Effect of carbon black on dynamic properties.

Even though natural rubber was discovered centuries ago, there were very few applications for natural rubber until about a 150 years ago. Users found it difficult to work with solid natural rubber. Furthermore, articles made from natural rubber turned tacky in warm weather and hardened in cold weather. Two major technological developments in the 19th century overcame these problems and laid the foundations for the polymer industry. In 1820, Thomas Hancock invented a machine that could masticate, mix and soften rubber. Once softened, natural rubber could then be easily shaped. The next major breakthrough came in 1839, when Thomas Hancock and Charles Goodyear independently discovered the process of sulfur vulcanization. During vulcanization, polymer chains are chemically crosslinked to form a viscoelastic network. Hence, vulcanized articles retain their shape and properties over a wide range of ambient temperatures.

The use of fillers in rubber is almost as old as the use of rubber itself. Initially, fillers were used to extend and cheapen the compound. Zinc oxide was used as a whitening pigment and was also briefly used as an active filler. Hancock patented the use of carbon black in the form of lamp black to stiffen compounds in 1830. It was not until 1904 that S.C. Mote demonstrated that the addition of carbon black to natural rubber appreciably enhanced its tensile strength. Yet, zinc oxide was still the filler of choice until about 1912. That is when J.D. Tew of B.F. Goodrich invented the use of the carcass cord that spurred the development of longer life tires through the use of carbon black. Yet it was not until 1925 before the general public accepted black tires. Since then, to optimize compound properties, carbon blacks have been the predominant and most widely used reinforcing fillers. This article will focus on the effects of carbon black on the dynamic properties of elastomers.

Effect of carbon black reinforcement on elastomer modulus

As the addition of carbon black significantly improves the static and dynamic properties of elastomers, carbon blacks are commonly referred to as reinforcing fillers. In general, the addition of carbon black results in an increase in modulus, tensile strength, tear strength, abrasion resistance, fatigue life, elongation to break, viscosity and decreases in compression set and die swell. The extent of reinforcement depends not only on carbon black loading, but also on the particle size, structure, surface area and surface activity levels. Particle size refers to the diameter of the quasi-spherical primary particles of which the aggregates are composed (ref. 1). In a tree aggregate, the particles have partly lost their individual identities as a result of their fusion when they form aggregates. Primary particle size is most accurately measured utilizing electron microscopy. Structure is the term used to describe the degree of aggregation of particles. A low structured black may have fewer than 20 particles per aggregate, while a highly structured black may have up to 200 particles per aggregate (refs. 2 and 3). As carbon black properties are distributional, for a given average value there is a wide distribution of aggregate sizes within a grade. The volume of void space between aggregates increases with the number of particles per aggregate. In addition, non-spherical aggregates pack differently from spheres. Structure is usually measured by filling the void spaces with a liquid. The dibutyl phthalate absorption (DBPA) test is commonly used to characterize the structure of a filler (ref. 2). Surface area defines how much of the aggregate surface is available for interaction with the elastomer. It largely depends on the size of the primary particle. The heat history and resulting texture of the surface (porosity) can also strongly influence the available surface area. Some experimental carbon blacks reportedly have surface areas five to seven times higher than normal carbon blacks having the same particle size. Nitrogen or iodine adsorption techniques are well-established methods (ref. 3) for measuring surface area. The chemical nature of carbon blacks is one variable that has been difficult to understand and control. Slight variations in oil feedstock composition or in the combustion process can affect the surface activity. New carbon blacks are produced with a greater degree of consistency to overcome the detrimental effects of variations in surface activity. Numerous groups, including carboxyl, phenol, quinone and lactone and others, have been detected on the surface of carbon blacks. These chemical groups can strongly influence the rate of vulcanization in a large number of elastomer compounds. Surface activity can also affect the physical adsorption of elastomer chains, and thus directly influence rubber properties (ref. 4). The effect of surface activity is not directly measured, but indirectly inferred by testing ASTM standard recipes.

According to Payne (ref. 1), four main factors contribute to the modulus of a carbon black filled vulcanizate. These factors are;

* Pure gum: This contribution is directly proportional to the crosslink density of the elastomer. Therefore, increasing the crosslink density increases the modulus.

