The electrorheological properties of polyaniline suspensions

The Electrorheological Properties of Polyaniline Suspensions C. J. G O W AND C. F. ZUKOSKI IV ~ Department of Chemical Engineering, University of Illinois, Urbana, Illinois 61801 Received June 8, 1989; accepted August 1, 1989 The electrorheological properties of suspensions containing polyaniline particles in silicon oil are reported for a range of suspension volume fractions, applied field strengths, shear stresses, and particle dielectric constants. Suspension viscosity at a fixed stress is found to increase slowly as the field strength is raised to a value of E*. Over a very narrow field strength range near E* the suspension viscosity is found to increase 106-108 Pa s. At field strengths greater than E*, the suspensions take on solid-like behavior. The scaling of yield stress on volume fraction and field strength is similar to that reported on other systems and the yield stress is found to increase monotonically with particle dielectric constant. © 1990 Academic Press, Inc.

I. INTRODUCTION

found to depend only on volume fraction 4, and Mason number, Mn = nc3"/2eoEo(flE) 2, which is a measure of the relative importance of hydrodynamic shear forces to electric polarization forces acting on particles in the suspension. Here n and nc are the suspension and continuous phase viscosities, e0 is the permittivity of free space, and ec is the dielectric constant of the continuous phase. The shear rate is 3' and E is the applied electric field strength. The particle dipole coefficient,/3, is defined as (ep - E~)/(e v + 2E~) and is a measure of the particle's ability to polarize in the presence of the electric field relative to that of the continuous phase. Marshall et aI. found that for low values of Mn (i.e., high field strengths or low shear rates), ~/nc scales as Mn-1, but for large shear rates n / nc approaches a value of n~ / n~ independent of field strength, where ~ is the high shear viscosity of the suspension in the absence of an electric field. The observed scaling suggests that at low values of 3" or high values of E, large values of n/nc are due to increased interactions between polarized particles. As 3" is raised or E is diminished (Mn increases), shear forces become large enough to overcome the interparticle polarization forces and the suspension begins to behave as with no applied electric field.

The electrorheological (ER) effect is noted for a rapid and reversible change in suspension viscosity upon application of an electric field (1-8) and an accompanying change in the suspension structure where, from an initially random distribution, particles from columns or fibers which span the electrode gap ( 1, 35, 9-11, 19). Suspensions displaying these changes are usually nonaqueous and composed of systems where there is a large dielectric mismatch between the particles and continuous phase ( 1 - 3 ) . Reviews covering the recent literature on the ER effect and its potential applications in stress transfer devices can be found in Refs. (12-17). There is a growing evidence that the dramatic changes in transport and structural properties accompaning the application of the electric field are due to the interaction of polarized particles. For example, Marshall et al. (8) recently analyzed the interparticle forces acting in an ER suspension and concluded that electrified suspension properties were dominated by polarization and viscous forces. For a wide range of field strengths and shear rates, the relative suspension viscosity, n/~c, was 1 To whom all correspondence should be addressed. 175

0021-9797/90 $3.00 Journal of Colloid and Interface Science, Vol. 136, No. 1, April 1990

Copyright © 1990 by Academic Press, Inc. All rights of reproduction in any form reserved.

176

GOW AND ZUKOSKI

Rheological data reported in the literature suggest that a wide variety of ER suspensions display a yield stress ry, which scales as E 2 ( 1, 4, 6). The work of Marshall et al. also supports these findings where they conclude for their system that rync/n~ has a linear dependence on suspension volume fraction. The scaling of the yield stress on E 2 again suggests that at low shear rates, ER suspension rheology is dominated by interactions of polarized particles. The importance of the interaction of polarized particles in ER suspensions has been included in two recent descriptions of ER response which attempt to link interparticle forces, suspension structure, and rheological behavior ( 19, 20). Klingenberg and Zukoski (9, 19) developed models for the yield stress and the continuous shear response of ER suspensions based upon observations that particle strands formed upon application of an electric field behave as elastic solids for small shear strains but yield above a critical strain. The model considers ER suspensions where the only interparticle forces are due to electrical polarization and assumes a simplified suspension structure where single particle chains are aligned with the electric field. By considering only pair interactions, a restoring stress which resists strains perpendicular to the electric field is found to increase to a maximum value with growing strain. The maximum restoring stress is found to scale as ¢~oEc(/3E)2f~,

Ill

where ~ is the volume fraction of solids and fm is the dimensionless maximum restoring force dependent on ~ and ep but not on E or (9, 19). For stresses larger than this maxim u m value, the suspensions are predicted to flow. As a result, the maximum restoring stress is associated with a yield stress. The model predicts that the strain at yielding is independent of field strength. A favorable comparison was found between model predictions and the work of Marshall et al. (8). Adriani and Gast (20) have developed a model for ER suspensions based on the susJournal of Colloid and InterfaceScience, Vol. 136, No. 1, April 1990

pension structure predicted by Hayter and Pynn (37) for polarized particles interacting in an electric field where the static suspension structure is determined by a balance between dipolar and thermal forces. Upon application of an oscillatory rate of strain, this structure is perturbed and the resulting stresses are averaged to determine the suspension viscosity. The analysis of Adriani and Gast is applicable to suspensions of Brownian particles at low field strengths (large Mason numbers) and, due to the linear nature of the analysis, cannot predict a yield stress. Both of the models of Klingenberg and Zukoski and Andriani and Gast attempt to relate details of suspension microstructure to rheological response and are based on polarization interactions between particles being the origin of the ER effect. The magnitude of polarization interactions is governed by the mismatch in particle and solvent polarizabilities. Little work has been reported with which to test these models where particle polarizability is varied as an independent parameter. Uejima (6) studied the effect of water in suspensions of microcrystalline cellulose and found that the ER effect increases with increasing water content until a maximum is reached. The initial increase can be understood in terms of the water increasing particle polarizability (13). Kelly and Block (18 ) have recently reported that the ER effect goes through a maximum as the conductivity of the particles in suspension is increased. Again the initial increase can be attributed to increased polarization interactions. The maximum reported in both studies has not been fully explained. In this paper, we investigate the nature of the yield stress in ER suspensions and the effect of particle dielectric constant on ER response. For this study, particles composed of polyaniline were chosen as this polymer can be doped from a conducting to an insulating state using simple protonic acids. This allows for a change in particle dielectric constant and conductivity while keeping all other particle properties and suspension characteristics the same.

