Langmuir 1990,6, 3-6 (University of Utrecht, Netherlands) discussed smallangle scattering experiments to determine the microstructure of dispersions undergoing steady simple-shear flow, Th. F. Tadros (ICI, U.K.) gave an overview of the use of viscoelastic measurements in studying interactions in concentrated dispersions, C. J. van Oss (State University of New York a t Buffalo) gave an account of the different forces responsible for stability in concentrated dispersions with emphasis on acid-base interactions, C. Pidgeon (Purdue University) discussed the preparation of multilayered vesicles by reverse-phase evaporation and their use in separations, S. Nakai (University of British Columbia) described proteins in emulsion formation pertinent to the food industry and their effect on aggregation and gelation, and P. H. Teware (Norton Co., MA)
3
discussed colloidal and rheological properties of concentrated ceramic slurries. Finally, we have included a paper on concentrated dispersions as observed by dynamic light scattering by W. van Megen, who was unable to attend the meeting.
Bruce J. Marlow Department of Chemistry University of Massachusetts Amherst, Massachusetts 01003 Charles F. Zukoski Department of Chemical Engineering University of Illinois Urbana, Illinois 61801
Rheological Study of Concentrated Dispersions in Binary Liquids? P. S. Leung* and E. D. Goddard Union Carbide Corp., Specialty Chemicals Division, Tarrytown Technical Center, Tarrytown, New York 10591 Received August 31, 1988. I n Final Form: April 27, 1989 Rheological data for concentrated dispersions of particles in polyethers of different molecular weight are presented and analyzed by using Eiler’s maximum packing volume fraction concept. While the dispersion medium may affect the degree of dispersibility, the theoretical maximum packing volume fraction is ultimately governed by properties of the particles. For a given packing volume fraction, the viscosity of a dispersion must be a function of the medium viscosity. A binary liquid medium can be used to furnish desirable viscosity and chemical characteristics of the dispersion. However, the viscosity of the binary polymeric liquid system cannot be predicted by the Kendall logarithmic summation equation. A modified predictive analysis, based on critical “hole” size, is presented, with examples.
Introduction In many applications, it is desirable to have a suspension of high particle concentration but with low suspension viscosity to facilitate processing. If there is no interaction between the particles and the suspending medium, the viscosity of the suspension will depend on the particle concentration, shape, size, and size distribution and on the viscosity of the medium. Hence it may be beneficial to use a low-viscosity medium provided such a medium gives other satisfactory physical and chemical properties, such as volatility, suspendability, and stability, etc. This paper provides results of a study of some of these effects and includes the use of binary polymeric liquids. The predictive viscosity of binary polymeric liquids is also analyzed. In addition, results obtained by using a model polyether suspension have been further evaluated in a filled urethane foam system.
Theory Eyring and Reel developed a quantitative theory of viscosity based on molecular relaxation processes. In their Presented at the symposium on “Rheology of Concentrated Dispersions”, Third Chemical Congress of North America, Toronto, June 5-10, 1988. (1) Ree, T.; Eyring, H.J. Appl. Phys. 1955, 26, 793.
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approach, viscosity is a summation of component terms with different rate constants, the Newtonian component corresponding to infinite shear rate. In this region, many systems can be considered as showing “Newtonian” behavior. In treating the viscosity of solutions or suspensions, it is convenient to “remove” the contribution of the medium by expressing the viscosity in relative form, viz., as qr. For spherical particles at low concentration, Einstein2 stated that
+
qr = q / q o = 1 2.54 (1) where qo is the viscosity of the liquid medium, q is the viscosity of the dilute suspension, and 4 is the particle volume fraction. The equation implies that the relative viscosity is only dependent on the volume fraction 4. Mooney3 developed the following equation for more concentrated dispersions of spheres, introducing p the “packing factor”, whose value approximates the inverse of the maximum random packing fraction of spheres. Typical values of p are between 1.3 and 1.9: qr = exp[(2.54)/(1- p 4 ) l (2) The treatment assumes that specific particle-particle inter(2) Einstein,A. Ann Phys. 1911, 34, 519. (3) Mooney, M. J. J.Colloid Sci. 1951, 6, 162.
