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Behavior of Fine Particle Agglomerates in a Newtonian Molten Polymer Under a Shear Flow
Advanced Powder Technology 19 (2008) 507–521 www.brill.nl/apt
Original Paper Behavior of Fine Particle Agglomerates in a Newtonian Molten Polymer Under a Shear Flow Yoshiyuki Komoda a,∗ , Kanako Kameyama b , Emi Hasegawa b , Hiroshi Suzuki a , Hiromoto Usui a , Yoshiyuki Endo c and Atsushi Syudo c a
c
Department of Chemical Science and Engineering, Kobe University, Kobe 657-8501, Japan b Graduate School of Science and Technology, Kobe University, Kobe 657-8501, Japan Process and Production Technology Center, Sumitomo Chemical Co., Osaka 554-8558, Japan Received 2 August 2007; accepted 27 November 2007
Abstract The dispersing behavior of a particle agglomerate in a mixture consisting of spherical fine particles and a molten polymer was investigated with the application of shear in a cone–plate apparatus. After attaining a constant agglomerated state by applying a small shear, the shear rate was changed to a set value and kept constant over a certain time. Viscosity measurement during shear application and analysis of particle agglomeration in a solidified mixture were conducted. In a dispersing process, agglomerates were broken up to a steady dispersed state corresponding to the shear rate applied and the average number of agglomerated particles could be well correlated by a deformation of the mixture in each particle volume fraction. The viscosity of the mixture with a particle loading of 0.15 had a good relationship with the agglomerated number independent of shear rate; thus, the viscosity of suspension may help in the understanding of the dispersing behavior. However, the concentrated mixture could not achieve a complete dispersion and the viscosity was significantly affected by the time response of the agglomerated structure to shear application, although a dynamic rheological measurement of mixtures with different particle loadings provided much the same result. © Koninklijke Brill NV, Leiden and Society of Powder Technology, Japan, 2008 Keywords Particle dispersion, viscosity, phase angle
1. Introduction Polymer composites, which are composite materials consisting of a polymer and filler, have various applications for the improvement of functionality of a raw material product, such as enhancement of mechanical or/and thermal properties and *
To whom correspondence should be addressed. E-mail: [email protected]
© Koninklijke Brill NV, Leiden and Society of Powder Technology, Japan, 2008
DOI:10.1163/156855208X368599
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addition of a new characteristic to a raw polymer. The filler, which is an organic or inorganic fine particle or fiber, was originally invented for cost reduction by the decrease in a fraction of an expensive polymer. At present the filler is also used for the production of functional materials. The functionality of a polymer composite will depend on the volume fraction and shape of filler, interaction between filler and polymer, dispersed state of filler in a polymer (morphology), etc. In general, the mechanical or thermal properties are mainly affected by the fraction. However, the new functionality may be primarily influenced by the dispersed state. The relations between the dispersed state of particles and the functionality have been reported by Jager et al. [1]. Schueler et al. noted that an ionic additive increased agglomeration, and the morphology affected a threshold of electrical conductivity for the mixture of carbon black and epoxy resin [2]. Additionally, the mechanical properties of composites, such as strength and modulus, also depend on the dispersed state of the filler [3]. Composites including nano-size fillers were studied extensively and reviewed by Jordan et al. [4]. Although the fraction of filler will be widely different between applications, the morphology of filler will have considerable effects on the properties of products. Particle dispersion into a polymer has been usually conducted by applying excessive shear stress for a long time with particular equipment such as a kneading machine and extruder. In such equipment, the flow behavior is visualized by a computer simulation; however, the operating condition to control the particle dispersion is still decided semi-empirically. Although it is proposed that agglomerate splitting and particle erosion induce the dispersion of particle agglomerates, the mechanism and progress of particle dispersion in a shear flow has not yet been fully clarified. Moreover, several factors, such as the adhesion property at the interface between particles and fluid, and rheological characteristics of fluid, affect the behavior of fine particle dispersion. Thus, the dispersing behavior is very complicated and is still more so for practical equipment. As one of the simpler cases, the breakup process of a compressed particle agglomerate under simple shear flow has been well investigated [5–7]. However, comprehension of the dispersing behavior with the number of distributed particle agglomerates is indispensable for developing the exact control method of particle dispersion and an innovative technology. The relationship between the rheological property and dispersed structure of filler in a polymer composite has been well investigated by many researchers [8–11]. Most research paid attention to the relationship between the dynamic rheological properties including a storage modulus and loss angle of mixture in a certain dispersed state. Although the evolution of any rheological property when particles are dispersing or agglomerating should have a strong relationship with the dispersed state of particles in a polymer, the transition behavior of the agglomerate and corresponding rheological property have not been researched well. In this study, the observation and analysis of particle agglomerates in a molten polymer under a shear flow when dispersing or agglomerating was investigated; at the same time, the variation of rheological characteristics was measured. Finally, the correspon-
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dence between the state of agglomerated particles and the viscosity of the mixture was investigated. 2. Experimental 2.1. Materials and Preparation of Mixture Ethylene meta-methyl acrylate copolymer (EMMA) was used as a molten polymer. EMMA has a melting point of 67◦ C and the molten EMMA showed a constant shear viscosity independent of shear rate (Newtonian fluid). A spherical silica particle (KE-P250; Nihon shokubai), which is mono-dispersed and ranges from 2.25 to 2.75 μm in size, was used as filler, and the surface of silica particle was not modified (hydrophilic). The silica particles were mixed with molten EMMA and shear was applied to the mixture by using a cone–plate rheometer at a temperature higher than the melting point of EMMA. The specifications of shear applied to the mixture will be stated in a later section. Sudden cooling to room temperature after stopping the shear application can maintain the state of particle agglomeration during the solidification process of EMMA. The volume fraction of silica particle φ was adjusted to 0.15 and 0.25. In the process of mixture preparation, the EMMA pellet and silica particles were mixed with a small amount of ethanol. Although the void between silica particles results in small bubbles in the mixture, the remaining air is easily removed from the suspension consisting of EMMA, silica and ethanol. When heating this suspension at 200◦ C for 4 h, ethanol will be evaporated, and the mixture of molten EMMA and silica particle with no bubbles can be prepared. The amount of ethanol evaporated in the heating process can be checked by the weight difference and almost all of the ethanol can be removed. From the rheological and thermal analysis, no significant change in the physical properties of EMMA in the heating process could be observed. 2.2. Shear Application and Viscosity Measurement Shear at a defined shear rate was applied to the mixture at 120◦ C by using a cone– plate-type rheometer (SR-5; Rheometric Scientific). The cone fixture has a diameter of 4 cm and an angle of 0.04 rad. The molten mixture of EMMA and silica particles was placed on the plate, and the temperature was adjusted to 120◦ C by using a Peltier temperature controller following squeezing the mixture between the cone fixture and plate. Some agglomerates of silica particles will be extremely large just after the heating process. When evaluating the number of agglomerated particles in such agglomerates, it is difficult to distinguish the shape of each particle because the particles are relatively very small compared to the agglomerate. Furthermore, the initial distribution of agglomerated particle number is difficult to control in the mixture preparation process. Thus, in this study, a constant initial agglomerated state was obtained by applying shear for a long enough time with a shear rate of
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0.1 s−1 — an operation referred to as ‘pre-shearing’. The determined procedure of the pre-shearing condition is shown afterwards. After the establishment of the initial agglomerated state, the shear rate applied to a mixture was changed to 0.5–10 s−1 immediately and maintained for a defined period of time by using rheometer control software. Then, the rotation of the cone fixture was stopped and the mixture was cooled down to 25◦ C over several minutes. As a result, the circular thin film of the solidified mixture, in which particles in various dispersed states depending on the shearing conditions were included, was obtained. The thin film peeled from the cone fixture was cut off by using a microtome in order to observe the cross-sectional area. The circular specimen was cut off in a vertical direction for a radial section and the observed point was chosen randomly, because the applied shear must be constant over the whole mixture. In the process of shear application, viscosity measurement of the mixture was also conducted. The molten EMMA has a constant viscosity of approximately 200 Pa · s at 120◦ C over the range of shear rates investigated. Moreover, the dynamic rheological measurement was conducted for pure EMMA and mixtures in a steady agglomerated state by pre-shearing at 120◦ C. In that measurement, the angular frequency ranged from 0.1 to 100 rad/s and the strain amplitude was kept at 1%. 2.3. Analysis of Particle Dispersion Measurement of the number distribution of agglomerated particles was performed to evaluate the agglomerated state of particles in a mixture. The cross-section of the thin film was observed by using scanning electron microscopy (SEM, JSM-5610LVS; JEOL). In the SEM image as shown in Fig. 1, some particles are connected to each other and their cluster is treated as an agglomerate. However, an isolated particle that does not connect to any other particles was treated as an agglomerate consisting of one particle. In each shear condition, approximately 200 agglomerates of silica particles were picked out randomly from SEM images and
Figure 1. SEM images of the cross-sectional area of solidified mixtures for φ = 0.15 after 1000 s of pre-shearing.
