Viscous heating and reinforcement effects of fillers using the rubber process analyzer.

Since 1912, carbon black has been used in rubber compounding as the principle filler and reinforcing agent (ref. 1). The use of carbon black is usually essential to impart the desired reinforcement for significant improvements in abrasion and wear resistance, tensile strength, tear resistance, modulus and hardness. However, the use of carbon black also imparts higher hysteresis and heat buildup to the vulcanizate, as well as significantly increasing viscous heating during the mixing and processing of the compound. Being able to accurately measure and study the different amount of viscous heating imparted by different carbon blacks to a rubber batch during mixing is important. Commonly in a rubber mixing operation, a particular compound may require two, three or even more passes in a factory internal mixer before an acceptable state of dispersion is achieved. A major limiting factor for the time length of a mixing cycle is determined from viscous heating. If a reinforcing filler, such as certain carbon blacks, quickly raise the temperature of the batch to very high levels, the viscosity of the batch drops so low at these higher temperatures that little useful mixing action will take place, thus the need for multiple passes. It would be useful to be able to compare the viscous heating effects of different fillers in order to help predict the useful mixing time possible per batch.

Up to now, it has been very difficult to directly measure viscous heating with conventional equipment and instruments, especially with any acceptable repeatability. However, it was discovered that the existing RPA 2000 rubber process analyzer (hereafter referenced as the RPA) can be modified to directly measure rubber compound viscous heating with excellent repeatability.

A. Patel, W. Brown and J. Weaver established methods in the late 70s and early 80s using a capillary rheometer to measure what they called the "reinforcement factor" imparted to an uncured rubber formulation which they found related to after-cure physical properties (refs. 2-4): This reinforcement factor (RF) measured from the uncured compound could be an effective quality control property for helping to assure the uniformity of the cured properties. However, the capillary rheometer method had some characteristics (clean up time, laps time, repeatability, etc.) which made it far less than ideal for routine quality control testing. A second goal of this work was to determine if sinusoidal rheological measurements can also calculate an effective RF.

The RPA, through sinusoidal strain measurements, was found to be able to measure the uncured reinforcement factors. However, the RPA could take these measurements much faster than could be done with a capillary rheometer. Also, there was little clean up time required and much better repeatability. Therefore, with the same instrument (the RPA), both viscous heating and the uncured reinforcement factor can be measured rapidly and with good repeatability.

Experimental

From recent experimental work it has been found that the RPA 2000 is ideal for measuring viscous heating because of its favorable sample surface area to sample volume ratio and ability to apply high strains. As discussed in earlier works (refs. 5-7), the RPA is a special dynamic mechanical rheological tester which encloses and molds the rubber sample in a sealed, pressurized cavity (figure 1). Approximately 400 psi of pressure is maintained against the dies and rubber specimen. A very special motor moves the lower die sinusoidally, while the upper die measures the resulting torque response from the strain applied to the rubber sample. From the complex torque response (S*) and the phase angle ([Delta]), the elastic torque (S') and viscous torque (S") responses are measured. Besides providing a special sealed, pressurized, biconical die cavity, another advantage of the RPA is its ability to apply very high strains (up to [+ or -] 90 degrees arc). This was found to be an ideal condition for measuring viscous heating. The RPA die design has a very high surface area in relation to the mass of the sample itself. The rubber test piece is very thin. This design was deliberate in order to assure very rapid temperature recovery for the specimen once the dies close and the test starts when operating the RPA normally as a dynamic mechanical rheological tester (DMRT). However, this unique die cavity geometry also provides effective measurements of viscous heating when the RPA is properly modified.

[Figure 1 ILLUSTRATION OMITTED]

When the RPA is operated normally as a DMRT, very efficient foil heaters and a forced air cooling system (across the dies) enable the instrument to keep the temperature of the rubber sample to within [+ or -] 0.2 [degrees] C of the set temperature. When the RPA is normally measuring the dynamic properties of the rubber sample, every effort is applied to keep the temperature constant. (Dynamic property measurements such as G', G", [Eta]' and [Eta]* would not have much validity if the sample temperature was allowed to rise from viscous heating during testing). However, a special modification of the RPA disabled the forced air cooling system to allow the temperature of the upper and lower dies to freely rise from viscous heating. This heat from the sample resulted from carefully controlled high sinusoidal strain movement of the lower die.