POLYANILINE

SUSPENSION

The basic aniline polymer is blue in color, and has a low conductivity ( 10-9 S / c m ) . The protonated form of the polymer is green in color and exhibits metallic properties (conductivities of 10 S / c m have been reported (21-34)). Zuo et al. (31, 32) have recently reported extensive work on the AC conductivity of polyaniline as a function of protonation level. These studies provide a basis with which to compare the electrical and chemical properties of the polyaniline used here. Colloidal dispersions of polyaniline have recently been prepared using a steric stabilizer which is chemically grafted onto the polyaniline particles (33). The dried material was found to have a high conductivity when the solvent was removed. To avoid complications in interpretation of ER data due to the polymeric layer, in this study polyaniline was synthesized in the absence of a stabilizer. Here we report on the ER behavior of suspensions of polyaniline particles with different doping levels. The effects of volume fraction, field strength, and shear stress are considered. For a constant applied stress, we find a dramatic change from fluid-like to solid-like behavior over a narrow range of field strengths and that the field strength required to induce this transition diminishes with increasing particle dielectric constant. Scaling behavior similar to that reported by Marshall et al. (8) is found but discrepancies with the yield stress calculations of Klingenberg and Zukoski (19) are observed. II. E X P E R I M E N T A L

METHODS

Synthesis and Suspension Preparation Polyaniline was synthesized using the method of MacDiarmid et al. (27). Concentrated HC1 (Mallinckrodt) was slowly added to deionized water in a 4.0-liter Erlenmyer flask and placed in an ice bath. Freshly vacuum-distilled aniline (Aldrich) was added to the chilled acid solution and stirred continuously. After the aniline solution reached thermal equilibrium, an aqueous a m m o n i u m peroxydisulfate solution of the same temperature

ELECTRORHEOLOGY

177

was added to the reaction flask. The reaction started within 30 s as noted by the solution turning dark green and was allowed to proceed for 20 h. Initial reactant concentrations were 0.55 M aniline, 0.1 M (NH4)zS208, and 1 M HC1. After the reaction was complete the solution was centrifuged at 3320g for 90 rain. The solids, emerald green in color, were washed by sedimentation and resuspension in deionized water. The sedimentation/decantation process was repeated four times. The solids were then divided into four portions and brought to a volume of 250 ml with deionized water. The pH of the suspensions after the initial washes was 1.6. Aqueous sodium hydroxide was added to bring the pH of the separate bottles to 6, 7, 8, and 9, respectively. The pH was measured and adjusted over a period of days until it remained constant for 24 h. Hydrophobic powders were prepared through a wash procedure in which the samples were centrifuged and washed into an ethanol/water solution, then centrifuged and washed into pure ethanol three times, into a cyclohexane/ethanol solution twice, and then finally, into cyclohexane twice. For the purpose of labeling, the samples will be called P2 (the as-prepared suspension), P6, P7, P8, and P9. After drying by evaporation at room temperature, the samples were ground using a mortar and pestle and placed in a vacuum oven at room temperature until a constant weight was reached. The density of the dry polyaniline, measured using a Quantachrome micropycnometer, was 1.30 + 0.02 g / m l for all four sampies. The particle size was measured using a Horiba Capa-700 particle analyzer. All four samples showed the same distribution with a number average diameter of 0.30 + 0.28 ~zm. Infrared spectra of the polyaniline samples used in this study were compared with spectra of polyaniline reported in the literature. Spectra on samples P2, P6, and P9 all had peaks at the same wavenumbers and agree with the values of Ohira and co-workers (34). Elemental analysis performed on samples P2, P7, P8, Journal of Colloid and Interface Science, Vol. 136, No. 1, April 1990

178

GOW AND ZUKOSKI

and P9 also show the same ratios of C, H, and N as found in the literature (27). For conductivity measurements, pellets of each sample of dry polyaniline (0.05 g) were pressed at 1.8 X 10 7 Pa, coated top and bottom with gold and placed between two electrodes, 0.01 V was applied, and the current was measured. The conductivity was calculated using the surface area and the thickness of each pellet. An H P 4102A low-frequency impedance analyzer was used to determine dielectric constants. Suspensions used for the rheology experiments were 2.5, 5.0, 10.0 and 15.0 wt% polyaniline and were prepared by placing a predetermined mass of polyaniline into a mortar. A predetermined mass of poly(dimethylsiloxane) ( P D M S ) (Petrarch Systems) was then weighed into mortar and the mixture was ground together using a pestle. Mass fractions were converted to volume fractions using the measured density of the dry polyaniline and PDMS (0.95 g c m - 3 ) . The PDMS viscosity was measured to be 0.286 Pa s and the literature value of 2.72 was taken for the PDMS dielectric constant, co.

gram of the rheometer tools is presented in Fig. 1. The bob was grounded through an electrode immersed in the solvent trap while the isolated cup was made hot. A series of calibrations indicated that, over the range of stresses used, the added drag due to the vane produced a negligible contribution to the bob's rotation rate. A continuously variable 3-kV DC power supply was used in all the experiments. The voltage was monitored using a multimeter attached to a one-tenth voltage readout connection on the supply. The current was monitored using a multimeter attached in series to the ground wire of the solvent trap. All the experiments were carried out at room temperature which varied between 18 and 22°C. No appreciable changes in rheological response or suspension conductivity were noted within this temperature range. Viscosity measurements were made using the following procedure. Sufficient suspension was added to the cup so that the top of the bob was covered when it was lowered into place. The zero field strength viscosity was measured for a specific shear stress. The power

