24
Langmuir 1990, 6, 24-27
above forms of the Bingham equation indicate, good results will be obtained by ignoring the existence of structure entirely after yield and assuming the plastic viscosity is that of the suspension with no applied field. V. Conclusion The origin of the success of the Bingham constitutive equation for correlating the steady-shear rheological data of ER suspension lies in its capture of the importance of the rupture of polarization-induced suspension structures. These structures, which take the form of crosslinked chains and columns of particles spanning the electrode gap in a quiescent suspension, rupture when strained past a limiting value, allowing the suspension to flow. Here we have presented a calculation of the magnitude of the effective yield stress in ER suspensions subject to a continuous rate of deformation. While the particle distribution model used in estimating the strength of the solid is extremely simple, the resulting calculations nonetheless capture the magnitude and scaling behavior of the yield stress and critical strain observed experimentally. To further determine the effect of the residual structure on the suspension’s flow properties after continuous deformation has been achieved, a continuum model was developed incorporating our observations of the coexistence of regions behaving like an elastic solid (where polarization forces dominate) and regions behaving like a viscous fluid (where hydrodynamic forces dominate). In developing this model, some sort of suspension structure again had to be assumed, and a general volume fraction profile across the electrode gap was chosen to account for rearrangement of the fibrous structure after rupture. Balancing polarization and viscous forces a t the interface between the solid and fluid regions, and choosing a
volume fraction and field strength dependent yield stress for the solid, the flow behavior of an ER suspension over a range of field strengths, shear rates, and volume fractions was captured. The exponents extracted from this study suggest again the yield stress is controlled by polarization forces. The essential result of the shear zone model is that it predicts the observed flow properties but displays a weak sensitivity to the details of the solid structure degradation. Indeed, our results suggest that once a substantial gap has been produced between the solid-like regions the fluid has essentially reached the transition region from constant stress to constant viscosity behavior (Figures 17 and 18). In this region, incremental changes in viscosity with field strength are becoming small. As a consequence, the general features of the response of ER suspensions to combined shear and electric fields are well described by a summation of the two limiting types of flow occurring in the suspension resulting in a Bingham constitutive equation. Predicting the details of this transition will have to include a deeper understanding of the rearrangement of the structure under flow and the suspension mechanics in the fluid-like region sustaining the deformation.
Acknowledgment. We thank L. Marshall and J. W. Goodwin for their helpful discussions and providing access to the viscosity and field strength data gathered by L. Marshall a t Bristol University for her Ph.D. Dissertation. We would like to thank J. J. L. Higdon for helpful discussions and loan of the flow visualization channel. D. Klingenberg gratefully acknowledges the support of the Fannie & John Hertz Foundation. This work was supported by NSF under Grant CBT 86-57749.
Rheological Characteristics of Ceramic Injection-Molding Mixed Beebhas C. Mutsuddy 8667 West Bowling Green, Lancaster, Ohio 43130 Received October 11, 1988. In Final Form: March 29, 1989 This study is concerned with rheological characteristics of ceramic and polymer binder systems for injection molding. The influence of different types of polymers, plasticizing agents, and processing aids was investigated. These mixes were investigated from parallel plate rheometric data. The results indicate that different polymers can be used for injection-molding of ceramic powders by using suitable plasticizer(s) and/or processing aids. The viscosity, i.e., the ability of a mix to flow, can be adjusted with appropriate additives.
Introduction During the past 2o years, the interest in ceramics as high-temperature structural material has grown in the major industrial countries. Components for the hot flow t Presented at the Symposium on ”Rheology of Concentrated Dispersions”, Third Chemical congress of North ~ ~Toronto,~ June 5-10, 1988.
