Journal of Colloid and Interface Science242,306–313 (2001)doi:10.1006/jcis.2001.7882, available online at http://www.idealibrary.com on

Stability of Dispersions of Colloidal Nickel Ferrite Spheres

R. C. Plaza, J. de Vicente, S. G´omez-Lopera, and A. V. Delgado1

Department of Applied Physics, Faculty of Sciences, University of Granada, 18071 Granada, Spain

Received December 29, 2000; accepted June 27, 2001

The stability of suspensions of nickel ferrite spheres is investi-gated for different compositions of the dispersion medium, in theabsence and in the presence of an external magnetic field. Thetime-dependence of the optical absorbance of the suspensions isthe quantity used for experimentally determining the stability. Twoapproaches have been used for the calculation of the interactionenergy of the particles: first, the classical DLVO theory, in whichthe net interaction is considered as the superposition of electro-static double-layer repulsion and van der Waals attraction; andsecond, the so-called extended-DLVO model, in which short-rangehydrophobic (hydrophilic) attractions (repulsions) are also consid-ered. Calculation of all these interactions required the determina-tion of (i) the diffuse double-layer potential of the ferrite particles(that was approximated by the zeta potential, as deduced from elec-trophoresis measurements); (ii) the Hamaker constant of the par-ticles in aqueous media; and (iii) the acid/base components of thesurface free energy of the solids. The quantities in (ii) and (iii) abovewere obtained from contact-angle measurements for selected liquidson layers of the magnetic oxide. When a magnetic field is applied,another interaction, of magnetic origin, has to be accounted for. Itwas found that the suspensions are more stable the farther theirpH is from the isoelectric point, and the lower the ionic strengthof the medium is, in full agreement with the predictions of boththe classical and extended-DLVO models. The application of theexternal magnetic field was found to provoke significant changesin the rate of variation of absorbance with time: The results arecoherent with an increased velocity of particle aggregation due tomagnetic attractions between the magnetized colloids. The DLVOtheory (in any of its versions) including magnetic interactions canexplain this behavior, since the calculated force between particles ismore attractive when the field is present. C© 2001 Academic Press

Key Words: nickel ferrite spherical colloidal particles; suspensionstability; magnetic fluids; DLVO interaction energy.

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INTRODUCTION

The peculiar magnetic properties of ferrites give their spensions a number of characteristics and potential uses thnot shown by suspensions of nonmagnetic particles. That ismagnetic colloids have found an increasing number of app

1 To whom correspondence should be addressed. Fax: +34-958-243E-mail: adelgado@ugr.es.

eter-Thelso

300021-9797/01 $35.00Copyright C© 2001 by Academic PressAll rights of reproduction in any form reserved.

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tions in many different fields of technology (1–3), including tmanufacturing of ceramic magnets from concentrated sussions, the use of the particles as magnetic resonance im(MRI) contrasts (4), and even as nuclei of biodegradable pmer particles for transport and delivery of pharmaceutical din living organisms (5). However, the properties of such dispsystems are very sensitive to external magnetic fields, becof the strong magnetic interactions existing between magneparticles, affecting both their colloidal stability and rheologibehavior (6–9). In the present work, we focus on the stabilitsuspensions of magnetizable colloidal particles (so-called mnetorheological fluids) (i.e., on their tendency to reversiblyirreversibly aggregate, or rather remain dispersed as indivunits), both in the presence and in the absence of externalnetic fields, and in different conditions of the aqueous dispermedium.

Interest in this investigation is justified on two grounds: fithe variety of physical phenomena that can be shown by tcomplex systems, and, second, the fundamental role playethe state of aggregation of the colloidal particles when useapplications. For instance, the better the stability of the stasuspension, the lower the density of structural defects in thramic magnet obtained (3). Also, particle size is crucial wconsidering biomedical applications: diameters below 1µm arerequired to avoid clogging of the capillaries, and to favordiffusion of the particles into organic tissues when they aretravenously injected into the body for drug delivery (10, 11)

In order to make a study as quantitative as possible, mparticles homogeneous in size and shape should be usedmany other fields of colloid science. The possibility of preping inorganic particles with controlled size and shape has bthroughly explored by Matijevi´c (12). In particular, he and hco-workers have demonstrated that spheres of ferrites in theloidal size range can also be synthesized (13–15).