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then the number of particles belonging to those agglomerates was calculated. Most of the agglomerates consisted of less than 30 particles and no agglomerate consisting of more than 200 particles was observed in this study. From the SEM images, the three-dimensional structure of agglomerate is difficult to evaluate and it is possible to mistakenly count several agglomerates as one. In this study, however, just the agglomerates separated clearly from others were picked out and the number of particles on the surface of the agglomerate was evaluated. Strictly speaking, the number of particles in this study is different from the particles in the agglomerate, but is representative of the size of an agglomerate. The state of particle agglomeration or dispersion was evaluated by a cumulative frequency distribution of agglomerated particle number fn , defined as: n (i · NC (i)) (i · NC (i)) × 100, (1) fn = i
i=1
where NC (i) is the number of agglomerates consisting of i particles. Thus, fn means the ratio of the number of particles belong to agglomerates consisting of n particles or less to the number of particles belonging to all agglomerates. The average of the agglomerated number Nave , which is calculated by dividing the number of particles belonging to all agglomerates by the number of agglomerates, was given by: Nave = (i · NC (i)) NC (i) × 100. (2) i
i
3. Result and Discussion 3.1. Determination of Pre-shearing Condition After the pre-shearing, a constant agglomerated state, is irrespective of the agglomerated state after the mixture preparation process, was obtained with good reproducibility. The shear rate in the pre-shearing should be as small much as possible because the moderately agglomerated state is preferable for the investigation of the dispersing progress of particle agglomeration. Thus, the shear rate applied in the pre-shearing was determined as 0.1 s−1 because the shearing time will be too long below that shear rate. The time variations of the viscosity of mixtures and the average agglomerated number for both particle volume fractions are shown in Fig. 2. Due to the lack of shearing time, the agglomerated state must be influenced by the state before the pre-shearing and the resulting agglomeration will be erratic. As a result, at the beginning of the pre-shearing, the behavior of viscosity is not consistent. Nevertheless, after applying shear at 0.1 s−1 for more than 500 s, the viscosity approaches a constant value and the difference from that at 1000 s of shearing was less than 10%. Furthermore, when the shearing time exceeded 2000 s, the average agglomerated number also nearly attained a steady state. Moreover, both mixtures
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Figure 2. Variation of viscosity and agglomerated number in the pre-shearing process.
showed much the same average agglomerated number at more than 2000 s in shearing time, although those viscosities are of course different. It inferred the existence of the similar structure of particle agglomeration in both mixtures. At 1000 s of shearing, the good reproducibility of both viscosity and agglomerated number could be confirmed. In the viscosity measurement, the deviation is within approximately 10%. Thus, in the pre-shearing operation, the initial condition for evaluating particle dispersion after the stepwise change in shear rate was decided to be achieved by applying shear at a shear rate of 0.1 s−1 for 1000 s. In the initial agglomerated state, no agglomerate consisted of more than 200 particles and more than 50% of agglomerates consisted of 5–50 particles for both volume fractions. 3.2. Rheological Behavior The viscosity of a mixture of liquid and particles — a so-called suspension — is well known to show a shear thinning behavior because of the change of particle agglomeration. In addition, the delayed change of viscosity to the change in shear rate is one of the typical characteristics. The time variation of viscosities both of mixtures (φ = 0.15 and 0.25) and pure EMMA is shown in Fig. 3 during the pre-shearing and the following shear application after stepwise shear rate changes. EMMA has almost constant viscosity except for just after the change of the shear rate. Thus, molten EMMA is a Newtonian fluid and shows a good response of viscosity to time. On the other hand, the viscosity of mixtures varies slowly compared to EMMA and gradually approached a constant in each shear application process. In Fig. 3, the viscosity behavior in pre-shearing is quite different between the mixtures, probably because of the difference in the dispersed state before the pre-shearing. For example, since the particles in the mixture of φ = 0.25 may be more dispersed than that at a steady state of 0.1 s−1 shear rate, the viscosity increased slowly to the steady state. However, the viscosity of each mixture always approached an almost
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Figure 3. Change of apparent viscosity of EMMA and EMMA mixtures with silica particles.