0743-7463/90/2406-0024$Q2.50/0
path of heat engines are being extensively investigated. Shapes for most of these components are extremely complex. Furthermore, the components must meet strict dimension tolerances and maintain very high reliability these camin use, Even so, it is a Drereauisite to ponents in large’numbers a t a competitive cost. The complexity of the components and the need for large quantities the~consideration of, injection molding as ~ dictated i ~ a technologically and economically feasible fabrication 0 1990 American Chemical Society
Rheology of Ceramic Injection-Molding Mixes
Langmuir, Vol. 6, No. 1, 1990 25
Table I. Typical Properties of A16-SG Alumina physical characteristic mean particle size, fim particle size range, fim specific surface area, m2/g tap density, 7' 0 of theoretical
A16-SG alumina
LEGEND 0
0.62
= 57
+= 48 *= 32
8.0-0.1 9.078 28
approach. Successful ceramic injection molding depends on flow properties of a ceramic and polymer binder combination. The flow behavior of such materials is characterized from rheological measurements. This paper presents some experimental data on the rheological behavior of ceramic/polymer binder mix as a function of filler loading and type of polymer used. The polymers chosen in this study are not necessarily the exclusive or the best choice. Still, they are useful in underlining the rheological behavior of highly filled systems.
Experimental Procedure MaterialsSs Alcoa's A16-SG alumina was used in this investigation. The 16-SG alumina is a low-soda, high-purity ultrafine powder. It is a Bayer-processed alumina ground by special milling to the ultimate particle size. The entire study was conducted with a single (20-kg) batch powder which was fully characterized. Typical characteristics of A16-SG alumina are given in Table I. The powder was dried a t 150 "C for 24 h prior to mixing with polymeric binder. A low melting point (140-150 "C) atactic polypropylene and a copolymer of ethylene-vinyl acetate (AC-400) were used as primary binders. A polyethylene-derived wax (BASF-A) was used as flow modifier for atactic polypropylene, and butyl stearate was used as a plasticizer for ethylene-vinyl acetate. A combination of unsaturated fatty acid and phosphate ester was used as a processing aid. The volume fraction of solids was initially estimated from the model presented by Furnas.' I t should be pointed out that the model assumes spherical and noncohesive particles, which is not the case with the particular alumina used in this study. Ceramic powder was mixed with the primary binder and other additives a t 200 "C in a torque rheometer a t 50 rpm using a Sigma mixing head. The mix homogeneity was noted from the torque readouts of the rheometer for each mixture. Rheological Measurements. While there are many techniques that can be used to evaluate the flow behavior and the degree of homogeneity achieved in a given mix, the fastest way is by rheological analysis. Several rheological parameters can be investigated in a variety of experimental modes. Capillary rheometry provides apparent viscosity versus shear rate data which can be used in injection-molding flow analysis. Unfortunately, the high shear rates produced in a capillary rheometer mask the microscopic inhomogeneities that are of interest. This difficulty can be overcome by investigating the low shear rate behavior of the filled systems. The effect of particle migration can be minimized by performing the experiments in a dynamic oscillatory manner rather than in steady shear. The experimental facility consisted of parallel plates, one of which oscillated in a sinusoidal manner at frequencies between IO-' and 10' s-'. The instrument is made by Rheometrics, Inc., and measures dynamic viscosity and modulus as a function of oscillation frequency a t the temperature of interest. In measuring rheological properties with the oscillating plate method, one must be careful in selecting the percent strain used, because the strain is proportional to the total angle to which the plate is turning. In this study, strain versus shear stress was initially tested for a mix. From this test, 0.1% strain was chosen where the stress was independent of strain. Dynamic viscosity (n*) has two components, one real and the other mathematically imaginary: n* = n' - in' n* has shown to be equivalent to the apparent viscosity mea(1) Furnas, C. C. R e p . 1nuest.-US.,Bur. Mines 1928, No. 2894.
3 2
C
r'
F i g u r e 1. Viscosity curves for atactic polypropylene a t various Al6-SG A1,0, filler levels. sured in steady flow (i.e., by a capillary), with dynamic frequency ( w ) equivalent to shear rate (+), and n' is the viscous contribution associated with energy dissipation. n", the elastic component associated with energy storage, is related to the real component of the dynamic shear modulus (G') by the relationship G' = wn" = iG'/w These terms are very sensitive to structural changes of the particle network in the matrix. The presence and breakdown of agglomerates, therefore, is indicated by a n unexpected change in the complex viscosity or real component of the dynamic shear modulus as a function of oscillation frequency. All of the rheological evaluations in this study were performed a t 200 "C. The reproducibility of measuring viscosity was i 2 % for the higher (above 40%) ceramic loading.