* Strain amplification: When an elastomer is filled with carbon black, an equivalent volume fraction of the elastomer is replaced with a rigid non-deforming filler. When deformed, the volume fraction of the filler does not undergo deformation. Hence, the microscopic strain experienced by the elastomer chains is greater than the applied macroscopic strain. This phenomenon is called strain amplification and depends not only on loading, but also on filler type.

* Filler-elastomer bonds: The physical and/or chemical interactions between the filler and elastomer increase the apparent crosslink density of the system.

* Structure: At moderate filler loadings, high structure fillers form a three dimensional network throughout the elastomer matrix. This filler network tends to increase the modulus at low strains of up to 2%.

For the same external deformation, the local strain experienced by the chains in a filled compound is higher than that of an unfilled compound, due to strain amplification. Hence the measured modulus of a filled compound is greater than that of an unfilled compound. When discussing carbon black-elastomer interactions, the concept of bound rubber, shell rubber and occluded rubber should be understood. Rubber attached to the filler surface due to chemisorption is called bound rubber. Even in the uncured state, solvents cannot easily extract the rubber chains that are firmly attached to the surface. Only a fraction of the bound rubber actually consists of polymer molecules in direct contact with the surface. The majority consists of loops and dangling chains attached at localized sites (ref. 5). In addition to bound rubber, shell rubber and occluded rubber also surround the particles. Shell rubber may be conceived as a shell of constant thickness surrounding the particle. Therefore, the volume of the shell is equal to its thickness times the surface area of the particle. It may be thought of as rubber immobilized by attachments within the first layer of crosslinks. The concept of occluded rubber will be dealt with later in this section.

Guth and Gold (ref. 6) derived an equation based on the Einstein viscosity (ref. 7) law which was used to predict the viscosity of a filled Newtonian liquid ([[Eta].sub.f]) when spherical particles of volume fraction [Phi] are added to a liquid of viscosity [[Eta].sub.u]:

1 [[Eta].sub.f] = [[Eta].sub.u](1 + 2.5[Phi])

Taking into account nearest neighbor interactions, Guth and Gold added a third term to equation 1:

2 [[Eta].sub.f] = [[Eta].sub.u](1 + 2.5[Phi]) + 14.1[[Phi].sup.2])

For very dilute solutions, the third term can be ignored and the equation reverts back to the Einstein equation. Smallwood (ref. 8) used the Guth-Gold equation to predict the shear modulus of a filled elastomer ([G.sub.f]) knowing the volume fraction of the filler ([Phi]):

3 [G.sub.f] = [G.sub.u] (1 + 2.5[Phi] + 14.1[[Phi].sup.2])

Equation 3 can also be used to calculate the tensile modulus (E). It holds true for compounds filled with spherical particles such as medium thermal carbon blacks with very low structure levels and micrometer sized glass beads at low concentrations. For higher concentrations and structured carbon blacks, the measured modulus is higher than the predicted modulus. Equation 3 does not take into account the anisotropy due to the non-spherical morphology of carbon blacks (refs. 2, 3 and 5).

Due to occluded rubber, Medalia (refs. 2 and 9) postulated that the equivalent volume of an aggregate was greater than its solid volume (figure 1). As an aggregate is nodular, the solid volume is the volume of a sphere, which occupies the same space as the aggregate. The equivalent volume is the total of the solid volume plus occluded rubber. Occluded rubber is that volume fraction of rubber residing in the interstices of the aggregates and hence shielded from external deformation. Occluded rubber is now considered as being part of the filler, hence the volume of the equivalent sphere is greater than that of the solid sphere. The DBPA test, which estimates the volume of the equivalent sphere that can be occupied by the rubber chains, is used to calculate the effective volume fraction of the filler V. Due to their interdependent nature, occluded rubber, bound rubber and shell rubber can overlap. Some of the occluded rubber may be comprised of molecules that were bound to the filler before curing. Bound rubber can be greater or less than occluded rubber, depending on primary particle size and structure of the aggregates. If [Phi], the volume fraction of the filler is replaced by V, the effective volume fraction of the filler, then equation 3 can be written as:

4 [E.sub.f] = [E.sub.u] (1 + 2.5V 14.1[V.sup.2])

Where

5 V = 0.5[Phi]([1 + [1 + 0.2139DBPA]/1.46)

[Figure 1 ILLUSTRATION OMITTED]

The term within the parenthesis in equation 4 is called the strain amplification factor X. In the region of linear viscoelasticity, equation 4 can be reduced to:

6 [E.sub.f]= [E.sub.u]X

Where [E.sub.f] and [E.sub.u] are the tensile moduli of filled and unfilled elastomers, respectively.