Figure 4. Frequency dependency of storage modulus for pure EMMA and mixtures with silica particles.
constant value independent of the history of viscosity change. Therefore, in the dispersion process of 1 s−1 shear rate, since a steady agglomerated state could still be obtained in the pre-shearing, the change in viscosity showed good reproducibility for both volume fractions. After a sudden increase or decrease of shear rate, the viscosity of the mixtures varied gradually for approximately 200 s, and the rate of viscosity recovery is somewhat quicker than that of viscosity loss. Such delayed change in the viscosity of mixtures compared to molten EMMA indicates that the break-up or re-agglomeration of agglomerates progressed gradually after the shear rate change and the degree of delay may be dominated by the shear rate. The dynamic rheological measurement was reported to be helpful for detecting the agglomerated structure of particles in a polymer [8, 9]. The dependency of phase angle on angular frequency is shown in Fig. 4 for pure EMMA and mixtures
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of EMMA and silica particles in the steady agglomerated state after pre-shearing at 0.1 s−1 for 2000 s. For EMMA, the phase angle of almost 90◦ at a low shear rate meant that EMMA was mostly viscous fluid and its gradual reduction at a higher shear rate revealed the appearance of elasticity due to the entanglement of polymer chains. On the contrary, phase angles for both mixtures have a peak at an angular frequency of 6–10 rad/s. The well-known Cox–Merz rule indicates a good relationship between the dynamic viscosity as a function of frequency and the steady shear viscosity as a function of shear rate for the polymer melt [12]. Consequently, we can treat an angular frequency as a shear rate. A small phase angle at a low shear rate for mixtures indicated large elasticity because of the formation of particle agglomeration, and the gradual increase in phase angle up to a shear rate of 10 s−1 suggests the destruction of agglomerated structure with increasing shear rate and reconstruction with decreasing shear rate. Thus, the range of shear rate applied in this study is appropriate for the investigation of particle dispersion and re-agglomeration in a polymer melt. From this dynamic rheological analysis, the difference in the agglomerated structure between mixtures of different particle content could not be found at the shear rate investigated. 3.3. Progress of Particle Dispersion After attaining the initial agglomerated state by the pre-shearing, the shear rate was quickly changed to a certain value and kept constant over a certain time. The number distribution of agglomerated particles in the mixture after the shear application was calculated and the results are summarized in Fig. 5 for particle loading of 0.15. As the time of shear application increased, the number of agglomerated particles was reduced and the fraction of non-agglomerated particles increased. Since the rheometer controls shear rate according to the exerted shear stress (stress controlled rheometer), it takes at least 20 s to adjust the shear rate to a set value. Thus, in Fig. 5 the distribution of each shear rate condition provided similar results at the shearing time of 10 s and the difference among shear rates could be clearly seen for more than 100 s in shearing time. For the shear rate of 1 s−1 , the dispersion
Figure 5. Progress of particle dispersion for each shear rate condition (φ = 0.15).
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proceeded until 1000 s and the distribution was not changed by further shear application. Meanwhile, for the shear rate of 10 s−1 the fraction of large agglomerate was reduced to until 5000 s of shearing, although that of isolated particles does not change so much. Since the change in shear rate was not so large for the shear rate of 0.5 s−1 , the termination of the distribution could not be clearly seen. The time variations of the average number of agglomerated particles at shear rates of 0.5, 1 and 10 s−1 for φ = 0.15 and 1 s−1 for φ = 0.25 are shown in Fig. 6. The averaged agglomerated numbers after the pre-shearing were 7.2 for φ = 0.15 and 9.6 for φ = 0.25, and the average agglomerated number for φ = 0.15 was about 5 and 3.5 at shearing times of 10 and 20 s. This indicates that the particle dispersion progressed rapidly in the transition process where the shear rate was changing to the set value. After that, the behavior of particle dispersion was affected by the shear rate. Thus, the number of agglomerated particles at the shearing time of 20 s for φ = 0.25, which was not evaluated in this work, will be lower compared to the solid line in Fig. 5. In a field of shear flow, the effect of particle dispersion should be balanced by that of agglomeration (shear agglomeration) and the stable agglomerated state must be strongly dependent on shear rate. Furthermore, the time to attain the stable agglomeration may be affected by shearing intensity. Thus, both dispersed state and required shearing time at a steady state were different from different shear rates, as shown in Fig. 6. Here, considering the particle dispersion will be accompanied by deformation of molten EMMA, the particle agglomeration may be influenced by the extent of deformation in the shearing process. As shown in Fig. 7, the average number of agglomerated particles has a strong relationship with the deformation or strain of EMMA, which is defined as the product of the shear rate and shearing time, for each particle volume fraction. The relationship between strain and particle agglomeration was affected not by shear rate, but by volume fraction. In a large strain
Figure 6. Time variation of average agglomerated number in the dispersing process.
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Figure 7. Relationship between strain and average agglomerated number.
region corresponding to a long shearing time, since particle dispersion does not proceed further, the average agglomerated number approached a constant and the deviation from the correlated line was observed. Therefore, particle agglomeration will be dispersed according to that relationship up to a dispersed limit, which is different for different shear rates. After that, it is supposed that the average number will reach a plateau when the shearing time is long enough. 3.4. Behavior Comparison Between Particle Dispersion and Re-agglomeration The viscosity of the mixture changed according to the shear rate applied as shown in Fig. 3 and the dispersed state in the mixture varied as stated above. As with the dispersion of particle agglomeration by the increase in shear rate, the dispersed particles should agglomerate again when the shear rate is reduced, even though the particles are dispersed well by applying shear for a long time. Nevertheless, the behavior of particle re-agglomeration has not been well investigated. In this study, as well as the dispersing behavior, the time variation of agglomerated particle number in a re-agglomeration process was measured and the results are shown in Fig. 8 accompanied with those for particle dispersion. Figure 8 shows the behavior of dispersion at a shear rate of 1 s−1 after pre-shearing and that of re-agglomeration at a shear rate of 0.1 s−1 following the dispersion process for φ = 0.25. For the case of dispersion, the agglomerate was particularly destroyed within 100 s; however, the particle dispersion progressed slowly and achieved a nearly steady state at 1000 s. On the other hand, the re-agglomeration within 1000 s was limited as the increase of large agglomerate, and then agglomerates consisting of relative small numbers of particle were formed; but it might take much longer than the dispersion process to attain a steady state. It may take approximately 10 000 s to establish a steady state at a shear rate of 0.1 s−1 if the re-agglomerating process is influenced by strain as well as that of dispersion.
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Figure 8. Dispersion and re-agglomeration behavior of agglomerated number distribution (φ = 0.25).
3.5. Correspondence Between Agglomerated State and Viscosity The existence of particles in a molten polymer is thought to increase the mixture viscosity compared to that of the molten polymer, as observed for ordinary suspensions consisting of liquid and particles. Further, the agglomeration of particles induces a further rise in viscosity. When comparing flow curves with upward and downward shear rate variation, a different viscosity can often be observed even at the same shear rate. Such hysteresis must be caused by a poor time response of the agglomerated structure to the change of shear rate. The extent of the viscosity increase is frequently evaluated by a relative viscosity, which is the ratio of apparent viscosity of the mixture to the dispersing fluid (e.g., Ref. [13]). A dynamic viscosity measurement gives us useful information concerning the agglomerated structure of a mixture, as already discussed. However, such a measurement is difficult to carry out in a manufacturing process for polymer composites. Meanwhile, a shear viscosity can be roughly estimated from the axial torque of mixing equipment. Thus, a shear viscosity will be a valuable index to evaluate particle dispersion, if the agglomerated number has a clear dependency on a shear viscosity. The relationship between the agglomerated particle number and the relative viscosity of the mixture of φ = 0.15 is summarized in Fig. 9 at various shear rates. Figure 9 shows the evolution of the relationship with time at both the pre-shearing and the following dispersion process, and an approximately linear relationship can be obtained over the whole of the dispersing process from the initial to the terminated agglomerated state. The relative viscosity at complete dispersion, where the average agglomerated number is unity, is about 1.3. At the same time, the fully dispersed relative viscosity of the mixture was calculated as 1.6 for φ = 0.15 by the use of Simha’s cell model [14], which is one of the proposed models to predict the relative viscosity of a suspension. Therefore, the mixture with φ = 0.15 could be mostly treated as an ordinal suspension when estimating agglomerated characteristics from shear viscosity.
