Two Roles of Nonionic Surfactants on the Electrorheological Response

JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.

183, 568–578 (1996)

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Two Roles of Nonionic Surfactants on the Electrorheological Response YOUNG DAE KIM

DANIEL J. KLINGENBERG 1

AND

Department of Chemical Engineering and Rheology Research Center, University of Wisconsin, Madison, Wisconsin 53706 Received March 18, 1996; accepted June 19, 1996

The influence of three nonionic surfactants (Brij 30, GMO, and GTO) on the electrorheological response of various alumina/silicone oil suspensions is investigated. The dependence of the dynamic yield stress on such variables as surfactant type and concentration, water and ion content, and electric field strength and frequency is reported. The prevalent feature common to all formulations is that the yield stress, t 0 , initially increases with surfactant concentration, passes through a maximum, and then decreases with surfactant concentration. Below the maximum, the yield stress increases quadratically with the field strength, E, while above the maximum, yield stress increases slower than E 2 . The increase in the yield stress with surfactant concentration is due to surfactant-enhanced interfacial polarization, which may arise from increased proton transport via neighboring hydrogen bonds. The nonlinear behavior observed at large surfactant concentrations (i.e., t 0 }/ E 2 ) arises from field-induced phase separation of a surfactant-rich phase as opposed to field-dependent conductivity of a homogeneous continuous phase. q 1996 Academic Press, Inc. Key Words: electrorheology; nonionic surfactants; suspensions; polarization.

1. INTRODUCTION

The electrorheological (ER) response is defined as the dramatic change in rheological properties of a suspension of small particles due to the application of a large electric field transverse to the direction of flow. ER suspensions are typically composed of nonconducting or semiconducting particles dispersed in a nonconducting continuous phase. A large ER effect was first reported by Winslow in 1949 (1), and has been reviewed in several publications (2–8). The simplicity of engineering designs based on ER materials has facilitated the development of specifications for a broad range of devices, such as dampers, clutches, and adaptive structures (2). Although many ER devices have been brought successfully to the prototype stage, and despite much industrial activity in the United States and abroad, the anticipated com1 To whom correspondence should be addressed at Department of Chemical Engineering, University of Wisconsin, 1415 Engineering Drive, Madison, WI 53706. [email protected].

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0021-9797/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.

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mercialization of these devices has yet to be realized. The main limitation of ER technology development is a lack of effective fluids (3, 9). Most applications require fluids that possess a large field-induced yield stress, are stable to settling and irreversible aggregation, are environmentally benign, and draw limited current. Our inability to design such acceptable fluids stems largely from a lack of a fundamental understanding of the mechanisms that control ER behavior. Surfactants are added to ER suspensions for a variety of reasons (1, 4–7, 10–15), and can be used to tailor suspension properties. They are often used to promote colloidal stability, which is necessary to keep particles from irreversibly flocculating, and to control rheological properties in the absence of the electric field. Surfactants can also be used to ‘‘activate’’ suspensions. Some suspensions display little or no ER activity unless a small amount of water or surfactant is added, while other suspensions exhibit a significantly enhanced response with activators present [10–17]. Enhancing ER activity with surfactants offers advantages over other approaches, such as adding water which severely limits the allowable temperature range of operation, promotes corrosion, and increases suspension conductivity and power consumption. Furthermore, additional independent variables (i.e., type and amount of surfactants) give flexibility to designing desired properties that is not possible by simply varying the materials of the disperse and continuous phases. In this paper, the influence of several nonionic surfactants on ER suspension properties is presented. In the following sections, sample preparation and experimental methods are briefly described, followed by a discussion of experimental results. The dependence of the dynamic yield stress on the surfactant type and concentration, particle type, water content, and electric field strength and frequency is presented, along with suspension dielectric properties. At small concentrations, surfactants increase the dynamic yield stress by increasing the particle polarizability via enhanced interfacial polarization. At large surfactant concentrations, a surfactantrich phase is formed, decreasing the yield stress which no longer scales with the square of the electric field strength. The underlying mechanism is similar to that proposed in Refs. (18, 19) in that the yield stress is limited by increased conductance in the interparticle gap. The mechanism pro-

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over molecular sieves (Aldrich, 4- to 8-mesh beads) prior to Brij 30 and water adsorption experiments. Molecular sieves were dried for 7 h under vacuum ( 010 psig) at 1857C before use. Surfactants were used as received.