Equation 1 gives the theoretical energy loss from a sinusoidal cycle (ref. 8). This energy loss translates into viscous heat which raises the temperature of both the upper and lower dies.

(1) [Epsilon] = [Pi] G" [[Gamma]o.sup.2]

Where: [Epsilon] = energy dissipated per cycle from oscillating sinusodial deformation; G" = loss shear modulus of rubber specimen; [[Gamma]o.sub.2] = peak strain.

From figure 1, one can see that there is a rubber seal between the lower seal plate and lower die, as well as another rubber seal between the upper seal plate and upper die. Since it is the lower die which imparts a strain to the sample when oscillating, this rubber seal also imparts a small amount of frictional heat buildup from this movement. This temperature contribution from the lower seal must be accounted for and subtracted from the total temperature rise for the lower die when a rubber specimen is being tested. This can be done by comparing the temperature of the lower die of the RPA when run empty vs. the lower die temperature when run with the rubber specimen. Both dies have low mass and will change temperature rapidly from the viscous heating of a rubber sample. Accurate platinum resistant thermometers (PRTs) are present in both the lower and upper dies, as shown in figure 1.

Test conditions for measuring viscous heating of uncured rubber compounds

Several preliminary experiments were performed to determine the best test conditions of temperature, strain and frequency for producing and measuring viscous heating in an uncured rubber compound. Figures 2 and 3 show the rise in the temperature of the upper and lower dies, respectively, of the specially modified RPA using an SBR compound with 75 phr of N351 carbon black (table 1). The figures show results from sinusoidal movements at different combinations of strain and frequency. For uncured rubber, it was found that a frequency of 20 cycles per minute (cpm) (0.33 Hz) and a strain of 90 [degrees] arc (1,256% strain) gave the highest measured viscous heating as measured at the upper and lower dies with very good repeatability. Figures 4 and 5 show the temperature of the upper and lower dies when the test conditions are repeated with the RPA die cavity empty. When the lower die cavity is empty, the temperature rises about 2 [degrees] C above the starting temperature due solely to the lower rubber seal. Since the upper die does not move and has no direct contact with the lower die, there is no heat input from the upper seal, and the recorded temperatures of the upper die with the cavity empty drop with time. By subtracting the temperatures of the lower and upper empty cavity ([t.sub.Le] and [t.sub.Ue]) from the apparent temperature rise of the lower and upper dies with a filled cavity ([t.sub.appL] and [t.sub.appU]), the "delta temp." ([Delta] T) is respectively calculated in equations 2 and 3 and illustrated in figures 6 and 7.

[Figure 2-7 ILLUSTRATION OMITTED]

Table 1 - internal mixer mix of masterbatch

                                     Phr           Wt.

SBR 1500                          100.00        580.56
Zinc oxide                          3.00         17.42
Stearic acid                        1.50          8.71
Aromatic oil                       15.00         87.08
TMQ                                 1.00          5.81
Carbon black or filler             75.00        435.42
Total                             195.50      1,135.00

Mill mix

Masterbatch                       195.50        788.90
Sulfur                              1.75          7406
TBBS                                1.00          4.04
Total                             198.25        800.00

(2) [Delta] [T.sub.Lower] = [t.sub.appL] - [t.sub.Le]

(3) [Delta] [T.sub.Upper] = [t.sub.appU] - [t.sub.Ue]

As can be seen from figure 7, the calculated [Delta] T is significantly higher from the lower die compared to the upper die, even after correcting for the heat contribution from the lower seal. This is probably because the heat starts predominately at the lower die.

For viscous heat measurements reported in this study of uncured rubber compounds, the RPA test configuration shown in table 2 was used. As already discussed, for uncured compound measurements, applying a [+ or -] 90 degree arc strain (1,256% strain) at 20 cpm (0.33 Hz) was most effective. As table 2 shows, the RPA test specimens were first molded and conditioned at 80 [degrees] C to assure good flow in the sealed pressurized cavity. Then using the variable temperature analysis (VTA) feature of the RPA, the temperature was ramped from 80 [degrees] C to 50 [degrees] C in three minutes. After a wait period of one minute (to assure the specimen has reached thermal equilibrium), the temperature control mechanism (both heating and cooling) is automatically disabled and a [+ or -] 90 degree arc strain at 0.33 Hz is applied for five minutes. The temperature changes for the lower and upper dies are automatically recorded.

