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Practical rheology of rubber compounds.

Uncured rubber compounds are heterogeneous viscoelastic materials that exhibit a number of peculiar flow properties calling for special rheometrical techniques, with appropriate handling care and testing procedure. Basically, any rheometry test consists of either applying a controlled rate of deformation and measuring the corresponding stress or vice versa. Measured quantities (e.g., force, torque, pressure, speed, output, etc.) are converted into the appropriate rheological parameters through so-called rheometrical equations that are theoretically derived, according to a number of hypotheses, namely an ideal behavior of the tested material. (Filled) rubber compounds are far from behaving in an ideal manner, even a linear viscoelastic one, and this obviously questions the meaning of test results.

By combining a number of techniques, not only rheological testing but also physico-chemical methods (e.g., bound rubber measurement [refs. 1 and 2]) and advanced characterization techniques (e.g., solid NMR [ref. 3]), a clearer picture has recently emerged about the very nature of filled rubber compounds. Nowadays one would see such materials as soft tri-dimensional networks (ref. 4) with the capability to evolve not only versus time and temperature, but also according to their particular (shear) history. Obviously, practical rheology of rubber compounds has to take such a complex nature into account, as well as the resulting non-linear viscoelastic character.

This article reports experiments on a SBR standard rubber formulation that demonstrate how significant and reproducible rheological properties can be measured providing one takes into account the peculiar character of such materials. Interpretation of observed behavior in terms of practical data, as measurable on the factory floor, is offered.



A SBR masterbatch whose formulation is given in table 1 was prepared in an internal mixer (2.25 liter; fill factor: 0.65) according to an upside down procedure. By varying the overall mixing time, three compounds were prepared with different mixing energies: 620, 1,270 and 1,930 MJ/[m.sup.3]. Microscopic examination of the compounds showed that even at the lowest mixing energy level, no undispersed carbon black agglomerates could be detected. After dump, compounds were sheeted off after one minute on an open mill (except a small quantity that was kept as such) and stored under dark cover at room temperature.
Table 1 - SBR compound

Ingredient Phr

SBR 1500(a) 100
N330 carbon black 50
Zinc oxide 5
Processing oil (aromatic) 5
Stearic acid 3
Permanax TQ(b) 2

(a) [M.sub.n] = 1.5 x [10.sup.5] g/mol;
[M.sub.w] = 7 x [10.sup.5] g/mol

(b) trimethylquinoline, polymerized

(c) N-isopropyl-N'-phenyl-p-phenylene diamine

Testing techniques

Mooney rheometer tests were performed at 100 [degrees] C, according to ASTM D1646, in order to obtain the so-called Mooney peak and ML(1+4). Viscoelastic properties were measured at 100 [degrees] C with a harmonic torsional tester for rubber materials, RPA 2000. Preliminary strain sweep tests at 1 Hz demonstrated that even in the lowest part of the strain range investigated (i.e., [Gamma] = 0.2 deg.), no linear viscoelastic response is observed with the test compounds, quite a common behavior of filled elastomers. Frequency sweep tests were therefore performed at 0.5 deg. within a 0.2 - 200 rad/s frequency range.

Bound rubber was measured according to a standard procedure developed in the laboratory: Around 1 g of material, cut in small pieces, is placed in a steel wire cage and immersed in 100 ml toluene for one week, with one replacement of the solvent in order to avoid saturation by extractable rubber. Bound rubber is determined by weighing the cage and the residue after vacuum drying.

Pressure-temperature treatment

Bound rubber and rheological properties are known to vary on storage at room temperature. In order to further document this effect, samples with various histories were prepared according to the schematic in figure 1. In addition, parts of sheeted off samples were submitted to pressure-temperature treatments (in 4 mm thick mold, under 20 MPa pressure at 100 [degrees] C for various periods), then stored at room temperature under dark cover.



Mooney viscometer

Experimental results are given in table 2. As expected, the higher the mixing energy when preparing the compound in the internal mixer, the lower the viscosity, and milling for one minute further decreases both the Mooney peak and ML(1 + 4). Moreover, storing compounds at room temperature produces significant increases in Mooney data. Figure 2 illustrates the effects of both (internal) mixing and milling using data measured just after dump. Sheeting off obviously adds some mixing energy to compounds, but this energy is actually not measured.