The effect of increasing carbon black loading (N1100, DBPA = 112 and N990, DBPA = 41) on the storage modulus is given in figure 2. As expected, N110, which has higher structure than N990, has a more profound effect on the modulus.

[Figure 2 ILLUSTRATION OMITTED]

Viscoelasticity

The response of an elastomer to an excitation is both time-dependent and instantaneous. Therefore, elastomers are called viscoelastic materials. The instantaneous response is the elastic component, while the time dependent response is the viscous component. Figure 3 is a simple four-parameter model that can be used to describe the response of an elastomer to an excitation. This model consists of a Voigt and a Maxwell model in series. The response of the Maxwell model spring is the transient elastic response, while that of the combined Maxwell and Voigt model dashpot's are the time dependent viscous response. This figure graphically represents the response of the model to a constant load (creep). When the load is applied at time t = 0, the spring of the Maxwell model instantly deforms, followed by the deformation of the dashpot of the Maxwell model, along with the spring and dashpot of the Voigt model. When the load is removed, the Maxwell model spring recovers instantly, while the Voigt model exhibits a time dependent recovery. Unlike the dashpot of the Voigt model, the dashpot in the Maxwell model does not experience any restoring forces, and thus retains its deformation. This residual deformation is often called permanent set.

[Figure 3 ILLUSTRATION OMITTED]

As a result of the viscoelastic behavior of elastomers, a fraction of the mechanical energy input is converted to heat. This phenomenon of energy conversion is often called hysteresis, and leads to a temperature rise of the component. The dynamic properties and rate of heat generation are strongly dependent on factors such as temperature, frequency and the extent of deformation (strain). Other factors, such as amount and type of filler, crosslink density and presence of plasticizers, also strongly influence the dynamic properties. A rise in temperature can decrease the service life and/or lead to catastrophic failure of the component. For example, in an automobile, hysteresis leads to energy losses by the tire, and hence a reduction in fuel economy.

Dynamic mechanical properties of elastomers

Since many elastomeric components undergo cyclic deformations during service, dynamic mechanical properties of elastomers have been extensively studied. Some examples of these components are tire treads, rubber rolls, stators of positive displacement motors, engine mounts and vibration isolators.

The response of a perfectly elastic or a perfectly viscous material to a deformation only has one component, while the response of a polymer has both viscous and elastic components. If a cyclic deformation (strain) is applied to such a material, then the response (stress) and excitation will be out of phase (figure 4) (ref. 10). The elastic component of the response is in phase with the deformation, while the viscous component is 90 [degrees] out of phase with the deformation. The elastic response is the stored energy, while the viscous response is the energy that is dissipated. The angular difference between the response and the excitation is the phase angle [Delta] which is a function of the amplitude, frequency and temperature. When a sinusoidal strain [Epsilon](t) is applied, the resultant dynamic stress f(t) has two components, f'(t) the elastic response and f"(t) the viscous component of the response. These terms can be expressed as:

(7) [Epsilon](t) = [Epsilon] sin ([Omega]t)

(8) f(t) = E* [Epsilon] sin ([Omega]t + [Delta])

(9) f'(t) = E" [Epsilon] sin ([Omega]t)

(10) f"(t) = E" [Epsilon] cos ([Omega]t)

[Figure 4 ILLUSTRATION OMITTED]

Where [Omega] is the angular frequency, E*, E' and E" are the complex dynamic, storage and loss moduli, respectively.

