Measurement of the Amplitude Dependence of the Shear Modulus of NR Elastomers
Purpose
The influence of deformation on the shear modulus is used to show the limits of linear behavior.
Sample
NR elastomers vulcanized with 2 phr sulfur with different carbon black contents. The carbon black content varied between 0 and 60 phr.
Conditions
Measuring cell: DMA/SDTA861e with shear sample holder
Sample preparation: Cylinders of 5-mm diameter were punched out from a 1.8-mm thick film and mounted in the shear sample holder with 5% predeformation.
DMA measurement: The measurement was performed at 27.8 °C with 1 Hz. The displacement amplitude was varied logarithmic steps between 30 nm and 0.8 mm.
Interpretation
The measurements were performed in the rubbery plateau. With unfilled material, a value of 0.5 MPa was obtained for the storage modulus, The value is practically independent of the displacement amplitude. The sample exhibits linear behavior over the entire range of amplitudes. Small amounts of carbon black (10 phr) strengthen the material, i.e. they increase the storage modulus to 0.6 MPa with only less deviation of the linear behavior at large amplitudes. With larger concentrations of carbon black (30 phr), the storage modulus increases to 1.8 MPa. However, a continuous decrease of the modulus is observed from a displacement amplitude of 10 Pm onward (a shear deformation of 0.6%). The sample exhibits non-linear behavior. This decrease in the modulus with displacement amplitude is known as the Payne effect. The reason for this behavior is the reversible destruction of carbon black clusters. If the elastomer contains more carbon black, the storage modulus increases to 9 MPa. The limit of linearity is however already reached at an amplitude of 2 µm. This corresponds to a shear deformation of 0.1%.
Conclusions
Amplitude-dependent DMA measurements can be used to measure the linear behavior of filled materials. The linear range can be quickly measured in a trial experiment. For example, in a dynamic measurement of the sample with 30 phr carbon black, the displacement amplitude should not be greater than 10 Pm. The amplitude-dependence of the shear modulus depends not only on the carbon black filler concentration, but also on the interaction between the polymer and the filler. The type of filler used can also be characterized by performing specific measurements.
Measurement of the Amplitude Dependence of the Shear Modulus of NR Elastomers | Thermal Analysis Handbook No.HB458 | Application published in METTLER TOLEDO TA Application Handbook Elastomers, Volume 2