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Effects of PEG molecular weights on rheological behavior of alumina injection molding feedstocks
Materials Chemistry and Physics 78 (2002) 416–424
Effects of PEG molecular weights on rheological behavior of alumina injection molding feedstocks Wei-Wen Yang, Kai-Yun Yang, Min-Hsiung Hon∗ Department of Materials Science and Engineering (Mat32), National Cheng Kung University, Tainan, Taiwan Received 16 October 2001; received in revised form 19 March 2002; accepted 8 April 2002
Abstract The rheological behaviors of alumina injection molding feedstocks containing polyethylene glycol (PEG) binders having different molecular weights were analyzed using capillary viscometer. The results indicate that the feedstock containing larger molecular weight PEG shows a higher yield stress and shear stress. The relative viscosity of feedstocks with PEG binder system is small, which show a good fluidity, and the viscosity decreases with increasing both temperature and shear rate. However, when temperature is above 90 ◦ C, the fluidity of feedstocks with PEG1K and PEG1.5K is too high to catch powder, which may induce dissociation occurring between the binder and the powder particles. Based on the results, feedstock D containing PEG20K as the binder has the lowest fluidity, however, it possesses viscosities smaller than 103 Pa s for all working temperatures. The feedstocks all show pseudoplastic behavior with n value in the range 0.41–0.66, which would be accepted for injection molding. In addition, feedstock D with PEG20K shows a lower temperature dependence of viscosity in the temperature range just below the nozzle temperature. It has the best rheological properties and is most suitable for injection molding. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Power-law index; Injection molding; Rheological behavior; Polyethylene glycol; Molecular weight
1. Introduction
fluid that shows quasi-plastic behavior with a yield stress τ y , it should obey the expression:
Injection molding for ceramic feedstocks containing binders that impart flow during processing is an attractive method for near-net and complex shape production of engineering products [1–5]. The feedstocks that consists of the ceramic powder and together with the binders are first injected into a shape forming mold cavity. Subsequently, the binders are removed before sintering the ceramic. The mold injection stage, which determines the shape of the green part, represents a critical step in the PIM process. Mold filling with the PIM feedstock is dependent on viscous flow of the mixture into the die cavity, and this requires specific rheological characteristics [6,7]. The steady flow of melt feedstock and the filling of the mold is a key feature for successful molding. Initially, for successful molding, the ceramic–binder mixtures should have either Bingham or pseudoplastic flow characteristics, since increasing shear rates produce lower viscosities that will assist mold filling [8]. However, for the
τ − τy = Kγ n
∗ Corresponding author. Tel./fax: +886-6-2380208. E-mail address: [email protected] (M.-H. Hon).
(1)
Here τ and γ represent the shear stress and the shear rate, respectively. K is the consistency coefficient which is a constant related to the flow characteristics of a real fluid, and n is the power-law exponent which is defined as flow behavior index of a fluid. For Bingham or pseudoplastic like flow behavior n < 1, for a Newtonian fluid n = 1. If n > 1 the mixtures will be dilatant and result in the separation of the binders from the ceramic powders. It is clear that the binder is the key that provides the rheological properties and determines whether the resulting feedstock can be injection molded without introducing defects. Many different powder and binder systems have been used for PIM. The most widely applied system is polymer/wax system such as mixture of polypropylene, paraffin wax, and stearic acid (SA) or polyethylene [9–11]. The advantages claimed for waxes are the low viscosity and superior wetting characteristics. Wax is the major portion of the binder to lower the viscosity of feedstocks. The thermoplastic polymer such as polypropylene or polyethylene, acts as a backbone material to give the strength of system in
0254-0584/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 2 ) 0 0 2 0 3 - 1
W.-W. Yang et al. / Materials Chemistry and Physics 78 (2002) 416–424
the green state and offers the general rheological properties required. SA is commonly used as a surfactant that helps the binder wet the powder particles and promotes flow. Many problems are associated with using these polymer/wax systems such as low green strength and very narrow processing windows [12]. Most of the organic solvents frequently adopted in solvent debinding are flammable, carcinogenic and environmentally unacceptable. Additionally, the green compacts soften in these debinding solvents and expensive machined debinding substrates are necessary if any shape retention is to be achieved [13]. From these considerations and an environmental point of view, polyethylene glycols (PEGs) are used to eliminate the use of unsound solvents to modify the pattern of debinding in alumina injection molding, as they are soluble in water [12,14]. The unique characteristics of PEG is water soluble and thermoplastic. In addition, they are very safe chemicals and are used quite extensively in food industry; permission was obtained from the local water authorities to dump the water/PEG containing solvents into the drain after debinding [12]. In view of the literatures, many publications have reported useful results concerning the influence of binder composition on the rheological properties of wax-based feedstock [15–17]. However, the rheological behavior of alumina injection molding feedstock with PEG binder system has not been extensively studied. Owing to the PEG molecular weight has considerable effect on the debinding behavior of the specimen according to our previous investigation [18], the main objective of this research is to characterize in detail the effects of PEG molecular weights on rheological behavior of alumina injection molding feedstock. The flow properties of all feedstocks were measured in a capillary viscometer over a wide range of shear rate and working temperature. The corresponding rheological parameters such as fluidity, pseudoplasticity, and flow energy were determined or generated from the measured viscosity data and the influence of PEG molecular weight on these parameters was analyzed statistically and discussed. These studies will help establish an understanding of the advantages of PEG on rheology for the injection molding feedstock.