Table 2

Subtest               0 Ready
           Temp.                         80 [degrees] C
Subtest               1 Timed
           Time                                    1 mm
           Temp.                         80 [degrees] C
           Freq                                  30 cpm
           Strain                        0.05 [degrees]

Subtest               2 Variable temperature analysis
           Strain                        0.05 [degrees]
           Freq.                                 10 cpm

           Time                                 Temp. C
           (min.)
           0.00                                      80
           3.00                                      50

Subtest               3 Timed
           Time                                    1 mm
           Temp.                         50 [degrees] C
           Freq.                                 30 cpm
           Strain                        0.05 [degrees]
                                  "Interpolate" checked

Subtest               4 Variable temperature analysis
           Time                                   5 m.m
           Freq.                                 20 cpm
           Strain                          90 [degrees]

Test conditions for measuring heat buildup of cured rubber compounds

If the RPA can be used to measure viscous heating of uncured rubber compounds by applying combinations of high strains and frequencies, it is also logical that similar test conditions could also be applied to rubber compounds in the cured state to measure the degree of heat buildup which could relate to product performance. Of course in the cured state, usually there is a limit to the level of strain that can be applied with the RPA (normally not more than a maximum of 40 to 100% strain for most compounds). As seen previously from figures 2 and 3 for viscous heating, increasing the frequency is almost as effective for increasing the specimen temperature as increasing the strain. Since there is a much greater limit to the maximum strain that can be applied to a cured rubber specimen (compared to an uncured specimen), it was found that a strain and frequency combination of 39% strain and 12 Hz starting at 40 [degrees] C, worked best for measuring heat buildup of a cured rubber compound. Table 3 shows the details of the RPA test configuration used to measure heat buildup of cured rubber compounds. In this configuration, the RPA was programmed to cure the experimental compounds at 180 [degrees] C for 10 minutes and using the VTA feature discussed earlier, dropping the temperature down to 40 [degrees] C and holding it there for five minutes before starting the heat buildup test by oscillating the cured specimen at 12 Hz and 39% strain for six minutes. This condition worked very well for measuring heat buildup of cured rubber specimens.

Table 3

Subtest                  0 Ready
          Temp.                                  180 [degrees] C

Subtest   Time           1 Cure
          Temp.                                            10 mm
          Freq.                                  180 [degrees] C
          Strain                                         100 cpm
                                                           1.40%

Subtest                  2 Variable temperature analysis
          Strain                                           1.95%
          Total time                          9 mm freq. 0.10 Hz
          Time (min.)                                    Temp. C
          0.00                                             180.0
          4.00                                              40.0
          9.00                                              40.0
                                           "Interpolate" checked
Subtest                  3 Variable temperature analysis
          Total time                                       5 m.m
          Freq.                                          12.0 Hz
          Strain                                             39%

Reinforcement factors

As discussed earlier, Patel, Brown and Weaver introduced the concept of reinforcement factors (RF). Their initial work consisted of comparing the viscosity imparted to a raw polymer (such as EPDM or SBR) by a selected carbon black or filler at a specific concentration vs. the viscosity of the unfilled polymer. Thus, this reinforcement factor is calculated by the equation given below:

(4) RF = [[Eta].sub.f]/[[Eta].sub.u]

Where: RF = the reinforcement factor

[[Eta].sub.f] = the filled viscosity

[[Eta].sub.u] = the unfilled viscosity

When different fillers are mixed in rubber, they have differing tendencies to form an aggregate network with varying degrees of interaction among the filler aggregates and the polymer matrix (refs. 9 and 10). The extent of these interactions (which are determined by the filler particle size, structure, surface activity, nature of the rubber, etc.) determine what the compound processability characteristics will be, as well as what some of the cured physical properties will be (such as tensile strength, modulus and tear resistance) (ref. 11). This RF is sometimes used as a single parameter to summarize the level of reinforcement imparted by a specific filler to a given rubber compound.

The original reinforcement factor work by Patel, Brown and Weaver was determined by measuring the viscosity of unfilled and filled elastomers with a capillary rheometer. In this experiment, we wanted to determine if dynamic viscosity measurements from the RPA could substitute for steady state shear rate capillary rheometer measurements for calculating RF.

