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Shear viscosity of carbon black filled polypropylene at very low shear stresses.


Carbon black has long been the major reinforcing filler fill·er 1  
One that fills, as:
a. Something added to augment weight or size or fill space.

b. A composition, especially a semisolid that hardens on drying, used to fill pores, cracks, or holes in wood, plaster,
 used in polymers, its most important application being with elastomers for tires. It also plays a useful role with thermoplastics because of its electrical conductivity Not to be confused with electrical conductance, a measure of an object's or circuit's ability to conduct an electric current between two points, which is dependent on the electrical conductivity and the geometric dimensions of the conducting object.  as well as reinforcing qualities. There have been many studies of the rheological rhe·ol·o·gy  
The study of the deformation and flow of matter.

 properties of carbon black filled polymer melts (1-23). These investigations show the presence of carbon black particles increases the viscosity of the melts. The extent of viscosity rise was found to increase with volume loading and with decreasing particle size Particle size, also called grain size, refers to the diameter of individual grains of sediment, or the lithified particles in clastic rocks. The term may also be applied to other granular materials.  (7). As early as 1930, Scott (24) concluded that rubber compounds with many different small particle fillers exhibited yield values, i.e. a stress below which there is no flow. Generally, investigators (1-5, 7-9) for the next half century did not test this hypothesis. In 1972, Vinogradov et al. (6) concluded on the basis of shear shear: see strength of materials.

A straining action wherein applied forces produce a sliding or skewing type of deformation.
 viscosity measurements that the rubber-carbon black compounds they were studying seemed to exhibit yield values. Since 1979, one of us (JLW JLW Junior League of Washington
JLW Junior League of Wichita
JLW Junior League of Waco
JLW Junior League of Worcester
JLW Junior League of Wilmington, Inc.
JLW Junior League of Wheeling
) and co-workers (10-23) have confirmed this for a range of thermoplastics, elastomers, and carbon blacks.

The experimental measurement of shear viscosities of polymer melt-carbon black compounds may be divided into four generations. The first shear flow Shear flow is:-
in a solid body, the gradient of a shear stress force through the body;
in a fluid, it is the flow induced by such a force gradient - see Viscosity for a fuller treatment.
 measurements of viscosity on polymer-carbon black compounds were for rubber and used capillaries Capillaries
The smallest arteries which, in the lung, are located next to the alveoli so that they can pick up oxygen from inhaled air.

Mentioned in: Adult Respiratory Distress Syndrome, Birthmarks, Platelet Count

 (1, 4, 5, 7-9). Typically the shear rates Shear rate is a measure of the rate of shear deformation:

For the simple shear case, it is just a gradient of velocity in a flowing material.
 were above 10 [sec.sup.-1] and involved viscosities only as high as [10.sup.5] Pa.s. In the second generation (6, 10, 11, 14, 18, 20), which begins with Vinogradov et al. (6), rotational rheometers with cone-plate and biconical geometries were usually used as were sandwich rheometers operated at constant shear rate. Shear rates as low as 0.01 [sec.sup.-1] were achieved and viscosities of [10.sup.7] Pa.s were measured. From those measurements, which show an increasing unbounded viscosity at low shear rates and stresses, the probable existence of yield values in particle filled compounds is clear. The third generation (12, 13, 17) of studies, which somewhat overlap the second generation, involve creep measurements. The first creep measurements were reported in 1962 by Zakharenko et al. (3), but yield values were not suspected. Creep experiments indicating yield values were first described for carbon black compounds by Toki and White (12). Shear rates of [10.sup.-6] [sec.sup.-1] were achieved and viscosities as high as [10.sup.10] Pa.s determined. These measurements indicated a continued rapid rise in the shear viscosity as the stress continued to be lowered and increased the arguments for yield values. The fourth generation of measurements have involved actual determination of yield values. This was begun by modifying a sandwich creep instrument through weight compensation of the central member. Osanaiye et al. (21, 22) and Li and White (23) have made measurements of stresses so low that rubber-carbon black compounds only sustain limited and not continuous deformations. Through such experiments, yield values were actually measured.

[TABULAR tab·u·lar
1. Having a plane surface; flat.

2. Organized as a table or list.

3. Calculated by means of a table.


resembling a table.