Table 2 - Mooney viscometer results

 Milling At dump Stored 1 day

Mixing Operation Total
energy MJ/ energy MJ/ Peak ML(1+4) Peak ML(1+4)
[m.sup.3] [m.sup.3]

 620 None 137.9 85.1 145.0 85.1
1,270 None 109.6 66.9 108.0 66.9
1,930 None 97.8 62.5 98.2 62.2
 620 1 min. 900 124.5 79.0 123.0 78.7
1,270 1 min. 1,550 105.7 66.8 105.0 66.8
1,930 1 min. 2,210 97.7 61.6 95.4 62.3

 Stored 8 days Stored 29 days

energy MJ/ Peak ML(1+4) Peak ML(1+4)

 620 148.0 86.6 148.0 88.6
1,270 116.0 67.7 119.0 69.3
1,930 103.0 62.6 106.0 64.1
 620 128.0 80.4 132.0 81.4
1,270 109.0 67.5 110.1 68.6
1,930 99.4 62.7 102.0 63.8

The pattern of figure 2 suggests, however, that by horizontally shifting data measured on milled samples, one could estimate how much energy is added during one minute on an open mill.

This extra mixing energy can indeed be estimated using a graphical shifting procedure but a more elegant method consists in considering that Mooney data, either the peak or ML(1+4), vary with mixing energy according to a simple exponential decay equation, i.e.:

(1) Y(ME) = [Y.sub.stab] x[1 + exp(-[Beta] x ME)]

where Y(ME) is the property measured on a sample having been prepared in the internal mixer with an energy equal to ME (MJ/[m.sup.3]), [Y.sub.stab] is the same property at optimum mixing level and [Beta] is a fitting parameter. By non-linear regression, [Y.sub.stab] and [Beta] are easily obtained using Mooney data measured on samples without milling. The extra mixing energy brought by the milling operation is then calculated through:

(2) [ME.sub.mill] = 1/[Beta] *ln [[Y.sub.stab]/Y(ME) - [Y.sub.stab]] - [ME.sub.mixer]

where [ME.sub.mixr] is the mixing energy level reached in internal mixer operation. Results are given in table 3 with likely unrealistic data between brackets. Scatter is very large and milling energy estimated from Mooney peak data is generally higher than from ML(1+4) data. Simply averaging all values gives 282 MJ/[m.sup.3], so we concluded that one minute milling adds some 280 MJ/[m.sup.3] to compounds (see third column in table 2).
Table 3 - assessing extra mixing energy through
one minute milling

 Estimated milling energy (MJ/[m.sup.3])

Sample aging From Mooney peak From ML(1+4) data

Unaged 227 145
 275 155
 281 214
1 day 325 151
 447 143
 (1,293) (31)
8 days 337 136
 483 170
 (1,151) (96)
29 days 285 168
 525 241
 804 171

As illustrated in figure 3, in the case of the unaged compound (i.e., measurements were made within one hour after dump), milling effects on Mooney data are now clearly understood as further steps towards the optimum development of rheological properties. In equation 1, two parameters are needed to describe the evolution of the rheological property with the mixing energy: [Beta] ([m.sup.3]/MJ) and the optimum level [Y.sub.stab] of the property considered. Table 4 gives these parameters for compounds with different storage periods.

Table 4 - effect of (mixing and milling) energy
on Mooney data using equation 1; parameters
vs. storage periods at room temperature

 Mooney peak at ML(1+4) at 100 [degrees] C
 100 [degrees] C

Storage [Peak.sub. [Beta] ML [Beta]
 (day) stab] ([m.sup.3]/MJ) (1+4)stab ([m.sup.3]/MJ)

 0 90.6 1.16 [10.sup.-3] 57.7 1.24 [10.sup.-3]
 1 91.5 1.18 [10.sup.-3] 58.3 1.30 [10.sup.-3]
 8 94.5 1.14 [10.sup.-3] 58.2 1.22 [10.sup.-3]
 29 95.9 1.13 [10.sup.-3] 59.5 1.23 [10.sup.-3]

As can be seen, storage affects the (stabilized) rheological property, either the Mooney Peak or ML(1+4) but, for a given property, [Beta] shows marginal changes that suggest: (i) that mean values could be considered, i.e., [Beta] = 1.16 [10.sup.-3] for the Mooney peak and [Beta] = 1.25 [10.sup.-3] for ML(1+4); and (ii) that one has only to consider how the stabilized values, [Peak.sub.stab] and ML[(1+4).sub.stab], vary with storage time. Such a storage effect can be simply treated using:

(3) [Y.sub.stab](t) = [Y.sub.stab](0) + [[Y.sub.stab]([infinity]) - [Y.sub.stab](0)](1 - [e.sup.-kt])

where [Y.sub.stab](0) and [Y.sub.stab]([infinity]) are, respectively, the stabilized property (i.e., at optimum mixing energy) measured either immediately (t = 0) or after an infinite storage time.