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Figure 9. Dependency of agglomerated number on relative viscosity (φ = 0.15).
Figure 10. Dispersion and re-agglomeration process in the viscosity–agglomerated number diagram (φ = 0.15).
On the other hand, the mixture with large particle loading showed an interesting behavior in the relationship between viscosity and agglomerate size as shown in Fig. 10. In the dispersing process including the initial agglomerated state (1000 s of pre-shearing), the relative viscosity showed a linear relationship with the agglomerated number as well as the mixture of φ = 0.15. However, the plateau viscosity in the pre-shearing at shearing times of 2000 and 5000 s was higher than that in the dispersing process at the same agglomerated number. Furthermore, the relative viscosity and agglomerated number were not reduced further from 2.5 and 4. When particles are dispersed completely and the agglomerated number becames unity, the
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relative viscosity is predicted to be 2.8 by Simha’s cell model. Thus, this model is not appropriate for the prediction of the mixture viscosity at a higher particle loading and, in this mixture, the agglomerated particles will not be dispersed completely. In the re-agglomerating behavior, the viscosity increased within 500 s after the change in shear rate in spite of the constancy of the agglomerated number and after that the agglomerated number also increased with the viscosity to a steady agglomerated state corresponding to the shear rate of 0.1 s−1 . When reviewing the change of agglomerated number distribution during the first 500 s in Fig. 8, the constant average agglomerated number was caused by the decrease in the fraction of large agglomerates and the increase in that of small agglomerates. Both the plateau relative viscosity and agglomerated number in the re-agglomeration and pre-sharing processes, which are operated at the same share rate of 0.1 s−1 , showed good agreements. Thus, in the dispersing process from the steady state at 0.1 s−1 , the agglomerated number will decrease gradually following the sudden decrease of the relative viscosity with constant agglomerated number (indicated as a dotted arrow in Fig. 10) in the same way with re-agglomeration. In the case of the suspension consisting of less viscous solvent with constant particle content, the transition of particle agglomeration after the change in shear rate is relatively quick and the relative viscosity is determined just by the agglomerated state. Thus, the discrepancy in the dependency of viscosity on agglomerated number between the mixtures with φ = 0.15 and 0.25 suggests that the higher particle loading polymer composite could not be treated as a suspension. Moreover, the difference in particle contents could not be explained from a dynamic rheological evaluation. One of the reasons is the dependency of the distribution of agglomerated number on the viscosity. The effect may be significant at a higher particle loading and the viscosity prediction model has to be developed to treat these mixtures as a kind of suspension. Another reason is the poor affinity of hydrophobic silica particles with molten polymer. Since the void space around silica particles, which is sometimes observed as shown in Fig. 1, may cause the delay of the change in viscosity to the change in agglomerated number, the surface modification of silica particles may clearly explain this discrepancy. 4. Conclusions In order to understand the variation of particle agglomeration under a shear flow, a defined shear rate was applied to molten polymer containing silica particles with a volume fraction of 0.15 and 0.25. The agglomerated particle number, which was the number of connected particles making up a cluster, was measured, and then the agglomerated state was evaluated by their distribution and average in the dispersing and re-agglomerating processes. Measurement of viscosity of the mixture was also conducted and the relationship with the agglomerated state was studied.
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After attaining a constant agglomerated state by pre-shearing, the shear rate was changed to a defined value in a short time. Agglomerate gradually approached a steady dispersed state corresponding to the shear rate and the time to the steady state was different depending on the shearing condition. When the agglomerated particles were dispersing, the average agglomerated number could be well correlated by a strain of molten polymer for each particle fraction. Thus, the particle dispersion in a Newtonian molten polymer is dominated by the deformation of the polymer. When decreasing the shear rate, the dispersed particles again agglomerated slowly. At the particle loading of 0.15, a good agreement between the agglomerated number and viscosity could be observed independent of shear rate. Thus, the agglomerated state in the dispersing process will be estimated via the viscosity of the mixture of this composition. On the other hand, for a mixture with a particle content of 0.25, the viscosity at the same agglomerated state was different according to the shear rate. Furthermore, when the shear rate is increased or decreased, the viscosity of the mixture will change in spite of a constant agglomerated number. Accordingly, the behavior of the particle agglomerate and mixture viscosity under a shear flow must be particularly affected by the particle content. Shear viscosity provides a possibility to evaluate the particle agglomeration in the mixture. At the same time, there are some problems to overcome for the further understanding of agglomerate behavior via shear viscosity. The distribution of agglomerated number and the affinity between materials, which may affect the viscosity, has to be taken into account for detailed comprehension. References 1. K. M. Jager and D. H. McQueen, Fractal agglomerates and electrical conductivity in carbon black polymer composite, Polymer 42, 9575–9581 (2001). 2. R. Schueler, J. Petermann, K. Schulte and H. P. Wentzel, Agglomeration and electrical percolation behavior of carbon black cispersed in epoxy resin, J. Appl. Polym. Sci. 63, 1741–1746 (1997). 3. Y. Lee and I. Z. Manas, Analysis of titanium dioxide agglomerate dispersion in linear low density polyethylene and resulting properties of compounds, Polym. Eng. Sci. 35, 1037–1045 (1995). 4. J. Jordana, K. I. Jacobb, R. Tannenbaumc, M. A. Sharafb and I. Jasiukd, Experimental trends in polymer nanocomposites — a review, Mater. Sci. Eng. A 393, 1–11 (2005). 5. S. P. Rwei and I. Z. Manas, Observation of carbon agglomerate dispersion in simple shear flow, Polym. Eng. Sci. 30, 701–706 (1990). 6. Y. Lee, D. L. Feke and I. Z. Manas, Dispersion of titanium dioxide agglomerates in viscous media, Chem. Eng. Sci. 48, 3363–3372 (1993). 7. A. Scurati, D. L. Feke and I. Z. Manas, Analysis of the kinetics of agglomerate erosion in simple shear flow, Chem. Eng. Sci. 60, 6564–6573 (2005). 8. G. Wu, J. Lin, Q. Zheng and M. Zhang, Correlation between percolation behavior of electricity and viscoelasticity for graphite filled high density polyethylene, Polymer 47, 2442–2447 (2006). 9. G. Wu, S. Asai, M. Sumita, T. Hattori, R. Higuchi and J. Washiyama, Estimation of flocculation structure in filled polymer composites by dynamic rheological measurements, Colloid. Polym. Sci. 278, 220–228 (2000).
