Modulus and Compliance - METTLER TOLEDO

Modulus and Compliance

Purpose

The mechanical behavior can be described both by the complex modulus and by the compliance. The purpose of the experiment is to illustrate this by comparing the corresponding curves. 

 

Sample

Unfilled unvulcanized SBR (VSL5025-0) 

 

Conditions

Measuring cell: DMA/SDTA861e

Sample preparation: The material was pressed to a 1-mm thick film. Cylinders of 4-mm diameter were punched out and mounted in the shear sample holder with 10% predeformation.

DMA measurement: The measurement was performed at 1 Hz and a heating rate of 2 K/min. In the first heating run the sample was heated to 200 °C. Maximum force amplitude 5 N; maximum displacement amplitude 10 Pm; offset control zero.

 

Interpretation

The uppermost diagram displays the storage (G') and loss (G") moduli, the middle diagram the loss factor, tan G, and the lowest diagram the real and imaginary part of the compliance as a function of temperature. All the curves were all obtained from the same measurement. At low temperatures below the glass transition (less than –25 °C) the sample is rigid. The storage modulus, G', is more than 500 MPa and G" is less than G'. The loss factor, tan g, is less than 0.1. For compliance, the real part, J', is also larger than the imaginary part, J". The value of J' is about 10 Pa-1.

 At the glass transition, G' decreases by several decades. The G' step is accompanied by a peak in G". The loss factor, tan G, also exhibits a peak. At the glass transition, the compliance, Jƍ, shows a step with a height of several decades that is coupled with a J" peak. A comparison of the peak maxima of G", tan g and J" shows that the maxima do not occur at the same temperature. The maximum of J" (about –8 °C) is shifted to higher temperature in comparison with the 'G"-maximum (about –20 °C). The maximum of tan G lies in the middle between the two peaks (about –12 °C). After the glass transition region, the rubbery plateau begins at about 10 °C. Both G' and J' are almost constant here and G" and J" are less than the corresponding real parts. Since the sample measured was unvulcanized material, the loss factor, tan g, increases somewhat with temperature. This slight increase can also be seen with G" and J". 

 

Conclusions

Both the modulus and the compliance can be used to characterize the viscoelastic behavior of materials. Both quantities have a real and an imaginary part. While the real part of the modulus is large with hard materials and small with soft materials, the compliance, J', behaves in the opposite sense. A glass transition is accompanied by a peak in the imaginary parts, G" and J". The peak maximum of the imaginary part of the compliance is always at a higher temperature than the maximum of the G" peak.

Both quantities can be used equally well to describe the experimental results, but depending on the matter being considered, one discusses either the modulus or the compliance.

 

Modulus and Compliance | Thermal Analysis Handbook No.HB420 | Application published in METTLER TOLEDO TA Application Handbook Elastomers, Volume 1