TABLE 1 Properties and Chemical Compositions of the Activated Alumina Particles [21] Alumina particles Basic pH of 5% aqueous suspension (stirred) Surface area (m2/g) Cl0 (mval/g) Na2O (%) Fe2O3 (% max) SiO2 (% max)

9.5 { 0.3 155 — 0.4 0.02 0.02

Neutral

7.5 { 0.5 155 0.03 0.4 0.02 0.02

Acidic

4.5 { 0.5 155 0.14 0.4 0.02 0.02

posed here differs, however, in that the increased conductance does not arise from a field-dependent continuous phase conductivity, but rather from the field-induced phase separation of a more conducting phase (the conductivity of each phase is independent of field strength). This phenomenon is likely to occur in many ER formulations that contain surfactants. 2. MATERIALS AND METHODS

Suspension Preparation Three different types of activated alumina particles were employed: acidic, neutral, and basic (Aldrich, rp Å 3970 ˚ ). The acidity is adkg/m 3 , average pore diameter Å 58 A justed by washing with dilute mineral acids (presumably HCl) (20). The properties and chemical compositions of these particles are presented in Table 1 (21). The alumina particles were approximately spherical and sieved to obtain diameters in the range of 63–90 mm. Nonionic surfactants investigated were glycerol monooleate (GMO, Chemical Service), glycerol trioleate (GTO, Chemical Service), and Brij 30 (C12H25 (OCH2CH2 )4OH, Aldrich). The particles were used as received (‘‘nondried’’ suspensions), were dried for 3 h under vacuum ( 010 psig) at 587C (‘‘dried’’ suspensions), or were dried for 4 h under vacuum ( 010 psig) at 1607C (‘‘highly dried’’ suspensions). The water contents of the particles were determined by Karl Fisher titration. The results of this analysis are presented in Table 2, along with the water contents of silicone oils and surfactants. Alumina suspensions were prepared by first adding the desired amount of surfactant to silicone oil (SF96, General Electric, hc Å 0.0968 Pars, rc Å 968 kg/m 3 ). The particles were then added to the surfactant solution and stored in a desiccator to minimize contact with air. Suspensions were allowed to equilibrate for at least 24 h before experiments. The silicone oil was used as received for all rheological and dielectric measurements, and stored for more than 1 week

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Rheological Measurements Rheological experiments were performed at 237C on a Bohlin VOR rheometer fitted with parallel plates, and modified for the application of large electric fields (13–15). Potential differences were supplied by a function generator (Stanford Research Systems, Model DS345) and amplified with a Trek amplifier (Model 10/10). Experiments were conducted with an electric field frequency of 500 Hz (except for the frequency sweep experiments), in order to avoid electrode polarization and the heating due to excessive current observed at significantly smaller frequencies. The influence of surfactants on ER activity was determined by their effect on the dynamic yield stress. Samples were placed between the parallel plates and sheared for 1 min at a large shear rate ( ú40 s 01 ) and zero field strength to ensure a uniform particle distribution. The desired electric field was then applied for 1 min with no shear prior to measurements. Rheological measurements were performed by shearing the suspensions at a constant shear rate under the applied electric field, and recording the shear stress transmitted by the suspension. Experiments were performed with decreasing and then increasing shear rates, to obtain plots of shear stress as a function of shear rate. Values for the dynamic yield stress, t 0 , were determined by extrapolating the shear stress–shear rate data to zero shear rate, using data over the range of shear rates 0.01 s 01 õ gh õ 0.1 s 01 . Dielectric and Conductivity Measurements Suspension capacitance and loss were measured using a General Radio GR 1689M RLC Digibridge, which probes TABLE 2 Water Contents of Particles, Silicone Oil, and Surfactants Determined by Karl Fisher Titration Material Nondried neutral alumina Nondried acidic alumina Nondried basic alumina Dried neutral alumina Dried acidic alumina Dried basic alumina Highly dried neutral alumina Dried deionized acidic alumina Silicone oil (SF96) Dried silicone oil (SF96) GMO Brij 30 GTO

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Water content (wt%) 3.47 4.26 1.51 1.20 1.28 1.18 0.53 1.26 0.113 0.065 0.460 0.239 0.022

{ { { { { { { { { { { { {

0.12 0.12 0.12 0.09 0.09 0.09 0.09 0.09 0.003 0.003 0.003 0.003 0.003

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FIG. 1. Yield stress as a function of surfactant concentration for 20 wt% dried neutral alumina suspensions in silicone oil ( fE Å 500 Hz): (a) Brij 30, (b) GMO, and (c) GTO.