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Original Paper Behavior of Fine Particle Agglomerates in a Newtonian Molten Polymer Under a Shear Flow Yoshiyuki Komoda a,∗ , Kanako Kameyama b , Emi Hasegawa b , Hiroshi Suzuki a , Hiromoto Usui a , Yoshiyuki Endo c and Atsushi Syudo c a
c
Department of Chemical Science and Engineering, Kobe University, Kobe 657-8501, Japan b Graduate School of Science and Technology, Kobe University, Kobe 657-8501, Japan Process and Production Technology Center, Sumitomo Chemical Co., Osaka 554-8558, Japan Received 2 August 2007; accepted 27 November 2007
Abstract The dispersing behavior of a particle agglomerate in a mixture consisting of spherical fine particles and a molten polymer was investigated with the application of shear in a cone–plate apparatus. After attaining a constant agglomerated state by applying a small shear, the shear rate was changed to a set value and kept constant over a certain time. Viscosity measurement during shear application and analysis of particle agglomeration in a solidified mixture were conducted. In a dispersing process, agglomerates were broken up to a steady dispersed state corresponding to the shear rate applied and the average number of agglomerated particles could be well correlated by a deformation of the mixture in each particle volume fraction. The viscosity of the mixture with a particle loading of 0.15 had a good relationship with the agglomerated number independent of shear rate; thus, the viscosity of suspension may help in the understanding of the dispersing behavior. However, the concentrated mixture could not achieve a complete dispersion and the viscosity was significantly affected by the time response of the agglomerated structure to shear application, although a dynamic rheological measurement of mixtures with different particle loadings provided much the same result. © Koninklijke Brill NV, Leiden and Society of Powder Technology, Japan, 2008 Keywords Particle dispersion, viscosity, phase angle
1. Introduction Polymer composites, which are composite materials consisting of a polymer and filler, have various applications for the improvement of functionality of a raw material product, such as enhancement of mechanical or/and thermal properties and *
To whom correspondence should be addressed. E-mail: [email protected]
© Koninklijke Brill NV, Leiden and Society of Powder Technology, Japan, 2008
DOI:10.1163/156855208X368599
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addition of a new characteristic to a raw polymer. The filler, which is an organic or inorganic fine particle or fiber, was originally invented for cost reduction by the decrease in a fraction of an expensive polymer. At present the filler is also used for the production of functional materials. The functionality of a polymer composite will depend on the volume fraction and shape of filler, interaction between filler and polymer, dispersed state of filler in a polymer (morphology), etc. In general, the mechanical or thermal properties are mainly affected by the fraction. However, the new functionality may be primarily influenced by the dispersed state. The relations between the dispersed state of particles and the functionality have been reported by Jager et al. [1]. Schueler et al. noted that an ionic additive increased agglomeration, and the morphology affected a threshold of electrical conductivity for the mixture of carbon black and epoxy resin [2]. Additionally, the mechanical properties of composites, such as strength and modulus, also depend on the dispersed state of the filler [3]. Composites including nano-size fillers were studied extensively and reviewed by Jordan et al. [4]. Although the fraction of filler will be widely different between applications, the morphology of filler will have considerable effects on the properties of products. Particle dispersion into a polymer has been usually conducted by applying excessive shear stress for a long time with particular equipment such as a kneading machine and extruder. In such equipment, the flow behavior is visualized by a computer simulation; however, the operating condition to control the particle dispersion is still decided semi-empirically. Although it is proposed that agglomerate splitting and particle erosion induce the dispersion of particle agglomerates, the mechanism and progress of particle dispersion in a shear flow has not yet been fully clarified. Moreover, several factors, such as the adhesion property at the interface between particles and fluid, and rheological characteristics of fluid, affect the behavior of fine particle dispersion. Thus, the dispersing behavior is very complicated and is still more so for practical equipment. As one of the simpler cases, the breakup process of a compressed particle agglomerate under simple shear flow has been well investigated [5–7]. However, comprehension of the dispersing behavior with the number of distributed particle agglomerates is indispensable for developing the exact control method of particle dispersion and an innovative technology. The relationship between the rheological property and dispersed structure of filler in a polymer composite has been well investigated by many researchers [8–11]. Most research paid attention to the relationship between the dynamic rheological properties including a storage modulus and loss angle of mixture in a certain dispersed state. Although the evolution of any rheological property when particles are dispersing or agglomerating should have a strong relationship with the dispersed state of particles in a polymer, the transition behavior of the agglomerate and corresponding rheological property have not been researched well. In this study, the observation and analysis of particle agglomerates in a molten polymer under a shear flow when dispersing or agglomerating was investigated; at the same time, the variation of rheological characteristics was measured. Finally, the correspon-
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dence between the state of agglomerated particles and the viscosity of the mixture was investigated. 2. Experimental 2.1. Materials and Preparation of Mixture Ethylene meta-methyl acrylate copolymer (EMMA) was used as a molten polymer. EMMA has a melting point of 67◦ C and the molten EMMA showed a constant shear viscosity independent of shear rate (Newtonian fluid). A spherical silica particle (KE-P250; Nihon shokubai), which is mono-dispersed and ranges from 2.25 to 2.75 μm in size, was used as filler, and the surface of silica particle was not modified (hydrophilic). The silica particles were mixed with molten EMMA and shear was applied to the mixture by using a cone–plate rheometer at a temperature higher than the melting point of EMMA. The specifications of shear applied to the mixture will be stated in a later section. Sudden cooling to room temperature after stopping the shear application can maintain the state of particle agglomeration during the solidification process of EMMA. The volume fraction of silica particle φ was adjusted to 0.15 and 0.25. In the process of mixture preparation, the EMMA pellet and silica particles were mixed with a small amount of ethanol. Although the void between silica particles results in small bubbles in the mixture, the remaining air is easily removed from the suspension consisting of EMMA, silica and ethanol. When heating this suspension at 200◦ C for 4 h, ethanol will be evaporated, and the mixture of molten EMMA and silica particle with no bubbles can be prepared. The amount of ethanol evaporated in the heating process can be checked by the weight difference and almost all of the ethanol can be removed. From the rheological and thermal analysis, no significant change in the physical properties of EMMA in the heating process could be observed. 2.2. Shear Application and Viscosity Measurement Shear at a defined shear rate was applied to the mixture at 120◦ C by using a cone– plate-type rheometer (SR-5; Rheometric Scientific). The cone fixture has a diameter of 4 cm and an angle of 0.04 rad. The molten mixture of EMMA and silica particles was placed on the plate, and the temperature was adjusted to 120◦ C by using a Peltier temperature controller following squeezing the mixture between the cone fixture and plate. Some agglomerates of silica particles will be extremely large just after the heating process. When evaluating the number of agglomerated particles in such agglomerates, it is difficult to distinguish the shape of each particle because the particles are relatively very small compared to the agglomerate. Furthermore, the initial distribution of agglomerated particle number is difficult to control in the mixture preparation process. Thus, in this study, a constant initial agglomerated state was obtained by applying shear for a long enough time with a shear rate of
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0.1 s−1 — an operation referred to as ‘pre-shearing’. The determined procedure of the pre-shearing condition is shown afterwards. After the establishment of the initial agglomerated state, the shear rate applied to a mixture was changed to 0.5–10 s−1 immediately and maintained for a defined period of time by using rheometer control software. Then, the rotation of the cone fixture was stopped and the mixture was cooled down to 25◦ C over several minutes. As a result, the circular thin film of the solidified mixture, in which particles in various dispersed states depending on the shearing conditions were included, was obtained. The thin film peeled from the cone fixture was cut off by using a microtome in order to observe the cross-sectional area. The circular specimen was cut off in a vertical direction for a radial section and the observed point was chosen randomly, because the applied shear must be constant over the whole mixture. In the process of shear application, viscosity measurement of the mixture was also conducted. The molten EMMA has a constant viscosity of approximately 200 Pa · s at 120◦ C over the range of shear rates investigated. Moreover, the dynamic rheological measurement was conducted for pure EMMA and mixtures in a steady agglomerated state by pre-shearing at 120◦ C. In that measurement, the angular frequency ranged from 0.1 to 100 rad/s and the strain amplitude was kept at 1%. 2.3. Analysis of Particle Dispersion Measurement of the number distribution of agglomerated particles was performed to evaluate the agglomerated state of particles in a mixture. The cross-section of the thin film was observed by using scanning electron microscopy (SEM, JSM-5610LVS; JEOL). In the SEM image as shown in Fig. 1, some particles are connected to each other and their cluster is treated as an agglomerate. However, an isolated particle that does not connect to any other particles was treated as an agglomerate consisting of one particle. In each shear condition, approximately 200 agglomerates of silica particles were picked out randomly from SEM images and
Figure 1. SEM images of the cross-sectional area of solidified mixtures for φ = 0.15 after 1000 s of pre-shearing.