2. Experimental Commercial purity alumina powder (Japan, Showa Denko, AL-160-SG4) was used in this study. The average particle size was 0.6 m and specific surface area was 0.41 m2 kg−1 . A multi-component binder system was used to prepare the alumina feedstock. The binders used in the experiment are listed in Table 1. To understand the effect of PEG molecular weight on rheological behavior of alumina injection molding feedstocks, different PEG molecular weights range from 1K to 20K were used, respectively, as the major binder. For these binders, the major portion consisted of PEGs (PEG1K,
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Table 1 The characterization of polymeric binder used in this study Binder
Mw
Source
Density (g cm−3 )
PEG PEG PEG PEG
1K 1.5K 4K 20K
Merck Merck Merck Merck
1.16 1.17 1.21 1.22
Allied Merck
0.93 0.94
PE wax SA
Table 2 The compositions of binder system employed in this study for Al2 O3 powder Feedstock
Binder (45 vol.%)
Mixing temperature (◦ C)
A B C D
PEG1K/PE wax/SA PEG1.5K/PE wax/SA PEG4K/PE wax/SA PEG20K/PE wax/SA
90 90 100 110
1.5K, 4K, 20K), the backbone was polyethylene wax (PE wax) for good strength during debinding, and SA was used for improving flow ability. The total alumina powder content was 55 vol.%, and the remaining 45 vol.% consisted of the aforementioned polymers with a weight ratio of PEGs:PE wax:SA = 65:30:5. Table 2 illustrates the compositions of binder systems used in this study. Six feedstocks were prepared by using a sigma-type blade kneader having a rotation frequency of 50 rpm. The alumina powder was initially added into the kneader and preheated at 100 ◦ C for 30 min in order to achieve the uniform temperature distribution. The binders were subsequently added and mixed for 90 min. Granules were obtained by continuously rotating the blade during cooling from 100 to 50 ◦ C. Viscosity of the feedstocks was measured in a Rosand capillary rheometer (RH-14), using the standard procedure with temperature control of ±0.5 ◦ C, the schematic diagram of capillary viscometer is shown in Fig. 1. The pressure drop across the length of the die was measured using a pressure transducer situated adjacent to the die entrance. The piston velocity of the rheometer was varied in order to obtain different shear rates and the corresponding pressure drops were measured to calculate the shear stress. Shear stress divided by shear rate gives the apparent viscosity.
3. Results and discussion 3.1. Yield stress Fig. 2 shows the shear stresses of the alumina feedstocks with different PEG molecular weights at 90 ◦ C for different shear rates, where shear stress increased with increasing
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following equation [19]: τ = τy + µp γ
Fig. 1. Schematic diagram of capillary viscometer.
(2)
where µp is the plastic viscosity. The yield stress τ y can be evaluated from the intercept value of the τ –γ for each feedstock as shown in Table 3. µp values are also listed in Table 3 and become larger with increasing PEG molecular weight. The results indicate that the feedstock containing high molecular weight PEG shows a higher yield stress compared to which a low molecular weight PEG was used as the major binder. Since the yield stress can be considered as the minimum force required to make a relative movement between particle assemblies, the greater value of the yield stress could be considered as a result of the lower fluidity of the higher PEG molecular weight. In addition, it is interesting to note that the yield stresses for feedstocks A and B were negative within the limitation of experimental error. The method cannot, therefore, measure the yield stress and the implication of the results is that, for the feedstocks A and B, yield stress is very low at 90 ◦ C. It was observed during rheological measurements that the A and B feedstocks showed a very low viscosity at 90 ◦ C, even they could flow without force induced. The low τ y values confirm this and could be a drawback as they flowed into the mold cavity during injection molding. 3.2. Power-law index It is clear that τy τ from Fig. 2 and therefore, Eq. (1) could be rewritten as τ = Kγ n
Fig. 2. Apparent shear stress versus apparent shear rate graphs for various feedstocks at 90 ◦ C.
shear rate. The results indicate that τ versus γ plot shows a linear relationship with correlation coefficients greater than 0.96 for all the mixtures. Therefore, these mixtures show Bingham-like behavior, which can be expressed by the
(3)
Eq. (3) has been widely used to correlate the data of shear stress to shear rate for pseudoplastic and dilatant fluids, which is known as the power-law equation. The exponent n of the power-law index indicates the shear sensitivity. Smaller n of feedstock indicates a higher shear sensitivity and more pseudoplastic behavior of the feedstocks. Some molding defects such as jetting are associated with small n, i.e., higher shear sensitivity. The mathematical significance of n can be more clearly obtained from the logarithmic form of the above power-law equation: log10 τ = log10 k + n log10 γ
(4)
Table 3 Yield stress, plastic viscosity, fluidity, activation energy for viscous flow of the feedstocks used in the study Feedstocks
A B C D
Rheological parameters τ y (kPa) (90 ◦ C)
µp (Pa) (90 ◦ C)
Fluidity, 1/η (×10−3 Pa−1 s−1 ) (110 ◦ C, γ = 300 s−1 )
Activation energy, Eη (kJ mol−1 ) (γ = 300 s−1 )
– – 16.76 29.68
67.03 74.11 100.53 128.49
68.26 56.56 15.10 9.17
69.21 64.98 51.82 50.22
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Fig. 3. Variation of apparent shear stress with apparent shear rate for feedstock D at different temperatures.
