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Rheological Properties of Carbon Black Suspensions in a Silicone Oil Masami Kawaguchi,* Maki Okuno, and Tadaya Kato Chemistry Department for Materials, Faculty of Engineering, Mie University, 1515 Kamihama, Tsu, Mie 514-8507, Japan Received April 16, 2001. In Final Form: July 23, 2001 Transient shear stresses, steady-state viscosities, and linear dynamic moduli of the furnace carbon black suspensions in a silicone oil were measured as a function of the carbon black concentration. Except for the lowest carbon black concentration, from the transient shear flow experiment structural breakdown is observed at the lower shear rate, whereas at the higher shear rate structural buildup is observed. A crossover point between structural breakdown and structural buildup is decreased with an increase in the carbon black concentration. For the lowest carbon black concentration at the higher shear rate, stress overshooting appeared. Every suspension exhibits shear thickening under steady shear flow, and the critical shear rate corresponding to the onset of steady shear thickening is almost coincident with the shear rate where structural buildup or stress overshooting is first observed. The carbon black suspensions show solidlike viscoelastic behavior under linear responses for dynamic modulus measurements.
Introduction Furnace carbon black particles are prepared from the oil furnace method, and their primary particles usually tend to form a primary aggregate, so-called “structure”. With an increase in the carbon black concentration, such primary aggregates are gathering to form a secondary aggregate, namely, an agglomerate.1 The furnace carbon black particles dispersed in liquids and solids are widely used in many application fields, such as tires, paints, coating, printing, inks, batteries, and so forth.1 Understanding of the dispersing state, namely, the stability and the flocculated structure of the furnace carbon black particles in the dispersion media, is one of the most important issues. However, current understanding is insufficient, and the main reason sufficient knowledge cannot be obtained is the presence of the flocculated structures of carbon black particles in the dispersions. Thus, it is impossible to avoid taking into account such flocculated structures for the investigation of carbon black dispersions. Furthermore, the presence of the flocculated structures in the carbon black dispersions yields various rheological properties:2-5 there is shear thinning, shear thickening, or yield stress for shear stress-shear rate (shear flow) experiments accompanied with the deformation or partial breaking of the structures, whereas solidlike viscoelastic behavior is observed for oscillatory (dynamic) experiments with linear responses, where no deformation of the structures occurs. In other words, it is expected that we can obtain information on the flocculated structures through careful rheological experiments and the resulting information will clarify the interactions between carbon black particles themselves. In addition to the steady-state rheological behavior, transient shear stress, instantaneous stress during the transient start-up period at a fixed shear rate, gives information about rates of structural rearrangement within a deforming dispersed system, leading to under(1) Dannenberg, E. M. In Vanderbilt Rubber Handbook, 12th ed.; R. T. Vanderbilt Co.: New York, 1977. (2) Boonstra, B. B. Polymer 1979, 20, 691. (3) Rigbi, Z. Adv. Polym. Sci. 1980, 36, 21. (4) Amari, T.; Watanabe, K. J. Rheol. 1990, 34, 207. (5) Amari, T.; Uesugi, K.; Suzuki, H. Prog. Org. Coat. 1997, 31, 171.