This kind of particle is used in the present study, and a tough surface characterization of spherical nickel ferriteticles is performed with the aim of estimating all the cotributions to the overall particle–particle interaction enerThe results are used for explaining, to the greatest posextent, the experimentally observed stability, based on dminations of the optical absorbance of the suspensions.fundamental effect of externally applied magnetic fields is adiscussed.

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COLLOIDAL NICKEL

EXPERIMENTAL

Materials

Colloidal nickel ferrite (NiFe2O4) spheres were synthesizeby a process of coprecipitation of nickel hydroxide and ferrohydroxide gels in the presence of nitrate ions, followingmethod first proposed by Regazzoni and Matijevi´c (15). Thestarting point of the process was the mixing of two solutiosolution A contained 1.5 cm3 of 0.15 M KNO3 and 4.5 cm3 of0.112 M KOH, and solution B consisted of 1 cm3 of 0.025 MNiNO3 and 4 cm3 of FeSO4 (0.1 M, acidified to pH 2 withH2SO4). Both solutions were bubbled for 1 h with pure nitrogen,in order to avoid the presence of oxygen as much as possiblechemicals were of analytical quality from Merck (Germanand the water used was of Milli-Q grade (Milli-Q AcademiMillipore, France).

The coprecipitation of the gels was performed by mixinglutions A and B with sufficient water to reach 20 cm3 of finalsolution that was purged again with N2 for 2 h in a50-cm3 stop-pered Pyrex tube. After completion of the mixing process,tubes were kept at 90.0◦ ± 0.2◦C for 4 h in apreheated Mem-mert (Germany) oil bath. After cooling in ice water, the soliobtained were washed in a 1 M HNO3 solution for 60 min, in or-der to dissolve the unreacted hydroxides. The remaining sonot dissolved by nitric acid, were easily shown to be magneThus, repeated decantation in the presence of a permanentnet (B = 340 mT) placed at the bottom of the container, aredispersion in Milli-Q water, was the method used to cleansuspension of unreacted ions. When the conductivity of sunatant was below 2µS/cm, the particles were considered cleaand dried at 60◦C under vacuum.

Methods

Transmission electron microscope (TEM) observations wused to ascertain the spherical shape of the particles, andsize homogeneity. Figure 1 is an example of the picturestained: the particles are spherical and moderately monodispwith an average diameter of 810± 90 nm.

The electrical surface characteristics of the particles werealyzed by electrophoretic mobility measurements, performat 25.0◦ ± 0.5◦C in a Malvern Zetasizer 2000 device (MalveInstruments, UK). The effects of pH and NaCl concentraton the electrophoretic mobility of the ferrite particles weinvestigated.

A thermodynamic analysis of the particle surface was acarried out. To that aim, contact angles of selected liquids wmeasured on ferrite layers deposited on microscope glass sThe method used to obtain a flat, homogeneous surface consof covering the glass with a 100 g/L suspension of particles,allowing it to dry slowly at room temperature for 24 h. Finallthe slides were heated for 6 h at 50◦C in a convection oven, andstored in a desiccator. The surface free energy,γS, of the solids

LW + −

was characterized by three parameters,γS , γS , andγS , corre-sponding, respectively, to the Lifshitz–van der Waals, electro

FERRITE SPHERES 307

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FIG. 1. TEM picture of the nickel ferrite particles synthesized. Bar leng600 nm.

acceptor, and electron-donor contributions to the surfaceenergy. According to van Oss (16),γS can be written

γS = γ LWS + 2

√γ+S γ

−S [1]

and a similar equation applies to the liquid phase in contact wthe particles,γL . The solid/liquid interfacial free energy,γSL,can be related to theγ components of both the solid and thliquid. In fact, using Young’s equation,

γS− γSL= γL cosθ, [2]

we can write (16)

γL (1+ cosθ ) = 2√γ LW

S γ LWL + 2

√γ+S γ

−L + 2

√γ−S γ

+L , [3]

whereθ is the contact angle of the liquid on the solid. Mesuringθ for three liquids of knownγL components, three equations like Eq. [3] are solved in the unknownsγ LW

S , γ+S , γ−S .The liquids used were water (γ LW

L = 21.8 mJ/m2; γ+L =γ−L = 25.5 mJ/m2), diiodomethane (γ LW

L = 50.8 mJ/m2; γ+L =γ−L = 0), and formamide (γ LW

L = 39.0 mJ/m2; γ+L = 2.28 mJ/m2;γ−L = 39.6 mJ/m2). The probe liquids were analytical qualitfrom Merck, and their surface-tension parameters were tafrom Ref. (16). A Ram´e-Hart (USA) 100-07-00 goniometer waused to measureθ .