For a given temperature, n is the slope of the τ and γ curve plotted on log axes. Figs. 3 and 4 show the log τ –log γ curves of feedstocks D and A at a working temperature range from 70 to 130 ◦ C. The results show that the shear stress decreased with increasing the working temperature. In addition, the temperature effect on the decrease of shear stress is more evident for the feedstock A. Fig. 5, comparing the shear stress for feedstocks used in this study at 110◦ C, indicates that the shear stress of feedstocks increased as the molecular weight of PEG increased.
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The exponent n represents the shear sensitivity and can be calculated from the slope of the curves in Figs. 3 and 4. It may be of considerable interest if the index n can be expressed as a function of temperature and Fig. 6 shows the resulting curves for feedstocks used in this study. The results show that the n values of feedstocks C and D were smaller than 1 and fall between 0.41 and 0.74 for all the working temperatures, which shows the flow behavior of feedstocks C and D obeys the pseudoplastic fluid, and the change of n value is small. However, for the feedstocks A and B, the results indicate that the n values were larger than 1 for temperatures above 80 ◦ C and the change of n value was larger apparently than that of feedstocks C and D. It reveals that feedstock with PEG1K and PEG1.5K owned a dilatant behavior in which separation of binder and powder could occur when the working temperatures were greater than 80 ◦ C. In addition, it can be seen that as the temperature increased, the index n decreased for feedstocks C and D, however, for feedstocks A and B, the index n increased with increasing temperature. It seems to show the inconsistent results, nevertheless, if we consider the relationship between the apparent viscosity (η) and power-law index n as follows: τ Kγ n η= = = kγ n−1 (5) γ γ It is evident that the value of |n − 1| represent the sensitivity of viscosity to shear rate. The relationship between |n − 1| and temperature for feedstocks studied is plotted in Fig. 7. The results indicate that the value of |n − 1| increased with increasing the temperature for all feedstocks,
Fig. 4. Apparent shear rate against apparent shear stress of feedstock A at different temperatures.
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Fig. 5. Apparent shear stress as a function of apparent shear rate for various feedstocks at 110 ◦ C.
which means that the higher the temperature, the higher the sensitivity of viscosity to shear rate. Since the flow behavior of the feedstock under shear is dependent on the hydrodynamic interaction between the particles and the molten binder, and the viscosity of the molten binder also affects the particle mobility in the molten binder. A decrease in binder viscosity due to temperature rise may induce the increase of the particle mobility, and therefore, the sensitivity of viscosity to shear rate increased with increasing the temperature.
3.3. Effect of shear rate on viscosity The effect of temperature and shear rate on the viscosity of feedstock D is shown in Fig. 8. Feedstock D with PEG20K apparently exhibited pseudoplastic flow behavior and the shear viscosity decreased with increasing the shear rate for all the working temperatures. The decrease in viscosity with increasing shear rate indicates particle (or binder molecule) orientation and ordering with flow, and may reflect an improved homogeneity. In addition, it has been
Fig. 6. Relationships between power-law index n and temperature for various feedstocks.
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Fig. 7. Relationships between |n − 1| and temperature for various feedstocks used in this study.
suggested that for ceramic injection molding, the shear rates can vary from 100 to 1000 s−1 and the flow rate during molding required a viscosity less than 1000 Pa s [20,21]. Viscosity of feedstock D shown in Fig. 8 matched the request. Accompanying the decrease in the PEG molecular weight, from 20K to 1K, the flow behavior changed apparently. The effect of PEG molecular weight on the shear viscosity of feedstocks at 110 ◦ C as shown in Fig. 9 indicates that shear viscosity increased with increasing PEG molecular weight. The viscosities of all feedstocks were smaller than 1000 Pa s which matched the request for injection molding. However, the fluidity was necessary but insufficient criterion for
ceramic injection molding feedstocks. Accompanying the decrease of the PEG molecular weight, the fluid behavior changed from pseudoplastic to dilatant behavior at 110 ◦ C. It is worthy to note that the viscosity of the feedstocks with PEG1K and 1.5K had a minimum at 200 S−1 , followed by an upward trend with further increase in shear rate. This in turn may be a result of possible dissociation occurring between the binder and the powder particles when the binder was sheared away from their surface. Initially, the particles in the feedstock formed agglomerates or partially ordered regions prior to shear. At high shear rates the particles dilated (increase in volume) as they slid past one another,
Fig. 8. Apparent shear viscosity versus apparent shear rate for feedstock D at different temperatures.