0 1990 American Chemical Society
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Langmuir, Vol. 6, No. 1, 1990
Leung and Goddard
% = [1 + M 4 / 4 J / ( l - 4/4JI2 It can be rearranged to give
-
20,
action is absent, and thus the viscosity is “Newtonian“. The equation developed by Eiler4 is of the form
I
(3)
(ar1’2- I ) / $ = k/& + 1/b#d%1’2 - 111
(4) The value of @-, the apparent maximum packing fraction, can be derived from the slope of a plot of (qr’/2 1)/4 vs (qr1j2- 1). It is a function of the size and shape of the particles. Furthermore, one can deduce that, as 4 0, the equation reduces to Einstein’s equation; k is uniquely related to Einstein’s constant and depends on particle shape. In many applications, an initially liquid suspension is processed to produce a solid composite. Kerner developed an equation in which the modulus of the composite has a dependence on the volume fraction of the filler in a way similar to the dependence of the viscosity of the liquid suspension on this same parameter. Chong’ showed that the Eiler equation has utility in this respect as applied to the modulus of filled cross-linked and amorphous viscoelastic materials. Thus, the properties of the solid composite produced from its dispersion precusor can be partly predicted by the dispersion viscosity.
-
0
Results Figure 1 shows the relative viscosity of suspensions of aluminum trihydrate (ATH) particles in four homologous polyethers of different molecular weight (ranging (4) Eiler, H. Kolloid-2. 2. Polym. 1941, 97,313. (5) Chong, J. S.; Christriansen, E. B.; Bear, A. D. J . Appl. Polym. Sci. 1971, 15,2007. ( 6 ) Kulkarni, R. D.; Leung, P. S.; Goddard, E. D. Colloids Surf. 1982, 5, 321.
(7) Saunders, J. H.; Frisch, K. C. Polyurethanes Chemistry and Technology;R.E.Krieger: 1978.
30
20
40
50
Volume Percent
Figure 1. Relative viscosity of suspensions of aluminum trihydrate particles in four homologous polyethers of different molecular weight.
Experimental Section A Haake Rotovisco RV-3 was used to study the viscosity of suspensions a t 25 OC a t a shear rate sufficiently high (400 s-l) to essentially overcome particle-particle interactions where the shear stress vs shear rate plot became linear. A description of the viscometer can be found in a previous publication? In d i e d systems, where Newtonian behavior can be expected, we used a Cannon-Fenske viscometer to obtain the viscosity. The dispersions were prepared by adding the powder in the dispersion medium and mixing with a high-shear Cowles mixer made by Hockmeyer Equipment Corp. until uniform (-5 min). The urethane foam samples were made by using the specified polyethers and 10% excess of toluene diisocyanate (TDI). Three parts of water, based on the total formulation, were included.‘ The so-called indentation load deflection (ILD) was obtained by using Instron equipment. A 15 X 15 X 4 in. thick foam sample was compressed to 60% of its thickness, and the load (psi) was recorded. Tear strength was also measured by using the Instron with a 6 X 1 X 1 in. sample presplit at one end to a 1in. depth. Aluminum trihydrate (A) grade C331 was obtained from Alcoa Corp. Scanning electron micrography showed that the average particle size was 7 pm with a small level of agglomerates. Other particles used included calcium carbonate (B) from Thompson and Whiteman (size 2 pm), dicalcium phosphate (C) from Monsanto (size 10 pm), and walnut shell flour (D) from Agrashell Inc. (irregular mass, over 10 pm in size). The dispersion media, polypropylene glycol polyethers, were obtained from Union Carbide Corp. The molecular weight can be found in the corresponding figures. Poly(dimethylsi1oxanes) of different viscosity, which we used, are products of Union Carbide Corp.
10
04
0
1
qr
2 ’/2-1
3
4
Figure 2. Eiler plots of the same systems presented in Figure 1.
10
PD /
9
A
: l y 21
04
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
8
0
7r”2-l
Figure 3. Eiler plot of suspensions of four different particles (see text) in a polyether with MW 2600.
from 450 to 3000) and viscosity. This plot shows that the data fall onto a master curve indicating ideal relative viscosity behavior which does not depend on the molecular weight or viscosity of the medium. Figure 2 shows an Eiler plot for the same systems. Here we again see the line fits the data from all four systems. This result is reasonable, since all four systems contain the same particles &e., the shape and the packing would be the same), and the liquid media have similar chemical characteristics. On the other hand, if we change the particles but use the same liquid carrier, the data cannot fit a master line, as indicated in Figure 3. The data set for each type of particle can fit a line of different slope which reflects the packing, size, and shape of the particles. Although in the Eiler plot, which uses a function involving the relative viscosity, the data fall on a master line, the absolute viscosities of the suspensions are significantly different because of the differences in viscosity of the liquid media. The approach of lowering
Langmuir, Val. 6, No. 1, 1990 5
Concentrated Dispersions in Binary Liquids
the viscosity of a particular suspension by replacing the liquid with a similar one of lower viscosity may be acceptable, provided other properties remain satisfactory. There is, however, another approach affording formulating flexibility that is provided by the use of mixtures of liquids rather than a single liquid. It turns out that there is no really satisfactory theory for the viscosity of binary mixtures. Kendall’ derived an equation of fluidity (f) for ideal liquids of very similar nature. His approach was based on the dependence of fluidity upon the activation free energy, viz.