Results and Discussions Viscosity of Alumina and Atactic Polypropylene Mixes. A16-SG alumina was mixed in the atactic polypropylene at volume loadings of 32, 48, and 57%. Figure 1 shows the viscosity of different mixes. It is obvious that the viscosity increases by 1 order of magnitude with the addition of alumina powder (56.7 vol 5% ). This particular grade of atactic polypropylene was highly plastic even in the presence of large volume fraction of ceramic, so it was necessary to reduce the plasticity of this polymer by blending with BASF-A wax. The replacement of atactic polypropylene with BASF-A wax does not exhibit much change in viscosity (Figure 2) as compared with the mix containing atactic polypropylene alone as a binder. However, the physical examination of the mix containing BASF-A shows some reduction in plasticity. The addition of processing aids to a mix containing simply A16-SG alumina and atactic polypropylene reduces the viscosity markedly; for example, at a frequency of 10 rad/s, viscosity of the mixes with and without processing aids is 0.75 X lo4 and 0.5 X lo5 P, respectively. Furt h e r m o r e , t h e addition of processing a i d s in the mix containing both atactic polypropylene and BASF-A wax brings the mix viscosity close to the viscosity of pure atactic polypropylene. Viscosity of Alumina and Ethylene-Vinyl Acetate (EVA) Mixes. The viscosity profile in Figure 3 of alumina-EVA mix is significantly different from alumina-atactic polypropylene, particularly a t shear rates approaching 100 s-l, where the viscosity of the aluminaEVA is almost close to that of pure EVA. Now the addi-
26 Langmuir, Vol. 6, No. I , 1990
3 3
0
*
10-1
,
'
1
LEGESD
= A-p =A-P = A-? = A-?
- A16 A 1 2 0 3
-
= A-?
8'
Mutsuddy
"
'
A16 A 1 2 0 3 A16 AlgOg A16 A 1 2 0 3
,
-- AIDS
BASF-A
- BASF-A
+
AIDS
x
'i
5
A +
= = =
AC-400 AC-400 AC-400
= A-? = A-P = A-P
-- A16 +
+
LEGEND
A1203 A16 A 1 2 0 3 A16 A 1 2 0 3 A16 A 1 2 0 3
+
+
+
BASF-A AIDS BASF-A
+
AIDS
I
1b
id
w (RAD 6%)
Id
LZGESD z =AC-400
o = A-P A
A.
Figure 2. Viscosity of A16-SG A1,0, and atactic polypropylene (A-P) mixes: 0,100% A-P; 0 , 43.3 vol % A-P + 56.7 vol % A120,; A, 20 V O ~70 A-P + 20 VOI % BASF-A + 60 V O ~Yo A1,0,; +, 38.5 V O ~70 A-P + 57.3 VOI '70 A1,0, + 4.2 V O ~?& of processing aids; X , 17.4 vol % A-P + 16.0 vol YO BASF-A + 58.1 vol YO A1,0, + 8.5 vol % processing aids.
1
.. .