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then the number of particles belonging to those agglomerates was calculated. Most of the agglomerates consisted of less than 30 particles and no agglomerate consisting of more than 200 particles was observed in this study. From the SEM images, the three-dimensional structure of agglomerate is difficult to evaluate and it is possible to mistakenly count several agglomerates as one. In this study, however, just the agglomerates separated clearly from others were picked out and the number of particles on the surface of the agglomerate was evaluated. Strictly speaking, the number of particles in this study is different from the particles in the agglomerate, but is representative of the size of an agglomerate. The state of particle agglomeration or dispersion was evaluated by a cumulative frequency distribution of agglomerated particle number fn , defined as: n (i · NC (i)) (i · NC (i)) × 100, (1) fn = i
i=1
where NC (i) is the number of agglomerates consisting of i particles. Thus, fn means the ratio of the number of particles belong to agglomerates consisting of n particles or less to the number of particles belonging to all agglomerates. The average of the agglomerated number Nave , which is calculated by dividing the number of particles belonging to all agglomerates by the number of agglomerates, was given by: Nave = (i · NC (i)) NC (i) × 100. (2) i
i
3. Result and Discussion 3.1. Determination of Pre-shearing Condition After the pre-shearing, a constant agglomerated state, is irrespective of the agglomerated state after the mixture preparation process, was obtained with good reproducibility. The shear rate in the pre-shearing should be as small much as possible because the moderately agglomerated state is preferable for the investigation of the dispersing progress of particle agglomeration. Thus, the shear rate applied in the pre-shearing was determined as 0.1 s−1 because the shearing time will be too long below that shear rate. The time variations of the viscosity of mixtures and the average agglomerated number for both particle volume fractions are shown in Fig. 2. Due to the lack of shearing time, the agglomerated state must be influenced by the state before the pre-shearing and the resulting agglomeration will be erratic. As a result, at the beginning of the pre-shearing, the behavior of viscosity is not consistent. Nevertheless, after applying shear at 0.1 s−1 for more than 500 s, the viscosity approaches a constant value and the difference from that at 1000 s of shearing was less than 10%. Furthermore, when the shearing time exceeded 2000 s, the average agglomerated number also nearly attained a steady state. Moreover, both mixtures
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Figure 2. Variation of viscosity and agglomerated number in the pre-shearing process.
showed much the same average agglomerated number at more than 2000 s in shearing time, although those viscosities are of course different. It inferred the existence of the similar structure of particle agglomeration in both mixtures. At 1000 s of shearing, the good reproducibility of both viscosity and agglomerated number could be confirmed. In the viscosity measurement, the deviation is within approximately 10%. Thus, in the pre-shearing operation, the initial condition for evaluating particle dispersion after the stepwise change in shear rate was decided to be achieved by applying shear at a shear rate of 0.1 s−1 for 1000 s. In the initial agglomerated state, no agglomerate consisted of more than 200 particles and more than 50% of agglomerates consisted of 5–50 particles for both volume fractions. 3.2. Rheological Behavior The viscosity of a mixture of liquid and particles — a so-called suspension — is well known to show a shear thinning behavior because of the change of particle agglomeration. In addition, the delayed change of viscosity to the change in shear rate is one of the typical characteristics. The time variation of viscosities both of mixtures (φ = 0.15 and 0.25) and pure EMMA is shown in Fig. 3 during the pre-shearing and the following shear application after stepwise shear rate changes. EMMA has almost constant viscosity except for just after the change of the shear rate. Thus, molten EMMA is a Newtonian fluid and shows a good response of viscosity to time. On the other hand, the viscosity of mixtures varies slowly compared to EMMA and gradually approached a constant in each shear application process. In Fig. 3, the viscosity behavior in pre-shearing is quite different between the mixtures, probably because of the difference in the dispersed state before the pre-shearing. For example, since the particles in the mixture of φ = 0.25 may be more dispersed than that at a steady state of 0.1 s−1 shear rate, the viscosity increased slowly to the steady state. However, the viscosity of each mixture always approached an almost
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Figure 3. Change of apparent viscosity of EMMA and EMMA mixtures with silica particles.