By combining equations 1 and 3, the effects of both the mixing energy and storage time are considered; for instance in the case of the Mooney peak (at 100 [degrees] C), one writes:

(4) Peak (ME, t) = {[Peak.sub.stab] (0) + [[Peak.sub.stab]([infinity]) - [Peak.sub.stab] (0)] (1 - [e.sup.-kt])} x [1 + [e.sup.-[Beta]ME]]

Equation 4 was used to draw the 3D map in figure 4, with [Peak.sub.stab] (0) = 906; [Peak.sub.stab]([infinity]) = 95.9; k = 0.165; and [Beta] = 1.16 [10.sup.-3], in order to compare it with experimental data. As can be seen, the fit is excellent and a similar 3D plot is obtained for ML(1 + 4).


Bound rubber

Bound rubber data are given in table 5. As can be seen, bound rubber varies with mixing energy and there are some effects due to milling, but variations on storage are not consistent. In agreement with the previous section, we accounted for milling effects by assigning 280 MJ/[m.sup.3] extra mixing energy to open-mill treatment. Furthermore, according to a purposely simple model previously suggested (ref. 5) for filler wetting and dispersion and bound rubber formation, experimental data can be fitted with:

(5) [[%BdR].sub.ME] = [[%BdR.sub.max]] {1 - [k.sub.2]/[k.sub.2] - [k.sub.1] exp(-[k.sub.1] ME) + [k.sub.1]/[k.sub.2] - [k.sub.1] exp(-[k.sub.2] ME)}

where [[%BdR].sub.ME] and [[%BdR.sub.max]] are, respectively, the bound rubber for a given mixing energy level and the maximum bound rubber that can be obtained for the rubber-filler system considered, [k.sub.1] and [k.sub.2] are process constants for filler wetting and bound rubber formation, respectively, and ME is the mixing energy. (Note: In order to avoid overflow problems with non-linear regression algorithms that fit equation 5 to experimental data, ME values must be expressed in [10.sup.-3] MJ/[m.sup.3]).
Table 5 - bound rubber data

 Mixing Storage: 1 day 8 days 29 days
 energy Milling Bound Bound Bound
 MJ/ rubber rubber rubber

 620 None 13.9 14.9 14.8
 1,270 None 19.3 20.7 19.6
 1,930 None 20.4 21.9 20.7
 620 1 min. 14.4 15.8 15.0
 1,270 1 min. 19.5 22.4 19.8
 1,930 1 min. 20.4 22.6 20.7

By non-linear regression, equation 5 is used to fit the curve drawn in figure 5 to experimental data, yielding [k.sub.1] = 5.89, [k.sub.2] = 2.19 and [[%BdR.sub.max]) + 22.1%, with [r.sup.2] = 0.94. Because an upside-down procedure is used in preparing SBR batches, the wetting and dispersion of carbon black particles are relatively rapid, as reflected by the value of [k.sub.1] when compared to [k.sub.2].


Dynamic properties

G' and G" dynamic moduli are given in table 6. As shown in figure 6, mixing energy level significantly affects the complex modulus G* function in the terminal region; milling further changes test results.

Table 6 - dynamic moduli - RPA at 100 [degrees] C, strain = 0.5 deg.
- samples stored one day at []

Mixing 1,270 MJ/ 1,930 MJ/
energy: 620 MJ/[m.sup.3] [m.sup.3] [m.sup.3]
Milling: None None None
w(rad/s) G'(kPa) G"(kPa) G'(kPa) G"(kPa) G'(kPa) G"(kPa)
 0.2 131.59 86.45 85.69 59.67 76.51 54.32
 0.5 163.72 106.34 113.23 79.57 107.11 72.68
 0.99 193.56 125.47 138.47 97.16 126.23 88.75
 2 229.52 149.19 167.55 117.82 156.07 109.40
 5 293.78 185.91 223.40 152.25 211.15 143.83
 10 357.28 214.98 280.01 180.55 265.47 170.61
 50 543.19 278.48 454.44 240.99 439.91 231.05
 100 640.35 296.84 552.37 252.47 530.95 248.64
 200 740.57 309.08 641.11 266.24 629.64 262.41
 Mixing 1,270 MJ/ 1,930 MJ/
energy: 620 MJ/[m.sup.3] [m.sup.3] [m.sup.3]
Milling: 1 min. 1 min. 1 min.
w(rad/s) G'(kPa) G"(kPa) G'(kPa) G"(kPa) G'(kPa) G"(kPa)
 0.2 116.29 77.27 89.51 61.97 77.27 53.55
 0.5 142.30 92.57 110.17 76.51 104.81 71.15
 0.99 170.61 111.70 139.24 97.93 125.47 88.75
 2 210.39 136.94 169.84 116.29 155.31 107.87
 5 273.12 174.43 226.46 150.72 211.15 141.53
 10 332.03 201.97 282.30 176.73 266.24 168.31
 50 514.88 263.18 458.27 237.93 439.91 228.75
 100 608.22 279.24 547.01 253.23 530.95 245.58
 200 705.38 293.78 648.76 269.30 626.58 260.88