From previous studies, we know that this may be possible through the Cox Merz rule. Cox and Merz in the early 1950s published the following empirical relationship they found between capillary rheometer apparent viscosity ([[Eta].sub.app]) measured under conditions of steady shear rate and dynamic complex viscosity ([Eta]*) which is measured by sinusoidal deformations (and constantly changing shear rates) with a DMRT (refs. 12 and 13). This equation is given below as equation 5.

(5) [[Eta].sub.app]([Gamma]) = [Eta]* ([Omega])| [Omega] = [Gamma]

Where: [[Eta].sub.app] = the apparent (uncorrected) capillary viscosity at a steady shear rate of [Gamma] (in. [sec..sup.-1]) n* = dynamic complex viscosity measured at an oscillatory frequency of [Omega] (in radians per second).

If it is assumed that the Cox Merz relation is valid, then the RPA could be used to directly measure RFs with equation 6.

(6) RF = [[Eta].sub.f]*/[[Eta].sub.u]* Where: [[Eta].sub.f]* = the filled dynamic complex viscosity; [[Eta].sub.u] = the unfilled dynamic complex viscosity.

Formulations and mixing

For measuring the viscous heating and reinforcement effects we just discussed, the SBR formulation shown in table 1 was used where different carbon blacks and mineral fillers were compared at 75 phr loading. Table 4 lists the selected carbon blacks and fillers used in this study with typical values for CTAB adsorption no. (ASTM D3765) and CDBP absorption no. (ASTM D3493) to characterize the colloidal properties. Also, another study was performed with the SBR formulation in table 5, where filler loading levels for N110, N347 and N650 carbon black and "Al" Whiting (ground calcium carbonate) were varied in increments of 15 from 15 phr to 75 phr. These three carbon blacks were selected because they have similar structure, even though they differ greatly in particle size. From the previous work reported by Patel, Brown and Weaver for measuring reinforcement factors, they found from studying various carbon blacks in a recipe based on SBR with a capillary rheometer could result in values exceeding the critical shear stress value for their test conditions. However, we felt it was important to use SBR in this study; therefore, 15 phr of aromatic oil was also included in the SBR test formulations to avoid this effect.

Table 4

N110                              CDBP(*)       CTAB(**)
N115                                   98            126
N220                                   96            128
N234                                  100            111
N299                                  100            119
N326                                  105            104
N330                                   69             83
N347                                   88             82
N351                                  100             67
N550                                   98             73
N650                                   88             42
N660                                   87             38
N762                                   75             36
N774                                   57             29
N787                                   62             29
N990                                   74             31
HiSil 210 silica                       40              9
Air floated hard clay                   -              -
Alumina trihydrate (ATH)                -              -
Mistron Vapor talc                      -              -
Calcium carbonate whiting               -              -

(*) Compressed DBP absorption no. as given for each "N number" carbon black as listed in ASTM D1765.

(**) A special surfactant adsorption no. as given for each "N number", carbon black as listed in ASTM D1765

Table 5 - internal mixer mix of masterbatch

                                   Phr

SBR 1500                        100.00
Zinc oxide                        3.00
Stearic acid                      1.50
Aromatic oil                     15.00
TMQ                               1.00
Carbon black or filler        15 to 75

Test conditions for the MPT capillary rheometer

The original work performed by Patel, Brown and Weaver to measure reinforcement factors was a Monsanto automatic capillary rheometer, Model 3501-H which was a constant stress instrument with precise temperature and pressure controls. For this study, we used a Monsanto MPT capillary rheometer and programmed it to move the piston in the barrel at predetermined speeds in order to apply sequentially shear rates of 30, 100, 300 and 1,000 [sec.sup.-1] to the rubber samples as it is extruded through a 0.059 inch orifice die with an L/D of 20:1. The test temperature selected was 100 [degrees] C.

Test conditions for the rubber process analyzer

The RPA test configurations for measuring viscous heating of uncured rubber compounds and heat buildup of cured rubber compounds were shown earlier as tables 2 and 3, respectively. Another configuration (table 6) was used to calculate the reinforcement factors with the RPA. This configuration is the new standard configuration from the recently accepted ASTM D6204 standard which achieved industrial acceptance last year. It is a very rapid test which has a test length of only 2.73 minutes. In addition, another more detailed RPA configuration (table 7) was used to also calculate reinforcement factors.