The stability of the suspensions was followed by turbidity dterminations as a function of time with a Spectronic 601 Milt

n-Roy UV–vis spectrophotometer, for a wavelength of 394 nm (thewavelength of maximum absorbance of the solids) and a 1-cm

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308 PLAZA

light path. Optical absorbance was recorded at 1-s intervals400 s, or at 15-s intervals for 1800 s, and suspensions conta5 g/L of solids and different NaCl concentrations and pH valuwere analyzed. The effect of an external magnetic field onstability of nickel ferrite suspensions was studied by placingspectrophotometer cuvette at the center of a pair of Helmhcoils (Phywe, Germany). The magnetic field inside the cuvewas vertical, and its strength (2.5 mT in all cases) was measwith a Hall-effect probe using a Phywe (Germany) teslameNo field variations higher than 10% were detected throughthe sample volume.

The magnetic properties of the particles were analyzedmeasuring their magnetization,M , as a function of the appliedmagnetic field,H , in a Manics DSM-8 (France) magnetosuceptometer. Magnetic fieldsH ranging between−5000 and+5000 Oe (−398 and+398 kA/m) were applied. Measuremenwere performed at room temperature (293 K).

RESULTS AND DISCUSSION

Electrokinetic Characterization

In order to evaluate the electrostatic repulsion betweenpersed ferrite particles, the electrical surface potential (in fthe diffuse potential) must be estimated. Our best approachsuch a potential is the electrokinetic or zeta potential (ζ ), com-puted from electrophoretic mobility (µe) measurements usingO’Brien and White’s theory (17). The effect of pH onζ is de-picted in Fig. 2, for three different NaCl concentrations. As oserved, the isoelectric point, pHiep (pH of zeroζ ), ranges between

FIG. 2. Zeta potential (ζ ) of nickel ferrite particles as a function of pH, forthe concentrations of NaCl indicated.

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FIG. 3. Zeta potential (ζ ) of nickel ferrite particles as a function of NaCconcentration for different pH values.

6.6 and 6.8 whatever the concentration of sodium chloride,proving to be an indifferent electrolyte for this oxide/aqueosolution interface. Other authors (15) found a pHiep ≈ 6.7, usingKNO3 as supporting electrolyte; so our results agree reasonwell with previous findings.

The indifferent nature of NaCl is confirmed by data in Fig.whereζ is plotted as a function of [NaCl] for three pH vaues. Note that only an overall decrease is observed withcentration, due to the double-layer compression expectedelectrolyte solution undergoing no specific interactions withoxide surface.

Surface Free Energy of the Ferrite Particles

As described, all the information concerning the surfaceenergy,γS, of the particles was deduced from contact-angleθ )measurements. Since the stability of the suspensions wassured as a function of both pH and NaCl concentration, the eof these quantities onγS components was also investigated.that aim, solid layers were deposited on the glass slides ascribed in the Experimental section, but the starting suspensused to deposit the particles had the required pH and/or istrength. Once the layer was dry, the contact angles weresured for water, formamide, and diiodomethane.

Table 1 shows the results. As observed, nickel ferrite is ansentially monopolar, electron-donor (γ−S À γ+S , γ

+S ∼ 0) solid.

