Master Curves of Differently Vulcanized SBR Samples
Purpose
Investigation of the influence of vulcanization conditions on master curves measured by DMA.
Sample
The samples are described in Section 4.2.2.
Conditions
Measuring cell: DMA/SDTA861e with shear sample holder
Sample preparation: Cylinders of 5-mm diameter were punched out from a 1-mm thick film and mounted in the shear sample holder with 10% predeformation.
DMA measurement: The measurement was performed in isothermal steps between –40 °C and 120 °C. The temperature steps used in the range –40 °C to 60 °C were 10 K, afterward 20 K. The frequency range was from 10-1 Hz and 103 Hz. The full frequency range (10-3 Hz to 103 Hz) was only used for the measurements at –10 °C. Maximum force amplitude 10 N, maximum displacement amplitude 10 µm, offset control zero.
Evaluation
Master curves were constructed by horizontally shifting the measured curves according to the time-temperature superposition principle. These curves reflect the mechanical behavior of a material over a large frequency range. A reference temperature of 20 °C was chosen. The storage and loss part of the shear modulus are shown in the following diagrams for samples with different degrees of crosslinking. When constructing the master curves, it is important to shift G' and G" to the same extent in order to obtain optimum results.
Master curve of the unvulcanized material
Master curve of SBR1
Master curve of SBR2
Master curve of SBR3
Master curve of SBR4
Interpretation
It can be seen from the master curves that the frequency of the relaxation region changes with the degree of cross-linking. The curves allow information to be obtained concerning the frequency- and temperature-dependence of the mechanical properties of the materials. For example, it is possible to evaluate how the damping changes with the degree of vulcanization at a frequency of 10 kHz, or to determine the frequency at which the material begins to become rubbery elastic.
The most noticeable effects of the cross-linking density are apparent at low frequencies in the rubbery plateau. The storage modulus of the unvulcanized material shows only a relatively short plateau between 104 Hz and 102 Hz, whose position is determined by the degree of polymerization and the molar mass distribution. Afterward the storage modulus decreases and the material exhibits viscous flow. The flow relaxation is the reason for the peak in the loss modulus in this frequency region.
The point of intersection of the storage and loss modulus at low frequency characterizes the gel point. Gel formation is no longer possible even with the minimum cross-linking density of SBR1. The material behaves rubbery elastic even at the lowest frequencies. This is shown by the fact that G' is always greater than G" in this frequency range. The loss modulus however still exhibits flow relaxation. With SBR2 only a small degree of flow relaxation is observed. The storage modulus reaches an almost constant value. From SBR3 onward, flow relaxation can no longer be measured. The cross-linking density is so large that flow no longer occurs. As expected, in the frequency range observed, the storage modulus increases with the degree of cross-linking. The loss modulus decreases. With SBR4, the difference between the storage and loss modulus at 10-13 Hz is largest. Here tan g is 3.4103. The logarithm of tan g is the difference log G' - log G".
Comments
The modulus curves in the low frequency region were obtained from measurements at higher temperatures. Since the heavily cross-linked samples SBR3 and SBR4 behave almost as an ideal network, an increase of the modulus with temperature was measured. This effect was taken into account in the construction of the master curve by a slight vertical shift. The storage and loss moduli were thereby shifted to the same extent so that tan g was not affected.
Conclusions
The master curves describe the temperature- and frequency-dependent mechanical behavior of the materials. They provide information on the fine structure of the relaxation behavior. The flow behavior and the network structure can be specified. The curves allow the macroscopic properties to be measured and information to be obtained about molecular structure and interactions.
Master Curves of Differently Vulcanized SBR Samples | Thermal Analysis Application No. HB448 | Application published in METTLER TOLEDO TA Application Handbook Elastomers, Volume 2