standing the structures formed by the particles.6-9 However, no systematic transient shear stress experiments of carbon black dispersions have been reported. In this study, we report transient shear stress, steadystate shear viscosity, and dynamic measurements of carbon black particles suspended in a silicone oil as a function of the carbon black concentration. The molecular weight of the silicone oil is less than the chain entanglement molecular weight of 47 × 103 of poly(dimethylsiloxane);10 it is not necessary to take account of the chain entanglements of silicone oils. However, the silicone oil chains could adsorb on the surfaces of the carbon black particles through van der Waals interactions. Thus, the resulting rheological properties of the carbon black suspensions can be mainly considered in terms of the interactions between the carbon black particles themselves and between the silicone oil and the particles. Experimental Section Samples. Silicone oil KF96-100 was kindly supplied from Shinetsu Chemical Co. and used without further purification. The silicone oil has a viscosity of 100 mPas, a molecular weight of 6.6 × 103, and a density of 0.965 g/cm3, according to the manufacturer. Furnace carbon black powder designed as no. 2600 was supplied from Mitsubishi Chemical Co., and it was dried under vacuum at ambient temperature. From the manufacturer of the no. 2600 carbon black, the primary silica particle has an average diameter of 13 nm, a surface area of 390 m2/g, and a density of 1.8 g/cm3. For preparation of the carbon black suspensions in silicone oil, a weighed amount of no. 2600 carbon black was added to the silicone oil in a cylindrical bottle, it was mixed at 2000 rpm for 25 min by a T. K. Robo Mics homomixer (Tokushu Kika Co., Osaka), and then the mixture was treated by a HM-500 hybridmixer (Keyence Co., Osaka) to remove air bubbles for 2.5 min. The carbon black concentrations in the resulting suspensions were 7.5, 10, 12.5, and 15 wt %. Rheological Measurements. Rheological experiments were carried out on a Paar Physica MRS-300 rheometer. A cone(6) Kosinski, L. E.; Caruthers, J. M. J. Non-Newtonian Fluid Mech. 1985, 17, 69. (7) Kosinski, L. E.; Caruthers, J. M. Rheol. Acta 1986, 25, 153. (8) Kosinski, L. E.; Caruthers, J. M. J. Appl. Polym. Sci. 1986, 32, 3393. (9) Nakai, Y.; Ryo, Y.; Kawaguchi, M. J. Chem. Soc., Faraday Trans. 1993, 89, 2467. (10) Fox, T.; Allen, V. J. Chem. Phys. 1964, 41, 344.
10.1021/la010560r CCC: $20.00 © 2001 American Chemical Society Published on Web 09/06/2001
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Figure 1. Evolution of transient shear stress of the 7.5 wt % carbon black suspension in a silicone oil with time for various shear rates, s-1: 4, 100; 0, 500; 2, 1200; 9, 2000. The inset shows the short-time behavior of the transient shear stress of the 7.5 wt % carbon black suspension.
Figure 2. Evolution of transient shear stress of the 10 wt % carbon black suspension in a silicone oil with time for various shear rates, s-1: O, 50; ], 800; b, 1000. Other symbols are the same as in Figure 1. The inset shows the short-time behavior of the transient shear stress of the 10 wt % carbon black suspension. plate fixture having a cone angle of 1° and a diameter of 25 mm was used for the carbon black suspensions, whereas for the silicone oil a different cone-plate fixture having a cone of 1° and a diameter of 50 mm was used. Experiments were conducted under both steady shear flow and dynamic oscillatory shear at 25 °C. For every rheological measurement, as soon as a carbon black suspension was preconditioned under the same method as described previously in the preparation of the suspensions, the resulting suspension was newly placed on the fixture and it was kept for 5 min to obtain reproducible data. For each steady shear flow experiment, at given shear rates ranging from 5 to 2000 s-1 the carbon black suspension was subjected to achieve a steady state as a function of time. Dynamic experiments were mainly carried out at frequency sweeps changed from 0.1 to 100 rad s-1 at a constant strain where the linear response range was confirmed by strain sweeps (an increase in the strain amplitude by discrete steps).
Results and Discussion As mentioned earlier, for rheologically complex substances such as carbon black suspensions, it is convenient to study the transient behavior before examining the steady-state behavior. Figures 1-3 show typical stress developments of the 7.5, 10, and 15 wt % carbon black suspensions at various shear rates. For the 10 and 15 wt % carbon black suspensions (Figures 2 and 3), the shear stress decreases sigmoidally with an increase in time at the lower shear rate, namely, structural breakdown is observed, whereas at the higher shear rate a sigmoid increase of the shear stress with increasing time, that is, structural buildup, is observed. Similar rheological properties are observed for the 12.5 wt % carbon black suspension though the data are not
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Figure 3. Evolution of transient shear stress of the 15 wt % carbon black suspension in a silicone oil with time for various shear rates. Symbols are the same as in Figures 1 and 2. The inset shows the short-time behavior of the transient shear stress of the 15 wt % carbon black suspension.