500
Exp-By Mole % /
loot
0
f = ( V d ( h N A d exp[-(XIAGl* ) + X2AG2*)/RTl (5) Here NAvis Avagadro’s number, AG* is activation free energy for the activated jump process of viscosity (related to Eyring’s mechanism), h is Planck’s constant, and X, and X, are mole fractions. The equation is subject to a limiting assumption that V,, the “molar volume” of the mixture, is not very different from that of the individual components. In a homologous or closely resembling series of polymers, segments of similar length should have close values of “molar volume”. The equation then simplifies to log f = Xi log f i
+ Xz log f 2
.
I
Theo>eticol
20
60
40
80
100 B
%E
A
Figure 4. Composite viscosity of a binary polyether mixture A and B vs mole or weight fraction. Polyether A has a molecular weight of 1000 and B of 2600. 1000
8 +I 6
a u
Q
._ 3 5
(6)
so that
0
A Theoretical
A
0 Experimental
loo/
x,
log 9 = log 9, + x2 1% 1 2 (7) Our experience has been that, for polymeric liquids of different molecular weight, the above equation gives large deviations from the experimental values. We found, however, that if X, and X,are expressed as weight fractions rather than mole fractions, the calculated result is much more consistent with that observed. It is recognized that in dealing with a mixture of components of significantly different molecular weight the use of mole fraction to express a concentration ratio can have drastic consequences. However, the success of using weight fractions in this activation model would mean the moieties responsible for the jump mechanism have the same molecular weight. It should, however, be pointed out here that the responsible moiety may not necessarily be the monomeric unit of the polymer but, rather, a segment of similar length. Using weight fractions is not without theoretical basis. Eyring’s treatment” of viscosity utilized the concept of the free energy of activated jumps to “vacant holes”. We submit that in this approach the whole polymer molecule should not (need not) be considered as jumping into a vacant hole, but rather a portion of the molecule could be involved at a particular time. This is consistent with the critical free volume per molecule concept of Doolittle.” With this interpretation, the calculation of “mole fraction” should not be based on the molecular weight of the whole molecule. As a consequence, if the molecules of a binary mixture are of sufficiently high molecular weight that both molecules are larger than the hole, their “jump molecular weight” would be similar and be determined by the size of the hole. In the cases studied here, the effective mole fraction would then be given by the weight fraction. We recognize that in a mixture comprising a high molecular weight liquid with a very low molecular liquid, the weight fraction approach again would (8) Kendall, J. Meddel. Vetenskapsakad. Nobelinst. 1913,2, 25.
(9) Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rate Processess; McGraw-Hill: New York, 1941; p 501. (10) Eyring, H. J. Chem. Phys. 1936,4, 283. (11) Doolittle, A. K.;Doolittle, D. B. J.Appl. Phys. 1957, 28, 901.
1 1000
0
1
1 E4 MW of the Lower MW Component
:5
Figure 5. Composite viscosity of a binary poly(dimethylsi1oxane) (10 wt 70 of MW 6 3 000 and 90 wt % of a lower MW) vs molecular weight of the lower molecular weight component.
Table I. Comparison of Viscosity of Liquids and Compression Modulus and Tear Strength of Composite Foams ~
~~
50
parts ATH in 100 parts of
50% A/50% B
B”
275
520
1.8 1.35
1.25 0.85
liquid medium viscosity, CPat 25 “C 60% ILD,b psi tear strength, lb/in. “ A polyether, MW 1OOO; B Indentation load at 60% deflection.
polyether,
MW
2600.
