*3.3. Dynamical Mechanical Properties*

The e ffects of various carbon blacks in the SBR matrix on the temperature dependence of the elastic (storage) modulus is summarized in Figure 3. These curves describe the temperature region, where the hard and brittle material behavior is replaced by the rubbery or viscoelastic behavior. The modulus decreased strongly in the glassy transition region. The elastomer chain mobility, and thereby the glass temperature, is noticeably a ffected by various additives in the rubber compound. The presence of filler, the amount, an increase in the surface area, or the structure can restrict the chain's movement ability and lead to the shift of the glassy region to higher or lower temperatures [9].

During heating, the elastic modulus of the studied compounds decreased in the temperature range from −50 ◦C to −25 ◦C. The most rapid decrease of the elastic modulus was observed for the compound containing the N 990 carbon black type. On the other hand, the highest values of the elastic modulus were obtained for the compounds with the N 110 and N 330 carbon black types. This is connected with the decreasing carbon black particle sizes and the increasing surface area.

The glass transition temperature for the rubber compounds determined from the loss factor (*tan* δ) curve of three measurements was in the low temperature region, namely −31.9 ± 0.6 ◦C, −32.5 ± 0.5 ◦C, −32.2 ± 0.6 ◦C, and 31.1 ± 0.8 ◦C for the N 110, N 330, N 550, and N 990 types, respectively (see Figure 4). The di fferences in the glass temperature between compounds were less than 10%. The shift in glass transition temperature was probably caused by sample thickness inhomogeneity and the slightly di fferent clamping forces of each compound. As a result, no significant e ffect was observed for the particle size on the glass transition temperature. In addition, the damping properties of the rubber compounds can be evaluated from this figure. It is evident that the loss factor increased with an increase in the primary particle size.

**Figure 3.** Temperature dependence of the tensile storage modulus.

**Figure 4.** Temperature dependence of the loss factor.

The dynamic stiffness of the tested rubber mixtures is measured by the complex modulus of elasticity. The frequency dependencies of the storage modulus and the loss factor at 25 ◦C are demonstrated in Figures 5 and 6.

Significant changes of the storage modulus depending on the frequency for SBR compounds with the N 110, N 330, and N 550 carbon blacks are evident in Figure 5. There is a moderate increase of the storage modulus with the frequency up to 180 Hz. The filler with the smallest primary particle size (N 110) exhibited the highest storage modulus values, while N 990 gave the lowest values. This is connected with the filler–polymer interaction. This fact depends on the filler's primary particle size, as well as its structure [28].

It was found that the loss factor *tan* δ at low frequencies up to 100 Hz showed similar behavior for all carbon black compounds (see Figure 6). Generally, the loss factor increased with an increase in the frequency. While for the more reinforced carbon black type (N 110) the increase of *tan* δ was slower, in the case of the N 990 type the loss factor increased more significantly.

**Figure 5.** Frequency dependence of the tensile storage modulus (displacement x = 5 μm, T = 25 ◦C).

**Figure 6.** Frequency dependence of the loss factor (displacement x = 5 μm, T = 25 ◦C).

The next measurement was performed in order to evaluate the deformation dependence of the tested samples on their dynamic properties. The elastic modulus dependence on the displacement is shown in Figure 7. The effects of the carbon black particle size and structure were measured by this experiment. The compound with the smallest primary particle size gave the highest elastic modulus value, while that with the largest particle sizes showed almost no stiffening effect and had almost constant elastic modulus during the whole deformation range. High elastic moduli at low deformation levels are caused by the filler–filler interaction, as explained by Payne [31]. The smallest particles with higher carbon black structures created stronger filler–filler network in comparison with larger particles and a lower carbon black structures. With the increasing deformation, the filler network is destroyed and the interaction between the rubber and carbon black becomes the main factor.

Incorporated carbon black particles, which are already known as aggregates, create a filler–filler network. Inside the rubber compound, carbon black aggregates are formed by van der Waals forces into so called agglomerates. If a small deformation is applied, a high elastic modulus value is obtained.

The reason for this phenomenon is the strong interaction between filler particles that are not broken. From Payne's point of view, some of the rubber is immobilized on the filler surface, and in addition some of the rubber is also immobilized inside the branched structure of the agglomerate

(known as occluded rubber). If the deformation increases, the agglomerates are broken into smaller sizes, and therefore the elastic modulus decreases. This phenomenon is caused by more mobile smaller units inside the rubber compound. At high deformation levels a plateau can be reached, whereby individual mobile aggregates units are set into motion. This behavior is known as the Payne effect [31–36].

**Figure 7.** Displacement dependence of the tensile storage modulus (f = 20 Hz, T = 0 ◦C).

The dependence of the loss modulus on the sample deformation is presented in Figure 8. The loss modulus increased with a decrease in the primary particle size. The stronger filler–filler interaction led to higher energy dissipation. With the increasing deformation, the loss modulus maximum was found around the displacement amplitude of 35 μm for the compounds with the N 110 and N 330 carbon black types. The highest damping properties were obtained in this area. Apparently, the values of the loss modulus were low for the N 550 and N 990 carbon black types, while damping properties were especially negligible for the N 990 type.

**Figure 8.** Displacement dependence of the tensile loss modulus (f = 20 Hz, T = 0 ◦C).

Shear amplitude deformation was measured using a rubber process analyzer. This test describes similar behavior of the rubber compounds as the DMA measurements, but in shear deformation mode.

The dependence of the filler–filler interaction for compounds with the N 110, N 330, N 550, and N 990 carbon black types is depicted in Figure 9. A strong dependence of the shear storage modulus on the filler particle size is visible, similarly to the DMA testing. Large carbon black particles (N 990) are characterized by a low reinforcing effect, while small particles (N 110) cause a pronounced increase of the storage modulus. Figure 10 shows the strain amplitude dependence of the loss modulus of four carbon black grades. Similarly to the DMA measurements, the shear loss modulus was highest for the N 110 type, while for the N 990 type it was the lowest. The maximum value of the loss modulus was observed at 1% strain, which is fully connected with the maximal damping properties.

**Figure 10.** Strain amplitude dependence of the shear loss modulus.