Rheometry A Bohlin constant stress rheometer (Bohlin Reologi AB, Lund, Sweden) was used for the electrorheology experiments. The instrument was fitted with a stainless-steel cup (inner diameter 15.4 m m ) and bob (diameter 14 m m ) . The cup consisted of a stainless-steel sleeve in a plastic (Delrin) insulating mount. The bob was fitted with a Delrin uppershaft which insulated it from the rest of the rheometer. As the bob floats on an air bearing, it was necessary to make electrical contact without disturbing the balance of the shaft or adding unnecessary drag. This was accomplished through the use of an aluminium vane attached below the Delrin spacer on the bob. When the bob was lowered into the cup, the vane made contact with a solvent trap containing 1 M a q u e o u s potassium nitrate. A diaJournal of Colloid and Interface Science, Vol. 136, No. 1, April 1990

Co:

Sol

FIG. 1. Diagram of rheometer tool. Electrical contact is made to bob through an electrode immersed in a solvent trap containing 1 M potassium nitrate. The aluminum vane also immersed in electrolyte is attached to the stainless-steel bob through a set screw. The cup consists of a stainless-steel sleeve set in a Delrin holder, Electrical contact is made to the cup through a set screw in the top of the sleeve.

POLYANILINE

SUSPENSION

supply was then set to a specific voltage and after 20 s a constant stress was applied. Typically, the creep compliance was monitored for a time period of 250 s after which the stress was turned off and the recovery compliance was followed for 250 s. At the end of this time, the voltage was turned off and a large shear stress was applied to break up any structure which might have formed and the process was repeated at a different field strength. The field strength was increased in 143 k V / m increments until the region where the suspension changed from fluid-like to solid-like was determined. To investigate the behavior near this critical field strength, 29 k V / m increments were used. Steady-state viscosities were independent of the order in which the field strength was applied. The applied shear stresses ranged from 0.2 to 150 Pa. The field strength range of 0 to 3143 k V / m . III. R E S U L T S

(/t) Particle and Zero Field Strength Suspension Characterization As mentioned earlier, polyaniline can be doped from an insulating to an electrically conducting state by simple protonic acids. Table I summarizes the conductivity and dielectric constants (at 10 Hz) of pressed polyaniline pellets as a function of the pH of the solution with which the polymer had been equilibrated prior to drying. These results compare favor-

TABLE I S a m p l e C o n d u c t i v i t i e s a n d Dielectric C o n s t a n t s Sample P2 P6 P7 P8 P9

o-(S/cm) 6.02 2.13 2.12 6.34 1.47

× X × × X

10 -3 10 -4 10 7 10 -8 10 -9

C

~ (Zuo)b

---

-724 95.0 66.6 22.1

-

-

61.0 21.0

a Dielectric c o n s t a n t m e a s u r e d at 10 H Z . b I n t e r p o l a t e d f r o m t h e values r e p o r t e d b y Z u o et al. (32).

ELECTRORHEOLOGY

179

ably with those of MacDiarmid et al. (25) who did not wash their solids into an organic liquid prior to drying. The eight orders of magnitude range of conductivity upon doping is accompanied with a change in the dielectric constant of the polyaniline. Zuo et al. (32) have recently reported results on the complex impedence of polyaniline samples with DC conductivities in the range studied here. For purposes of comparison, dielectric constants for our samples were calculated by fitting their data to the equation log c = A log a + B,

[2]

where ~ is the dielectric constant at 10 Hz, and is the DC conductivity, and A and B are fitting parameters with values of 0.2937 and 3.938, respectively. The values of the dielectric constant determined in this study are very close to the estimated values obtained by Zuo et al. for samples P8 and P9 giving us confidence in using Eq. [ 2 ] to estimate the dielectric constant of P6 and P7 (Table 1 ). Broad particle size distributions were found for samples P9, P8, and P7 in PDMS. However, little variation was observed between samples and the number average particle diameter was 0.30 + 0.28 #m. Particles with sizes of 100 to 0.1 #m were found in all samples. The broad size distribution is primarily due to the suspension preparation technique. The similarity between the suspensions is supported by the zero field strength viscosities which are substantially the same at a given shear stress (Fig. 2). At 7.5 and 11.4 vol% all the samples exhibited a yield stress. The yield stress was determined by applying successively lower shear stresses until the suspension behaved like an elastic solid (i.e., complete strain recovery when the stress is released) for the time period of the experiment (250 s). Zero field strength yield stress values are given in Table II. The presence of zero field strength yield stress is attributed to the agglomeration and network formation. In this study, we investigate the effects of changing the particle's dielectric properties on Journal of Colloid and Interface Science, Vol. 136, No. 1, April 1990

180

GOW AND ZUKOSKI 0.2 P9P8P7-

0.1~

7.5 V

.~"0.1 8

o

l

%

~

0.05 1.8 Vol%

0.0 0.0

10.0'

2010 Stress (Pa)

30.0

FIG. 2. Zero field strength viscosities for suspensions of polyaniline particles suspended in PDMS at volume fractions of 0.018 and 0.075.

the ER response of a suspension. As a consequence, variations in agglomerate strength with doping level are of concern. For polyaniline particles in PDMS, agglomerate structure and strength are primarily determined by attractive van der Waals interactions which, in turn, are governed by the magnitude of the particle Hamaker constant. A series of flocculation experiments were carried out on aqueous suspensions of polyaniline doped to different levels to determine if large changes in Hamaker constant accompany increased doping levels (35, 36). The experiments were carried out with aqueous dispersions of polyaniline held at the pH to which the polyaniline particles had been equilibrated. Suspensions at the same weight fraction were prepared at several ionic strengths and the degree of floc-

culation was monitored over a 24-h period by following the suspension turbidity. A sudden decrease in the turbidity as the salt concentration was increased was taken as the critical flocculation concentration (CFC). We found the CFC to be 0.02 __+0.005 M for a pH range of 3 to 9 (this corresponds to a range of particle conductivities of 1 0 - 3 10 9 S / c m ). These resuits do not reflect changes in particle surface charge as the electrophoretic mobilities of the samples at an ionic strength of 10 -3 M, (but at equilibrium with different pHs) were essentially constant at +2.5 × 10 -8 m2/V. These qualitative experiments support our theological data in suggesting that the flocculated structure of polyaniline particles in PDMS and the strength of these structures are relatively unaffected by the level of doping (i.e., particle conductivity).