Table 6

          0 Ready                          Subtest
Temp.                                          100
          1 Timed                          Subtest
Time                                        1 min.
Temp.                              100 [degrees] C
Freq.                                       30 cpm
Strain                           0.2 [degrees] arc

          2 Frequency sweep                Subtest
Temp.                              100 [degrees] C
Strain                           0.5 [degrees] arc

          Frequency
          cpm                 6, 120 and 1,200 cpm

Table 7

          0 Ready                                 Subtest
Temp.                                                 100
          1 Timed                                 Subtest
Time                                               1 min.
Temp.                                     100 [degrees] C
Freq.                                              30 cpm
Strain                                  0.2 [degrees] arc

          2 Frequency sweep                       Subtest
Temp.                                     100 [degrees] C
Strain                                  0.5 [degrees] arc

          Frequency
          cpm                 2, 5, 10, 20, 50, 100, 200,
                                 500, 1,000 and 2,000 cpm

Results and discussion

Repeatability of the viscous heating at [+ or -] 90 [degrees] arc strain and 20 cycles per minute frequency was measured and found to be very good. Table 8 shows the coefficients of variation for the measured lower and upper dies from replicate testing of the SBR based compounds given in table 1. The grand average coefficient of variation (CV) of the RPA temperature rise measurements was found to be 0.31%. Repeatability for traditional isothermal dynamic viscosity measurements with the RPA was also found to be quite excellent, as documented earlier from a RMA interlaboratory cross-check (ref. 14).

Table 8 - coefficient of variation for RPA temperature measurements from repeat tests of the same SBR compound

Die temp. after x    Coef. of variation   Coef. of variation
number of minutes      for lower die        for upper die
testing

1.0 minutes                 0.47%                O.19%
2.0 minutes                 0.33                 0.24
3.0 minutes                 0.36                 0.28
4.0 minutes                 0.36                 0.29

Uncured compound viscous heating vs. dynamic viscosity Figure 8 shows the corrected measured delta temperature ([Delta] T) values from the lower die. As discussed earlier, this viscous heating was generated from sinusoidal oscillations of 20 cpm (0.33 Hz) and [+ or -] 90 [degrees] arc strain for five minutes after initially stabilizing at 50 [degrees] C (reference table 2, discussed earlier). Figure 8 gives the [Delta] T values in decreasing order. Also shown are the corresponding responses for the dynamic complex viscosity ([Eta]*) measured isothermally under the new ASTM test conditions of 2 Hz, 7% strain and 100 [degrees] C from the separate RPA series of tests using the configuration given in table 6. As can be seen, the viscous heating is highest for the very fine particle size carbon blacks and lowest for the large particle mineral fillers with the semi-reinforcing carbon blacks falling in between. The imparted [Eta]* values are very close to the same pattern. In fact, figure 9 shows that [Eta] * vs. [Delta] T has a very good correlation of [R.sup.2] = 0.975.

[Figure 8 ILLUSTRATION OMITTED]

It was observed that a moderate RPA frequency such as 120 cpm (2 Hz) or a non-standard frequency such as 50 cpm gave the best correlations of RPA isothermal rheological properties with RPA [Delta] T for the 20 rubber compounds just discussed. From figure 9, the best correlation is achieved with the lower die [Delta] T vs. the RPA isothermal dynamic complex viscosity [Eta]*. As indicated from the calculated correlation coefficients (R) shown in table 9, comparisons using the RPA real dynamic viscosity [Eta]' are not as good as [Eta]* in predicting viscous heating. The [Delta] T from the lower die correlates better to the isothermal dynamic viscosity values than the upper die [Delta] T. It was also found that the uncured tan [Delta] (calculated by dividing the viscous response by the elastic response) did not correlate well to viscous heating.

[Figure 9 ILLUSTRATION OMITTED]

Table 9 - correlation coefficients of RPA [Delta]T vs. ASTM RPA dynamic viscosity testing

Combination of test conditions                 R       [R.sup.2]

n* at 2 Hz vs. [Delta]T from lower die        0.99        0.98
n' at 2 Hz vs. [Delta]T from lower die        0.93        0.87
n* at 2 Hz vs. [Delta]T from upper die        0.92        0.84
n' at 2 Hz vs. [Delta]T from upper die        0.89        0.79

The typical colloidal properties for the carbon blacks included in this study (table 4 from ASTM D 1765) were used to relate to the [Delta] T measurements from the lower die for viscous heating through multiple linear regression. For the carbon blacks chosen for this study, there was no significant correlation between the CTAB and CDBP values ([R.sup.2] = 0.61). On the other hand, CTAB alone mildly correlated to the RPA viscous heating (with an [R.sup.2] = 0.85) and CDBP alone also mildly correlated ([R.sup.2] = 0.87). However, through multiple linear regression analysis using CTAB as [X.sub.1] and CDBP as [X.sub.2], a very useful predictive equation was established for viscous heating as shown in tables 10 and 11 and figure 10 with an [R.sup.2] = 0.97.