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Fig. 9. Effects of temperature and shear rate on the flow characteristics of various feedstocks at 110 ◦ C.
thereby consuming energy and increasing the viscosity. The critical level of shear rate may well be the point at which particles came into contact with one another. 3.4. Temperature dependence of viscosity Fig. 10 shows the viscosity results of feedstock A with PEG1K over a range of shear rate for temperatures from 50 to 120 ◦ C. On the whole, the flow behavior of feedstock A at 50 and 60 ◦ C obeyed the pseudoplastic flow. However, at a low shear rate 200 s−1 , the viscosity of feedstock A was 1021 Pa s at 50 ◦ C and was thus above the previously
suggested [20,21] limit of 1000 Pa s. In addition, the viscosity of feedstock A did not change apparently with shear rate at 70 and 80 ◦ C, which was analogous to Newtonian fluid. When the temperature was larger than 80 ◦ C, although the viscosity of feedstocks A was smaller than 1000 Pa s for all the measured shear rate, however, the viscosity of feedstock A owned a dilatant behavior and they were rather unstable. As we mentioned above in Section 3.1, the particle mobility in the molten binders was affected by the viscosity of molten binders. A decrease in binder viscosity due to temperature rise may induce an increment of interparticle
Fig. 10. Apparent shear viscosity versus apparent shear rate for feedstock A at different temperatures.
W.-W. Yang et al. / Materials Chemistry and Physics 78 (2002) 416–424
interaction. The viscous force (or hydrodynamic interaction) was comparatively lower than the interparticle interaction when the binder became less viscous at some critical temperatures. Under such condition, a weakly bonded particle network may be developed and caused a viscosity increase. This formation of particle network suggests some degrees of instability of the feedstock as shown in Fig. 10. In addition to affecting the controllability of viscosity within a molding machine by controlling the temperature of barrel, nozzle and mold, the temperature dependence of viscosity may have an effect on the response of the material to the sudden non-uniform cooling within the cavity. For example, during the molding stage, the feedstock was forced into the mold where it immediately began to cool. If the cooling was accompanied by a rapid increase in the viscosity, the result may be incomplete filling the mold and introduced cracking or porosity in molded parts. Therefore, a low temperature dependence was desired to minimize problems arising from fluctuating molding temperature; thereby minimizing stress concentration, cracks, and shape distortion The value of flow activation energy Eη represents the influence of temperature on the viscosity of the feedstock, as expressed by Eq. (6), is an important parameter for
injection molding Eη η = η0 exp RT
423
(6)
where R is the gas constant, T the temperature and η0 the reference viscosity. Taking nature logarithm at both sides, Eq. (7) was obtained Eη 1 ln η = ln η0 + (7) R T With a shear rate of 300 s−1 , which fell in the normal range of shear rates for injection molding of CIM feedstocks, by plotting ln η against the reciprocal of temperature as shown in Fig. 11, the activation energies of viscous flow could be calculated and are given in Table 3. The activation energies in Table 3 could cast some lights on the nature of polymer blend. The results indicate that the activation energy of feedstocks decreased with increasing PEG molecular weight. The lowest activation energy, 50.22 kJ mol−1 , was established for feedstock D, indicating that the sensitivity of its viscosity to temperature was the lowest. This feedstock could thus be injection molded in a relatively wide
Fig. 11. Correlation of apparent shear viscosity and temperature for feedstocks: (a) A, (b) B, (c) C, (d) D at shear rate of 300 s−1 .
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temperature range. In addition, the highest activation energy was 69.21 kJ mol−1 for feedstock A. A high Eη value indicates a drastic viscosity increase upon cooling, and thus feedstock A required a more accurate temperature control during injection molding. Otherwise, mold temperature distribution will cause non-uniform flow, which induced internal stresses.
4. Conclusion The rheological behavior of alumina–PEG injectionmolded feedstocks has been investigated in terms of PEG molecular weights and working temperatures (50–130 ◦ C), over a wide range of shear rate. The results reveals that the feedstock containing high molecular weight PEG as the major binder leads to a higher yield stress and shear stress. The relative viscosity of feedstocks with PEG binder system was small which shows good fluidity and the viscosity was decreased with increasing both temperature and shear rate. However, when temperature was above 90 ◦ C, the fluidity of feedstocks with PEG1K and PEG1.5K was too high to catch powder. It may induce possible dissociation occurring between the binder and the powder particles when the binder was sheared away from their surface. With respect to the dependence of viscosity on temperature, experimental results indicate that the activation energy of feedstock decreased with increasing PEG molecular weight. The lowest activation energy, 50.22 kJ mol−1 , was established for feedstock D, indicating that the sensitivity of its viscosity to temperature was the lowest. The highest activation energy was 69.21 kJ mol−1 for feedstock A, which indicates a more drastic viscosity increase upon cooling, and thus required a more accurate temperature control during injection molding. Otherwise, mold temperature distribution will cause non-uniform flow that induced internal stresses. Based on the above results, although feedstock D containing PEG20K as the binder has the lowest fluidity, however, it possessed viscosities smaller than 103 Pa s for all working temperatures and the feedstocks all show pseudoplastic behavior with n values in the range 0.41–0.66, which would be accepted for injection molding. In addition, the PEG20K should have a stronger adhesion to powder than the other lower molecular weight PEG, giving a more excellent flow stability; therefore, feedstock D with PEG20K shows a lower temperature dependence of viscosity in the temperature range just below the nozzle temperature. It had the best general rheological properties and was most suitable for injection molding.
