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The science of mixing rubber.

The mixing of rubber involves many variables, some of them are material and others are of a mechanical nature.

Quite often one variable has a decisive influence on the entire mixing process. However, it is not possible to discuss all the variables in one presentation. Therefore, I shall limit the discussion to gum rubber characterization (ref. 1) and mixing mechanisms (ref. 2).

Gum rubber characterization

Characterization of a polymer involves an effort of relating structure to property. Here, the structure is the molecular architecture of gum rubber and the property is its viscoelastic property. In the industrial operation, the structure must be related to the conditions of polymerization and post-reactor processing. The properties must be related to processability.

Molecular architecture

The characterization method varies depending upon the type of polymerization. Gum rubbers made by anionic polymerization have no branches unless it is so designed. The molecular weight distribution is very narrow and often called monodispersed. Therefore, the only variable is molecular weights. When branches are incorporated, they are usually of equal length, emanating from a single branch point.

When gum rubber is made through a coordinated metal-complex, like cis-1,4-polybutadiene, the rubber often has long branches which are neither of equal length nor joined to the backbone chain at a single joint. Characterization requires not only the degree of branching, but also the length of branches.

In the above two types of gum rubbers, the molecular weight distribution may be characterized with size-exclusion chromatography (GPC), although only relative information is obtainable with irregularly branched polymers.

The emulsion polymerized rubber has more complex architecture. Because of the chain-transfer reaction inherent in free radical polymerization, molecules with many long branches are generated. Since chain transfer preferentially occurs with large molecules, a branched molecule becomes more branched (ref. 3), generating gigantic molecules, macro-gel. Sometimes, a disfunctional co-monomer is used to generate crosslinked particles, micro-gel. With the emulsion rubbers, the GPC method is meaningless because gels and large molecules are removed by filtration.

Because generating the branched structure dominates over molecular weight distribution, the degree of branching and gel-content are the most important structural variables. The gel-content may be determined by filtration, which gives a relative value depending upon the pore size of the filter (ref. 4).

Analytical methods are available for sequencing comonomer distribution and for micro-structure determination such as cis-trans or 1.2 ~ 1.4 addition in diene rubbers. However, no technique is available for determining branch structure, such as the number and length of branches and branch-point distribution. Perhaps the most important challenge in the science of characterization is the precise determination of branch patterns. At present, a combination of the knowledge of polymerization mechanism and a proper use of viscoelastic measurements is the only way to obtain relative and quantitative information on the branch patterns and gel structure ref. 1).

Viscoelastic properties

The science of viscoelasticity has been around quite a while, but it is often very vaguely understood in the rubber industry. Therefore, I shall begin with the viscoelastic definition of rubber. "For a flexible chain polymer, when its molecular weight is high enough, there is a rubbery state within a given time-temperature window. If the time is shorter or temperature is lower than those defined by the window, the polymer becomes glassy via transition zone. If the time is longer or temperature is higher and if there is no degradation, the polymer becomes fluid via transition." Although some gum rubber behavior falls outside of the window, the rubbery state is the primary concern here.

The rubbery state is characterized by its unique behavior large deformation without break and almost 100% recovery of the deformation. Thus, the rubber is called an elastomer. However, there is a heat generation accompanying the deformation and this is due to the viscous energy dissipation. Viscosity arises from internal friction but not from flow.

Prior to this writer's work, theories of large deformation are primarily limited to equilibrium condition, i.e. elasticity theories of crosslinked rubbers (ref. 5). No consideration was given to uncrosslinked rubber and its time dependent behavior. Viscoelasticity theory was primarily at very small deformation, i.e. linear viscoelasticity (ref. 6). Although there were nonlinear theories, they were not given as a simple form suitable for gum rubber characterization (ref. 7).

This author developed a simple yet adequate characterization scheme from these reasonings: Because gum rubber is practically incompressible, only shear and elongational deformation need to be considered. The time and temperature dependence may be summarized through time-temperature correspondence (ref. 6).

The time and strain dependence, the latter being a measure of nonlinearity, may be summarized through strain-time correspondence (ref. 8). The applicability of both correspondence principles must be examined with experimental data. With an exception of plasticized nitrile rubbers, the time-temperature correspondence is applicable to all gum rubbers examined to date over the temperature range of processing. The strain-time correspondence is also applicable to many gum rubbers with the strain-shift factor being a universal constant of the elongation ratio. For shear deformation it is the elongation equivalent value expressed by deformation of the axis.