B. Electrorheological Results Typical creep and recovery curves for the polyaniline suspensions are shown in Figs. 3 and 4 for an applied stress of 4 Pa at various field strengths. After 250 s the stress was re-

8000

0 kV/m

0~ 6000 571 kV/rn o c- 4000 E~ Q_ E

~

2000

TABLE II Zero Field Strength Yield Stresses Sample

Volume% solids in suspension

P9 P8 P7 P9

7.5 7.5 7.5 11.4

0

r~ (Pa) 0.5 0.5 1.0 10.0

IIIIll'lll~llll'lll[lllll[[llllllll

o

_+ 0.1 ± 0.1 ± 0.1 ± 2.0

Journal of Colloid and Interface Science, Vol. 136,No. 1, April 1990

lOO

IIIl[lllllllll

eoo

30o

Time

(s)

4oo

50o

FIG. 3. Creep and recovery compliance as a ['unction o f

time after a stress of 4 Pa was applied to a suspension containing sample P8 particles at a volume fraction of 0.018. The creep and recovery curves are shown at zero field strength and 571 k V / m . For this sample E* = 1128 4- 15 k V / m .

POLYANILINE SUSPENSION ELECTRORHEOLOGY 0.04

181

I0 g 30

10 8 10 7

1143 k V / m o

E3_

0.03

10 Po l i

10 6

2 Po

10 5

© o 0.02 co CL

I-

Pa

50 Pa

Pa

P°

1 Po

lO4i

1429 k V / m

10 3.

"~o lo 2i ~ 10

E CO)0.01

1

10-1__, 0.00

10 ~ 2 -

,,,,,IIIIIIJ,,,,,,,IIIIpI*,,II,,,t,~IIIIIII,,,,IT

0

1 O0

200

.300

400

Time (s)

500

0

500

1000

Strength (kV/m)

Field

1500

FIG. 4. Creep and recovery compliance curves for the same suspension and stress as those in Fig. 3 but at higher field strengths. For this suspension E* = 1128 _+ 15 kV/m.

FIG. 6. Viscosity of a suspension containing particles of sample P8 at a volume fraction of 0.075 as a function of field strength at various stresses.

leased and the creep recovery was followed. At low field strengths, the suspensions rapidly reached a steady-state viscosity and showed a small elastic recovery w h e n the stress was released. U n d e r these conditions, the recovery curves show overshoots due to the m o m e n t u m o f the bob (Fig. 3 ). Steady-state viscosities increased slowly with field strength (Fig. 5). A b o v e a critical field strength denoted E*,

the suspensions no longer acquired a steady-

10 8 ,

50 10 ' Po15 Pa

10 71__-

Q,..

2

Pa

J__.~ _=_ ,

,

,

,

,

15 Po

PA

~

,

,

0

,

i

,

500

Field

,

,

,

,

,

,

,

1047

2 103

jjJ

10

~2-

~'

i

"c% 10 2. 0

10

10 Pa

10 5

1°3!

10"1

Pa

10 6

r

1

107:

Pa

Pa

k

10 5. 10 4.

(Figs. 4 - 7 ). T h e creep and recovery c o m p l i a n c e (defined as the strain divided by applied stress) for sample P8 ( 1.8% by v o l u m e at a stress o f 4 Pa) are s h o w n for two field strengths above E * in Fig. 4. A n initial rapid increase in c o m pliance is followed by a region where the corn-

: Pc

10 6;

o

30

state viscosity and behaved like elastic solids

102; .o

1C

>

1

J

10 -1 ,

i

,

,

,

,

1000

,

,

,

,

,

1500

Strength (kV/m)

FIG. 5. Viscosity of a suspension containing particles of sample P9 at a volume fraction of 0.075 as a function of field strength at various stresses.

10 - 2 " 0

200

Field

400

600

800

1000

Strength (kV/m)

FIG. 7. Viscosity of a suspension containing particles of sample P7 at a volume fraction of 0.075 as a function of field strength at various stresses. Journal of Colloid and Interface Science, Vol. 136, No. I, April 1990

182

GOW AND ZUKOSKI

pliance does not change with time. When the stress is released the suspension recovers, but there is not a full recovery. Thus, some irreversible strain occurs during the first j u m p after the stress is applied. Long-time creep compliance studies demonstrated solid-like behavior of the samples above E*. At field strengths of 2 × E*, after an initial jump, the strain did not increase for time periods of 4 ks. At each stress, the suspension viscosity increases by a factor of 3 to 4 as the field strength is raised to just below E*. The dramatic increase in suspension viscosity with small changes in field strength near E* is evident in Figs. 5-7 where changes in viscosity on the order of 10 6 t o 10 8 Pa s occur for a variation in field strength of less than 30 k V / m . All of the suspensions investigated in this study displayed behavior similar to that shown in Figs. 3-7. A sample containing hydrated polymethylacrylate in a chlorinated hydrocarbon as investigated by Marshall et aL (8) showed the same qualitative behavior. For the experiments described above, the voltage was applied before the shear stress. This was the simplest method to ensure reproducible results. For field strengths well above or below E*, steady-state viscosities were found to be independent of the order in which the stress and voltage were applied and steady state was reached within 30 s. For field strengths near E*, however, steady-state viscosities were found to be sensitive to the order of application of field and stress, and to the time interval between applying the field and the stress. Wait times of less than 20 s caused irreproducible and erratic results near E*, while for wait times greater than 20 s, the resuiting steady-state viscosities were reproducible and independent of wait time. The nature of the irrecoverable strain observed in Fig. 4 was explored in experiments where the stress was applied to a sample several times without turning off the electric field. Figure 8 shows the results of a series of creep and recovery curves carried out at 429 and Journal of Colloid and Interface Science,

Vol.