frequencies in the range of 12 Hz to 100 kHz, and operates with potential differences in the range of 0.01–1.0 V (rms). A three-terminal, guarded dielectric cell was employed. Suspension dielectric constants and loss tangents were determined for decreasing and increasing field frequencies. The samples’ dc conductivities were measured with a picoammeter (Keithley 4853), with blocking circuitry to allow measurements at large electric field strengths.

yield stress initially increases with surfactant concentration and then passes through a maximum; the surfactant concentration at the maximum is insensitive to the applied electric field strength E, especially at large field strengths, but does depend on the surfactant type. Brij 30 and GMO increase the yield stress much more than GTO. The dependence of the yield stress on particle water content is presented in Fig. 2 for 20 wt% neutral alumina suspensions containing various amounts of Brij 30 (E Å 1.5 kV/ mm and fE Å 500 Hz). The yield stress again passes through a maximum at approximately 3 wt% Brij 30 at all water contents. The ER enhancement increases with water content; water must be present in order for surfactants to increase the yield stress. For the nondried neutral alumina suspensions, there appears to be a threshold surfactant concentration for yield stress enhancement. The dependence of the yield stress on particle type is presented in Fig. 3 for 20 wt% dried alumina suspensions (acidic, neutral, and basic alumina; E Å 1.0 kV/mm and fE Å 500 Hz), using Brij 30 as a surfactant. All particles show similar trends, with the maximum yield stress varying with particle type. Acidic alumina shows the largest yield stress and basic alumina shows the smallest yield stress; neutral alumina shows the largest relative increase in yield stress, approximately 1000% at 2 kV/mm. As shown in Table 1, the main difference in the chemical compositions among the three types of alumina particles is the chloride ion content. To further probe the effect of ion content, suspensions of deionized acidic alumina particles were prepared. Acidic alumina particles were placed in dialysis tubing and dialyzed against deionized water. The deionized water was replaced daily for 60 days. The particles were then filtered, allowed

Adsorption Measurements The adsorption isotherm of Brij 30 on neutral alumina particles in SF96 was obtained spectrophotometrically using the difference method (using a Beckman DU Series 60 spectrophotometer). A characteristic adsorption peak for Brij 30 was found at a wavelength of 276 nm. Dried neutral alumina suspensions (5 wt%) with various Brij 30 concentrations were sealed and equilibrated for 24 h. Suspensions were then put in test tubes and centrifuged at 1550 rpm for 30 min. UV spectra of the supernatants were obtained, and the adsorbed amount was determined by difference. Water adsorption was determined by difference using Karl Fisher titration. 3. RESULTS

Rheological Data The dependence of the dynamic yield stress on Brij 30, GMO, and GTO concentration is presented in Fig. 1 for 20 wt% dried neutral alumina suspensions. For all cases, the

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FIG. 2. Yield stress as a function of Brij 30 concentration for 20 wt% neutral alumina suspensions in silicone oil, with varying water contents. Nondried, 3.47 wt% (g H2O/100 g dried alumina); dried, 1.20 wt%; highly dried, 0.53 wt% (E Å 1.5 kV/mm, fE Å 500 Hz).

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FIG. 3. Yield stress as a function of Brij 30 concentration for 20 wt% dried alumina suspensions in silicone oil (E Å 1.0 kV/mm, fE Å 500 Hz).

to dry at ambient conditions, and then dried at 587C ( 010 psig) for 6 h. The water content of the deionized acidic alumina particles was 1.26 wt%, comparable to that of dried acidic and neutral alumina particles. The yield stress of 20 wt% dried deionized acidic alumina suspensions is plotted as a function of Brij 30 concentration in Fig. 4, along with the data for acidic and neutral alumina suspensions. Deionizing the acidic particles reduces the yield stress, to values similar to those of neutral alumina suspensions, as expected from the yield stress dependence on the particle type (i.e., the chloride ion content). This result confirms that the yield stress and its enhancement with added surfactant are sensitive to the particle ion content.

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FIG. 5. Brij 30 adsorption isotherm on dried neutral alumina particles in SF96 (Cequil is the equilibrium surfactant concentration in the continuous phase).

