Dynamic properties of rubber.

Carbon black

Effect of carbon black properties

Carbon black has a major influence on the dynamic properties of compounded rubber. This effect depends quantitatively on the basic properties of the carbon black, such as surface area, structure and surface activity. These properties form the basis for modifying a rubber's dynamic properties through the following processes [refs. 34 and 35]:

* hydrodynamic-occlusion; * rubber to filler linkages; * interaggregate interaction.

The hydrodynamic-occlusion is due to a dilution of the rubber by the carbon black particles. The resulting increase in elastic modulus is partially accounted for by Einstein's equation for the viscosity of a liquid containing suspended spherical particles. When substituting modulus for viscosity, the equation is:

E = [E.sub.o] (1 + 2.5C + 14.1[C.sup.2])

where:

E = modulus of filled elastomer 

[E.sub.o] = modulus of unfilled elastomer

C = volume fraction of filler

This equation is valid for fillers such as glass beads or thermal blacks. However, highly structured fine particle size blacks produce compounds having moduli larger than predicted from this equation. This increase is partially due to a filling of the voids in the carbon black structure. The rubber occluded in these voids is shielded from any imposed deformation: with the net result that the total rubber volume available for deformation is reduced. This occlusion of a portion of the rubber. to,ether with the dilution effect predicted from the Einstein equation. cause an increase in elastic modulus. Higher structure blacks, having a higher void volume, give a higher elastic modulus. The total contribution of the hydrodynamic-occlusion depends on the carbon black structure and volume. When inducing a sinusoidal deformation on the rubber, the total dilution effect remains unchanged. It therefore dissipates no energy and has no influence on tan [delta].

The rubber to filler linkages are chemical bonds between the elastomer and the carbon black. These bonds function as crosslinks and increase the elastic modulus of the rubber. The number and intensity of these linkages are functions of the carbon blacks' surface activity. They form the molecular basis for the Mullins effect, which is shown in figure 29 [ref. 36]. In this illustration, two carbon black particles are together by a series of elastomer chains. When placing a strain on the system, the distance between the particles increases and the elastomer chains become stretched. It is postulated that as the elongation increases, more and more the chains are pulled loose from the carbon black. When reaching point 3 in the illustration, the chains are fully stretched. In the process of becoming fully stretched, energy is dissipated in pulling the chains loose from the particles. When removing the strain, the chains do not immediate reattach themselves to the particles. Therefore, the application of a continuous sinusoidal deformation dissipates a reduced level of energy after the first cycle. The total effect of the rubber to filler linkages is to increase the elastic modulus without affecting the tan [delta].

Interaggregate interaction is caused by the carbon black aggregates being in close contact with one another and forming a network of agglomerates. A rubber compound containing such an agglomerate network has a relatively high electrical conductivity, indicating that the aggregates are either touching or are separated by only a few angstroms [ref. 37]. When a cyclic strain is placed on a rubber compound, these agglomerate networks are broken up and the elastic modulus decreases. The amount of network break-up and accompanying reduction in elastic modulus varies with the strain amplitude. The total effect of this phenomenon on dynamic properties is illustrated in figure 30 [ref. 35]. At low strain levels (< 1%) the network is not broken and the elastic modulus remains constant. Since no energy is dissipated, both the loss modulus and the loss tangent are low. At higher strains (1 to 10%) the agglomerates are partially broken and the elastic modulus decreases. However, since the break-up of the network is not severe, the agglomerates reform before the next strain cycle. Due to this constant breaking-up and reforming of the network, energy is dissipated and both the loss modulus and loss tangent reach maximum values at these strain levels. At much higher strain levels (> 10%), the agglomerate network is completely broken down and the elastic modulus reaches a minimum value. Here, the network break-up is so severe that it does not reform between deformation cycles and the energy dissipated is very low. Consequently, both the loss modulus and the loss tangent are low. This complete break-up of the agglomerate network is confirmed by a measured reduction in electrical conductivity at high strain amplitudes. The loss modulus is related to the change in elastic modulus in going from low to high strain amplitudes [ref. 36]. The energy absorption therefore is related to the quantity of agglomerate networks present in the rubber compound. These agglomerate networks are in turn related to the surface area of the carbon black.

The combined effect of all these processes on the change in elastic modulus with increasing strain amplitude is shown in figure 31 [ref. 38]. All of the change in elastic modulus is due to the interaggregate interaction. None is due to the rubber to filler linkages, or the hydrodynamic-occlusion effect The effect of carbon back properties on the strain amplitude dependence of the elastic modulus can be better shown by comparing a series of carbon blacks with widely varying surface areas and structures. The curves in figure 32 are plots of elastic modulus vs. % strain for an unloaded gum stock and six rubber compounds containing 50 phr of six different carbon blacks [ref. 39]. At first glance it is apparent that the curves for N330 and N327 are parallel; and the curves for N568, N539 and N440 are parallel. N220 has a different Slope than the other two sets. The change in elastic modulus ("E") in going from low to high strain amplitudes is approximately the same for the carbon blacks in each of these sets. The carbon blacks with the highest surface area have the largest change in elastic moduli. The more extensive agglomerate network of the higher surface area blacks dissipate a higher level of energy during a cyclic deformation. The other two parameters influencing the elastic modulus, namely the hydrodynamic-occlusion effect and the rubber to filler linkages are not affected by the variation in strain levels. Changes in carbon black structure should therefore relate to the higher strain elastic modulus. The data from these curves verify this, and the elastic modulus at 10% is higher for the compounds containing the highest structure carbon black. Surface activity is not believed to change much from one black to another. Its effect on elastic modulus is therefore fairly constant. In summary, the elastic modulus at high strains is dependent upon the carbon black volume, structure and surface activity, while at low strains, it is dependent on all these parameters plus surface area. When a high surface area low structure black like N327 is compared to a low surface area high structure black like N539, the curves actually cross-over at a higher strain amplitude.