[Figure 10 ILLUSTRATION OMITTED]

Cured heat buildup measurements with RPA

The RPA was also configured as indicated in table 3 to cure the rubber compounds and measure cured heat buildup at 40 [degrees] C. (Since these heat buildup measurements were performed on cured specimens, the strain was limited to only 39%, but the frequency was increased to 720 cycles per minute). The rubber compounds in this study were from the formulation given in table 1. They were cured in situ at 180 [degrees] C for 10 minutes. The temperature was reduced to 40 [degrees] C for effective heat buildup measurements with the RPA. Figure 11 shows the level of cured heat buildup and uncured viscous heating imparted to the SBR compound by the respective fillers tested. As can be seen, fillers which imparted high viscous heating to the uncured SBR compound, also impart high heat buildup to the cured compound. Also, selected RPA heat buildup data correlated to the heat buildup imparted by the Goodrich Flexometer shown in figure 12 for the carbon black loaded compounds only. (Variations in compound thermal conductivity will have a much greater effect on the Goodrich Flexometer heat buildup measurements than they have on the RPA measurements. Siliceous fillers impart significantly poorer thermal conductivity than carbon black.) Also, within the restraints of the fillers selected for this study, there is a very good correlation between the cured heat buildup imparted and the uncured viscous heating imparted by the different fillers. Of course, with the formation of crosslinks through vulcanization, the elastic modulus increases greatly in relation to the loss modulus. Therefore, the amount of heat generated from the vulcanizate is considerably less than from the corresponding uncured stock, as clearly seen from figure 11.

[Figures 11-12 ILLUSTRATION OMITTED]

Reinforcement factors

In accordance with equation 4, reinforcement factors (RF) were calculated from MPT capillary rheometer data from the testing of the SBR formulation with different fillers, as shown in table 1. Likewise, RPA testing was also performed on these same compounds, and the respective RF values are calculated from the RPA data in accordance with equation 6. Figure 13 shows the descending comparison of the RF calculated from MPT apparent viscosity data vs. the RF calculated from RPA complex dynamic viscosity data. Figure 14 gives an [R.sup.2] of 0.91, which is a good correlation. Some of the scatter observed is probably due to the poorer repeatability of the MPT capillary compared to the RPA.

[Figures 13-14 ILLUSTRATION OMITTED]

As stated by Patel, Brown and Weaver, the higher the calculated RF implies a greater level of reinforcement to the vulcanizate. Figure 15 shows a comparison of the uncured RF vs. the imparted cured elastic modulus as measured by the RPA. Figure 16 shows a very good correlation of [R.sup.2] = 0.97. This implies that if there is no variation in curatives and crosslink density, we should be able to largely control the cured dynamic properties of a given compound by controlling the uncured dynamic properties. This can be done by controlling the uncured rheological properties measured by the RPA.

[Figures 15-16 ILLUSTRATION OMITTED]

Loading effects

With a rise in the concentration of a fine-particle, reinforcing filler such as carbon black or precipitated hydrated silica, an agglomerate "network" forms above a "threshold" concentration (ref. 15). It is generally believed that the attractive force to create this network for carbon black is due to the Van der Waals force (refs. 16 and 17). However, for silica, it is generally believed that the stronger hydrogen bonding force is responsible (refs. 18 and 19). So, above this threshold concentration, the density of this filler network becomes significantly greater. Previous work has shown that this threshold concentration point is somewhere around 30 phr for an N300 type carbon black (ref. 20). As this network builds, more energy is absorbed to break it up during mixing. The energy required to destroy this network ends up being dissipated as heat during the mixing process.