Acknowledgements The authors wish to thank the National Science Council of Taiwan, ROC, for their support under the project (NSC-87-2216-E-006-042).
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Effects of PEG molecular weights on rheological behavior of alumina injection molding feedstocks Wei-Wen Yang, Kai-Yun Yang, Min-Hsiung Hon∗ Department of Materials Science and Engineering (Mat32), National Cheng Kung University, Tainan, Taiwan Received 16 October 2001; received in revised form 19 March 2002; accepted 8 April 2002
Abstract The rheological behaviors of alumina injection molding feedstocks containing polyethylene glycol (PEG) binders having different molecular weights were analyzed using capillary viscometer. The results indicate that the feedstock containing larger molecular weight PEG shows a higher yield stress and shear stress. The relative viscosity of feedstocks with PEG binder system is small, which show a good fluidity, and the viscosity decreases with increasing both temperature and shear rate. However, when temperature is above 90 ◦ C, the fluidity of feedstocks with PEG1K and PEG1.5K is too high to catch powder, which may induce dissociation occurring between the binder and the powder particles. Based on the results, feedstock D containing PEG20K as the binder has the lowest fluidity, however, it possesses viscosities smaller than 103 Pa s for all working temperatures. The feedstocks all show pseudoplastic behavior with n value in the range 0.41–0.66, which would be accepted for injection molding. In addition, feedstock D with PEG20K shows a lower temperature dependence of viscosity in the temperature range just below the nozzle temperature. It has the best rheological properties and is most suitable for injection molding. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Power-law index; Injection molding; Rheological behavior; Polyethylene glycol; Molecular weight
1. Introduction
fluid that shows quasi-plastic behavior with a yield stress τ y , it should obey the expression:
Injection molding for ceramic feedstocks containing binders that impart flow during processing is an attractive method for near-net and complex shape production of engineering products [1–5]. The feedstocks that consists of the ceramic powder and together with the binders are first injected into a shape forming mold cavity. Subsequently, the binders are removed before sintering the ceramic. The mold injection stage, which determines the shape of the green part, represents a critical step in the PIM process. Mold filling with the PIM feedstock is dependent on viscous flow of the mixture into the die cavity, and this requires specific rheological characteristics [6,7]. The steady flow of melt feedstock and the filling of the mold is a key feature for successful molding. Initially, for successful molding, the ceramic–binder mixtures should have either Bingham or pseudoplastic flow characteristics, since increasing shear rates produce lower viscosities that will assist mold filling [8]. However, for the
τ − τy = Kγ n
∗ Corresponding author. Tel./fax: +886-6-2380208. E-mail address: [email protected] (M.-H. Hon).
(1)
Here τ and γ represent the shear stress and the shear rate, respectively. K is the consistency coefficient which is a constant related to the flow characteristics of a real fluid, and n is the power-law exponent which is defined as flow behavior index of a fluid. For Bingham or pseudoplastic like flow behavior n < 1, for a Newtonian fluid n = 1. If n > 1 the mixtures will be dilatant and result in the separation of the binders from the ceramic powders. It is clear that the binder is the key that provides the rheological properties and determines whether the resulting feedstock can be injection molded without introducing defects. Many different powder and binder systems have been used for PIM. The most widely applied system is polymer/wax system such as mixture of polypropylene, paraffin wax, and stearic acid (SA) or polyethylene [9–11]. The advantages claimed for waxes are the low viscosity and superior wetting characteristics. Wax is the major portion of the binder to lower the viscosity of feedstocks. The thermoplastic polymer such as polypropylene or polyethylene, acts as a backbone material to give the strength of system in
0254-0584/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 2 ) 0 0 2 0 3 - 1
W.-W. Yang et al. / Materials Chemistry and Physics 78 (2002) 416–424
the green state and offers the general rheological properties required. SA is commonly used as a surfactant that helps the binder wet the powder particles and promotes flow. Many problems are associated with using these polymer/wax systems such as low green strength and very narrow processing windows [12]. Most of the organic solvents frequently adopted in solvent debinding are flammable, carcinogenic and environmentally unacceptable. Additionally, the green compacts soften in these debinding solvents and expensive machined debinding substrates are necessary if any shape retention is to be achieved [13]. From these considerations and an environmental point of view, polyethylene glycols (PEGs) are used to eliminate the use of unsound solvents to modify the pattern of debinding in alumina injection molding, as they are soluble in water [12,14]. The unique characteristics of PEG is water soluble and thermoplastic. In addition, they are very safe chemicals and are used quite extensively in food industry; permission was obtained from the local water authorities to dump the water/PEG containing solvents into the drain after debinding [12]. In view of the literatures, many publications have reported useful results concerning the influence of binder composition on the rheological properties of wax-based feedstock [15–17]. However, the rheological behavior of alumina injection molding feedstock with PEG binder system has not been extensively studied. Owing to the PEG molecular weight has considerable effect on the debinding behavior of the specimen according to our previous investigation [18], the main objective of this research is to characterize in detail the effects of PEG molecular weights on rheological behavior of alumina injection molding feedstock. The flow properties of all feedstocks were measured in a capillary viscometer over a wide range of shear rate and working temperature. The corresponding rheological parameters such as fluidity, pseudoplasticity, and flow energy were determined or generated from the measured viscosity data and the influence of PEG molecular weight on these parameters was analyzed statistically and discussed. These studies will help establish an understanding of the advantages of PEG on rheology for the injection molding feedstock.