shown. Thus, there is a crossover region between structural buildup and structural breakdown and the shear rate where the crossover region appears decreases with an increase in the carbon black concentration. The respective transient shear stresses tend to attain a steadystate value, and the steady-state shear stress does not always increase with an increase in the shear rate. At shear rates higher than 1000 s-1, the 15 wt % carbon black suspension was often spun out from the cone-plate fixture and no reproducible shear stress data were obtained. On the other hand, note that the stress development at the higher shear rate for the 7.5 wt % carbon black suspension (Figure 1) is quite different from those for the carbon black suspensions with concentrations higher than 10 wt %. At a shear rate higher than 1000 s-1, a kind of stress overshooting is observed, whereas at a shear rate lower than 1000 s-1 only structural breakdown occurs. The steady-state shear stress increases with an increase in the shear rate. Thus, the resulting carbon black suspensions show structural breakdown, structural buildup, and stress overshooting behavior and such complex rheological properties should be related to the presence of the flocculated structures of carbon black particles in the suspensions. The volume fraction of carbon black particles φ in this study is very low; namely, the φ value is 0.0420.086, corresponding to the carbon black concentration of 7.5-15 wt %. Only the assumption that the effective disperse volume fraction is much higher is possible to explain the observation of structural breakdown, structural buildup, and stress overshooting behavior. The much higher effective volume fraction could be guaranteed by the open, loosely packed carbon black aggregates, which may not be impossible to form by taking account of the aggregation character of the furnace carbon black particle. At the lowest carbon black concentration of 7.5 wt %, the appearance of the stress overshooting means that some structures of the carbon black suspension formed by the initial shear flow at the higher shear rate are partially breaking down with an increase in time, corresponding to an increase in strain. The structures formed by the shear flow at the higher shear rate could be mechanically weaker than those for the carbon black suspensions with concentrations higher than 10 wt % where only rheopexy is observed. Figure 4 shows steady data (steady-state viscosity against shear rate) of the 7.5, 10, 12.5, and 15 wt % carbon black suspensions. An increase in viscosity due to shear thickening is more appreciable in the carbon black
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Figure 4. Double logarithmic plots of steady-state viscosities of the 7.5 (O), 10 (4), 12.5 (0), and 15 (b) wt % carbon black suspensions in a silicone oil as a function of shear rate.
concentrations higher than 10 wt %. The critical shear rate corresponding to the onset of steady shear thickening is an important parameter, and the parameter decreases with an increase in the carbon black concentration, namely, 1200, 1000, 775, and 750 s-1 in the order of the carbon black concentration. Such a concentration dependence of the critical shear rate is similar to those reported previously.11 Moreover, the critical shear rate nearly coincides with the shear rate where rheopexy or stress overshooting is first observed. Many experiments of shear thickening have been performed on suspensions of monodisperse spheres with higher volume fractions of solids, where the particles are stabilized by steric and electrostatic repulsion.11 On the other hand, a few shear thickening results have been obtained for fumed silica suspensions with lower volume fractions of silicas in strongly hydrogen-bonding12,13 or weakly hydrogen-bonding fluids,13 where the particles are in the state of nonflocculated sol12,13 or colloidal gel.13 The critical shear rate obtained in this study is much larger than those for the fumed silica suspensions.12,13 The larger critical shear rate may stem from the lower volume fraction of solids and the presence of the flocculated structures in the carbon black suspensions. To explain shear thickening, there are two microstructural models:11,12 one is the order-disorder transition theory, and the other is the cluster-formation theory. We believe that our results give evidence in support of the cluster-formation theory since above the critical shear rate structural buildup or overshooting behavior is always observed, namely, is characterized by the presence of flowinduced clusters (aggregates). Moreover, there is little possibility of forming an ordered arrangement of carbon black particles at low shear rate due to the absence of repulsive forces between the particles themselves and the observation of structural breakdown behavior. The viscoelastic behavior of the 7.5 and 12.5 wt % carbon black suspensions is illustrated in Figure 5a,b in terms of a strain sweep. The experiment was carried out from low to high strain amplitudes at a constant frequency of 6.28 rad s-1. The storage modulus G′ is considerably greater than the loss modulus G′′ at low strain amplitude, and the linear region where the G′ value is independent of the strain is below 1% strain amplitude. Moreover, the G′ value decreases more rapidly with an increase in the strain amplitude than G′′, and it ultimately is much (11) Van Egmond, J. W. Curr. Opin. Colloid Interface Sci. 1998, 3, 385 and references therein. (12) Raghavan, S. R.; Khan, S. A. J. Colloid Interface Sci. 1997, 185, 57. (13) Raghavan, S. R.; Walls, H. J.; Khan, S. A. Langmuir 2000, 16, 7920.