Figure 4. Frequency dependency of storage modulus for pure EMMA and mixtures with silica particles.
constant value independent of the history of viscosity change. Therefore, in the dispersion process of 1 s−1 shear rate, since a steady agglomerated state could still be obtained in the pre-shearing, the change in viscosity showed good reproducibility for both volume fractions. After a sudden increase or decrease of shear rate, the viscosity of the mixtures varied gradually for approximately 200 s, and the rate of viscosity recovery is somewhat quicker than that of viscosity loss. Such delayed change in the viscosity of mixtures compared to molten EMMA indicates that the break-up or re-agglomeration of agglomerates progressed gradually after the shear rate change and the degree of delay may be dominated by the shear rate. The dynamic rheological measurement was reported to be helpful for detecting the agglomerated structure of particles in a polymer [8, 9]. The dependency of phase angle on angular frequency is shown in Fig. 4 for pure EMMA and mixtures
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of EMMA and silica particles in the steady agglomerated state after pre-shearing at 0.1 s−1 for 2000 s. For EMMA, the phase angle of almost 90◦ at a low shear rate meant that EMMA was mostly viscous fluid and its gradual reduction at a higher shear rate revealed the appearance of elasticity due to the entanglement of polymer chains. On the contrary, phase angles for both mixtures have a peak at an angular frequency of 6–10 rad/s. The well-known Cox–Merz rule indicates a good relationship between the dynamic viscosity as a function of frequency and the steady shear viscosity as a function of shear rate for the polymer melt [12]. Consequently, we can treat an angular frequency as a shear rate. A small phase angle at a low shear rate for mixtures indicated large elasticity because of the formation of particle agglomeration, and the gradual increase in phase angle up to a shear rate of 10 s−1 suggests the destruction of agglomerated structure with increasing shear rate and reconstruction with decreasing shear rate. Thus, the range of shear rate applied in this study is appropriate for the investigation of particle dispersion and re-agglomeration in a polymer melt. From this dynamic rheological analysis, the difference in the agglomerated structure between mixtures of different particle content could not be found at the shear rate investigated. 3.3. Progress of Particle Dispersion After attaining the initial agglomerated state by the pre-shearing, the shear rate was quickly changed to a certain value and kept constant over a certain time. The number distribution of agglomerated particles in the mixture after the shear application was calculated and the results are summarized in Fig. 5 for particle loading of 0.15. As the time of shear application increased, the number of agglomerated particles was reduced and the fraction of non-agglomerated particles increased. Since the rheometer controls shear rate according to the exerted shear stress (stress controlled rheometer), it takes at least 20 s to adjust the shear rate to a set value. Thus, in Fig. 5 the distribution of each shear rate condition provided similar results at the shearing time of 10 s and the difference among shear rates could be clearly seen for more than 100 s in shearing time. For the shear rate of 1 s−1 , the dispersion
Figure 5. Progress of particle dispersion for each shear rate condition (φ = 0.15).
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proceeded until 1000 s and the distribution was not changed by further shear application. Meanwhile, for the shear rate of 10 s−1 the fraction of large agglomerate was reduced to until 5000 s of shearing, although that of isolated particles does not change so much. Since the change in shear rate was not so large for the shear rate of 0.5 s−1 , the termination of the distribution could not be clearly seen. The time variations of the average number of agglomerated particles at shear rates of 0.5, 1 and 10 s−1 for φ = 0.15 and 1 s−1 for φ = 0.25 are shown in Fig. 6. The averaged agglomerated numbers after the pre-shearing were 7.2 for φ = 0.15 and 9.6 for φ = 0.25, and the average agglomerated number for φ = 0.15 was about 5 and 3.5 at shearing times of 10 and 20 s. This indicates that the particle dispersion progressed rapidly in the transition process where the shear rate was changing to the set value. After that, the behavior of particle dispersion was affected by the shear rate. Thus, the number of agglomerated particles at the shearing time of 20 s for φ = 0.25, which was not evaluated in this work, will be lower compared to the solid line in Fig. 5. In a field of shear flow, the effect of particle dispersion should be balanced by that of agglomeration (shear agglomeration) and the stable agglomerated state must be strongly dependent on shear rate. Furthermore, the time to attain the stable agglomeration may be affected by shearing intensity. Thus, both dispersed state and required shearing time at a steady state were different from different shear rates, as shown in Fig. 6. Here, considering the particle dispersion will be accompanied by deformation of molten EMMA, the particle agglomeration may be influenced by the extent of deformation in the shearing process. As shown in Fig. 7, the average number of agglomerated particles has a strong relationship with the deformation or strain of EMMA, which is defined as the product of the shear rate and shearing time, for each particle volume fraction. The relationship between strain and particle agglomeration was affected not by shear rate, but by volume fraction. In a large strain
Figure 6. Time variation of average agglomerated number in the dispersing process.
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Figure 7. Relationship between strain and average agglomerated number.
region corresponding to a long shearing time, since particle dispersion does not proceed further, the average agglomerated number approached a constant and the deviation from the correlated line was observed. Therefore, particle agglomeration will be dispersed according to that relationship up to a dispersed limit, which is different for different shear rates. After that, it is supposed that the average number will reach a plateau when the shearing time is long enough. 3.4. Behavior Comparison Between Particle Dispersion and Re-agglomeration The viscosity of the mixture changed according to the shear rate applied as shown in Fig. 3 and the dispersed state in the mixture varied as stated above. As with the dispersion of particle agglomeration by the increase in shear rate, the dispersed particles should agglomerate again when the shear rate is reduced, even though the particles are dispersed well by applying shear for a long time. Nevertheless, the behavior of particle re-agglomeration has not been well investigated. In this study, as well as the dispersing behavior, the time variation of agglomerated particle number in a re-agglomeration process was measured and the results are shown in Fig. 8 accompanied with those for particle dispersion. Figure 8 shows the behavior of dispersion at a shear rate of 1 s−1 after pre-shearing and that of re-agglomeration at a shear rate of 0.1 s−1 following the dispersion process for φ = 0.25. For the case of dispersion, the agglomerate was particularly destroyed within 100 s; however, the particle dispersion progressed slowly and achieved a nearly steady state at 1000 s. On the other hand, the re-agglomeration within 1000 s was limited as the increase of large agglomerate, and then agglomerates consisting of relative small numbers of particle were formed; but it might take much longer than the dispersion process to attain a steady state. It may take approximately 10 000 s to establish a steady state at a shear rate of 0.1 s−1 if the re-agglomerating process is influenced by strain as well as that of dispersion.
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Figure 8. Dispersion and re-agglomeration behavior of agglomerated number distribution (φ = 0.25).
3.5. Correspondence Between Agglomerated State and Viscosity The existence of particles in a molten polymer is thought to increase the mixture viscosity compared to that of the molten polymer, as observed for ordinary suspensions consisting of liquid and particles. Further, the agglomeration of particles induces a further rise in viscosity. When comparing flow curves with upward and downward shear rate variation, a different viscosity can often be observed even at the same shear rate. Such hysteresis must be caused by a poor time response of the agglomerated structure to the change of shear rate. The extent of the viscosity increase is frequently evaluated by a relative viscosity, which is the ratio of apparent viscosity of the mixture to the dispersing fluid (e.g., Ref. [13]). A dynamic viscosity measurement gives us useful information concerning the agglomerated structure of a mixture, as already discussed. However, such a measurement is difficult to carry out in a manufacturing process for polymer composites. Meanwhile, a shear viscosity can be roughly estimated from the axial torque of mixing equipment. Thus, a shear viscosity will be a valuable index to evaluate particle dispersion, if the agglomerated number has a clear dependency on a shear viscosity. The relationship between the agglomerated particle number and the relative viscosity of the mixture of φ = 0.15 is summarized in Fig. 9 at various shear rates. Figure 9 shows the evolution of the relationship with time at both the pre-shearing and the following dispersion process, and an approximately linear relationship can be obtained over the whole of the dispersing process from the initial to the terminated agglomerated state. The relative viscosity at complete dispersion, where the average agglomerated number is unity, is about 1.3. At the same time, the fully dispersed relative viscosity of the mixture was calculated as 1.6 for φ = 0.15 by the use of Simha’s cell model [14], which is one of the proposed models to predict the relative viscosity of a suspension. Therefore, the mixture with φ = 0.15 could be mostly treated as an ordinal suspension when estimating agglomerated characteristics from shear viscosity.