Such observations are obviously in line with the Mooney data discussed above and suggest that a similar shifting procedure could be used to estimate the extra mixing energy brought by the open-mill treatment. However, as shown in figure 7, one needs to assign the open mill treatment a mixing energy that depends on the frequency at which the complex modulus is measured: The higher the frequency, the lower the mixing energy to be assigned to milling in order to get a good alignment of G* vs. ME data. For G* measured at [Omega] = 2 rad/s, the shifting value is 140 MJ/[m.sup.3], i.e., half what is needed with Mooney results (for which shear rate is around 1.57 [s.sup.-1]). Once the right shift factor is used, G* vs. ME data at each frequency can be fitted using equation 1. As shown by the dashed curves in figure 7, the fit is excellent.


Effect of pressure at constant temperature on rheological properties

Most rheometrical techniques for rubber compounds are, in fact, performed under pressurized conditions. For instance, the Mooney and RPA cavities are maintained closed through hydraulic pressure of several MPa, and capillary rheometry is obviously a pressure flow technique. Long ago, Leblanc and Swidersky reported peculiar Mooney and capillary rheometer results on rubber compounds with reinforcing fillers when extended preheating time is used while materials are maintained under pressurized conditions (ref. 6). More recently, we observed with carbon black and silica filled SBR compounds a shift in dynamic modulus measured with the RPA, when samples are maintained for long periods in the test cavity (ref. 7). Such effects could be due, either to instrumental artifacts or - more likely - to variations in rubber-filler interaction that directly reflect on rheological properties.

In order to study such effects, samples were submitted to a pressure-temperature (PT) treatment (20 MPa, 100 [degrees] C) for various periods, using 4 mm thick molds. Then, rheometrical tests and bound rubber measurements were performed as described earlier.

Mooney and bound rubber results are given in table 7. As can be seen, PT treatment significantly changes the properties of compounds: Mooney peak and ML(1 + 4) drastically increase with longer molding times, while bound rubber increases by several percent. PT treatments and the associated experiments were performed on samples having received different (mixing and milling) energies over three consecutive days; therefore, a (likely minor) storage effect further adds on PT induced changes. It seems, moreover, that PT effects are stronger than storage ones, as seen when comparing the data on samples mixed up to 2,210 MJ/[m.sup.3] and stored either 10 or 29 days (bottom of table 7). Quite a complex picture emerges when mixing energy and pressure-temperature effects are considered simultaneously, as illustrated by the three-dimensional graph in figure 8. Simply stated, higher mixing energy decreases the rheological properties, but maintaining compounds under pressure (at 100 [degrees] C) for a sufficient time restores a significant part of the lost [of Mooney peak in figure 8, but a similar picture is obtained with ME(1+4)].

Table 7 - effect of pressure-temperature on Mooney data
and bound rubber

 Mixing Molding time Mooney at
 energy under 20 MPa at 100 [degrees] C Bound
MJ/[m.sup.3] 100 [degrees] C h. Peak ML(1+4) rubber
 900 0 128.0 80.4 15.8
(aged 8 d.) 1 133.0 81.5 17.2
 5 137.0 82.9 17.9
 16 144.0 84.3 20.0
 1,550 0 109.0 67.5 20.8
(aged 9 d.) 1 115.2 69.3 20.8
 5 120.7 71.0 21.6
 16 132.0 72.7 22.5
 2,210 0 99.4 62.7 21.9
(aged 10 d.) 1 107.0 64.2 21.5
 5 117.0 66.2 21.4
 16 128.3 72.1 23.9
 2,210 0 102.0 63.8 20.7
(aged 29 d.) 1 104.0 64.2 20.9
 5 111.0 66.3 21.7
 16 128.0 70.3 23.5

Similar significant effects of pressure-temperature treatment are also observed on dynamic properties as measured with the RPA at 100 [degrees] C. Results are given in table 8. Both the elastic and viscous moduli of any sample prepared under given conditions (internal mixing energy and milling time) significantly increase with longer pressure-temperature treatment. The conditions of preparation (mixing energy level) further complicate the variation, as illustrated in figure 9 with complex modulus at 2 rad/s.