This means that it might have acid/base interactions (hydroprepulsion or hydrophobic attraction) with phases of any po

+ −

ity (having eitherγ or γ , or both, different from zero), butthat such interactions do not contribute to the cohesion of this

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COLLOIDAL NICKEL

TABLE 1Contact Angle θ (Degrees) of the Liquids Indicated and Surface

Free Energy Parameters of Nickel Ferrite Particles as a Functionof pH for 10−3 M NaCl Concentration

pH θwater γ−S (mJ/m2)

4 26± 3 44± 35 22.4± 2.3 47.0± 1.96 28± 3 42± 37 25± 4 44± 48 28± 3 42± 39 29± 5 40± 5

10 28± 6 41± 5

Note.In all cases,θformamide= 10.2± 0.8,θdiiodomethane= 4.5± 0.9,γ LWS =

50.6± 0.1 mJ/m2, andγ+S ∼= 0.

material. Note also that neither pH nor NaCl concentration ha significant effect onγ LW

S or γ−S . Only the latter componenshows a slight decrease when the pH is shifted away fromtrality, but we found that such small changes have a negligeffect on the interaction energy.

Magnetic Properties

Figure 4 shows the magnetization loop of the nickel ferpowder. Its saturation magnetization is∼22 kA/m, not verydifferent from the literature value [37 kA/m; see Ref. (18)]. Frothe plot in Fig. 4 it is found that NiOFe2O3 is a soft magneticmaterial, given its practically zero coercive field and remaneLet us also mention that from these data, when the externalis 2.5 mT (the one to be applied in stability determinations;below), the magnetization isM = 716 A/m.

Stability of the Suspensions: Effect of pH and Ionic Strengt

Information about the colloidal stability of ferrite suspensiocan be inferred from data on their optical absorbance variat

FIG. 4. Magnetization of nickel ferrite powder, at room temperatu(293.0± 0.2 K), as a function of the external field.

FERRITE SPHERES 309

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FIG. 5. Time-dependence of the optical absorbanceA, relative to its ini-tial (t = 0) value,A0, of NiFe2O4 suspensions for different pH values. Ionstrength: 10−3 M NaCl. Inset: first 50 s of the absorbances, with their lineregressions.

with time. Figure 5 is an example where the absorbanceA, rela-tive to itst = 0 value,A0, is plotted as a function of time (aftesonicating the suspension) for different pH values, and a consconcentration of NaCl. Although the overall tendency ofA/A0

is to decrease with time because of particle sedimentationcurves do not superimpose, indicating that there is a clear eof pH on the sedimentation rate. Such effect, in turn, is a mifestation of the change with pH of the interfacial interactiobetween particles.

Since the light scattering and absorption properties of cloidal particles forming complex aggregates are not furesolved from a theoretical point of view (19), absorbanceturbidity values have some meaning only at the very early staof aggregation, whereA changes only for two reasons: sedimetation of the particles, or formation of doublets from individuparticles. So we restrict our discussion to the initial time variatof A/A0: Thus, Fig. 6 shows the initial slopes of the absorbacurves in Fig. 5 (10−3 M NaCl), and similar data correspondinto NaCl 10−2 M and 10−1 M, as a function of pH. The effect oNaCl concentration on the slope, at a natural pH of 6, is depicin Fig. 7.

In all cases,S= [d(A/A0)/dt ]t=0 is negative (i.e., any influ-ence from either pH or ionic strength is superimposed onoverall decrease of turbidity), provoked by the gravitational stling of the suspensions. However, it is clear that the slopmaximum (less negative) at approximately pH 6, close toisoelectric point of the particles, and furthermore, that chanwith pH are less significant the higher the ionic strength (Fig.The maximum inScan be related to the absence of electrostrepulsion between the particles in the vicinity of pHiep: parti-cle aggregation will be more likely in such conditions. For tsizes and wavelength involved, the extinction cross sectio

retwo particles is smaller than that of a single aggregate of twicethe volume of the individual particles (19, 20): This means that,

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310 PLAZA

FIG. 6. Initial slopes of absorbance curves like those in Fig. 5, for differeNaCl concentrations and pH 6.

in the absence of settling, the turbidity of the suspension shoincrease in the initial stages of aggregation. Since sedimentawill always be present, the net effect would be a slower ratedecrease inA/A0 (less negative values ofS) when aggregationis more likely, in agreement with data in Fig. 6. The screeningelectrostatic interactions at high ionic strengths must be respsible for the damping of pH effects onS observed at 10−2 and10−1 M NaCl in Fig. 6. Concerning the effect of ionic strength othe initial slope,S, Fig. 7 shows that the latter quantity increaswith ionic strength below 1 mM; the screening mentioned abowill favor attraction between the particles, and hence increain turbidity, and less negative slopes, as NaCl concentratioraised. For higher concentrations, the slope tends again to mnegative values. Apparently, for such thin double layers thegregation must be very rapid, and the absorbance decreasto settling is faster than its increase by aggregation.