Surfactant Adsorption The Brij 30 adsorption isotherm for the dried neutral alumina particles in dried SF96 (237C) is presented in Fig. 5. Brij 30 adsorption increases with surfactant concentration and reaches a plateau at large concentrations. Assuming that ˚ 2 (reported for adsorption at the the adsorbate area is 46 A air–water interface (22)), monolayer coverage corresponds to approximately 3.5 1 10 06 gmol/m 2 . The pore volume of the neutral alumina particles is approximately 0.225 cm3 /g; the amount of Brij 30 ( rsur f Å 0.95 g/cm3 , MW Å 362.56) required to fill the pores is approximately 3.8 1 10 06 gmol/ m 2 . Comparison with Fig. 5 clearly indicates that Brij 30 forms aggregates or multilayers on the particle surface at large concentrations. Aggregate formation may arise from dipole–dipole and/or hydrogen bonding interactions between the hydroxyl groups (23). However, whether adsorption within the pores is monolayer or multilayer is uncertain. Brij 30 adsorption was found to be insensitive to particle water content over the range 0.53–3.47 wt% (15). This indicates that the dependence of surfactant activation of the ER response with water content does not arise from a change in the amount of adsorbed surfactant, but may be due to the variation of the structure of the adsorbed phase. Water Adsorption

FIG. 4. Yield stress as a function of Brij 30 concentration for 20 wt% dried acidic, neutral, and deionized acidic alumina suspensions in silicone oil (E Å 1.0 kV/mm and fE Å 500 Hz).

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Neutral alumina suspensions (20 wt%) with 3 wt% Brij 30 were prepared by adding known amounts of water and equilibrating the sealed samples for 24 h. The suspensions were then put in test tubes and centrifuged at 1550 rpm for 30 min. The supernatant water concentrations were measured by Karl Fisher titration. The adsorbed amount and equilib-

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FIG. 6. Water contents of the particles and supernatants as a function of the added water amount for 20 wt% dried neutral alumina suspensions with 3 wt% Brij 30 in SF96.

rium water concentration (in the liquid phase) are presented in Fig. 6. The adsorption increases linearly with the added water, while the equilibrium water content is essentially constant up to 0.5 g H2O added/g particle. This equilibrium water content ( É0.01 wt%) is insensitive to surfactant concentration between 1 and 10 wt% Brij 30 (15). Since the total water content in ER suspensions used in this study is typically less than 0.1 g H2O/g particle (see Table 2), most of the water will be adsorbed on the particles in this range. 4. DISCUSSION

the surface normal) around the particle surface, is thus quadratic in the applied electric field strength. The yield stress is therefore also quadratic in the applied electric field strength, as commonly observed, and increases monotonically with the particle polarizability. Considerable evidence indicates that surfactants enhance the rheological properties of ER suspensions by increasing particle polarizabilities. Specifically, surfactants appear to facilitate interfacial polarization. The evidence supporting this hypothesis is reviewed below. The yield stress and suspension dielectric constant for 20 wt% dried neutral alumina suspensions, with and without surfactant, are plotted as a function of electric field frequency in Fig. 8. The yield stresses in this figure were measured at a field strength of 1.5 kV/mm, while the dielectric constants were measured under a small field strength ( õ2 V/mm). In the absence of surfactants, both the yield stress and the suspension dielectric constant decrease with frequency over the range of 10–10,000 Hz, consistent with interfacial polarization (5). When surfactant is added, the yield stress and dielectric constant increase, and the decrease with increasing frequency becomes more pronounced, supporting the hypothesis of enhanced interfacial polarization. The low-frequency dispersion is enhanced with added surfactant (Fig. 8), suggesting that surfactants increase either the number or the mobility of charge carriers within the pores or on the surfaces of the particles. Other evidence supporting the notion that adsorbed surfactants enhance interfacial polarization is: • Adsorption studies showed that surfactants and water are predominantly associated with the surface or the pores of the particles (Figs. 5 and 6).

The dependence of the yield stress on the electric field strength is depicted in Fig. 7. Here, the yield stress divided by the field strength squared is plotted against Brij 30 concentration ( fE Å 500 Hz). At small Brij 30 concentrations, the curves at different electric field strengths superpose and the yield stress scales with E 2 (linear polarization region; see below). However, for Brij 30 concentrations ú3 wt%, the yield stress deviates from the E 2 dependence, increasing approximately linearly with field strength (nonlinear polarization region). Since the behavior of the ER response in the linear and nonlinear regions is quite different, they will be discussed separately. Linear Polarization Region The electrostatic polarization model of ER attributes the field-induced rheological properties to electrostatic polarization interactions between particles (8, 24–29). In this model, polarization in each phase is assumed to be linear. The net electrostatic force on each particle, which may be obtained by integrating Maxwell’s stress tensor (dotted into

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FIG. 7. Yield stress divided by the electric field strength squared as a function of Brij 30 concentration for 20 wt% dried neutral alumina suspensions in silicone oil ( fE Å 500 Hz).