2. Experimental Commercial purity alumina powder (Japan, Showa Denko, AL-160-SG4) was used in this study. The average particle size was 0.6 m and specific surface area was 0.41 m2 kg−1 . A multi-component binder system was used to prepare the alumina feedstock. The binders used in the experiment are listed in Table 1. To understand the effect of PEG molecular weight on rheological behavior of alumina injection molding feedstocks, different PEG molecular weights range from 1K to 20K were used, respectively, as the major binder. For these binders, the major portion consisted of PEGs (PEG1K,
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Table 1 The characterization of polymeric binder used in this study Binder
Mw
Source
Density (g cm−3 )
PEG PEG PEG PEG
1K 1.5K 4K 20K
Merck Merck Merck Merck
1.16 1.17 1.21 1.22
Allied Merck
0.93 0.94
PE wax SA
Table 2 The compositions of binder system employed in this study for Al2 O3 powder Feedstock
Binder (45 vol.%)
Mixing temperature (◦ C)
A B C D
PEG1K/PE wax/SA PEG1.5K/PE wax/SA PEG4K/PE wax/SA PEG20K/PE wax/SA
90 90 100 110
1.5K, 4K, 20K), the backbone was polyethylene wax (PE wax) for good strength during debinding, and SA was used for improving flow ability. The total alumina powder content was 55 vol.%, and the remaining 45 vol.% consisted of the aforementioned polymers with a weight ratio of PEGs:PE wax:SA = 65:30:5. Table 2 illustrates the compositions of binder systems used in this study. Six feedstocks were prepared by using a sigma-type blade kneader having a rotation frequency of 50 rpm. The alumina powder was initially added into the kneader and preheated at 100 ◦ C for 30 min in order to achieve the uniform temperature distribution. The binders were subsequently added and mixed for 90 min. Granules were obtained by continuously rotating the blade during cooling from 100 to 50 ◦ C. Viscosity of the feedstocks was measured in a Rosand capillary rheometer (RH-14), using the standard procedure with temperature control of ±0.5 ◦ C, the schematic diagram of capillary viscometer is shown in Fig. 1. The pressure drop across the length of the die was measured using a pressure transducer situated adjacent to the die entrance. The piston velocity of the rheometer was varied in order to obtain different shear rates and the corresponding pressure drops were measured to calculate the shear stress. Shear stress divided by shear rate gives the apparent viscosity.
3. Results and discussion 3.1. Yield stress Fig. 2 shows the shear stresses of the alumina feedstocks with different PEG molecular weights at 90 ◦ C for different shear rates, where shear stress increased with increasing
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following equation [19]: τ = τy + µp γ
Fig. 1. Schematic diagram of capillary viscometer.
(2)
where µp is the plastic viscosity. The yield stress τ y can be evaluated from the intercept value of the τ –γ for each feedstock as shown in Table 3. µp values are also listed in Table 3 and become larger with increasing PEG molecular weight. The results indicate that the feedstock containing high molecular weight PEG shows a higher yield stress compared to which a low molecular weight PEG was used as the major binder. Since the yield stress can be considered as the minimum force required to make a relative movement between particle assemblies, the greater value of the yield stress could be considered as a result of the lower fluidity of the higher PEG molecular weight. In addition, it is interesting to note that the yield stresses for feedstocks A and B were negative within the limitation of experimental error. The method cannot, therefore, measure the yield stress and the implication of the results is that, for the feedstocks A and B, yield stress is very low at 90 ◦ C. It was observed during rheological measurements that the A and B feedstocks showed a very low viscosity at 90 ◦ C, even they could flow without force induced. The low τ y values confirm this and could be a drawback as they flowed into the mold cavity during injection molding. 3.2. Power-law index It is clear that τy τ from Fig. 2 and therefore, Eq. (1) could be rewritten as τ = Kγ n
Fig. 2. Apparent shear stress versus apparent shear rate graphs for various feedstocks at 90 ◦ C.
shear rate. The results indicate that τ versus γ plot shows a linear relationship with correlation coefficients greater than 0.96 for all the mixtures. Therefore, these mixtures show Bingham-like behavior, which can be expressed by the
(3)
Eq. (3) has been widely used to correlate the data of shear stress to shear rate for pseudoplastic and dilatant fluids, which is known as the power-law equation. The exponent n of the power-law index indicates the shear sensitivity. Smaller n of feedstock indicates a higher shear sensitivity and more pseudoplastic behavior of the feedstocks. Some molding defects such as jetting are associated with small n, i.e., higher shear sensitivity. The mathematical significance of n can be more clearly obtained from the logarithmic form of the above power-law equation: log10 τ = log10 k + n log10 γ
(4)
Table 3 Yield stress, plastic viscosity, fluidity, activation energy for viscous flow of the feedstocks used in the study Feedstocks
A B C D
Rheological parameters τ y (kPa) (90 ◦ C)
µp (Pa) (90 ◦ C)
Fluidity, 1/η (×10−3 Pa−1 s−1 ) (110 ◦ C, γ = 300 s−1 )
Activation energy, Eη (kJ mol−1 ) (γ = 300 s−1 )
– – 16.76 29.68
67.03 74.11 100.53 128.49
68.26 56.56 15.10 9.17
69.21 64.98 51.82 50.22
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Fig. 3. Variation of apparent shear stress with apparent shear rate for feedstock D at different temperatures.