These qualitative arguments can be made more quantitaif the interaction forces between the particles are estimated

FIG. 7. Initial slopes of absorbance curves (relative to theirt → 0 values)as a function of NaCl concentration, for pH 6.

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that aim, a potential energy of interaction,V(s) is calculatedfollowing two approaches. According to the classical DLVtheory (21), the total potential energy consists of two terelectrostatic double-layer repulsion,VEL(s), and Lifshitz–vander Waals attraction,VLW(s). Here,s= r − 2a, with r beingthe center-to-center distance between the particles anda theparticle radius. The potential used to account for electrosrepulsion (21) is

VEL(s) = 2πεr ε0aζ 2 ln(1+ e−κs), [4]

where it has been assumed that the particle has a constanmoderate surface potential, and that the electrokinetic orpotential,ζ , is a good estimation of the diffuse layer potentiIn Eq. [4], εr ε0 is the dielectric permittivity of the dispersiomedium, andκ is the reciprocal double-layer thickness. The vder Waals attraction is given by the potential (22)

VLW(s) = − A

6

[2a2

s(4a+ s)+ 2a2

(2a+ s)2+ ln

s(4a+ s)

(2a+ s)2

],

[5]

whereA is the Hamaker constant. Its value can be obtained ftheLWcomponent of the solid/liquid interfacial free energy,γ LW

SL(16), by

A = 24πs20

(√γ LW

S −√γ LW

L

)2

, [6]

where the best estimation fors0 is 1.58± 0.08 A (16).Using the thermodynamic data of Table 1, we obtainedA =

1.1× 10−20 J. The DLVO interaction forceFDLVO(s) is givenby

FDLVO(s) = − d

ds(VEL+ VLW). [7]

The second approach is the so-called extended-DLVO moin addition to electrostatic and van der Waals interactions,drophilic (hydrophobic) repulsions (attractions) must be conered. These can be related to the acid/base contribution tinterfacial free energy, which in turn can be expressed in teof the electron-donor and electron-acceptor components oγS

andγL as (16)

VAB(s) = 4AB exp

(s0− s

λ

), [8]

whereλ is the so-called correlation length of water moleculthat can be estimated to be∼1 nm (16) and

4AB = −4πaλ

(√γ+S γ

−S +

√γ+L γ

−L −

√γ+S γ

−L −

√γ−S γ

+L

).

[9]

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COLLOIDAL NICKE

FIG. 8. Force between nickel ferrite particles as a function of particle sarations for different pH values and 10−3 M NaCl ionic strength. Dashed lineclassical DLVO model; solid lines: extended-DLVO theory.

The force between particles is in this case

F E−DLVO = − d

ds(VEL+ VLW+ VAB). [10]

Figures 8 and 9 show the variation of the force with distafor both approaches, and different pH values (Fig. 8) and istrengths (Fig. 9). Note that the inclusion of theAB term in theforce manifests only at very short distances between the pcles, owing to the rather short range of acid/base interactFor distancess above roughly 15 nm, the extended and classDLVO evaluation of the force practically coincide. Whatevermodel used, it is clear that our stability data can be explainethe force calculations: Thus, the repulsion between particlminimum when the pH is in the 6–7 interval, and increases amove to either more-acid or more-basic values, and henclow stability of the ferrite particles in the pH 6–7 region (Fig.

FIG. 9. Same as Fig. 8, but for different NaCl concentrations, and pH 6

FERRITE SPHERES 311

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FIG. 10. Relative absorbanceA/A0 as a function of time for the NaCconcentrations indicated and pH 6. Open symbols: no magnetic field apfull symbols: vertical 2.5-mT field.

Similarly, when the effect of NaCl concentration, is conside(Figs. 7 and 9), it is seen that the systems are less stablhigher concentration, as experimentally observed (Fig. 7).