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FIG. 8. Yield stress (at 1.5 kV/mm, open symbols) and dielectric constant (filled symbols) as a function of electric field frequency for 20 wt% dried neutral alumina suspension with (squares) and without (circles) 3 wt% Brij 30.

• Activation increases with water content, with very little activation when particles are highly dried (Fig. 2). Water is believed to enhance the ER effect by enhancing polarization through increased interfacial polarization (4, 5). • Enhancement depends on the surfactant type, particle type, and ion content ( Figs. 1, 3, and 4 ) . This is reasonable as the facilitation of charge transport should clearly depend on the chemical species that associate with the charge carriers. • The ER response and its dependence on surfactant concentration depend on the particle surface area (15), consistent with interfacial polarization.

Enhanced electrostatic polarization through interfacial polarization is thus a very likely mechanism for the surfactant activation of the ER response. However, the mechanism by which surfactants enhance particle polarization is not as clear. We speculate that the surfactants act to increase the mobility of protons and/or other ions, thus increasing particle polarizability. Some evidence for this speculation is described below. Many solids containing hydroxyl groups show a dielectric dispersion which is considerably larger, and occurs at much lower frequencies, than that of substances of similar chemical constitution, but with other polar groups (30). Such is the case for certain modifications of primary and secondary long-chain alcohols (31, 32), and glycerides of fatty acids (33). High dielectric loss (conduction) in such systems has been argued to be due to proton transfer through hydrogen bonds between hydroxyl groups (31–34). As water adsorbs to hydrophilic surfaces through the formation of hydrogen bonds (35), conduction via proton mi-

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gration through neighboring hydrogen bonds on particle surfaces is possible (4, 30, 31, 34, 36). Indeed, the increase in shear stress (at 2 kV/mm) of aluminum dihydrotripolyphosphate/silicone oil suspensions with temperature has been correlated with an increase in proton mobility with NMR measurements (37). Proton transport was assumed to occur through hydrogen bonds. The hypothesis that proton transport can control particle polarization in ER suspensions is consistent with the observation that the ER response of many suspensions of hydrophilic particles increases with water content (for small water concentrations). The ER response depends on the particle type (Fig. 3), with the acidic alumina particles showing the largest yield stresses. The acidic alumina particles differ from the basic and neutral particles only in that more surface hydroxyl groups have been replaced by chloride ions. The halogen has a higher electron affinity than a surface hydroxyl group, causing the residual surface hydrogen to be more acidic (35). Thus the energy barrier for proton transport is lower, resulting in a larger surface conductivity, larger particle polarizabilities, and larger yield stresses than for the neutral and basic particles. Rheological experiments suggest that surfactants play a role similar to that of water. Brij 30 and GMO, which contain hydroxyl groups, show an ER enhancement, while GTO, which does not contain hydroxyl groups, is not nearly as effective as an activator. We have also observed that Brij 30 and GMO associate strongly with water while GTO does not; aqueous solutions of Brij 30 and GMO form viscous homogeneous gel-like phases over a wide range of concentrations, while GTO/water mixtures separate into two liquid phases (15). We therefore speculate that adsorbed Brij 30 and GMO enhance the surface conductivity by providing a favorable surface environment for ion transport. It is likely that proton migration through hydrogen bonds contributes significantly to the conduction, but it is difficult to rule out the transport of other (e.g., impurity) ions with our existing evidence. Nonlinear Polarization Region At large surfactant concentrations, above the maximum in the yield stress (Fig. 7), the yield stress scales as E n , where n É 1, a feature that is not captured by enhanced linear interfacial polarization. Possible explanations for the nonlinear ER behavior are (i) nonuniform electric fields and (ii) field-dependent dielectric properties. For suspensions with zero conductivity, the electrostatic potential averaged over a volume containing many particles (but small relative to the electrode gap dimensions) will decrease linearly from the high to low potential electrodes. As the suspension conductivity increases, as observed at large surfactant concentrations, space charge layers may build up near the electrodes, screening the electric field near

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FIG. 9. Shear stress as a function of shear rate for 20 wt% dried neutral alumina suspensions with varying Brij 30 ( E Å 2.0 kV /mm and fE Å 500 Hz ) .