If the dynamic stress amplitude ([f.sub.dyn]) is plotted as a function of the dynamic strain amplitude ([[Epsilon].sub.dyn]), then the resultant plot is a Lissajou Ellipse (figure 5). This plot can be used to calculate the energy dissipated per deformation cycle [W.sub.e]. The area on the rectangle enclosing the ellipse is the energy input per deformation cycle W, and is:

(11) W = [f.sub.dyn] [[Epsilon].sub.dyn]

[Figure 5 ILLUSTRATION OMITTED]

The area of the ellipse is the energy dissipated/deformation cycle/unit volume and is:

(12) [W.sub.e] = ([Pi]/4) [f.sub.dyn] [[Epsilon].sub.dyn] sin[Delta]

For the small phase angles normally encountered in elastomers, the magnitude of the sine and the tangent of the phase angle are approximately equal. Hence, equation 12 can be rearranged to obtain:

(13) [W.sub.e] = ([Pi]/4) [f.sub.dyn] [[Epsilon].sub.dyn] tan[Delta]

The total energy dissipated (H) per unit time (in seconds), is the energy dissipated per cycle multiplied by the total number of deformation cycles in that time period, which usually is the frequency of deformation (Hz). Thus, H can be calculated using the following equation:

(14) H = [W.sub.e] Hz

Approximately 7-9% of the energy losses in an automobile are attributed to the tire (ref. 11). Of these losses, 60-70% are due to hysteresis in the tread and the carcass. Thus, the rubber in fires is responsible for approximately 5-6% of the total energy losses of an automobile. It is also important to note that this dissipation mechanism is also responsible for traction. Thus, there is a delicate balance between rolling resistance and traction; reducing the rolling resistance to maximize the fuel economy could lead to a reduction of wet and dry traction. The complex dynamic modulus is the slope of the ellipse and is given by:

(15) E* = [f.sub.dyn]/[[Epsilon].sub.dyn]

The relationship between complex dynamic modulus E* (figure 6) and its two components, the storage (E') and loss (E"), is:

(16) E' = E*cos[Delta]

And

(17) E" = E*sin[Delta]

[Figure 6 ILLUSTRATION OMITTED]

For a perfectly elastic solid, ([Delta] = 0 [degrees] hence sin[Delta] = 0) E' is equal to E* and E" is zero. On the other hand, for a perfectly viscous fluid, ([Delta] = 90 [degrees], cos[Delta] = 0) E" = E*, which implies all the energy input is dissipated as heat. In general, for filled elastomers, E' is approximately 10 times E". Next, the difference in constant strain and constant stress deformations as well as the effect of filler type/loading on properties, will be examined.

Effect of deformation mode

The measured material properties are strongly dependent on the test parameters, such as geometry, frequency, temperature and mode of deformation. For the majority of test instruments, the most common mode of deformation is constant dynamic strain amplitude (figure 7). However, many rubber components such as tank track pads and tire treads experience either constant dynamic stress amplitudes or a combination of both modes (constant dynamic stress and constant dynamic strain), during normal service conditions (ref. 12). In a tire, as the tread enters the footprint region, it flexes (constant strain), which is followed by compression (refs. 10, 12 and 13) (constant stress). Therefore, when studying dynamic properties, it is important to understand the effect of deformation mode on properties, and to select the correct mode of deformation for laboratory evaluation of a compound.

[Figure 7 ILLUSTRATION OMITTED]

Constant dynamic strain

Under these conditions, the dynamic strain amplitude is kept constant. When the filler loading is increased, the microscopic strains experienced by the elastomer chains are amplified in proportion to the strain amplification factor over the macroscopic strain experienced by the component. This leads to greater energy dissipation or heat build-up in the component. As seen in figure 7 for a stiffer material (higher filler loading), the stress required to deform a sample to constant strain is greater. Thus, both the energy input (area of the rectangle enclosing the ellipse, figure 5) and energy dissipation (area of the ellipse) are greater for a stiffer sample. The relationship between energy dissipation and the modulus can be calculated as shown below. Since the cosine of a small angle is approximately equal to 1, E' is approximately equal to E*. Thus, equation 15 can be rearranged as follows:

(18) [f.sub.dyn] = E' [[Epsilon].sub.dyn]

If [f.sub.dyn] in equation 13 is substituted by equation 18, one obtains:

(19) [W.sub.e] = ([Pi]/4) [([[Epsilon].sub.dyn]).sup.2] tan[Delta] E'

Furthermore:

(20) tan[Delta] = E"/E'

Finally, one obtains:

(21) [W.sub.e] = ([Pi]/4) [([[Epsilon].sub.dyn]).sup.2] E"

From equation 19 it can be seen that the energy dissipation is proportional to the storage modulus and to the square of the dynamic strain amplitude. Thus, increasing the modulus would lead to higher heat build-up in a rubber component experiencing constant dynamic strains. Furthermore, higher carbon black loadings also result in an increase in E". This would also result in an increase in energy dissipation (equation 21).