With some EP rubbers, linear behavior persists over a large range of deformation such that neither the application of strain-time correspondence nor linearization are necessary.

With gum rubbers having long branches and macrogels, linearization requires not only the strain-time correspondence but also an adjustment on the modulus. The magnitude of the adjustment is a measure of strain-hardening or strain-softening. The former arises from entanglement of branches acting as constraints against deformation and the latter from slipping of branches. Whether the branches give constraints or slipping, provides rheological differentiation between long and short "long-branches" (ref. 9).

Once linearized, the modulus functions of shear and elongation should agree with a factor of three, and it is indeed the case, except for rubbers that exhibit strain-induced crystallization and strain-induced association (refs. 9 and 10).

The above described characterization scheme is applicable and found adequate for many grades of gum rubbers examined to date, NBR, SBR, polyethylacrylate, polyepichlorohydrin, polyisobutylene, EP(D)M and cis-1,4-polybutadiene.


It is customary to rate a given gum rubber as easy or difficult in processing. I would like to challenge this rating. In 1966 Tokita and White (ref. 11) described a mill processability of gum rubbers, where the rubber behavior was classified into four regions. Among the four regions only one (region II) gives a good processing behavior, whereas in the other three regions, each gives poor processing for different reasons. Therefore, rating a rubber as poor processing is quite inadequate and certainly not a scientific description. Moreover, a rubber failing in region I at room temperature, may be satisfactorily milled at a higher temperature or with an addition of a process oil. A rubber falling in region IV may be handled by upside-down mixing. Therefore, much more in-depth analyses are required. Although the four regions of processability provide a starting point for a classification, the mill-processability is only one of the requirements. A high-loading of carbon black may not be possible with a rubber giving a processability in region II. Instead, a rubber tending to go to Region I behavior may be used for this case. Even though the above mill processability provides a yard-stick for evaluating gum rubbers, it in itself is not a science.

This author had interpreted the four regions of the rubber behavior in terms of modulus and elongation at break (ref. 12). This provided the starting point for the scientific approach to mill processability. The above properties are rate and temperature dependent as is the mill processabillity. The rate here is the deformation rate which is primarily controlled by the opening of the mill-gap (ref. 13) when the roll-speed is fixed. However, the modulus depends on the magnitude of strain as well as the rate and temperature. In much later works with polyethylacrylate rubbers (ref. 4) and with cis-1,4-polybutadiene rubbers (ref. 5), the dynamic shear modulus, G', values were found to relate well with the mill-processability. It indicates that the behavior of rubber at small shear and rather slow deformation controls the initial response of rubber touching the mill-roll.

At the same time, it has been recognized that rubber is stretched during milling so that large elongational deformation also plays an important role. Thus, not only linear viscoelasticity but also nonlinear viscoelasticity must be considered. Hence, the previously described characterization of gum rubbers according to their viscoelastic behavior provides an understanding of the processing behavior (refs. 14 and 15). The processability in the internal mixer may also be interpreted on the basis of nonlinear viscoelastic behavior.

Mixing mechanisms

Here, I am going to discuss mixing mechanisms primarily with a tangential internal mixer. The interpretation of mechanisms may be modified appropriately to suit other types of mixers. Also, discussions will be limited to mixing of rubber with reinforcing fillers, mainly carbon black. The steps of mixing are mastication of rubber, incorporation and dispersion of fillers with simultaneous improvement of filler distribution.

Heretofore, most of the knowledge on the subject has been derived from personal observation such that conclusions are limited to particular cases and lack generality. Recently, efforts have been made to treat rubber-mixing as a subject of engineering. These involve computer-simulation with the use of a hydrodynamic model. That is, gum rubber is treated as a high viscosity fluid (refs. 16 and 17). By viscosity, it meant viscosity of fluid in the steady-state, laminar shear flow.