the center of the electrode gap. Within the framework of the electrostatic polarization model, the decreased electric field strength would lead to a decreased yield stress, and an apparent field strength scaling less than quadratic. However, it was found that the electric field across the ER suspensions, even at high surfactant concentrations, is uniform above an electric field frequency of 100 Hz (15), indicating that the effect of electrode polarization on the ER response is negligible at 500 Hz. The nonlinear ER behavior does not arise from dramatic changes in the suspension dielectric properties with surfactant concentration at small electric fields. Dielectric properties ( e*, e9 ) of neutral alumina suspensions increase smoothly with surfactant concentration, showing no abnormal behavior (15). This result suggests that the enhanced interfacial polarization should provide enhanced stress transfer even at large surfactant concentrations, if there are no other impeding phenomena. Indeed, nonlinear behavior is observed only at small shear rates. Figure 9 shows the shear stress as a function of shear rate for 20 wt% dried neutral alumina suspensions with varying Brij 30 concentrations. At large shear rates, the shear stress at large surfactant concentrations is larger than at smaller surfactant concentrations. Here, the shear stress is proportional to E 2 , indicating that polarization is linear and that the increased stress transfer with increasing surfactant concentration arises from enhanced interfacial polarization. However, at small shear rates, the shear stress at large surfactant concentrations ( ú3 wt% Brij 30) decreases below that for suspensions with smaller surfactant concentrations. Here, the response is nonlinear at large surfactant concentrations. Small and large shear rates differ primarily in the state of aggregation. At sufficiently large shear rates, particles are

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well dispersed and hydrodynamic forces degrade large aggregates. At small shear rates, particles form large columnar aggregates due to the strong electrostatic polarization interactions. Within the aggregates, particles remain in close contact. The electric field strength in an interparticle gap can be much larger than the nominal field strength. These features suggest that the mechanism producing nonlinear ER behavior arises from the large electric fields between closely spaced particles. A promising explanation for nonlinear ER behavior is nonlinear, nonhomogeneous conduction. Conductivities of many fluids may increase at field strengths comparable to those expected between particles in ER fluids due to fieldenhanced dissociation of electrolytes (38–40). Foulc et al. (18, 19) have shown that increased conductivity due to fieldenhanced dissociation in the fluid between conducting particles under dc electric fields can lead to electrostatic interactions and yield stresses that increase slower than E 2 . However, this model assumes that the continuous phase is homogeneous. In contrast, we have found that under large electric fields, surfactants in solution can phase separate, forming a surfactant-rich phase which appears in the interparticle gap. As discussed below, this leads to nonlinear conduction only on a macroscopic scale—conduction within each phase appears to be independent of field strength. Thus the mechanism for nonlinear ER behavior, with yield stresses increasing slower than E 2 , arises from a different mechanism than that proposed in Refs. (18, 19). Field-Induced Formation of a Surfactant-Rich Phase Brij 30 solutions (3 wt%) were visualized to probe their behavior under electric fields. Video images for various applied field strengths ( fE Å 500 Hz) are presented in Fig. 10. The solutions appear to be homogeneous up to an applied electric field strength of 128 V/mm (Fig. 10a). At 256 V/ mm, surfactants phase-separate as droplets and begin to form surfactant-rich fibers spanning the electrodes (Fig. 10b). With increasing field strength, more droplets are incorporated into the thickening fibers. Phase separation is complete at some large field strength ( É600 V/mm), with no more structure evolution with increasing field strength (Fig. 10c). When the electric field is removed, the fibers immediately break up into droplets, but the new phase persists (Fig. 10d). The formation of the surfactant-rich phase between fixed glass beads under ac electric fields was also observed. Two glass beads (420-mm diameter) were glued to a microscopic slide at a separation of É12 mm, and between electrodes separated by 8 mm. The glass beads are nonporous and hence most surfactants are initially in the continuous phase. A nominal electric field strength of 513 V/mm ( fE Å 500 Hz) was applied for different Brij 30 concentrations and video images were acquired. Representative images are presented in Fig. 11 for the beads immersed in solutions of 1, 3, and

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FIG. 12. Storage modulus as a function of electric field strength for 20 wt% dried neutral alumina suspensions with 1 and 7 wt% Brij 30. The oscillation frequency is 10 Hz, the edge shear strains are 2.4 1 10 04 (1 wt% Brij 30) and 1.3 1 10 04 (7 wt% Brij 30), and fE Å 500 Hz. FIG. 10. Sequential images of 3 wt% Brij 30 solutions in SF96 under an applied electric field ( fE Å 500 Hz); (a) E Å 0 V/mm, (b) E Å 256 V/mm, (c) E Å 641 V/mm, and (d) electric field is turned off.