Figure 5. Storage G′ (O) and loss G′′ (b) moduli as a function of strain amplitude for the 7.5 (a) and 12.5 (b) wt % carbon black suspensions in a silicone oil.
Figure 6. Double logarithmic plots of G′ (open symbols) and G′′ (filled symbols) as a function of angular frequency for the 7.5 (circle), 10 (triangle), 12.5 (square), and 15 (diamond) wt % carbon black suspensions in a silicone oil.
smaller than G′′; beyond strain amplitudes higher than 10%, the G′ value is somewhat scattered. This behavior is characteristic of a flocculated gel-like substance, and a larger deformation leads to a partial breakage of the flocculated structures. Other carbon black suspensions show similar viscoelastic behavior under strain sweeps though data are not shown. Figure 6 shows the linear viscoelastic response of the 7.5, 10, 12.5, and 15 wt % carbon black suspensions at a strain amplitude of 0.1%. The G′ value exhibits a frequency independence, irrespective of the carbon black concentration, and it increases with an increase in the carbon black concentration. Moreover, the G′ value is fairly large compared to the G′′ value for every carbon black suspension, and this is indicative of a solidlike viscoelastic behavior. A qualitative estimate of the strength of interaction between particles in the flocculated suspension can be expected from the power law dependence of G′ with the volume fraction φ of the solid particles in the suspension.14,15 The higher power in φ means strong interaction (14) Sonntag, R. C.; Russel, W. B. J. Colloid Interface Sci. 1987, 116, 485.
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between particles themselves. We find the carbon black suspensions to show a power law behavior, that is, G′ ∝ φn, where the G′ value is obtained at a frequency of 1 rad s-1. They have an exponent of n ) 2.6 fitting by the leastsquares method. The resulting exponent is much smaller than those for fumed silica particles dispersed in solvents16,17 and in polymer solutions,15,17 where the less the attractive interaction between the particles due to polymer adsorption on the silica particles, the smaller the exponent. Thus, adsorption of silicone oil chains onto carbon black particles allows weak attractive forces between the carbon black particles themselves, leading to the smaller exponent. Conclusions Furnace carbon black suspensions in a low molecular weight silicone oil exhibit complex transient shear flow (15) De Silva, G. P. H. L.; Luckham, P. F.; Tadros, Th. F. Colloids Surf. 1990, 50, 263. (16) Khan, S. A.; Zoeller, N. J. J. Rheol. 1993, 37, 1225. (17) Kawaguchi, M.; Mizutani, A.; Matsushita, Y.; Kato, T. Langmuir 1996, 12, 6183.
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behavior such as structural breakdown, structural buildup, and stress overshooting. Structural breakdown appears at the lower shear rate, whereas at the higher shear rate structural buildup or stress overshooting occurs. A crossover point between structural breakdown and structural buildup (or stress overshooting) is clear; it coincides well with the critical shear rate at incipience of steady shear thickening, and it decreases with an increase in the carbon black concentration. The resulting transient behavior gives evidence for an explanation of the shear thickening through a cluster-formation mechanism, which attributes the thickening behavior to the presence of flowinduced clusters, that is, the appearance of rheopexy or stress overshooting. Every carbon suspension behaves in a solidlike viscoelastic matter for the linear responses of dynamic measurements, and the power law between the storage moduli and the volume fraction of carbon black particles gives the relatively weak interaction between the carbon black particles themselves. LA010560R