136,

No.

1, April

1990

0.010 429 kV/m 0.008 ~

_

_

0.006 © L 0.004 714 kV/m o oo2

0.000

j

,

i 200

,

, 400

,

, 600

,

E 800

,

i 1000

,

i 1200

'

i 1400

,

, 1600

,

I 1800

, 2000

Time (s) FIG. 8. Strain as a function of time. The suspension consisted of sample P9 at a volume fraction of 0.075. A stress of 4 Pa was applied for 250 s and the sample was then allowed to recover by 250 s. Without changingthe field strength, creep and recoverycyclesof 250-s duration with the stress applied under creep of 4 Pa were then repeated. The response of the suspension at field strengths of 429 and 714 kV/m is shown. For this sample, at a stress of 4 Pa, E* = 343 _+ 15 kV/m.

714 k V / m , respectively, where a stress of 4 Pa was repeatedly applied and released (E* = 343 k V / m at this stress.) On first applying the stress at a field strength of 429 k V / m a strain of approximately 0.9% results. When the stress is released the sample recovers only approximately 0.15%. For subsequent applications of the stress the sample shows a trend toward a strain of 0.12% for both creep and recovery. The same qualitative behavior is observed for a field strength of 714 k V / m where after three applications of the stress, the strains on creep and recovery have the same values of 0.05%. These results suggest that above E*, the suspension structure is capable of sustaining the applied stress. However, application of the stress results in rearrangements of the structure to a more favorable configuration. The resulting "annealed" structure then acts like an elastic solid with the strain on creep being completely recovered when the stress is released. The strain of the suspension at the point of yielding can be estimated from the strain at

POLYANILINE SUSPENSION ELECTRORHEOLOGY the first field strength above the transition from fluid to solid-like b e h a v i o r ( t y p i c a l l y within 15 k V / m o f E * ) . F o r s a m p l e s P7, P8, a n d P9, the strain at yielding was f o u n d to scatter a b o u t a c o n s t a n t value over a stress range o f 0.5-15 Pa ( c o r r e s p o n d i n g to E * values ranging from 2 0 0 - 2 0 0 0 k V / m ) . F o r suspensions containing P7, P8, a n d P9 particles at a v o l u m e fraction o f 0.018, these critical strains were (8.6 + 2.1) X 10 -3, (2.5 + 0.8) X 10 -3, a n d (5.1 4- 1.0) X 10 -3, respectively. W h i l e the scatter is a large fraction o f the average critical strain, no systematic changes were observed as E * increased. These critical strains are smaller t h a n those in the m o d e l o f Klingenberg a n d Z u k o s k i ( 9 ) , b u t s u p p o r t the p r e d i c t i o n t h a t E R suspensions flow a b o v e a field s t r e n g t h - i n d e p e n d e n t strain. T y p i c a l l y in studies o f E R suspensions, a yield stress is defined as the stress where the suspension p r o p e r t i e s change f r o m solid-like to fluid-like at a given field strength. In o u r studies, the s a m e stress is a p p l i e d at several field strengths a n d at E * the suspension takes on solid-like behavior. C o n s e q u e n t l y , in this m o d e o f o p e r a t i o n , the yield stress is the s a m e as the a p p l i e d stress. Y i e l d stresses as a function o f field strength are s u m m a r i z e d in Figs.

102

•

o P9 n P8 • P7 EL_

183

10 3 _

o 1 . 8 VoI% a 335 Vol~ ~ 7.5 Vol~

102-

J / " ./~ /

~

o

a

10 -1

i

10

i

, l l

,

,

o

i l l

102

i

,

i

, , , l l

10

1

4

CriticGI Field Strength (kV/rn) FIG. 10. Summary plot of yield stress as a function of field strength for suspensions containing particles of sample P9 at four volume fractions. Solid lines are calculated from Eq. [3] in the text with r~ taken from Table 2.

9 a n d 10 where, at a given field strength, the yield stress increases with suspension v o l u m e fraction a n d particle dielectric constant. As observed with o t h e r E R suspensions ( 1, 4, 6, 8), the yield stress is f o u n d to scale as [3]

"ry = ]gE m,

where k is a c o n s t a n t a n d m has been f o u n d to t a k e on a range o f values b e t w e e n 1 a n d 3. F o r o u r samples, rn is f o u n d to lie very close to 2 ( T a b l e III).

oo

*'~

* °

°

TABLE III

1Q

Values of the Critical Mason Number .+~ (23 "zz

o= a

1

>-

7.5

10 -1

i 10

i

a

Vol~

i~lJlq 10 2

ao .

a

" 1.8

° Vol~

i

, ,,ll.

o

I 10 3

i

, IJ,~rl 10 4

Criticol Field Strength (kV/m) FIG. 9. Summary plot of yield stress as a function of held strength for suspensions containing particles of samples P7, P8, and P9 at volume fractions of 0.018 and 0.075.

Sample

V o l u m e fraction

ma

Mn*

P7 P7 P8 P8 P9 P9 P9 P9

0.018 0.075 0.018 0.075 0.018 0.038 0.075 0.114

1.92 2.03 1.91 1.80 2.02 2.25 1.56 1.85

0.10 0.67 0.050 0.32 0.035 0.10 0.30 0.29

a Value of the exponent m relating yield stress to field strength in Eq. [2].