7 wt% Brij 30. Without the applied electric field, all solutions are homogeneous. Upon applying the electric field, the solutions phase-separate and droplets move to the glass bead surfaces. The droplets move along the surface, accumulate in the interparticle gap, and form a surfactant-rich ‘‘bridge’’ between the particles. The volume of the surfactant-rich bridge increases with surfactant concentration.

FIG. 11. Surfactant structure formation between two glass beads. In surfactant solutions under an applied electric field of 513 V/mm ( fE Å 500 Hz); (a) 1 wt%, (b) 3 wt%, and (c) 7 wt% Brij 30. In a 1 wt% Brij 30 solution for different electric field strengths ( fE Å 500 Hz); (d) E Å 0 V/ mm, (e) E Å 256 V/mm, and (f ) E Å 641 V/mm.

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Video images of surfactant bridge formation in 1 wt% Brij 30 solutions under the various electric field strengths are also presented in Fig. 11. Without an electric field and up to a certain field strength, bridges do not form ( Fig. 11d ) . Above a critical field strength ( 190 õ Ec õ 250 V / mm) , surfactant-rich droplets accumulate on the particles and migrate to form a bridge between the glass beads. The bridge grows with increasing electric field strength ( Figs. 11e and 11f ) . Bridge formation between small alumina particles (diameters 63–90 mm) is difficult to image. However, evidence of bridges can be obtained from elasticity measurements, where suspensions with particles held together by such bridges display elasticity in the absence of an electric field. The storage modulus of 20 wt% dried neutral alumina suspensions containing 1 and 7 wt% Brij 30 were measured with and without an electric field (oscillation frequency Å 10 Hz, strain amplitude Å 3%). The results are presented in Fig. 12 where the storage moduli are plotted as a function of time. For an electric field strength of 2 kV/mm, both suspensions possess large storage moduli. When the field is removed, the modulus of the 1 wt% Brij 30 suspension decreases rapidly, while the modulus of the 7 wt% Brij 30 suspension initially increases, and then decreases slowly, consistent with a surfactant-mediated force holding the field-induced structure together. This result indicates the formation of surfactant-rich bridges between small alumina particles at large surfactant concentrations, consistent with the observations with large glass beads. Below, it is shown that the surfactant bridges have a larger conductivity than the continuous phase, decreasing electro-

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FIG. 13. DC conductivity as a function of dc electric field strength for 0, 0.5, 1, and 3 wt% Brij 30/SF96 solutions.

static particle interactions and shear stresses, thus producing a nonlinear ER response. Electrical Properties of Solutions and Suspensions with a Surfactant-Rich Phase The dc conductivity of Brij 30/silicone oil solutions is presented as a function of electric field strength in Fig. 13 for 0, 0.5, 1, and 3 wt% Brij 30. The dc conductivities of 0 and 0.5 wt% Brij 30 solutions are independent of field strength up to 2.0 kV/mm. For the 1 wt% Brij 30 solution, the conductivity is constant up to about 1.5 kV/mm and then increases with electric field strength. The conductivity of the 3 wt% Brij 30 solution increases immediately and then reaches a large field strength plateau. The solution conductivity apparently possesses two critical electric field strengths where the conductivity behavior changes. The conductivity is constant up to the first critical field strength and then increases with field strength. The conductivity reaches a plateau at the second critical field strength and then remains constant with further increases in the field strength. The critical field strengths are decreasing functions of surfactant concentration. This dc conductivity behavior of Brij 30 solutions is consistent with the visual observations of Brij 30 solutions in electric fields (Fig. 10). The solution is homogeneous at small field strengths and hence the conductivity is independent of the field strength. Above the first critical field strength, surfactants begin to phase-separate and form surfactant-rich fibers spanning the electrodes. The fibers provide a conduction path producing an increased apparent conductivity. With further increases in the applied electric field, the number and thickness of the surfactant-rich fibers increase, and thus the conductivity increases. Above the second criti-