It is the purpose of this paper to further investigate the shear viscosity of carbon black-thermoplastic polypropylene polypropylene (pŏl'ēprō`pəlēn), plastic noted for its light weight, being less dense than water; it is a polymer of propylene. It resists moisture, oils, and solvents.  melt compounds at low shear stresses shear stress
See shear.

shear stress

A form of stress that subjects an object to which force is applied to skew, tending to cause shear strain.
 in the neighborhood of the yield value. We present new results and contrast it to earlier data on carbon black compounds.



The polypropylene homopolymer (PP) used in this research was obtained from Millennium Petro-chemicals (Petrothene PP 8000-GK). The melt flow rate of this polymer is 5.0g/10 min.

Three different carbon blacks that have different particle sizes were used in this investigation. The carbon blacks were obtained from Cabot Corporation Cabot Corporation is a specialty chemicals and performance materials company. It operates in four segments: the Carbon Black Business, the Metal Oxides Business, the Supermetals Business, and the Specialty Fluids Business. Cabot's headquarters is located in Boston, Massachusetts.  and designated CB-1, CB-2 and CB-3. The characteristics of these carbon black are summarized in Table 1. The compounds prepared have 0.2 volume fraction carbon black.

All measurements were made at 180 [degrees] C.


The polypropylene/carbon black compounds investigated were prepared in a Moriyama (D3-7.5) laboratory internal mixer mixer, either of two electronic devices in which two or more signals are combined. In the type of mixer used in radio receivers, radar receivers, and similar systems, a signal is translated upward or downward in frequency.  at 185 [degrees] C.

Rheological Measurements

A sandwich rheometer rhe·om·e·ter
An instrument for measuring the flow of viscous liquids, such as blood.
 was used in this study for low shear rate measurement. The design and operation of this sandwich rheometer originally first used by Toki and White (12) has been modified in more recent studies (21-23). It was primarily used in the creep mode. Weight compensation of the inner member (22, 23) was considered but was not used at 180 [degrees] C. The shear stresses were calculated from

[Sigma] = F + W (inner member)/2A (1)

where F is the applied weight and W is the weight of inner member. The shear rates obtainable from this instrument depend on careful measurements, particularly at very low stresses. Displacements were monitored with time for each constant stress applied. Values of strain dependence on time were obtained by dividing displacements by sample thickness. The whole rheometer except the displacement gauge was enclosed en·close   also in·close
tr.v. en·closed, en·clos·ing, en·clos·es
1. To surround on all sides; close in.

2. To fence in so as to prevent common use: enclosed the pasture.
 in a 180 [degrees] C heat regulated chamber for temperature control. Nitrogen gas was used to prevent oxidative ox·i·da·tive
Of, relating to, or characterized by oxidation.

adj having the ability or property to oxidize.


pertaining to or emanating from oxidation.
 degradation. This instrument is shown in Fig. 1.

The capillary capillary (kăp`əlĕr'ē), microscopic blood vessel, smallest unit of the circulatory system. Capillaries form a network of tiny tubes throughout the body, connecting arterioles (smallest arteries) and venules (smallest veins).  rheometer used was an Instron Capillary rheometer with dies of diameter 1.5 mm and L/D L/D Labor and Delivery
L/D Lethal Dose
L/D Lift/Drag (ratio)
L/D Low Dynamic
L/D Limiter/Discriminator
L/D Loading / Discharging Rate (shipping) 
 ratios of 10, 20, and 30 to allow for end loss corrections. Weissenberg corrections for shear rate were also performed. The maximum shear rate investigated was about 1000 [sec.sup.-1].

At intermediate shear rates, a Rheometrics Mechanical Spectrometer spectrometer

Device for detecting and analyzing wavelengths of electromagnetic radiation, commonly used for molecular spectroscopy; more broadly, any of various instruments in which an emission (as of electromagnetic radiation or particles) is spread out according to some
 with a cone-plate fixture was used. Its diameter was 25mm and cone angle was 0.1 rad. This instrument was used only for PP. This was because of the inability to fully squeeze many samples into the 50 [[micro]meter] gap between the blunted tip of the cone and the plate. The sandwich instrument allowed measurements up to 0.1 [sec.sup.-1].


Creep Experiments

We have plotted the shear strain shear strain or shearing strain

See under strain.
 creep as a function of time for various shear stress levels for polypropylene/carbon black compounds in Figs. 2a, b, and c.