Journal of Colloid and Interface Science, Vol. 136, No. I, April 1990

184

GOW AND ZUKOSKI

At low field strengths, suspension response is not well described by Eq. [3] with a constant m for volume fractions is greater than 0.075. This change is due to the colloidal interactions that give rise to a flocculated network (and a yield stress, r,~) at zero field strength. As the applied field strength is increased, the polarization interactions grow and a crossover between a region where colloidal forces dominate to a region where polarization forces dominate is expected. Figures 9 and 10 show that the crossover field strength increases with volume fraction, suggesting that the field strength dependence of the yield stress in the ER suspensions studied here can be approximated by

7"yt = 7"yC+ ]gE m,

[41

where r~ is the total yield stress incorporating both colloidal and field strength dependencies. In Fig. 10, curves showing the applicability of this approximation are shown for sample P9 where ry is the measured zero field yield stress and the values of k and m are extracted from a least-squares fit to the data with E greater than 400 k V / m . The qualitative fit of this approximation may provide an explanation of reports that r t scales with m between 0 and 2 (14). If colloidal interactions dominate, ( k E m / r ~ ) is m u c h less than 1 and the yield stress scales as E ° while, if polarization interactions dominate, ( k E m / r ~ ) is m u c h greater than 1 and the yield stress scales as E 2. As particle conductivity increased, the suspensions began to draw measurable currents. At all volume fractions for suspensions containing sample P9, the current could not be measured with the available equipment, indicating that the current density was less than 10 # A i m 2 for all the field strengths applied. For suspensions containing P6, the current density exceeded 20 A / m 2 when 200 k V / m was applied for all volume fractions investigated. As a consequence of instrumental limitations, no electrorheological data could be collected on this sample. Figure 11 indicates Journal of Colloid and Interface Science, Vol. 136, No. 1, April t 9 9 0

A

E

1 ia

d o310'-1

•

P7

0

~E 10-2. << >, ~c l o-a(D c~ *6 10-4. ~_ = C) lO-s

0

mo

!

!

o ,,

P8

o

o 500

1000

1500

Field Strength (kV/m) FIG. 11. Current density in suspensions consisting of samples P7 and P8 at a volume fraction of 0.018. Current densities upon strain are the circles whereas current densities under recoveryare the squares. A stress of 4 Pa was applied and E* for these suspensions of P7 and P8 were 743 _+ 15 and 1128 _+ 15 kV/m, respectively. Note that the squares and circlescoincide for the highest three field strengths for suspensions containing sample P7.

that the current densities for P7 are m u c h higher than for P8, suggesting that the particles themselves carry current. This is further supported by changes in current density under creep and recovery. U p o n application of the electric field continuous particulate structures are observed to span the electrode gap. If the particles are in electrical contact and conduct, an increase in current-carrying capacity of the suspension would accompany this structural rearrangement. Continuous deformation of the sample produced by application of a stress above the yield stress is known to degrade these structures (9, 19). Consequently, one would expect the current carried by the suspension to drop. As seen in Fig. 11, the current density at low field strengths is larger under recovery (where the structures spanning the electrode gap have reformed) than when the sample is creeping under the applied stress. Above E*, the current densities upon application of the stress are very close to the values observed upon recovery, suggesting that above E * the suspension is capable of sustaining the applied

POLYANILINE

SUSPENSION

stress without rupture of electrode spanning particle structures. IV. D I S C U S S I O N

The behavior of ER suspensions is often described using the Bingham plastic model (6, 8, 10) Tap p = l"]pl"Y -[- Ty,

[5]

where ry is the yield stress, and %1 is the plastic viscosity which is found to equal ~%o,the high shear stress viscosity in the absence of an electric field. Using yield stress values extracted from Figs. 9 and 10, the Bingham model is found to describe our polyaniline suspensions well at low and high shear rates, but underestimates the stress for intermediate values of the shear rate. Klingenberg and Zukoski (9) suggest this is due to the form of the Bingham model which is the sum of two limiting behaviors (i.e., 3' -+ 0 and 7 --~ oo). The crossover zone is not captured by Eq. [ 5 ]. As discussed earlier, the zero field strength rheological behavior of suspensions composed of particles at different doping levels suggests that these suspensions, when at the same volume fraction, differ only in particle dielectric constant and conductivity. As a consequence, comparison of the ER behavior of suspensions studied here can be best characterized in terms of ry. Following the analysis of Marshall et al. (8), the Bingham equation is rewritten as

nl*loo = M n * / M n + 1,

[6]

where the critical Mason number, Mn*, characterizes the magnitude of the yield stress and is defined as Mn* = [ry/2eoEct32E2](~Tc/B~).

[7]

The solid line shown in Fig. 12 was calculated using Eq. [6] and provides an excellent fit to the data. Similar fits were found for all suspensions studied. Values of Mn* for the samples studied here are summarized in Table 3. Due to the nature of the constant stress instrument used in these studies, the middle

ELECTRORHEOLOGY

185

range of Mn values in Fig. 12 cannot be accessed. To gather data in this region a variable shear rate instrument is required. Marshall et al. (8), found Mn* that varied as q5n with n approaching unity. The suspensions studied here have a similar scaling giving an average n value of 1.28 + 0.05 Recently, Klingenberg and Zukoski (9) developed a model for the yield stress of ER suspensions that predicts a field-independent strain above which yield occurs (9). The yield stress from this model is found to scale as shown in Eq. [ 1 ] where values forfm are determined by solving for the force between two polarized particles suspended in a dielectric media using a multipole expansion technique (19). Klingenberg determinedfm out to values of a ( = ~p/ ec) of 15. For larger values, the multipole expansion technique did not converge. However, it is known that as a ~ ~ , j(m ----~ OO.