Table 8 - effect of pressure-temperature on (uncured)
dynamic properties; RPA at 100 [degrees] C, strain = 0.5 deg.

Mixing Pressure- Freq. = Freq. =
energy temperature 2 rad/s 200 rad/s
MJ/[m.sup.3] treatment G' G" G' G"
(= + 1 min. milling) h. kPa kPa kPa kPa

620 0 203.5 134.7 700.0 295.3
(aged 8 d.) 1 229.5 140.8 727.6 299.9
 5 231.8 139.2 730.6 291.5
 16 239.5 138.5 749.8 297.6
1,270 0 172.9 117.1 651.1 264.7
(aged 9 d.) 1 182.1 118.6 667.1 280.8
 5 190.5 120.1 680.9 273.1
 16 218.0 123.9 697.0 282.3
1,930 0 157.6 107.9 626.6 263.9
(aged 10 d.) 1 167.5 111.7 660.2 263.9
 5 169.1 110.2 649.5 266.6
 16 202.7 121.6 721.4 285.4

Discussion and conclusions

Reported data show that rheological properties of rubber compounds have a strong transient character. Whatever the technique used, any test result, either obtained in simple shear or in dynamic mode, is depending on the level of mixing energy received by the compound and on the storage period before performing the experiment. As we showed, most of the effects observed can be treated with relatively simple equations that model the variation as an evolution towards a plateau, or stabilized value, of the property considered. Mixing energy and storage modify Mooney peak and viscosity in reverse directions: A decrease with higher mixing energy, an increase with longer storage time.

We developed a simple technique to estimate how much mixing energy is brought to compounds by the milling operation, subsequent to internal mixing. By assigning the right level of energy to open mill treatment, the observed variations of rheological properties and bound rubber take a logical pattern, easily modeled with the appropriate equations. For instance, bound rubber varies with (mixing and milling) energy until a plateau value is reached. In agreement with a simple model previously proposed (ref. 5), essentially two subsequent operations take place when preparing a rubber compound: Wetting and dispersion of filler particles, then formation of bound rubber. The later process is the slow one, that requires quite an important level of energy to reach completion, and furthermore, a sufficient storage time before a stable bound rubber value is obtained. Because there is a direct relationship between bound rubber (as a parameter related to filled rubber morphology) and rheological properties, only transient flow properties can be measured before bound rubber formation is completed and stabilized. The significant variations in both rheological properties and bound rubber through pressurization at 100 [degrees] C suggest that the rubber-filler interactions are modified by the treatment. While these results shed some light on some peculiar effects observed with rubber rheometers, this calls for further works before a full understanding is gained.

Practical rubber rheology is consequently far from being a simple practice, would one want to obtain meaningful results. Ideally, the level of mixing energy and the age of the compound must be associated with any rheological measurement. On the factory floor, this means (i) that particular attention must be paid to the point of sampling with respect to the process line, and (ii) that the storage conditions (time as we showed and temperature most likely) of samples before testing are particularly important parameters.


(1.) B. Meissner, J. Appl. Polm. Sc., 50, 285 (1993).

(2.) J.L. Leblanc, J. Appl. Polm. Sc., 66. 2,257-2,268 (1997).

(3.) V.M. Litvinov and P.A.M. Steeman, Macromomolecules, 32 (25). 8,476-8,490 (1999).

(4.) J.L. Leblanc, Prog. Rubber Plastics Technol., 10, 112 (1994).

(5.) J.L. Leblanc and C. Barres, "Bound rubber: A key factor in understanding the rheological properties of uncurcd carbon black filled rubber compounds," ACS Rubber Division meeting, April 13-16, 1999, paper #70.

(6.) J.L. Leblanc and Z. Swiderski, Kautsch. Gummi, Kunstst., 40(9) 815-819(1987).

(7.) J.L. Leblanc and M. Cartault, "Studying the morphology of uncured filled rubber compounds by torsional dynamic methods," Intern. Symposium Eurofillers '99, Villeurbanne, France, Sept. 6-9, 1999, paper #49.

by Jean L. Leblanc, University P. & M. Curie, Paris
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Author:Leblanc, Jean L.
Publication:Rubber World
Date:Mar 1, 2001
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