In the case of PP and PP/CB-1 shown in Fig. 2a the materials flow at all stresses applied. For the CB-2, CB-3 compounds, there are stresses below which there is no flow but only finite deformations. This indicates the occurrence of a yield value. The minimum stress which we were able to obtain in this method was about 800 (796) Pa. The values of the measured yield stresses are summarized in Table 2.


Shear Viscosity Behavior

The shear viscosity obtained for all the compounds in the sandwich, capillary and rotational rheometers is shown in Fig. 3. The shear viscosity is plotted as a function of shear rate in Fig. 3a. The data range over about ten decades of shear rate from [10.sup.-7] to [10.sup.3] [sec.sup.-1]. In the low shear rate range the viscosity data spreads apart ranging from [10.sup.9] to [10.sup.10] Pa [center dot] s at a shear rate of [10.sup.-6] [sec.sup.-1]. At high shear rates the data on all the systems comes together. The data from all the instruments is quite consistent.


We have plotted the shear viscosity as a function of shear stress in Fig. 3b. It may be seen that the pure PP exhibits a zero shear viscosity [[Eta].sup.0] = 1.4 x [10.sup.4] Pa [center dot] s as determined by both the sandwich and cone-plate instruments and the shear viscosity decreases with further increases in shear rate.

In Fig. 3b, we may note the following:

1) The compounds with CB-2 and CB-3 exhibit yield values. The compound with CB-1 may also exhibit a yield stress, but it is not certain.

2) The CB-2 and CB-3 compounds exhibit a shear viscosity plateau in a low shear stress region that is at very high viscosities [approximately][10.sup.9] to [10.sup.10] Pa.s.

3) Comparing the CB-2 and CB-3 compounds we see the length of the plateau increases with decrease in particle size and increase in surface area. The large magnitude of the plateau in CB-3 results in yield values obtained from extrapolation (mathematics, algorithm) extrapolation - A mathematical procedure which estimates values of a function for certain desired inputs given values for known inputs.

If the desired input is outside the range of the known values this is called extrapolation, if it is inside then
 of the shear viscosity from higher stresses being significantly higher than the true value (9500 Pa compared to 2500 Pa).


Comparison of Results to Earlier Investigations

This is the first paper that proves the existence of yield values in carbon black-thermoplastic as opposed to carbon black-rubber compounds.

The high viscosity ([approximately][10.sup.9] to [10.sup.10] Pa.s) intermediate shear stress plateau we have observed in the polypropylene-carbon black compounds has not been previously discussed in the literature. We have carefully looked at all previously published data on compounds containing carbon black, where shear viscosities of at least [10.sup.8] Pa.s are reported. The papers describing such experiments (12, 13, 16, 17, 21, 23) all involve measurements in the creep mode. We list the carbon blacks used in Table 1. The matrices, loadings, temperatures and yield values are summarized in Table 3. We replot the data of Toki (12), Montes mon·tes  
Plural of mons.
 (13, 17), White (16), Osanaiye (21) and Li (23) and their co-workers in Figs. 4a, 4b, and 4c. These represent data from 1982, 1987-88 and 1993-96 respectively.

Figures 4a, 4b and 4c replotted from the investigations of Toki and White (12), Montes et al. (13, 17), and White et at. (16) show viscosities as high as [10.sup.9]-[10.sup.11], Pa.s, which suggest but do not measure or prove yield values. Osanaiye et al. (21, 22) and Li and White (23) both actually observed and measured yield values. Osanaiye et al. found viscosity plateaus at 0.2, 0.3 and 0.4, and 0.5 volume fraction that they did not clearly report in their paper. Li and White (23) observed a yield value but no plateau.

The CB-2 and CB-3 of our study of our Fig. 3b is consistent with the observations of Osanaiye et al. (21) in Fig. 4c. These compounds all have particles with sizes less than 0.024[Mu] and surface areas of 110-140 [m.sup.2]/g and exhibit viscosity plateaus in the intermediate shear stress region of the [Eta]-[[Sigma].sub.12] plot. The data of Li and White (23), which involves particles of size 0.070 [Mu] and very low surface area (20 [m.sup.2]/g), does not exhibit this behavior.