As mentioned in the Introduction, Eq. [ 1 ] arises from two contributions. The term e0ec/32E2fm accounts primarily for the interaction of pairs of polarized particles while the volume fraction dependence arises from an assumed structure. Supporting this model, Table 3 indicates that the yield stress of the polyaniline suspensions scales very nearly as E 2 above a field strength where polarization forces are capable of overcoming colloidal interactions. The qualitative features of the model are further supported by the field strength independence of the critical strain as described earlier. However, the simplified structure used in the model fails to capture the complicated particle stacking reported in the literature and observed for our samples. As a result, we suggest that the yield stress can be written in the form To = G ( (o )eOec132 E 2 f m,

[81

where G (q~) contains the volume fraction dependence of ro. Substituting r0 for Ty in Eq. [6] and noting that the only other volume fraction dependent variable is n~ suggests that if Journal of Colloidand InterfaceScience, Vol. 136, No. 1, April 1990

186

GOW AND ZUKOSKI 1010

10 9 .

10 8 10 7 °_

10 6,

03 © (.3 10 5. 03 o-~> 10 4. (D >

°-.-I-J

10 3.

c) (b £E

10 2.

10 1

10

-1

q i iiiiii q i 10 -10 10 - 9

i iiiiii

10 1

iiiiiii l_ i IIIIIHI

10 8

I IIIIIMI_ I IIIIIIq_ I IIIIII q_ I lllllH I

10-7

10 6

10 5

10 4

I I

10"3

m.q J i+,n. I i i'm.q I imid 1 0 - 2 10-1 1 10

Mn FIG. 12. Relativeviscosity,definedhere as ~/7+, as a functionof Mason numberfor a suspensioncontaining particles of sample P9 at a volume fraction of 0.018. The solid line was calculated from Eq. [5] using Mn* from Table 4.

G(~)nc/~+(~)~O',

[91

then Mn* can be rewritten as

comparison, his results for fm were fit to the form

fm = C a B Mn* = A4)'~fm,

[10]

where A is a parameter independent of volume fraction, particle polarizability, and field strength. Assuming the form of Mn* in Eq. [ 10] with n = 1.3, we are able to extract values of the term A f m for each sample type. The dimensionless force fm can be determined from the results tabulated in Ref. (9) and from the particle and solvent dielectric constants reported in Table 1. The dielectric constants of samples P7 and P8 are outside the range covered in Klingenberg's calculation. For the sake of Journal of Colloid and Interface Science,

V o l . 1 3 6 , N o . 1, A p r i l 1 9 9 0

[11]

for large a. The results (C = 0.051 and B = 0.369) were used to estimatefm for samples P7 and P8, and the values of A extracted are given in Table 4. The parameter A is expected to reflect suspension structure and multiparticle interactions. If the packing depends only on particle size and shape distributions, A would not be expected to vary between samples P9, P8 and P7. As can be seen, A increases monotonically with a. Accounting for the approximations made in estimating fm for samples P8 and P7 is in-

POLYANILINE SUSPENSION E L E C T R O R H E O L O G Y TABLE IV Values of the Structural Constant A in Eq. [ 10] Sample

Af~°

a

fmb

A

MGZ C P9 P8 P7

0.185 5.47 9.54 20.8

3.18 7.72 22.4 34.9

0.079 0.109 0.162 0.190

2.34 50.2 58.9 109.5

a Values determined from critical Mason number as shown in Eq. [10] with m = 1. b M a x i m u m restoring force calculated from dielectric constants given in Table 1.1 (9). c Data extracted from the paper of Marshall et al. (8).

sufficient to explain the trend in Table 4. fm calculated for sample P8 is not far outside the range of values calculated by Klingenberg (19) and comparison with the results of Marshall et al. (8) shows that A is not independent of particle polarizability. A large quantity of data was taken in these experiments in order that scaling of ~-yon volume fraction and field strength could be reliably determined. The consistency of the scaling of ry on E 2 and M n * on • for all samples (including those of Marshall et al.) suggests that changes in the parameter A are not associated with a particular volume fraction or field strength but are a characteristic of polarized particle interactions. As mentioned above, the scaling behavior of the model of Klingenberg and Zukoski (9) was derived for particles interacting only with nearest neighbors and in a pairwise additive fashion. The increase in yield stress at a rate faster than/32Jm as o~is increased suggests that polarization interactions are stronger than those invisioned in this model. Adriani and Gast (20) provide an analysis where multiparticle interactions are approximately accounted for through effective pair interactions that depend on suspension structure and show that the strength of pair interactions increases as the electrified structure is formed. Multiparticle interactions of this type m a y provide an explanation for the nonlinear dependence of Ty on ~2fm.

187

Kelly and Block (18) recently described work on the ER effect in which a m a x i m u m in the yield stress occurs as the particle conductivity is increased with the m a x i m u m occurring at 10 -7 S / c m . As mentioned earlier, we were unable to achieve an ER effect with sample P6 due to current carrying capacity associated with the solid's high conductivity. In order to obtain data at particle conductivities greater than 10-7 S / c m and volume fractions greater than 0.01, a power supply capable of providing a current greater than 20 A / m 2 at a fixed field strength is required. As our power supply was unable to deliver this current, we were unable to confirm the result of Kelly and Block. V. CONCLUSIONS

Suspensions composed of polyaniline particles in PDMS show a substantial ER response. Through the use of an electrified constant stress rheometer, we find that the transition from fluid to solid-like behavior occurs over a narrow range of field strengths ( + 15 k V / m ) . This transition is noted by a dramatic increase in viscosity and the appearance of solid-like creep and recovery behavior. Yield stresses are found to increase with field strength, volume fraction, and particle dielectric constant. The dependence of the yield stress on volume fraction and field strength is found to be independent of particle type and to follow the trends reported by Marshall et al. (8). A comparison of the data with yield stress predictions of Klingenberg and Zukoski (9) suggests that multiparticle polarization interactions may be important in determining the magnitude of a suspension's ER response. The trends of the data reported here clearly show that yield stresses in ER suspensions increase with disperse phase polarizability. Particle conductivity is identified as a factor limiting the use of highly doped polyaniline samples in ER suspensions. However, the results of this work and those of Marshall et al. (8) demonstrate Journal of Colloid and Interface Science, Vol. 136,No. 1, April 1990