Colloidal Stability: Effect of Magnetic Fields

According to the results found with other magnetorheologfluids (23), a significant effect of an externally applied magnfield on the sedimentation rate of the suspensions was texpected. Figure 10 shows that this is the case in our systthe settling of the ferrite particles follows quite different trenin the absence and in the presence of a 2.5-mT field apparallel or antiparallel (the results are not altered by chanthe orientation of the vertical field) to gravity. TheA/A0 curveswere fitted to a sigmoidal curve with the equation

A

A0= C1− C2

1+ e(t−Tc)/τ+ C2, [11]

and the effect of the field was analyzed for the initial slo[d(A/A0)/dt ]t=0, the characteristic timeTC (a measure of thetime needed forA/A0 to suffer a 50% reduction) and the timτ (this time is an indication of how steep the decrease insorbance is, since a shorterτ corresponds to a more abrupt fin A/A0). The effect of NaCl concentration and of the magnefield on these quantities is shown in Fig. 11. The presencthe field brings about a slower rate of decrease of absorbanshort times (Fig. 11a). This result is coherent with an increarate of aggregation of the system when the field is applied.latter magnetizes the particles and induces magnetic attrabetween them. Large flocculi are thus formed that probablycupy most of the suspension volume. However, owing tohigh density of the particles, such aggregates will breaksediment rapidly, and this explains the lowerτ values (Fig. 11b)in the presence of the field. The other parameter,TC, although

.

less affected by the field, tends to be longer when the mag-netic field is on, indicating that the suspensions take a slightly

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312 PLAZA

longer time to sediment. Comparing the behaviors ofτ andTC in Fig. 11b, we could say that when the field is applied, tsystem takes longer to start settling, but once the sedimetion process is initiated, it occurs at a faster rate. In fact, Bluet al. (24) analyzed the thermodynamic stability of magnetorhological fluids subjected to magnetic fields. They found thatthe region of instability (dependent on the field strength aparticle concentration), even small fluctuations in particle cocentration may provoke the rapid formation of large particle agregates. This is in qualitative accordance with our experimedata.

A quantitative picture of the kinetics of particle aggregatiocan be reached if the attractive magnetic force between theticles is added to either of the DLVO forces in Eqs. [7] an[10]. This force can be obtained from a potential energy funtion, V M (s), given by the following equation (25), where it iassumed that the magnetic dipoles associated to the interaparticles are aligned with the field.

V M (s) = −8πµ0M2a3

9(

sa + 2

)3 , [12]

whereµ0 is the magnetic permeability of vacuum, andM isthe magnetization of the particles forµ0H = 2.5 mT. Figure 12

FIG. 11. Initial slopes (a) and characteristic timesTC andτ (b) (see Eq. [11])of the curves in Fig. 10, as a function of NaCl concentration.

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FIG. 12. Total force between nickel ferrite spheres (Eq. [13]) as a functiondistance, for the NaCl concentrations indicated (pH 6). Solid lines: no magnfield applied; dashed lines:B = 2.5 mT.

shows the variation of the total force

FTOT= − d

ds(VEL+ VLW+ VAB+ V M ) [13]

with distance,s, for the NaCl concentrations investigated (fothe sake of brevity, only the extended-DLVO model is usedaccount for nonmagnetic interactions, mostly consideringshort range of the acid/base interactions, that makes bothclassical and extended-DLVO approaches indistinguishabllarge distances). As observed, the presence of the magneticreduces the repulsion due to double-layer electrostatic intetions, and in fact leads to net attractions when the particlessufficiently far apart and the ionic strength screening the surfcharge is high enough. In conclusion, the formation of loosegregates is thus favored by the field, mainly because the rangmagnetic attractions is typically above that ofEL forces. Thus,in spite of the complex particle structures formed in magntorheological fluids under external magnetic fields, the DLVtheory, modified to account for magnetic dipolar interactioncan give a satisfactory qualitative explanation for the obsermacroscopic behavior.

ACKNOWLEDGMENTS

Financial support by CICYT, Spain (Proj. No. MAT98-0940), and INTAS E(Proj. No. 99-0510) is gratefully acknowledged.

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COLLOIDAL NICKEL

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FERRITE SPHERES 313

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