Using the formulation shown in table 5, viscous heating measurements were made with the RPA. Figure 17 shows the rise in [Delta] T with an increase in the concentration of N347 carbon black. As can be seen, the [Delta] T value rises only a little from 15 phr to 45 phr; however, at higher concentrations, the [Delta] T rises very rapidly with each incremental increase in loading. This is due to the greater formation of a filler network which generates more heat when it is destroyed through the application of high strain. If the concentration is not high enough or the particle size small enough, then a filler network will not form and viscous heating will not be as great. The isothermal strain measurements with the RPA can measure the extent of this filler network by noting the shift in the critical strain [[Gamma].sub.c]. The critical strain [[Gamma].sub.c] is denoted when the measured storage modulus (G') and loss modulus (G") start to decrease as the strain increases. Generally, unfilled polymers on the RPA will show a [[Gamma].sub.c] of about 14% (ref. 21). However, as the density of a filler network forms, the [[Gamma].sub.c] starts to decrease. Decreasing the carbon black particle size and increasing the filler concentration can ultimately force the [[Gamma].sub.c] below 0.2% strain (ref. 22). By reviewing figures 18-20, one can see how the critical strain [Gamma]c goes to a lower strain value either because of smaller particle size or higher concentration. In figure 18, 15 phr of N110, N347, N650, or A1 (ground calcium carbonate whiting), produces a critical strain [[Gamma].sub.c] which is relatively high and the G' storage moduli are all about the same above the [[Gamma].sub.c] point. This indicates that at low concentration of filler, there is insufficient concentration of particles (or the particles are not small enough) to form a filler network. In figure 19, this comparison is made at 45 phr. This increase in concentration was not enough to affect the [[Gamma].sub.c] for A1 calcium carbonate whiting (because it has the largest particle size on the order of 1,000 nm and no significant structure). However, the critical strain for the semi-reinforcing N650 carbon black (particle size approximately 60 nm) is about 2% strain and the fully reinforcing N347 and N110 carbon blacks (particle size approximately 30 and 15 nm, respectively) show a much larger reduction in [[Gamma].sub.c]. Lastly, figure 20 clearly shows that the critical strain [[Gamma].sub.c] has be, en forced below 0.5% for all the carbon blacks; however, the A1 whiting does not have a sufficiently small particle size even at 75 phr to establish any filler network or effect the critical strain [[Gamma].sub.c]. Therefore, the ground calcium carbonate whiting generates relatively little viscous heat, as shown previously in figure 8. (The whiting filler generates about the lowest amount of viscous heat compared to all other fillers studied).

[Figures 17-20 ILLUSTRATION OMITTED]

Einstein, Guth and Gold equation

According to the Einstein, Guth and Gold equation (or EGG equation), the volume that the filler is occupying in a rubber compound will increase the rubber compound's viscosity, as shown in the equation below (refs. 23-25).

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

Where:

[[Eta].sub.f] = viscosity of filled compound

[[Eta].sub.u] = viscosity of unfilled compound

c = volume fraction of filler

This model is based on a filler having a perfect spherical particle shape. The factor in parentheses, which we will call the "Einstein, Guth and Gold reinforcement factor" (or simply the [RF.sub.EGG]), is part of this hydrodynamic formula which predicts that the filled polymer system will have a higher viscosity than the unfilled polymer. Table 5 gives the experimental SBR formulation used in which carbon black and ground calcium carbonate loadings at 15, 30, 60 and 75 phr were prepared. Table 12 gives the calculated [RF.sub.EGG] values for the carbon black and ground calcium carbonate filler. Different [RF.sub.EGG] values were calculated for the carbon black vs. calcium carbonate because the specific gravity of carbon black is 2.82 vs. the Ca[CO.sub.3] filler which is 2.70. The phr concentration is based on weight; however, equation 7 requires the concentration to be calculated as a volume fraction. Figure 21 compares the actual RPA complex dynamic viscosity values for four selected fillers with rising concentrations. The viscosity increase noted with the ground calcium carbonate whiting conforms somewhat to the Einstein, Guth and Gold equation just discussed. However, the viscosity responses from increased concentration of the three carbon blacks is very different from the EGG model. The viscosity values s for all three carbon blacks is significantly higher than what is predicted by EGG.