As defined earlier, gum rubber when it is in a rubbery state does not flow. It is an elastic solid. Its viscous effect is heat generation accompanying deformation. Therefore, the hydrodynamic model represents the farthest from reality. It is redundant to explain the unrealistic nature of the hydrodynamic model. Even so, it may be helpful to illustrate the contradiction the model presents against common sense in rubber mixing. For example, it is a fill factor and a necessity of having empty space in the chamber. In the hydrodynamic model, the most efficient use of a mixer is at 100% filled. In reality, if the mixer is filled to 100%, mixing is not effective and the contents need empty space to move around (ref. 18).

Another problem with the hydrodynamic model is that it assumes continuum. The presence of the empty space and its ever-changing shape and location makes it impossible to define boundary conditions for the continuum approach. Also, observation of material during the incorporation step (refs. 19 and 20) can hardly be described as a continuum. In addition, the presence of slip at the chamber wall presents another problem. It is not a steady slip but a type of slip-and-stick. This fact also makes definition of the boundary condition an almost impossible task. The growth of bound rubber is another important aspect which defies application of continuum.

Concerning distributive mixing, it was interpreted as a randomization, which would have been correct for a liquid. Rubber, being a solid, the mixing occurs through lamination (ref. 20). Overall mixing proceeds through communication of rubber domains (ref. 21) starting from a macroscopic size down to 1.0 ~ 0.1 [micro] m diameter (ref. 22). Because rubber is not fluid, viscosity contribution is a generation of heat, which is an energy. Likewise, elastic contribution is to store energy and fracture results in a consumption of energy. In summary, the mixing process of rubber is energy controlled. This fact has been recognized for a number of years (ref. 23). If the hydrodynamic-continuum model had been correct, time-based control would have given an adequate result. Instead, time-based control has been known to give a reproducibility problem. Energy-based control, for example, use of a power integrator is well-known for a better reproducibility (ref. 24).

A fundamental research on rubber mixing may start from examination of energy balance. This author, together with former colleagues at BFGoodrich, obtained data over a period from the beginning to the end of mixing (ref. 25).

An energy based modeling of mixing is possible and the basic approach has been mapped out already (ref. 2). Success of such a modeling and any other modeling must be accompanied with actual experimentation, because the overall result varies significantly depending upon a rubber sample, a choice of sequence of addition as well as other variables of operation.

Speaking of the dispersion mechanism of carbon black, "an onion" model was proposed by Shiga and Furuta (ref. 20), who had made a number of experimental observations. In short, carbon black pellets break up into several pieces in the beginning. Thereupon the pulverization into aggregates occurs layer-by-layer like the peeling of an onion. Such a mechanism is readily understandable, when the manufacturing process of carbon black involves rolling compared to the making of a snowball.

In order to peel the layer, shear must be applied to the surface of the carbon black agglomerate. The known fact is that elongational deformation is more effective than shear for dispersing carbon black. Seldom recognized is that the above observation is about the bulk deformation only.

In the presence of carbon black, the local, microscopic deformation is not the same as that of bulk, i.e. non-affine deformation. The fact is that bulk, elongational deformation provides more effective local shear around the carbon black agglomerate (ref. 26). The continuum approach generally assumes affine deformation and thus, is incapable of describing the dispersion mechanism.

Another aspect usually overlooked is the stress transmission from machine to the agglomerate. It is known to be most effective, when gum rubber is in the rubbery state, region II of Tokita-White. Some rubber, e.g. a low molecular weight or a narrow molecular weight distribution, tends to go to region IV, when temperature goes up. The rubber becomes a visco-elastic fluid and dispersion becomes ineffective.

Rubber mixing progresses through a continuous change of heterogeneous morphology. The situation may be described as a change of multi-phase morphology. Dizon and Parpazian (ref. 19) classified the contents of a mixer in the incorporation stage into nine kinds. It is possible to simplify them into several kinds, i.e. phases. A simplistic model of the phase change is illustrated in figure 1 (ref. 2).


Together with the energy consideration, the mixing mechanism may be modeled with changes of phase morphology.


At present, the most important problem in the science of mixing rubber is a lack of understanding of rubber as a material. It has two aspects. One is a lack of precise knowledge of branch patterns. This requires development of an analytical method for determining number, length and structure of junction for branches. Another aspect is a lack of understanding of viscoelastic properties of rubber. Science is available for this purpose and the problem is educational.