For a given temperature, n is the slope of the τ and γ curve plotted on log axes. Figs. 3 and 4 show the log τ –log γ curves of feedstocks D and A at a working temperature range from 70 to 130 ◦ C. The results show that the shear stress decreased with increasing the working temperature. In addition, the temperature effect on the decrease of shear stress is more evident for the feedstock A. Fig. 5, comparing the shear stress for feedstocks used in this study at 110◦ C, indicates that the shear stress of feedstocks increased as the molecular weight of PEG increased.
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The exponent n represents the shear sensitivity and can be calculated from the slope of the curves in Figs. 3 and 4. It may be of considerable interest if the index n can be expressed as a function of temperature and Fig. 6 shows the resulting curves for feedstocks used in this study. The results show that the n values of feedstocks C and D were smaller than 1 and fall between 0.41 and 0.74 for all the working temperatures, which shows the flow behavior of feedstocks C and D obeys the pseudoplastic fluid, and the change of n value is small. However, for the feedstocks A and B, the results indicate that the n values were larger than 1 for temperatures above 80 ◦ C and the change of n value was larger apparently than that of feedstocks C and D. It reveals that feedstock with PEG1K and PEG1.5K owned a dilatant behavior in which separation of binder and powder could occur when the working temperatures were greater than 80 ◦ C. In addition, it can be seen that as the temperature increased, the index n decreased for feedstocks C and D, however, for feedstocks A and B, the index n increased with increasing temperature. It seems to show the inconsistent results, nevertheless, if we consider the relationship between the apparent viscosity (η) and power-law index n as follows: τ Kγ n η= = = kγ n−1 (5) γ γ It is evident that the value of |n − 1| represent the sensitivity of viscosity to shear rate. The relationship between |n − 1| and temperature for feedstocks studied is plotted in Fig. 7. The results indicate that the value of |n − 1| increased with increasing the temperature for all feedstocks,
Fig. 4. Apparent shear rate against apparent shear stress of feedstock A at different temperatures.
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Fig. 5. Apparent shear stress as a function of apparent shear rate for various feedstocks at 110 ◦ C.
which means that the higher the temperature, the higher the sensitivity of viscosity to shear rate. Since the flow behavior of the feedstock under shear is dependent on the hydrodynamic interaction between the particles and the molten binder, and the viscosity of the molten binder also affects the particle mobility in the molten binder. A decrease in binder viscosity due to temperature rise may induce the increase of the particle mobility, and therefore, the sensitivity of viscosity to shear rate increased with increasing the temperature.
3.3. Effect of shear rate on viscosity The effect of temperature and shear rate on the viscosity of feedstock D is shown in Fig. 8. Feedstock D with PEG20K apparently exhibited pseudoplastic flow behavior and the shear viscosity decreased with increasing the shear rate for all the working temperatures. The decrease in viscosity with increasing shear rate indicates particle (or binder molecule) orientation and ordering with flow, and may reflect an improved homogeneity. In addition, it has been
Fig. 6. Relationships between power-law index n and temperature for various feedstocks.
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Fig. 7. Relationships between |n − 1| and temperature for various feedstocks used in this study.
suggested that for ceramic injection molding, the shear rates can vary from 100 to 1000 s−1 and the flow rate during molding required a viscosity less than 1000 Pa s [20,21]. Viscosity of feedstock D shown in Fig. 8 matched the request. Accompanying the decrease in the PEG molecular weight, from 20K to 1K, the flow behavior changed apparently. The effect of PEG molecular weight on the shear viscosity of feedstocks at 110 ◦ C as shown in Fig. 9 indicates that shear viscosity increased with increasing PEG molecular weight. The viscosities of all feedstocks were smaller than 1000 Pa s which matched the request for injection molding. However, the fluidity was necessary but insufficient criterion for
ceramic injection molding feedstocks. Accompanying the decrease of the PEG molecular weight, the fluid behavior changed from pseudoplastic to dilatant behavior at 110 ◦ C. It is worthy to note that the viscosity of the feedstocks with PEG1K and 1.5K had a minimum at 200 S−1 , followed by an upward trend with further increase in shear rate. This in turn may be a result of possible dissociation occurring between the binder and the powder particles when the binder was sheared away from their surface. Initially, the particles in the feedstock formed agglomerates or partially ordered regions prior to shear. At high shear rates the particles dilated (increase in volume) as they slid past one another,
Fig. 8. Apparent shear viscosity versus apparent shear rate for feedstock D at different temperatures.