Constant dynamic stress

On the other hand, for a constant dynamic stress, increasing the filler loading would lead to a decrease in energy dissipation. For a constant dynamic stress, the effect of modulus on the resultant strain for soft and hard elastomeric compounds is illustrated in figure 8. Here, increasing the modulus by increasing the filler loading results in a lower strain amplitude, and hence, lower energy dissipation. If [[Epsilon].sub.dyn] in equation 21 is substituted by equation 18 one obtains:

(22) [W.sub.e] = ([Pi]/4) [([f.sub.dyn]).sup.2] E"/[(E').sup.2]

[Figure 8 ILLUSTRATION OMITTED]

Thus, for a component experiencing a constant dynamic strain, the energy dissipation is inversely proportional to the square of the storage modulus. For a constant dynamic stress, figure 9 shows the effect of increasing the filler loading for N110 and N990 on E'. According to equation 22, it would be expected that [W.sub.e] would decrease with increasing filler loading. Indeed, this relationship is tree, as seen in figure 10. In summary, to accurately predict component performance from laboratory test results, first the actual mode or modes of deformation experienced by the component should be determined. Next, these deformation modes should be duplicated on a test instrument.

[Figures 9-10 ILLUSTRATION OMITTED]

Since most components experience both stress controlled and strain controlled deformations, the total energy dissipation ([W.sub.eT]) can be simplified as:

(23) [W.sub.eT] = a[W.sub.e[Sigma]] + b[W.sub.e[Epsilon]]

Where, "a" is the fraction of energy dissipated under stress controlled conditions ([W.sub.e[Sigma]]) and "b" is the fraction of energy dissipated under strain controlled conditions ([W.sub.e[Epsilon]]).

Other factors that influence dynamic properties

The above equations and examples have illustrated the effects of carbon black and test mode on dynamic properties. Other factors, such as strain, temperature, frequency and aging, also have a measurable effect on dynamic properties.

Strain

The effect of strain for two high performance carbon blacks, CD-2038 and HV3396 (table 1), can be seen in figure 11. This figure is a plot of G' (the storage modulus in shear) as a function of peak-to-peak strain, and illustrates carbon black networking, or the Payne effect. At very low strains ([is less than] 4% ptp) the three-dimensional network formed by inter-aggregate contact substantially increases the modulus. As the strain is increased, the network breaks down, which leads to a rapid decrease in G'. This relationship of a decrease in modulus with strain holds true over a wide temperature range, as seen in figure 14.

Table 1 - colloidal properties

Test                 CD-2038   HV3396

NSA ([m.sup.2]/g)      134      166
STSA ([m.sup.2]/g)     124      143
Iodine (g/kg)          141      175
DBPA (mL/100g)         174      135
CDBPA (mL/100g)        130      102
Tint (%ITRB)           112      133
Transmission (%)        97       99

[Figure 11 ILLUSTRATION OMITTED]

Temperature

The dynamic properties of an elastomer are also a function of temperature. The tire industry has established a good correlation between tire performance and dynamic properties in specific temperature regions. For example, the measurement of tan[Delta] at low temperatures (-30 to 0 [degrees] C) has been found to correlate well with wet traction. While higher temperature tan[Delta] in the range of 50 to 70 [degrees] C has good correlation with rolling resistance. Therefore, for a tire tread compound, it is desirable to maximize low temperature tan[Delta] and to minimize high temperature tan[Delta]. This approach would result in a tread compound with high traction and low rolling resistance performances. Figures 12 and 13 are plots of tan[Delta] as a function of temperature for CD-2038 and HV3396. The low temperature plot (figure 12) correlates with traction, and the high temperature graph (figure 13) correlates well with tire rolling resistance. In general, for a given carbon black, increasing loading results in an increase in tan[Delta] across the complete temperature range. However, the shape and slope of the tan[Delta] plot as a function of temperature remains relatively unaffected. The effect of temperature on G' can be seen in figure 14. As the temperature increases, G' decreases. Also, note that there is a decrease in G' with strain across all temperature ranges.