Once the viscoelastic nature of rubber is understood, the understanding of mixing mechanisms will follow. Instead, current effort ignores viscoelastic nature and erroneously assumes hydrodynamic model and continuum. The viscoelasticity and energy based approach is suggested, together with phase changes as a mixing model.


[1.] N. Nakajima, Polymer International, 36 105 (1995).

[2.] N. Nakajima, Polymer International, 41 23 (1996).

[3.] P. J. Flory, "Principles of polymer chemistry," Chapt. 9., Cornell Univ. Press, Ithaca, New York, 1953.

[4.] For example, ASTM D3616-77, American Society for Testing and Materials.

[5.] I.M. Ward, "Mechanical properties of solid polymers," 2nd ed. Chapts. 3 and 4, Wiley, New York, 1979.

[6.] J.D. Ferry, "Viscoelastic properties of polymers," 3rd ed., Wiley, New York, 1980.

[7.] For example, B. Bernstein, E.A. Kearsley and L.J. Zapas, Trans. Soc. Rheol., 7 391 (1963). R.A. Schapery, Polym. Eng. Sci., 9295 (1969).

[8.] N. Nakajima and E.R. Harrell, Rubber Chem. Technol., 59 305 (1986). N. Nakajima and E.R. Harrell, Rubber Chem. Technol., 56 1019 (1983).

[9.] N. Nakajima and Y. Yamaguchi, J. Appl. Polym. Sci, 61 1525 (1996).

[10.] N. Nakajima, J.J. Scobbo, Jr., and E.R. Harrell, Rubber Chem. Technol., 60 742 (1987).

[11.] N. Tokita and J.L. White, Appl. Polym. Sci., 10 1011 (1966).

[12.] N. Nakajima, Polym. Eng. Sci., 19 215 (1979).

[13.] N. Nakajima, Intern. Polymer Processing, 11 3 (1996).

[14.] N. Nakajima, R.A. Miller and E.R. Harrell, Intern. Polym. Process., 288 (1987).

[15.] N. Nakajima and Y. Yamaguchi, J. Appl. Polym. Sci., in press.

[16.] J.K. Kim, J.L. White, K. Min and W. Szydlowski, Intern. Polym. Process., 4 9 (1989).

[17.] I. Manas-Zloczower, A. Nir and Z. Tadmor, Rubber Chem. Technol., 55 1250 (1982).

[18.] H. Palmgren, Rubber Chem. Technol., 48 462 (1975).

[19.] E.S. Dizon and L.A. Papazian, Rubber Chem. Technol. 50 765 (1977).

[20.] S. Shiga and M. Furnta, Rubber Chem. Technol., 58 1 (1985).

[21.] N. Nakajima, Rubber Chem. Technol., 54 266 (1981).

[22.] W.M. Hess in "Reinforcement of elastomers," Chapt. 6, G. Kraus, ed., Wiley, New York, 1965.

[23.] P.R. VanBuskirk, S. B. Turetzky and P. F. Gunberg, Rubber Chem. Technol., 48 577 (1975).

[24.] F.S. Myers and S.W. Newell, Rubber Chem. Technol., 51 180 (1978).

[25.] N. Nakajima, E.R. Harrell and D.A. Seil, Rubber Chem. Technol., 55 456 (1982). N. Nakajima, Polymer International, 40 141 (1996).


"Trends in rubber mixing" is based on a paper given at the October, 1997 meeting of the Rubber Division.

"The science of mixing rubber" is based on a paper given at the October, 1997 meeting of the Rubber Division.

"Repeatable measurement of high-resistivity rubber and other materials" is based on a paper given at the October, 1997 meeting of the Rubber Division.


These acknowledgements were inadvertently left out of the February issue:

"HNBR and long term serviceability in modern automotive fluids" is based on a paper given at the October, 1997 meeting of the Rubber Division.

"Fuel permeation rates after changing fuel" is based on a paper given at the February, 1997 meeting of the Society of Automotive Engineers.

"Elastomer blends to extend heat life of NR based engine mounts" is based on a paper given at the May, 1997 meeting of the Rubber Division.

The figures in the February article "Fuel permeation rates after changing fuel" had the legends for 100% Fuel C and CE-10 reversed.
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Author:Nakajima, N.
Publication:Rubber World
Date:Mar 1, 1998
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