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Fig. 9. Effects of temperature and shear rate on the flow characteristics of various feedstocks at 110 ◦ C.
thereby consuming energy and increasing the viscosity. The critical level of shear rate may well be the point at which particles came into contact with one another. 3.4. Temperature dependence of viscosity Fig. 10 shows the viscosity results of feedstock A with PEG1K over a range of shear rate for temperatures from 50 to 120 ◦ C. On the whole, the flow behavior of feedstock A at 50 and 60 ◦ C obeyed the pseudoplastic flow. However, at a low shear rate 200 s−1 , the viscosity of feedstock A was 1021 Pa s at 50 ◦ C and was thus above the previously
suggested [20,21] limit of 1000 Pa s. In addition, the viscosity of feedstock A did not change apparently with shear rate at 70 and 80 ◦ C, which was analogous to Newtonian fluid. When the temperature was larger than 80 ◦ C, although the viscosity of feedstocks A was smaller than 1000 Pa s for all the measured shear rate, however, the viscosity of feedstock A owned a dilatant behavior and they were rather unstable. As we mentioned above in Section 3.1, the particle mobility in the molten binders was affected by the viscosity of molten binders. A decrease in binder viscosity due to temperature rise may induce an increment of interparticle
Fig. 10. Apparent shear viscosity versus apparent shear rate for feedstock A at different temperatures.
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interaction. The viscous force (or hydrodynamic interaction) was comparatively lower than the interparticle interaction when the binder became less viscous at some critical temperatures. Under such condition, a weakly bonded particle network may be developed and caused a viscosity increase. This formation of particle network suggests some degrees of instability of the feedstock as shown in Fig. 10. In addition to affecting the controllability of viscosity within a molding machine by controlling the temperature of barrel, nozzle and mold, the temperature dependence of viscosity may have an effect on the response of the material to the sudden non-uniform cooling within the cavity. For example, during the molding stage, the feedstock was forced into the mold where it immediately began to cool. If the cooling was accompanied by a rapid increase in the viscosity, the result may be incomplete filling the mold and introduced cracking or porosity in molded parts. Therefore, a low temperature dependence was desired to minimize problems arising from fluctuating molding temperature; thereby minimizing stress concentration, cracks, and shape distortion The value of flow activation energy Eη represents the influence of temperature on the viscosity of the feedstock, as expressed by Eq. (6), is an important parameter for
injection molding Eη η = η0 exp RT
423
(6)
where R is the gas constant, T the temperature and η0 the reference viscosity. Taking nature logarithm at both sides, Eq. (7) was obtained Eη 1 ln η = ln η0 + (7) R T With a shear rate of 300 s−1 , which fell in the normal range of shear rates for injection molding of CIM feedstocks, by plotting ln η against the reciprocal of temperature as shown in Fig. 11, the activation energies of viscous flow could be calculated and are given in Table 3. The activation energies in Table 3 could cast some lights on the nature of polymer blend. The results indicate that the activation energy of feedstocks decreased with increasing PEG molecular weight. The lowest activation energy, 50.22 kJ mol−1 , was established for feedstock D, indicating that the sensitivity of its viscosity to temperature was the lowest. This feedstock could thus be injection molded in a relatively wide
Fig. 11. Correlation of apparent shear viscosity and temperature for feedstocks: (a) A, (b) B, (c) C, (d) D at shear rate of 300 s−1 .
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temperature range. In addition, the highest activation energy was 69.21 kJ mol−1 for feedstock A. A high Eη value indicates a drastic viscosity increase upon cooling, and thus feedstock A required a more accurate temperature control during injection molding. Otherwise, mold temperature distribution will cause non-uniform flow, which induced internal stresses.
4. Conclusion The rheological behavior of alumina–PEG injectionmolded feedstocks has been investigated in terms of PEG molecular weights and working temperatures (50–130 ◦ C), over a wide range of shear rate. The results reveals that the feedstock containing high molecular weight PEG as the major binder leads to a higher yield stress and shear stress. The relative viscosity of feedstocks with PEG binder system was small which shows good fluidity and the viscosity was decreased with increasing both temperature and shear rate. However, when temperature was above 90 ◦ C, the fluidity of feedstocks with PEG1K and PEG1.5K was too high to catch powder. It may induce possible dissociation occurring between the binder and the powder particles when the binder was sheared away from their surface. With respect to the dependence of viscosity on temperature, experimental results indicate that the activation energy of feedstock decreased with increasing PEG molecular weight. The lowest activation energy, 50.22 kJ mol−1 , was established for feedstock D, indicating that the sensitivity of its viscosity to temperature was the lowest. The highest activation energy was 69.21 kJ mol−1 for feedstock A, which indicates a more drastic viscosity increase upon cooling, and thus required a more accurate temperature control during injection molding. Otherwise, mold temperature distribution will cause non-uniform flow that induced internal stresses. Based on the above results, although feedstock D containing PEG20K as the binder has the lowest fluidity, however, it possessed viscosities smaller than 103 Pa s for all working temperatures and the feedstocks all show pseudoplastic behavior with n values in the range 0.41–0.66, which would be accepted for injection molding. In addition, the PEG20K should have a stronger adhesion to powder than the other lower molecular weight PEG, giving a more excellent flow stability; therefore, feedstock D with PEG20K shows a lower temperature dependence of viscosity in the temperature range just below the nozzle temperature. It had the best general rheological properties and was most suitable for injection molding.
Acknowledgements The authors wish to thank the National Science Council of Taiwan, ROC, for their support under the project (NSC-87-2216-E-006-042).
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