If we consider 0.2 volume fraction carbon black compounds, our data and that of Osanaiye et al. (21) and Li and White (23) prove the existence of yield values for all compounds studied. However, only those compounds with particle diameter of 0.024 [Mu] or smaller and surface area of 110 [m.sup.2]/g or larger exhibit a plateau in their shear viscosity shear stress behavior. The data of Toki and White (12), Montes et al. (13, 17) and White et al. (16) give strong evidence of exhibiting yield values but do not suggest plateaus. They use particle sizes of 0.027 [micro] and surface areas of 80 [m.sup.2]/g.

What should be the effect of volume loading for the 0.3, 0.4 and 0.5 volume fraction carbon black compounds? The data of Osanaiye et al. (21) indicate larger yield values and larger plateaus. The data of Toki and White (12), Montes et al. (13, 17) at 0.3 loading indicate increasing yield values but do not prove their existence. Their results do not suggest plateaus.

The above results suggest as had been noted in the earlier literature that yield values arise first with increasing carbon black loading and decreasing particle size. The development of high viscosity plateaus subsequent to the yield values probably arise only for very small particle sizes. This effect is enhanced by higher loadings.

It should be noted that yield values accompanied by viscosity plateaus have been described by other investigators in different systems such as the observations of Hansen and Williams (25) on SBS See Small Business Server.  triblock copolymer copolymer: see polymer.  and Vliet and Hooijdonk (26) on low viscosity chocolate milk.

Mechanism of Yield Value

The generally believed mechanism of yield values in particle filled thermoplastics and elastomers is the agglomerates of very small suspended particles and the formation of percolation percolation /per·co·la·tion/ (per?kah-la´shun) the extraction of soluble parts of a drug by passing a solvent liquid through it.  networks through the samples. These particles small particles agglomerate agglomerate

Large, coarse, angular rock fragments associated with lava flow that are ejected during explosive volcanic eruptions. Although they may appear to resemble sedimentary conglomerates, agglomerates are igneous rocks that consist almost wholly of angular or rounded
 because of their high surface areas. This is readily observed in one's experiences with powders and may be seen in suspensions with an optical microscope optical microscope

See under microscope.
 (27). The above is a view that predates investigations of polymer melt systems. It is contained in papers by various investigations of the flow of suspensions of particles in low molecular weight matrices in the 1920s and 1930s such as McMillen (28) and Freundlich and Jones (27). The earliest attempt at modeling the formation and breakup breakup

The division of a company into separate parts. The most famous breakup to date was the 1984 division of AT&T (formerly, American Telephone & Telegraph Company). This breakup was intended to increase competition in the communications industry.
 of such structure and its relationship to shear viscosity and the dependent thixotropic behavior was by Goodeve and Whitfield (29) in 1938. Investigators of the flow of particle filled polymer systems have accepted this viewpoint though they have rarely quoted the old sources.

Osanaiye et al. (22) in our laboratories have recently reported studies of the system ethylene ethylene (ĕth`əlēn') or ethene (ĕth`ēn), H2C=CH2, a gaseous unsaturated hydrocarbon. It is the simplest alkene.  propylene propylene /pro·pyl·ene/ (pro´pi-len) a gaseous hydrocarbon, CH3CHdbondCH2.

propylene glycol  a colorless viscous liquid used as a humectant and solvent in pharmaceutical preparations.
 terpolymer-carbon black-oil. They note that if the oil content is increased relative to the rubber at fixed carbon black content, the behavior remains the same qualitatively but the shear viscosity and the measured yield value exhibit a significant decrease. These authors argue that the decrease in yield value means that its magnitude cannot be associated with a particle network alone. The mechanism for polymer compounds must involve a "particle polymer chain" network. With the addition of oil, the polymer chains are replaced by low-molecular-weight molecules that weaken the network and lower the yield value.

ACKNOWLEDGMENT acknowledgment, in law, formal declaration or admission by a person who executed an instrument (e.g., a will or a deed) that the instrument is his. The acknowledgment is made before a court, a notary public, or any other authorized person.  

The research described in this program is supported by Showa Denko Showa Denko K. K. (昭和電工株式会社   K. K. and Japan Polyolefins.