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cal field strength, phase separation is complete, and the conductivity is independent of field strength. The conductivity of pure Brij 30 was found to be independent of field strength up to 2.0 kV/mm. Therefore, the conductivity increase with increasing field strength for the Brij 30 solutions is caused by the formation of surfactant-rich fibers, with the conductivity within each phase evidently independent of field strength. The dc conductivities of 20 wt% dried neutral alumina suspensions with different surfactant concentrations were measured before, during, and after the application of large electric fields. Typical results are presented in Fig. 14. The dc conductivity with 1 wt% Brij 30 increases with the application of the electric field. Upon removal of the field, the conductivity returns to its original value, indicating that there is no significant bridge formation between particles. The dc conductivity with 3 wt% Brij 30 decreases when the large field is removed, but does not return to its original value, indicating that surfactants form some bridges between particles. The dc conductivity with 7 wt% Brij 30 remains essentially at its large field value when the field is removed, suggesting that the surfactant structure between particles is fully developed at this surfactant concentration. The ac conductivities of 20 wt% dried neutral alumina suspensions were measured after imposing large electric fields. The results are presented in Fig. 15 for different Brij 30 concentrations. The experiments were performed by imposing the desired field strength ( fE Å 500 Hz), and then waiting 1 min after removing the electric field before measuring sAC Å e0e9v. For the suspensions with 0 and 1 wt% Brij 30, the conductivities are essentially independent of the imposed field strength, indicating that there is no significant surfactant structure formation between particles. For 3 wt% Brij 30, the conductivity depends weakly on the imposed electric field strength. The conductivity of the 7 wt% Brij

FIG. 14. DC conductivity as a function of the electric field strength for 20 wt% dried neutral alumina suspensions with varying Brij 30 concentrations.

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in the gap is no longer proportional to the applied field strength, and thus the particle interactions and yield stress increase slower than E 2 . We note that this mechanism for nonlinear ER behavior is similar to that proposed in Refs. (18, 19) in that the yield stress is limited by an increase in gap conductance with field strength. The mechanism proposed here differs in that the increase in conduction does not arise from nonlinear conduction within a homogeneous phase, but rather results from phase separation of a more conducting phase. This mechanism can occur in a variety of ER systems that contain components in addition to particles and a pure oil. 5. CONCLUSION

FIG. 15. AC conductivity as a function of the imposed electric field strength for 20 wt% dried neutral alumina suspension with 0, 1, 3, and 7 wt% Brij 30, respectively ( fE Å 500 Hz). The conductivities were measured 1 min after the imposed electric field was removed.

30 suspension increases with the imposed field strength, indicating that surfactant bridges form between particles. These results are consistent with the dc conductivity behavior described above (Fig. 14). The connection between surfactant bridge formation and nonlinear ER behavior can be determined by considering the role of the conductivities of each phase on the interparticle forces. The dielectric data (Fig. 8) indicate that interparticle forces are determined by conductivity differences between the particles and the continuous phase (8, 41–43). When the particle conductivity ( sp ) is much greater than the fluid conductivity in the interparticle gap ( sgap ), the field strength in the gap between nearly touching particles is much greater than the applied field strength; pair electrostatic interactions are dominated by the large field strength in this region (8, 44). The yield stress is determined directly by the particle interactions (26, 29), and is thus influenced strongly by the field intensification between particles. At low surfactant concentrations, surfactants and water are located primarily in the particles. Therefore, sp @ sgap and the yield stress is relatively large. Since the conductivities of the disperse and continuous phases are independent of field strength, the field strength in the gap is proportional to the applied field strength and t 0 } E 2 . At large surfactant concentrations, sgap increases due to the presence of the surfactant bridges. The gap field strength is thus reduced, which reduces the particle interactions and the yield stress. The gap field intensification and yield stress decrease with further increases in surfactant concentration as the bridges continue to grow and the gap conductance further increases. The bridge volume also increases with increasing field strength; the field strength

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We have investigated the influence of three nonionic surfactants (Brij 30, GMO, and GTO) on the ER response of various alumina suspensions. Yield stresses initially increase with surfactant concentration, pass through a maximum, and then decrease with concentration. Below the maximum, the yield stress increases quadratically with the field strength, while above the maximum, yield stresses increase slower than E 2 . The increase in the yield stress with surfactant concentration is due to surfactant-enhanced interfacial polarization. The increased particle polarizability may arise from increased proton transport via neighboring hydrogen bonds. The nonlinear behavior observed at large surfactant concentrations (i.e., t 0 }/ E 2 ) arises from field-induced phase separation of a surfactant-rich phase which forms conductive interparticle bridges. This mechanism for nonlinear ER is similar to that proposed in Refs. (18, 19), in that the yield stress is limited by an increase in conductance in the interparticle gap. In contrast, the mechanism proposed here differs in that the conductance increase in the gap does not arise from a field-dependent continuous phase conductivity, but rather from phase separation of a more conducting phase. Each phase apparently possesses a field-independent conductivity, but the relative volumes of each phase depend on the field strength and surfactant concentration. This phenomenon is likely to occur in many ER suspensions that contain surfactants. ACKNOWLEDGMENTS Acknowledgment is made to the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. This work was also partly supported by the National Science Foundation (CTS-9401293).

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