188

GOW AND ZUKOSKI

that suspensions giving large changes in rheological behavior upon application of an electrical field can be achieved using particles with modest values of Eo/~cwhere current densities are low. ACKNOWLEDGMENTS The authors thank L. Marshall and D. J. Klingenberg for their insightful comments. This work was supported by the Amoco Foundation and the National Science Foundation through Grant NSF CBT 86-57749. REFERENCES 1. Winslow, W. M., J. Appl. Phys. 20, 1137 (1949). 2. Klass, D. L., and Martinek, T. W., J. Appl. Phys. 38, 75 (1967). 3. Deinega, Y. F., Popko, K. K., and Kovganich, N. Y., Heat Transfer-Soy. Res. 10, 50 (1978). 4. Klass, D. L., and Martinek, T. W., J. Appl. Phys. 38, 67 (1967). 5. Deinega, Y. F., Inzh. Fiz. Zh. 18, 994 (1970). 6. Uejima, H., JapanJ. Appl. Phys. 11, 319 (1972). 7. Lykov, A. V., Shulman, Z. P., Gorodkin, R. G., and Matsepuro, A. D., Inzh. Fiz. Zh. 18, 979 (1970). 8. Marshall, L., Zukoski, C. F., and Goodwin, J., J. Chem. Soc. Faraday Trans. 1 85, 2785 (1989). 9. Klingenberg, D. J., and Zukoski, C. F., Langmuir, in press. 10. Trapeznikov, A. A., Petrzhik, C. G., and Chertokova, O. A., Kolloidn. Zh. 43, 1134 (1981). 11. Shulman, Z. P., Deinega, Y. F., Gorodkin, R. G., and Matsepuro, A. D., Progress in Heat and Mass Transfer Vol. 4, p. 109. Pergamon, Oxford, 1971. 12. Deinega, Y. F., and Vinogradov, G. V., Rheol. Acta. 23, 636 (1984). 13. Gast, A. P., and Zukoski, C. F., Adv. Colloidlnterface Sci., (1989), in press. 14. Block, H., and Kelly J. P., J. AppL Phys. D 21, 1661 (1988). 15. Shulman, Z. P., Gorodkin, R. G., Korobko, E. V., and Gleb, V. K., J. Non-Newtonian Fluid Mech. 8, 29 (1981). 16. Scott, D., and Yamaguchi, J., J. Automotive Eng. 91, 61 (1983). 17. Scott, D., and Yamaguchi, J., J. Automotive Eng. 91, 75 (1983).

Journalof ColloidandInterfaceScience,Vol. 136,No. 1, April1990

18. Kelly, J. P., and Block, H., presented at 3rd Annual Chemical Congress of North America, Toronto, Canada, 1988. 19. Klingenberg, D. J., Studies on the Steady Shear Behavior of Electrorheological Suspensions, MS thesis, University of Illinois at Urbana--Champaign, 1989. 20. Adriani, P. M., and Gast, A. P., Phys. Fluids31, 2757 (1988). 21. Green, A. G., and Woodhead, A. E., J. Chem. Soc. 97, 2388 (1910). 22. de Surville, R., Jozefowicz, M., Perichon, J. H., and Buvet, R., Electrochim. Acta 13, 1451 (1968). 23. Diaz, A. F., and Logan, J. A., J. Electroanal. Chem. 111, 111 (1980). 24. Kobayashi, T., Yoneyama, H., and Tamura, H., J. ElectroanaL Chem. 161,419 (1984). 25. MacDiarmid, A. G., Chiang, J.-C., Halpern, M., Huang, W.-S., Mu, S.-L., Somasiri, N. L. D., Wu, W., and Yaniger, S. I., MoL Cryst. Liq. Cryst. 121, 173 (1985). 26. Chiang, J.-C., and MacDiarmid, A. G., Synth. Met. 13, 193 (1986). 27. MacDiarmid, A. G., Chiang, J.-C., Richter, A. F., Somasiri, N. L. D., and Epstein, A. J., in Conducting Polymers (L. Alcficer, Ed.), pp. 105-120. Reidel, Dordrecht, 1986. 28. Stafstr6m, S., Br6das, J. L., Epstein, A. J., Woo, H. S., Tanner, D. B., Huang, W.-S., MacDiarmid, A. G., Phys. Rev. Lett. 59, 1464 (1987). 29. Javadi, H. H. S., Angelopoulos, M., MacDiarmid, A. G., and Epstein, A. J., Synth. Met. 26, 1 (1988). 30. Nechtschein, M., Santier, C., Travers, J. P., Chroboczek, J., Alix, A., and Ripert, M., Synth. Met. 18, 311 (1987). 31. Zuo, F., Angelopoulos, M., MacDiarmid, A. G., and Epstein, A. J., Phys. Rev. B 36, 3475 (1987). 32. Zuo, F., Angelopoulos, M., MacDiarmid, A. G., and Epstein, A. J., Phys. Rev. B 39, 3475 (1989). 33. Armes, S. P., and Aldissi, M., private communication. 34. Ohira, M., Sakai, T., Takeuchi, M., Kobayashi, Y., and Tsuji, M., Synth. Met. 18, 347 (1987). 35. Hunter, R. J., Foundations of Colloid Science, Vol. 1. Claredon, Oxford, 1987. 36. Israelachvili, J. N., Intermolecular and Surface Forces. Academic Press, London, 1985. 37. Hayter, J. B., and Pynn, R., Mol. Phys. 53, 1527 (1984).