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Figure 9. Dependency of agglomerated number on relative viscosity (φ = 0.15).
Figure 10. Dispersion and re-agglomeration process in the viscosity–agglomerated number diagram (φ = 0.15).
On the other hand, the mixture with large particle loading showed an interesting behavior in the relationship between viscosity and agglomerate size as shown in Fig. 10. In the dispersing process including the initial agglomerated state (1000 s of pre-shearing), the relative viscosity showed a linear relationship with the agglomerated number as well as the mixture of φ = 0.15. However, the plateau viscosity in the pre-shearing at shearing times of 2000 and 5000 s was higher than that in the dispersing process at the same agglomerated number. Furthermore, the relative viscosity and agglomerated number were not reduced further from 2.5 and 4. When particles are dispersed completely and the agglomerated number becames unity, the
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relative viscosity is predicted to be 2.8 by Simha’s cell model. Thus, this model is not appropriate for the prediction of the mixture viscosity at a higher particle loading and, in this mixture, the agglomerated particles will not be dispersed completely. In the re-agglomerating behavior, the viscosity increased within 500 s after the change in shear rate in spite of the constancy of the agglomerated number and after that the agglomerated number also increased with the viscosity to a steady agglomerated state corresponding to the shear rate of 0.1 s−1 . When reviewing the change of agglomerated number distribution during the first 500 s in Fig. 8, the constant average agglomerated number was caused by the decrease in the fraction of large agglomerates and the increase in that of small agglomerates. Both the plateau relative viscosity and agglomerated number in the re-agglomeration and pre-sharing processes, which are operated at the same share rate of 0.1 s−1 , showed good agreements. Thus, in the dispersing process from the steady state at 0.1 s−1 , the agglomerated number will decrease gradually following the sudden decrease of the relative viscosity with constant agglomerated number (indicated as a dotted arrow in Fig. 10) in the same way with re-agglomeration. In the case of the suspension consisting of less viscous solvent with constant particle content, the transition of particle agglomeration after the change in shear rate is relatively quick and the relative viscosity is determined just by the agglomerated state. Thus, the discrepancy in the dependency of viscosity on agglomerated number between the mixtures with φ = 0.15 and 0.25 suggests that the higher particle loading polymer composite could not be treated as a suspension. Moreover, the difference in particle contents could not be explained from a dynamic rheological evaluation. One of the reasons is the dependency of the distribution of agglomerated number on the viscosity. The effect may be significant at a higher particle loading and the viscosity prediction model has to be developed to treat these mixtures as a kind of suspension. Another reason is the poor affinity of hydrophobic silica particles with molten polymer. Since the void space around silica particles, which is sometimes observed as shown in Fig. 1, may cause the delay of the change in viscosity to the change in agglomerated number, the surface modification of silica particles may clearly explain this discrepancy. 4. Conclusions In order to understand the variation of particle agglomeration under a shear flow, a defined shear rate was applied to molten polymer containing silica particles with a volume fraction of 0.15 and 0.25. The agglomerated particle number, which was the number of connected particles making up a cluster, was measured, and then the agglomerated state was evaluated by their distribution and average in the dispersing and re-agglomerating processes. Measurement of viscosity of the mixture was also conducted and the relationship with the agglomerated state was studied.
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After attaining a constant agglomerated state by pre-shearing, the shear rate was changed to a defined value in a short time. Agglomerate gradually approached a steady dispersed state corresponding to the shear rate and the time to the steady state was different depending on the shearing condition. When the agglomerated particles were dispersing, the average agglomerated number could be well correlated by a strain of molten polymer for each particle fraction. Thus, the particle dispersion in a Newtonian molten polymer is dominated by the deformation of the polymer. When decreasing the shear rate, the dispersed particles again agglomerated slowly. At the particle loading of 0.15, a good agreement between the agglomerated number and viscosity could be observed independent of shear rate. Thus, the agglomerated state in the dispersing process will be estimated via the viscosity of the mixture of this composition. On the other hand, for a mixture with a particle content of 0.25, the viscosity at the same agglomerated state was different according to the shear rate. Furthermore, when the shear rate is increased or decreased, the viscosity of the mixture will change in spite of a constant agglomerated number. Accordingly, the behavior of the particle agglomerate and mixture viscosity under a shear flow must be particularly affected by the particle content. Shear viscosity provides a possibility to evaluate the particle agglomeration in the mixture. At the same time, there are some problems to overcome for the further understanding of agglomerate behavior via shear viscosity. The distribution of agglomerated number and the affinity between materials, which may affect the viscosity, has to be taken into account for detailed comprehension. References 1. K. M. Jager and D. H. McQueen, Fractal agglomerates and electrical conductivity in carbon black polymer composite, Polymer 42, 9575–9581 (2001). 2. R. Schueler, J. Petermann, K. Schulte and H. P. Wentzel, Agglomeration and electrical percolation behavior of carbon black cispersed in epoxy resin, J. Appl. Polym. Sci. 63, 1741–1746 (1997). 3. Y. Lee and I. Z. Manas, Analysis of titanium dioxide agglomerate dispersion in linear low density polyethylene and resulting properties of compounds, Polym. Eng. Sci. 35, 1037–1045 (1995). 4. J. Jordana, K. I. Jacobb, R. Tannenbaumc, M. A. Sharafb and I. Jasiukd, Experimental trends in polymer nanocomposites — a review, Mater. Sci. Eng. A 393, 1–11 (2005). 5. S. P. Rwei and I. Z. Manas, Observation of carbon agglomerate dispersion in simple shear flow, Polym. Eng. Sci. 30, 701–706 (1990). 6. Y. Lee, D. L. Feke and I. Z. Manas, Dispersion of titanium dioxide agglomerates in viscous media, Chem. Eng. Sci. 48, 3363–3372 (1993). 7. A. Scurati, D. L. Feke and I. Z. Manas, Analysis of the kinetics of agglomerate erosion in simple shear flow, Chem. Eng. Sci. 60, 6564–6573 (2005). 8. G. Wu, J. Lin, Q. Zheng and M. Zhang, Correlation between percolation behavior of electricity and viscoelasticity for graphite filled high density polyethylene, Polymer 47, 2442–2447 (2006). 9. G. Wu, S. Asai, M. Sumita, T. Hattori, R. Higuchi and J. Washiyama, Estimation of flocculation structure in filled polymer composites by dynamic rheological measurements, Colloid. Polym. Sci. 278, 220–228 (2000).
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