[Figure 21 ILLUSTRATION OMITTED]

Table 12

Calculation of [RF.sub.EGG] values from formulation given in table 5 by the Einstein, Guth and Gold equation

Filler load-    [RF.sub.EGG] for ground calcium    [RF.sub.EGG] for
ing level              carbonate whiting             carbon black

15                            1.13                       1.20
30                            1.29                       1.47
45                            1.48                       1.78
60                            1.68                       2.11
75                            1.90                       2.45

[[Eta].sub.EGG] [approximately equal] [[Eta].sub.CaCO3] [is less than] [[Eta].sub.N650] [is less than] [[Eta].sub.N347] [is less than] [[Eta].sub.N110]

It is obvious that this EGG hydrodynamic formula underestimates the viscosity imparted by fillers with much finer particle size, such as carbon blacks. It is well known that when filler particle sizes are smaller than 100 nm, the hydrodynamic theory does not predict the resulting viscosity (ref. 26). The A1 ground calcium carbonate whiting has an average particle size of approximately 1,000 nm. As stated earlier, the average particle sizes of the N650, N347 and N110 are approximately 60 nm, 30 nm and 15 nm, respectively. Because of the agglomeration effects discussed earlier, the actual viscosity imparted by these semi-reinforcing and fully reinforcing carbon blacks is significantly higher than what the hydrodynamic theory would indicate. The smaller the filler particle size, the higher the resulting viscosity at a constant volume fraction. Medalia and Kraus have given detailed theoretical reasons and explanations regarding the causes of this phenomenon which include differences in particle size, primary and secondary structure, occluded rubber, etc. (ref. 27). Also, some theoretical models that post date the EGG model and are better in accounting for these effects are given by Pliskin and Tokita (ref. 28).

Conclusions

The following are conclusions from this study:

* Very repeatable viscous heating measurements were achieved using the RPA die design shown in figure 1.

* RPA high strain measurements were the most effective in measuring viscous heating of uncured compounds.

* Heat buildup of cured rubber specimens was successfully measured using the RPA die design shown in figure 1 with a combination of moderate strain and high frequency.

* Complex dynamic viscosity [Eta]* at moderate frequency (2 Hz) correlated to viscous heating values for the fillers studied.

* Directionally, fillers in the study which imparted high viscous heating in the uncured state also imparted high heat buildup in the cured state.

* Reinforcement factors could be measured by sinusoidal strain more rapidly, with better repeatability, and with far less clean up time, while still correlating well to the reinforcement factors calculated through capillary rheometer measurements for the fillers included in this study.

* The fillers in this study which had high reinforcement factors as measured by viscosity measurements also tended to impart higher reinforcement to their respective vulcanizates as indicated from the measured cured storage modulus values.

* A good correlation was achieved using multiple linear regression to relate CTAB adsorption and CDBP absorption properties of the selected carbon blacks to viscous heating imparted to the SBR formulation.

Table 10

                            X1 = CTAB
                            X2 = CDBP
Regression output
Constant                                    8.4987199
Std. err. of Y est.                         1.0668447
R squared                                   0.9682473
No. of observations                                14
Degrees of freedom                                 11
                                   X1              X2
X coefficient(s)             0.065503       0.1623736
Std. err. of coef.          0.0114838       0.0255674

Table 11

Carbon    CTAB    CDBP    Actual [Delta] T @    Predicted [Delta] T
black                        lower die after            @ lower die
                                      5 min.           after 5 min.

N110        126      98                  31.8                 32.66
N115        128      96                  34.5                 32.47
N220        111     100                  30.8                 32.01
N234        119     100                  32.8                 32.53
N326         83      69                  23.8                 25.14
N330         82      88                  28.8                 28.16
N351         73      98                  29.5                 29.19
N550         42      88                  25.9                 25.54
N650         38      87                  25.2                 25.11
N660         36      75                  23.6                 23.03
N762         29      57                  19.2                 19.65
N774         29      62                  20.1                 20.47
N787         31      74                  21.3                 22.54
N990          9      40                  16.8                 15.58

Acknowledgements

"Viscous heating and reinforcement effects of fillers using the rubber process analyzer" is based on a paper given at the April, 1999 meeting of the Rubber Division. "Electric in-situ measurement of vulcanization" is based on a paper given at the October, 1997 International Rubber Conference.

"Interlaboratory testing programs as a quality assurance tool for the rubber industry" is based on a paper given at the April, 1999 meeting of the Rubber Division.

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(21.) Ibid, p. 7.

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(27.) J. Mark, B. Erman and F. Eirich, chapter 8 by A. Medalia and G. Kraus, Science and Technology of Rubber, Academic Press, 1994, p. 400.

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