[Figures 12-14 ILLUSTRATION OMITTED]

Frequency

While increasing the strain or temperature leads to a decrease in modulus, increasing the frequency leads to an increase in measured modulus, as seen in figure 15. Going from 1 to 10 Hz for the same dynamic strain (2% peak-to-peak strain), the measured modulus is higher. As the modulus is higher at low temperatures and at high frequencies, testing at low temperatures can be used to calculate high frequency properties using the WLF time-temperature superposition principal. Most test instruments are limited to ~100 Hz, which is well below the frequencies that correlate well with traction attributes of a compound. Therefore, time-temperature superposition is useful in predicting the traction/handling characteristics of a compound.

[Figure 15 ILLUSTRATION OMITTED]

Aging

While aging is not a test condition, it can have a profound effect on properties (ref. 10). Figure 16 is a plot of the original and aged E" as a function of temperature. These NBR samples were aged at 150 [degrees] C for 72 and 168 hours in a fluid that is used to drill oil wells. After 72 hours aging, there was a 35% increase in E", and after 168 hours aging, a 53% increase in E". As the energy dissipation is directly proportional to E", the heat build-up would be significantly higher for the aged samples. The NBR compound used for these tests is used to fabricate positive displacement motors (PDM) that are used to drill directional oil wells. The stator of a PDM is made out of rubber. Therefore, if there is a detrimental change in compound dynamic properties with time, the motors can catastrophically fail. Figure 17 is an example of catastrophic failure due to hysteresis in the stator rubber. The first picture of a stator cross-section shows the early stages of hysteretic degradation in the thick sections of the lobes. Since rubber is an insulator, the thick sections can not readily dissipate hysteretic heat, and the temperature starts to rise. Excessive heat build-up is usually followed by catastrophic failure as seen in the second example. These examples clearly illustrate that a change in properties as a result of aging can lead to the premature blow-out of rubber components.

[Figures 16-17 ILLUSTRATION OMITTED]

Summary

Carbon black is the predominant reinforcing filler for elastomers, with the best balance of performance, cost and processability. The performance and service life of rubber components are vastly improved by the addition of carbon black. An overview of the mechanisms for reinforcement of elastomers by carbon black has been presented. The effect of carbon black on rubber compound properties is measured using a wide range of physical tests. However, dynamic testing is used routinely to understand and optimize the performance of rubber components. A review of the dynamic properties of carbon black reinforced elastomers has been presented, with the objectives to: a) highlight the effect of carbon black on the dynamic properties of elastomers, b) provide an understanding of dynamic properties and their measurements and, c) illustrate the effect of test conditions on the measured properties.

References

(1.) A.R. Payne, Reinforcement of Elastomers, G. Kraus Ed., Chap. 3, p. 192, 1965.

(2.) A.I. Medalia, Rubber Chem. Tech., Vol. 45, p. 1,171, 1972.

(3.) A.I. Medalia, Rubber Chem. Tech., Vol. 51, p. 437, 1978.

(4.) B.B. Boonstra, Rubber Technology, 2nd Ed., M. Morton Ed., Van Nostrand Reinhold, 1973.

(5.) A.I. Medalia, Rubber Chem. Tech., Vol. 47, p. 411, 1974.

(6.) E. Guth and O. Gold, Phys. Rev., 53, p. 322, 1938.

(7.) A. Einstein, Ann. Phys., Leipzig, 19, p. 289, 1906.

(8.) H.J. Smallwood, J. App. Phys., 15, p. 758, 1944.

(9.) A.I. Medalia, J. of Coll. and Int. Sci., 32, p. 115, 1970.

(10.) R. Lamba, Ph.D. Dissertation, The Univ. of Akron, 1995.

(11.) A.F. Halasa, ACS Rubber Div., 155th Technical Meeting, 1990.

(12.) R. Lamba, Educational Symposium, The Energy Rubber Group, 1995.

(13.) E.A. Meinecke, Rubber Chem. Tech., 64, p. 269, 1991.