1. J. H. Dillon and N, Johnston, Physics, 4, 224 (1993).

2. L. Mullins, J. Phys. Coll. Chem., 54, 539 (1950).

3. N. V, Zakharenko, F. S. Tolstukhina, and G. N. Bartenev, Rubber Chem. Technol. 35, 326 (1962).

4. P. P. A. Smit and A. K, van der Vegt, Kautschuk Gummi, Kunststoffe, 23, 147 (1970).

5. J. R. Hopper A tray, or chute, that accepts input to a mechanical device, such as a disk duplicator or printer. In the days of punch cards, millions of cards were numerically or alphabetically organized by placing them into the hopper of a card sorter, taking them out of all the stackers and putting , Rubber Chem. Technol., 40, 463 (1967).

6. G. V. Vinogradov, A, Ya. Malkin, E. P. Plotnikova, O. Y. Sabsai and N. E. Nikolayeva, Int. J. Polym. Mat., 2, 1 (1972).

7. J. L. White and J. W. Crowder, J. Appl. Polym. Sci., 18, 1031 (1974).

8. N. Nakajima and E. A. Collins, Rubber Chem. Technol., 4,8, 615 (1975),

9. N. Nakajima, H. H, Bowerman, and E. A. Collins, J. Appl. Polym. Sci., 21, 3063 (1977).

10. V. M. Lobe lobe (lob)
1. a more or less well-defined portion of an organ or gland.

2. one of the main divisions of a tooth crown.
 and J. L. White, Polym. Eng. Sci., 19, 617 (1979).

11. H. Tanaka and J. L. White, Polym. Eng. Sci., 20, 617 (1980).

12. S. Toki and J. L. White, J. Appl. Polym. Sci., 27, 3171 (1982).

13. S. Montes and J. L. White, Rubber Chent Technol., 53, 135 (1982).

14. C. Y. Ma and J. L. White, F. C. Weissert, and K. Min, J. Non Newt. Fluid Mech., 17, 275 (1985).

15. R. Brzoskowskt, K. Kubota, K. Chung, J. L. White, F. C. Weissert, N. Nakajima and K. Min, Int. Polym. Process, 1, 130 (1987).

16. J. L. White, Y. Wang, A. I. Isayev, N. Nakajima, F. C. Weissert, and K. Min, Rubber Chem. Technol., 60, 337 (1987).

17. S. Montes, J. L. White and N. Nakajima, J. Non Newt. Fluid Mech., 28, 182 (1988).

18. H. J. Song, J. L. White, K. Min, N. Nakajima, and F. C. Weissert, Adv. Polym. Technol., 8, 431 (1988).

19. S. Montes, J. L. White, N. Nakajima, F. C. Weissert, and K. Min, Rubber Chem. Technol., 61,698 (1988).

20. K. C. Shin shin (shin) the prominent anterior edge of the tibia or the leg.

saber shin  marked anterior convexity of the tibia, seen in congenital syphilis and in yaws.
, J. L. White, R. Brzoskowski, and N. Nakajima, Kautschuk Gummi, Kunststoffe, 43, 181 (1990).

21. G. Osanaiye, A. I. Leonov, and J. L. White, J. Non Newt. Fluid Mech., 40, 87 (1993).

22. G. Osanaiye, A. I. Leonov, and J. L. White, Rubber Chem. Technol., 68, 50 (1995).

23. L. L. Li and J. L. White, Rubber Chem. Technol., 69, 628 (1996).

24. J. R. Scott, Trans. Inst. Rubber Ind., 7, 169 (1931).

25, P. J. Hansen and M. C. Williams, Polym. Eng. Sci., 27, 586 (1987).

26. T. van Vliet and A. C. M. van Hooijdonk, Proc. IX th Int. Congr. Rheology, 4, 115 (1984).

27. H. Freundlich and A. D. Jones, d. Phys. Chem., 40, 1217 (1936).

28. E. L. McMillen, J. Rheology, 3, 179 (1932).

29. C. F. Goodeve and G. W. Whitfield, Trans. Faraday faraday /far·a·day/ (F ) (far´ah-da) the electric charge carried by one mole of electrons or one equivalent weight of ions, equal to 9.649 × 104coulombs.

 Soc., 34, 511 (1938).
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Author:Araki, Takumi; White, James L.
Publication:Polymer Engineering and Science
Date:Apr 1, 1998
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