It is apparent by now that by using structure and surface area properties, the type of carbon black used in a compound can be adjusted to give the optimum dynamic properties required for a particular application. Optimizing the dynamic properties depends on whether the compound functions under a constant energy, constant strain or constant stress condition. With a constant energy input, the change in modulus caused by carbon black structure variations has no effect on energy absorption and tan [delta] is proportional to the surface area. This is shown in figure 33 which is based on published data (table 8) [ref. 39]. The constant strain energy absorption (G' tan [delta]) accordingly is proportional to DBPA x iodine number (figure 34); and the constant stress energy absorption (tan [delta]/G') is proportional to iodine number/DBPA (figure 35). Therefore a compound, which functions under constant strain conditions, should contain a low surface area, low structure black for minimum heat build up; while a compound which functions under constant stress conditions, should contain a low surface area, high structure black for minimum heat build up.

[TABULAR DATA OMITTED]

Effect of volume

Increasing the carbon black level increases the agglomerate network, the hydrodynamic-occlusion, and the rubber to filler linkages. The effect of increased carbon black levels on the variation of elastic modulus and phase angle at different strains is shown in figures 36 [ref. 40] and 37 [ref. 41]. Increasing the black level produces a large increase in the change of elastic modulus in going from low to high strains. Accompanying this is an increase in the phase angle or tan [delta].

Effect of temperature

The effect of temperature on the low and high strain elastic modulus is shown in figure 38 [ref. 41]. Increased temperatures cause a large decrease in modulus at low strains, but the dependency on temperature becomes progressively less at higher strain amplitudes. This decrease in modulus is probably due to a reduction in the strength of the filler to filler linkages. In looking at the effect of both loading and temperature on low strain modulus, it is interesting to note that at high loadings and low temperature, the low strain modulus is dominated by the surface area of the carbon black, while at low loadings and high temperatures it is dominated by the structure.

Effect of dispersion

The degree of carbon black dispersion in a rubber has a large effect on the agglomerate network. Longer mixing times allow for a more complete break-up and dispersion of the agglomerate network. This is turn decreases G' and the phase angle [ref. 42]. When comparing the physical properties of different compounds, it is therefore imperative that they be given the same work input during mixing.

Temperature-frequency superposition 

The last area to be reviewed under carbon black is its effect on the temperature-frequency superposition. The dynamic properties of a gum rubber are based on the Maxwell model. At low frequencies there is much movement of the dashpot. At high frequencies, the dashpot becomes rigid and all the movement is associated with the spring. The modulus of the spring is due to a change in entropy, and the viscosity of the dashpot is due to molecular friction. The effect of varying the frequency or temperature is dependent on the relaxation time of the rubber. This relaxation time, however, is the average of an infinite number of small elements. Temperature and frequency variations have the same effect on each of these individual elements. Due to the interrelationship between temperature and frequency, a slight variation in temperature can be used to shift dynamic properties data over many decades of frequency. When carbon black is added to the rubber, new non-linear viscoelastic elements are added which cannot be represented by simple linear elements. The time associated with the breakdown and reforming of the agglomerate network is completely different from the relaxation time of the rubber.

Temperature and frequency have a different nonlinear relationship to this breakdown and reformation time. The shift factors for a filled compound are therefore different from those of the gum rubber. In spite of this, if caution is used, the technique of temperature-frequency superpositioning still has application in carbon black filled rubbers.

Non black fillers

Inorganic fillers have a similar effect on dynamic properties as is found with carbon black. Silica, for example, has a high surface area and a high structure [ref. 43]. The silanol groups on the surface of silica interact through hydrogen bonding to form a three dimensional lattice network in the rubber compound. The breaking down and reforming of this network during a cyclic strain dissipates energy and functions as a hysteresis source. The change in elastic modulus in going from low to high strains increases with increased surface area silicas. The addition of coupling agents increases the elastic modulus with a resulting reduction in tan [delta].

Clay, having a low surface area, no structure and only weak rubber to filler interaction, has a different effect on dynamic properties. It increases the elastic modulus through a dilution effect; but generates little hysteresis during a cyclic strain. The influence of other inorganic fillers on dynamic properties depends on their surface area, structure, filler to filler interaction and filler to rubber interaction.

References

[35.] A.I. Medalia, Rubber Chem. and Technol., 51, p. 437, (1978). [36.] M. Morton, Rubber Technology, Van Nostrand Reinhold, New York, p. 80, (1973). [37.] A.R. Payne, Rubber Chem. and Technol., 39, p. 915, (1966). [38.] A.R. Payne, in Reinforcement of Elastomers, G. Kraus, Ed., Interscience Publishers, New York, 1965, ch. 3. [39.] A.I. Medalia, Rubber World, 168, (5) p. 49, (1973). [40.] A.R. Payne, Rubber Plast. Age, Aug., 1961, p. 963. [41.] A.R. Payne, Rubber Chem. and Technol., 36, p. 432, (1963). [42.] A.R. Payne, Rubber Chem. and Technol., 39, p. 365, (1966). [43.] M.P. Wagner, Rubber Chem. and Technol., 49, 703, (1976).

Ron Schaefer is president of Dynamic Rubber Technology. He has 30 years experience in the rubber industry working at Zeon Chemicals and BFGoodrich in the Corporate, Tire and Chemical Divisions.