cx8-P
-
-
A16 AlzG3 A16 A1203 416 A1203
T
I
BC'TYL STEARATE BCTYL STEARATE
- AID
Figure 3. Viscosity of A1,0, with ethylene-vinyl acetate (AC400): 0,100% AC-400; O,60 V O ~% A1,0, + 40 V O ~% AC-400; A, 60 vol % A1,0, + 30 vol % AC-400 + 10 vol % butyl streate; +, 58.32 V O ~% A1,0, + 26.7 V O ~% AC-400 + 11.00 V O ~% butyl stearate + 4.0 vol % processing aid. tion of butyl stearate as a plasticizer does not cause any noticeable change in viscosity, while the addition of a processing aid to the mix reduces the viscosity at higher shear rates close to the viscosity of the pure EVA. The viscosity behavior of these systems at low shear rate indicates the presence of a network structure within the melt which could have resulted from the interaction of filler particles, possibly through active sites on their surface. The effect of this structure on the viscosity of these systems is dependent on the dynamic equilibrium between the breakup and re-formation of the filler particle structure. As the shear rate is increased, the equilibrium between breakup and re-formation shifts toward a decreasingly network-like structure, until at relatively high shear rates (greater than 1.0 s-l) breakup of the network is essentially complete. During this process, it is also likely that some of the polymeric binder may tend to migrate and cause an abrupt change in viscosity. The role of polyethylene-derived wax (BASF-A) to atactic polypropylene or use of butyl stearate as a plasticizer
Figure 4. Shear modulus of A16-SG A1,0, with atactic polypropylene mixes: 0,100% A-P; 0 , 43.3 vol % A-P + 56.7 vol % A120,; A, 20 V O ~% A-P + 20 V O ~% BASF-A + 60 V O ~70 A1,0,; +, 38.5 vol % A-P + 57.3 vol 70A1,0, + 4.2 vol 7'0 processing aids; X , 17.4 vol % A-P + 16.0 vol % BASF-A + 58.1 vol % A1,0, + 8.5 vol % processing aids. for ethylene-vinyl acetate is fairly complex, and a clear understanding is not yet being developed. The observations can only be explained on some assumptions: A plasticizer does not as a rule react with the polymer; rather, it forms a mechanical mixture with the polymer wherein molecules of the plasticizers are interspersed between the molecules of the polymer. This causes a change in the intermolecular energy and brings about a stiffness in the structure as is the case with atactic polypropylene-BASFA mixture, while a small dilution of the EVA might have occurred in the presence of butyl stearate. On the other hand, the presence of processing aid(s) has a pronounced influence on the viscosity and uniform dispersion of ceramic powder in these mixes. Functionally, processing aids can provide a multitude of effects, including modification of cohesive forces between the polymer and ceramic powder. These materials combine both polar and nonpolar moieties, usually a small polar head and long nonpolar chain. The polar head is adsorbed on the ceramic powder surface, allowing the long tail to become soluble with the polymer. A t the same time, a macromolecule adsorbed on the particle surface can maintain a uniform dispersion in a concentrated mix by counteracting the van der Waals forces and can minimize particle-particle interactions. Dynamic Shear Modulus. The dynamic shear modulus versus frequency curves for these mixes are shown in Figures 4 and 5. With both polymers, the irregularities in shear modulus are pronounced with mixes that do not contain either plasticizer and/or processing aids. These irregularities indicate that the mix is cot responding as a continuum but that some form of internal rearrangement occurs. It is likely that weakly bonded agglomerates start to break down at oscillatory frequencies above 2 s-'. With addition of BASF-A wax and processing aids in atactic polypropylene mixes, the overall shear modulus drops significantly, while the drop in shear modulus is relatively small with EVA mixes. In addition, the fact that the dynamic shear modulus drops or reduces in slope indicates that the maximum packing fraction has apparently increased, signifying that agglomerated particles have been broken down by the shear imparted by the oscillating plate.
Langmuir, Vol. 6, No. 1, 1990 27
Rheology of Ceramic Injection-Molding Mixes
1'
A
= AC-400 = AC-400
+
= AC-400
0
+
+ + +
o=MONOMODAL o = INFINITE MODEL A16 A1203 A16 A1203 A16 A l z 0 3
+
+
A
BUTYL STEARATE BUTYL STEARATE
10.'
I#
w,(RAD/SEC)
2:00
id
'
S
+
Table 11. Yield Stress Values for Different A16-G Alumina Mixes mix components composition, vol % yield stress, dyn/cm2 56.7 1.5 x 105 A1203 43.3 A-P 48.0 1.2 x lo6
A-P processing aids A1203
A-P BASF-A processing aids
52.0 60.0 20.0 20.0 57.3 38.5 4.2 58.1 17.4 16.0 8.5
LO 02
VOLUME 0 4 FRACTION oe OF SOLIDS 08
Figure 6. Relative viscosity a8 a function of composition.
