometry preferable to testing with another. Additionally, factors such as anisotropy and differences in strain dependence may yield variability in test results for different geometries.

Geometries are related to temperature systems and the specific applications. Different temperature systems will have a different set of geometries, depending upon the desired application.

General Tips for Choosing Geometries

The following should be considered when choosing test geometries:

• Cone and plate geometries are necessary when the tests are performed in the non-linear viscoelastic region (for example, flow experiments). Cone and plate geometries are limited to samples with small particle sizes (less than 1/10 of cone truncation gap) and are generally limited to isothermal measurements. The main advantage of a cone and plate geometry is that the shear rate is uniform throughout the sample. It is also favored because the first normal stress difference can be directly obtained from the measured normal force, as there is no contribution from the second normal stress difference.
• Parallel plate geometries are most appropriate for measurements in the linear viscoelestic region and have the advantage over cone and plate in that the gap between the plates can be varied, and they can therefore be used with samples containing larger particles. A good rule of thumb is that the gap size should be at least ten times as large as the maximum particle size. For non-linear measurements, the shear rate varies across the plate,from zero in the center to a maximum at the rim. The strain and shear rate reported by TRIOS software are those at the rim. The reported stress assumes that the sample is Newtonian or linearly viscoelastic, so this measuring system is also recommended for oscillatory experiments conducted within the sample's linear viscoelastic regime, for which the reported material functions are exact. Data from flow measurements made with parallel plates can be corrected by using the Rabinowicz stress correction transformation.

Although there is no theoretical minimum to the usable geometry gap, in practice any slight lack of parallelism between the plates will result in a measurement error, which increases as the gap is reduced. For this reason, the minimum usable gap is often taken to be 1% of the geometry diameter. The maximum usable gap will depend on the properties of the sample, but remember, if a temperature system is used that only heats from one side, then temperature gradients across the sample may result. This effect is eliminated if the UHP, EHP, or ETC are used. To eliminate slippage, the geometry can be serrated or roughened by sand blasting. Usually, a similarly textured cover plate is used in conjunction with geometries finished in this way.

• Concentric cylinder geometries are used for extremely low-viscosity fluids and materials containing larger particles. The drawbacks of the concentric cylinders are the relatively large sample size, the difficulty of loading the sample without excessively shearing it, and the presence of end-effects. The measuring system is not suited to high-viscosity samples. Rotors available for use with the Peltier concentric cylinder system are the standard size DIN (conforms to DIN 53019), recessed end, double gap, standard vane, and wide gap vane. The DIN rotor is the standard for use with the concentric cylinder system, and is used with the standard cup. The recessed end rotor has the same effective dimensions as the DIN, but is designed to reduce end effects by trapping a bubble of air below the rotor.

The double gap rotor is designed to provide a larger surface area than the standard single gap. The problem of sample loading is particularly marked for the double gap system and, for some samples, it may be impossible to fill the annulus fully. The standard vane rotor is used to eliminate wall slippage and the wide gap vane is used for samples containing large particles. The grooved cup is recommended for use with the vane rotors. For the concentric cylinder system, the shear stress and, hence, the shear rate, vary across the annulus. The effect on the reported viscosity is small for all the concentric cylinder systems provided by TA Instruments, except the wide-gap vane.

• Disposable plates should be used for curing or non-recoverable tests.
• Larger diameter geometries should be used for low-viscosity materials. Conversely, smaller diameter geometries should be used for high-viscosity materials.
• Small cone angle geometries are suggested for testing low viscosity materials at high shear rates.
• Large cone angle geometry are suggested for testing high viscosity materials, as this permits easier sample loading.
• Low-inertia geometries are suggested for testing low viscosity materials. For a given size geometry, one constructed from a lower-mass material will have a lower inertia.
• When testing corrosive samples (strong acid and alkali), geometries that resist corrosion are suggested.
• When the sample is volatile, solvent trap geometries and the solvent trap cover are suggested.
• If sample slip is a concern, serrated or cross-hatched plates are suggested.

Tips for Choosing Geometries Based on Sample Type

Recommendations for selection of a geometry based upon sample type are as follows:

• Fluids, Suspensions and Emulsions:  Test low viscosity fluids or suspensions of limited stability using either the concentric cylinder or double wall concentric cylinder geometry.  Test higher viscosity fluids and thicker suspensions and emulsions using parallel plates or cone and plate geometries.
• Solid Samples, Including Thermosets, Thermoplastics, and Elastomers:  Test these materials using the torsion rectangular geometry. Several inserts are available to accommodate many levels of sample thickness.
• Polymer Melts and Soft Solids:  Test melts using parallel plates or cone and plate geometries.
• Thermosetting Resins and other Curing Studies:  These materials are best tested using a parallel plate geometry.  Disposable plates are available for curing studies, or other reactive materials.

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Testing Limits and Instrument Compliance

• Instrument compliance is defined as the angular displacement, in radians, divided by the applied torque.
• Stiffness is the reciprocal of compliance.
• Torsional compliance is the shaft (motor and geometry) angular displacement, in radians, divided by the torque applied by the motor.
• Shaft displacement is measured by a position sensor on the motor shaft.
• Sample compliance is sample displacement, in radians, divided by the torque applied to the sample.

Both the shaft and sample exhibit compliance, so some of the commanded strain may deform the sample, and some of the strain may deform the shaft. If the shaft deformation is large relative to the sample deformation, errors in the measured sample modulus may result.

The AR utilizes an online hardware correction scheme to adjust for shaft compliance. The system determines sample deformation (strain) by subtracting the shaft compliance from the total measured signal.

Under "ideal" conditions, the sample deformation is relatively large, and the shaft displacement is small. The difference between the two deformations is therefore a large number, and the relative error associated with the measurement is small. However, this error becomes significant when very stiff samples are tested, and the shaft displacement is approximately equal to the total displacement.

Although measurements can be taken close to the limit, you are cautioned that accuracy may be affected. Measurements that are affected by transducer compliance report modulus values that are lower than the true modulus. One method of determining if transducer compliance is affecting the data is to switch to a different geometry and compare the results to the original test. If the data are unaffected by compliance, the results from the two geometries should be nearly identical.

Sample compliance and stiffness are related to both the modulus and geometry of the sample. Since the modulus of a material is a fixed, intrinsic property, sample dimensions may be adjusted to change sample stiffness/compliance. Alternatively, the geometry may be changed to alter sample stiffness/compliance altogether, to obtain the desired sample compliance. It is critical that the sample compliance is within the operational range of the instrument otherwise inconsistent or incorrect results will be obtained.

• NOTE: If compliance effects are large, samples should be made less stiff by either increasing sample gap, increasing sample length, or decreasing the sample cross-sectional area.

Determination of Operational Range

Operating range is defined as the region bounded by the maximum and minimum complex modulus (G*) in oscillation, or a minimum and maximum viscosity in flow tests for a specific geometry.

The geometry-specific dimensions will affect the operating range for each geometry. Additionally, the following instrument-specific factors affect the operating range of all geometries:

• Torque range that can be applied\measured
• Shaft compliance
• Strain\angular velocity that can be applied\measured

When the sample stiffness is comparable with the geometry's stiffness, the geometry compliance correction must be considered. The geometry compliance correction is done through TRIOS software by entering the geometry’s compliance values in the geometry setup. See Configuring a New Geometry for more information.

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