not apply. Figure 4 shows a plot of composite viscosity vs mole or weight fraction. The molecular weights of the individual polyether components are lo00 and 2600. When we assign different values to X (from 0 to 11, the theoretical values of the mixture viscosity are given by the solid lines. It is seen that the experimental data when expressed by weight fraction fit the theoretical curve almost perfectly, whereas there are significant departures when mole fractions are used. Furthermore, the actual viscosity of the mixture is lower than the arithmetic mean of the individual components (a line connecting the 0% and 100% points). This concept is further illustrated in Figure 5, where the viscosity of a mixture of 10% silicone with molecular weight of 63000 and 90% silicone oil with lower molecular weight is plotted against the molecular weight of the lower molecular weight component. It is seen that the calculated and experimental values are close when components have high molecular weight. However, if the molecular weight of one of the components is too low, the experimental value deviates from the theorectical calculation based on eq 7 with X values as weight fractions. This may be interpreted as indicating that, when the molecular weight of one of the component is
Langmuir 1990, 6, 6-14
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lower than the size of the “vacancy”,the molecular weight of the jump segments from the two components would be different. Thus, weight fraction cannot be used in the formulation in the limit of low molecular weight. Furthermore, in that limit, there would be no unique molal volume that could be used in the Kendall model. As an example of the approach of using a liquid mixture to facilitate the processing of a suspension, we have used a binary mixture of polyethers for making filled urethane foams containing a high level of aluminum trihydrate (ATH). Standard additions of isocyanate and catalyst were included in the formulation. Table I shows a comparison of the viscosity of the liquids and the com-
pression modulus and tear strength of the respective composite foams. It is seen that while the mixture gives low viscosity, it has superior properties. It must stressed that such benefits may not necessarily always be realized. The results will depend on the chemical nature and the reactivity of the individual components. Our purpose here is to show that a further degree of flexibility is possible in balancing the properties of the final composites and the viscosity of the liquid suspension employed to make them, a feature which could be of significant importance in processing. Registry No. ATH, 76566-01-3.
Materials and Mechanisms in Electrorheologyt H. Block,* J. P. Kelly, A. Qin,$ and T. Watson Centre for Molecular Electronics, School of Industrial Science, Cranfield Institute of Technology, Cranfield, Bedford, MK43 OAL, U.K. Received December 13, 1988. I n Final Form: April 20, 1989 The phenomenon of electrorheology is discussed in relation to possible mechanisms involving polarization of dispersions in flow. Data relating such polarization during flow are presented, and comparisons between electrorheological activity and dielectric properties are made. The importance of the rate of polarization as well as its magnitude is stressed. How such considerations led to electrorheological fluids based on dispersed semiconducting polymers as an alternative to traditional water containing polyelectrolytes is discussed, and some of the dielectric and electrorheological properties of these new electrorheological fluids are described.
Introduction Electrorheology (ER) is the term applied to the phenomenon in which the fluidity of liquids is modified by the application of electric fields. The ER fluids discussed here all comprise dispersions of solid particulates within an insulating oil, which under activating fields exhibit enhanced shear stresses (a) including in most cases the development of a static yield stress (uo); they become Bingham bodies under field. Some but by no means all the aspects of the mechanism by which the ER effect is manifest are understood, but there is a t present no satisfactory, quantifying theory for ER. ER thus presents a phenomenon which, on scientific grounds, is deserving of study. However, this is not the only reason why researchers have shown an interest in ER. Since its discovery,’p2 it has been recognized to have great potential in a number of hydraulic and robotic applications including heavyduty ones such as electric clutches and dampers in motor vehicles. Thus, the magnitude of the excess fieldinduced stresses that are achievable with fluids presently available is of order kilopascals for fields of order kilovolts per millimeter. There are, however, still problems to be solved before ER systems find extensive commercial applications. One
’
Presented at the symposium on “Rheology of Concentrated Dispersions”, Third Chemical Congress of North America, Toronto, June 5-10, 1988. Fudan University, Shanghai, People’s Republic of China. (1) Winslow, W. M. U S . Patent 2 417 850, 1947. (2) Winslow, W. M. J . A p p l . Phys. 1949, 20, 1137.
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of these, the apparent requirement that for optimum stress development the dispersed particles had to be wet, has recently been o ~ e r c o m e and ~ ’ ~ provides an example of how improvements in the understanding of the ER mechanism can lead to advancements in fluid design. Moist fluids are limited to a temperature range somewhere between -20 and 70 “C. It is also suspected that the presence of water may cause some of the conduction in such ER fluids, although the recently developed anhydrous fluids also show undesirable levels of conductance. Other improvements in fluids, particularly an increase in the developed stresses under field, would be highly desirable, but whether this is fundamentally possible is not known because of the lack of a firm theoretical foundation for the phenomenon. Solution of many of these problems and the development of better ER fluids do depend on improving our understanding of how the phenomenon depends upon the properties of the materials which make up ER fluids. It is therefore surprising that while there has been some research into the application of ER and there have been many patents describing various fluid formulations, little appears to have been undertaken to study the physics of the phenomenon. Many of the facts known about ER fluids were already recognized by Winslow1S2 over 40 years ago. As well as the observation that wet particulates were most active, he reported, among other factors, that the yield stress was proportional to the square of the field strength ( E ) , (3) Block, H.; Kelly, J. P. US.Patent 4 687 589, 1987. (4) Block, H.; Kelly, J. P. Proc. IEE Colloq. 1985, 14, 1
1990 American Chemical Society