Id
Figure 5. Shear modulus of A16-SG alumina with ethylenevinyl acetate (AC-400) mixes: 0,100% AC-400, 0,60 vol % A1203 4 0 V O ~% AC-400; A, 60 V O ~% A1203 + 30 V O ~% AC400 + 10 vol % butyl stearate; +, 58.32 vol % A1,03 + 26.7 vol % AC-400 + 11.0 vol % butyl stearate + 4.0 vol % processing aid.
BASF-A
BIMODAL
AID
!
a_
=
6.0 x 104
cosity (viscosity of the mixture over viscosity of the polymer) of a suspension. However, many of the complex phenomena associated with a flowing suspension cannot be explained by using the Newtonian description of a fluid with a relative viscosity. Such suspensions have to be treated as non-Newtonian fluids whose flow properties are influenced by a large number of variables. This study attempts to verify one of the empirical relations proposed to predict the viscosity of multimodal suspensions from the measured viscosity/concentration behavior of its unimodal distribution. The relative viscosity is given by 7, =
6.5 x 103 1.5 x 103
Yield Stress. The characteristic flow behavior of alumina filler with different polymer mixes is then considered from the standpoint of shear stress and shear rate. In general, non-Newtonian materials do not respond linearly to stress and sometimes exhibit a yield stress. The nonlinearity has been attributed to changes in the network structure and alignments within the network structure of the flowing material as the stresses change. This network structure can support a stress before any material flow can be initiated. This finite stress is known as the yield stress. All the alumina polymer mixes studied have shown a yield stress, and the resultant values are presented in Table 11. It is evident from this data that the yield stress is dependent on filler loading. Furthermore, the presence of wax and processing aids has lowered the yield point. The significance of relatively low yield stress lies in the fact that these mixes would require less energy to re-form and move quickly to a fluid state during injection molding. Relative Viscosity and Filler Loading. Various models2* have been proposed to predict the relative vis(2) Einstein, A. Ann. Physik. 1906, 19, 289. (3) Mooney, M. J. Colloid Sci. 1951, 6, 162. (4) Kreiger, I. M.; Dougherty, T. J. Trans. SOC.Rheol. 1959,3, 137-
152. (5) Frankel, N. A.; Acrivo, A. Chem. Eng. Sci. 1967, 22, 847-853. (6) Bartes-Biesel, D.; Acrivo, A. Jnt. J. Multiphase Flow 1973, I , 1-24.
(1- R)-"
where R is the volume fraction of solids and the constant n varies with the particle size distribution of powder. The significant feature of the mix with A16 alumina is that the viscosity is a function of ceramic concentration; however, the viscosity of this mix rises very stiffly as compared to F a r r i ~monomodal '~ viscosity (Figure 6). Applicability of such a model with an ultrafine and high surface area powder such as A16-SG is, therefore, restricted. The limitations might have been associated with the shape of the particles and the physicochemical interaction between the particle surfaces and the polymeric binder ingredients.
Summary In the final analysis, it can be stated that polymers from different chemical makeups can be effectively used for making injection-molded ceramics provided chemically appropriate plasticizer and/or processing aids are being chosen. Rheological behaviors or ceramic injection molding mixes are influenced by the minor additions. However, the physicochemical interaction of these minor additives on filled systems and their rheology are not fully understood. Registry No. Polyethylene, 9002-88-4; AC-400, 24937-78-8; polypropylene, 9003-07-0; butyl stearate, 123-95-5. (7) Farris, R. J. Tram. SOC.Rheol. 1968, 12(2), 281-301. (8) Material Suppliers. A16 SG alumina: Aluminum Company of America, Pittsburgh, PA. Atactic polypropylene:Novamont Corp., 1114 Avenue of the Americas, New York, NY 10036. AC400 EVA Allied Chemical, Special Chemicals Division,P.O. Box 1087R, Morristown, NJ 07960. Butyl stearate: Eastman Kodak Co., Rocheater, NY 14650. BASFA wax: BASF, Wyandotte Corp., 100 Cherry Hill Rd., Parsippany, NJ
07054.
