LINEAR AND NONLINEAR VISCOELASTIC BEHAVIOR OF OIL-IN-WATER EMULSIONS STABILIZED WITH POLYSACCHARIDES

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Linear and nonlinear viscoelastic behavior of veryconcentrated plate-like kaolin suspensions

Frédéric Bossarda)

Laboratoire de Rhéologie UMR 5520, BP 53, Université Joseph Fourier,1301 rue de la Piscine, 38041 Grenoble Cedex 9, France

Michel Moan and Thierry Aubry

Laboratoire de Rhéologie, 6 avenue Le Gorgeu - CS93837,29238 Brest Cedex 3, France

(Received 8 December 2006; final revision received 1 August 2007�

Synopsis

he viscoelastic behavior of very concentrated and electrostatically stabilized suspensions ofaolinite particles has been investigated in the linear and nonlinear regime as a function of volumeraction, ionic strength and in the presence of polymer at various concentrations. Materialroperties such as linear viscoelastic moduli and cohesive energy density are extensively enhancedy either increasing volume fraction or decreasing ionic strength. Attention has been paid to thearge amplitude oscillatory shear behavior of concentrated suspensions of plate-like particles,haracterized by a hump in G� curves. Rheological investigation shows the extreme sensitivity ofhe intensity of the strain hardening in G� to excluded volume, electrostatic and steric interactions.

physical interpretation of this nonlinear behavior has been proposed. © 2007 The Society ofheology. �DOI: 10.1122/1.2790023�

. INTRODUCTION

The anisometric character of kaolinite particles, combined with the electrostatic prop-rties of their surface, gives these clay suspensions quite specific structural properties.ndeed, at volume fraction ��*�0.1 corresponding to the onset of excluded volumenteractions, Jogun and Zukoski �1996, 1999� suggest that plate-like kaolinite particlesre aligned within domains. More recently, scanning electron cryomicroscopy observa-ions have pointed out that very concentrated kaolinite suspensions are organized inuasi-continuous neighboring domains of aligned, close-packed particles exhibiting aematic order over few micrometers �Moan et al. �2003��. Such microstructural organi-ation confers peculiar flow properties to kaolinite suspensions that have been thoroughlynvestigated. In the intermediate shear rate region, the presence of a “hesitation” point inhe steady state flow curve, associated with a negative minimum of the first normal stressifference, was shown to be reminiscent of nematic liquid crystalline polymer behaviorMoan et al. �2003��. The interpretation proposed by the authors suggests a competitionetween shear forces that tend to align domains and interactions between neighboring

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2007 by The Society of Rheology, Inc.1253. Rheol. 51�6�, 1253-1270 November/December �2007� 0148-6055/2007/51�6�/1253/18/$27.00

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1254 BOSSARD, MOAN, AND AUBRY

omains that oppose to their mutual alignment, leading to a progressive uniform align-ent of the domains in the flow direction, as the shear forces increase.By considering each plate-like clay particle with its ionic double layer as a new

ffective particle, the decrease of the ionic strength is known to increase the effectivearticle size through the expansion of the ionic double layer. Concurrently, long-rangelectrostatic repulsions are gradually strengthened, favoring the edge/face perpendicularonfiguration by minimizing their mutual repulsions �Mourchid et al. �1995�; Meyer et al.2001��. Consequently, on decreasing the ionic strength, a competition between the ten-ency of plate-like particles to align and the tendency to an isotropic ordering has beenhown �Rowan and Hansen �2002��. For large plate-like particles, such as bentonite, theelative change in the aspect ratio is less sensitive to ionic strength variation. So that,sotropic structure is expected to be favored when decreasing the ionic strength.

In the presence of polymers, three different mechanisms may occur: For nonadsorbingolymer chains at high concentrations, depletion flocculation takes place through phaseeparation �Sperry et al. �1981��. For polymer chains that adsorb on clay surface, adsorb-ng macromolecules may bridge particles at concentrations below the saturation of ac-essible clay surface �Lafuma et al. �1991�; Spalla and Cabane �1993��. They may formpolymeric layer around the particle at concentrations above the saturation of accessible

lay surface, leading to the increase of steric interactions �Napper �1983�; de Gennes1987��. Yziquel et al. �1999a, 1999c� have shown a great enhancement of rheologicalroperties of kaolinite suspensions at �=0.34 by adding high-molecular-weight poly-ers, such as carboxymethyl cellulose �CMC� or polyvinyl alcohol �PVA�.Flow curves express the rheological response at large deformations, whereas vis-

oelastic investigation techniques are measurements performed to provide material prop-rties of structured systems at very low deformations. The usual test consists of measur-ng the frequency dependence of storage and loss moduli in the linear viscoelastic regime,.e., in the low shear strain amplitude domain where the response is sinusoidal and both� and G� moduli are independent of strain amplitude. This spectromechanical techniqueas mainly two advantages: it is very sensitive to the microstructure and it can be treatedn a rigorous mathematical framework �Macosko �1994��. Besides, some works focus onhe rheological response of complex fluids in the nonlinear viscoelastic regime, where G�nd G� moduli are dependent on both frequency and strain amplitude. Among theseeasurements, the large amplitude oscillatory shear test �LAOS�, which consists of mea-

uring viscoelastic moduli as a function of shear strain amplitude from the linear up to theonlinear regime at a fixed frequency, has been shown to be useful to investigate theicrostructural state of various complex fluids �Yosick and Giacomin �1996�; Yosick et

l. �1997�; Hyun et al. �2002, 2003, 2006�; Sim et al. �2003a, 2003b��. However, LAOSeasurements carried out using commercial rheometers must be considered with caution

ince G� and G� moduli lose their physical meaning beyond the linear viscoelastic re-ime. Indeed, the stress becomes no longer sinusoidal and contributions of higher har-onics to viscoelastic moduli may be non-negligible �Dealy and Wissbrun �1990��. The

armonic contributions arising from nonlinear effects can be analyzed using Fourierransformation methods �Wilhelm et al. �1998, 1999, 2000, 2002�; See �2001�; Karis etl. �2002a, 2002b�� or using graphical analysis by drawing a Lissajous curve �Hyun et al.2003��. Very recently, a descriptive approach of viscoelasticity, extended in the nonlinearegime, has been proposed to interpret LAOS data �Cho et al. �2005��. Indeed LAOSeasurements have been used to classify the viscoelastic behavior of complex fluids in

our categories: type I, strain thinning �G� and G� decrease�; type II, strain hardening �G�nd G� increase�; type III, weak strain overshoot �G� decrease and hump in G� curve�;
ype IV, strong strain overshoot �hump in both G� and G� curves� �Hyun et al. �2002�;

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1255VERY CONCENTRATED KAOLIN SUSPENSIONS

im et al. �2003a��. The LAOS behavior of concentrated kaolinite suspensions has showno be classified in type III but the microscopic origin of G� hump has been scarcelyiscussed up to now. Simulation analysis using a modified Jeffreys model with a singleelaxation time and an energy dependent kinetic equation has shown to fit correctly theonlinear behavior of kaolinite suspension �Yziquel et al. �1999a��. This model assumeshat the breakdown of the suspension microstructure is related to the rate of energyissipated by oscillatory shear. Studies performed on fumed silica suspensions havehown that a particle network is required to develop the strain hardening in G� �Yziquelt al. �1999b��. According to the authors, the nonlinear viscoelastic behavior of concen-rated suspensions is governed by microstructural changes, which result from the com-etition between the breakup of the network under flow and its buildup due to Brownianotion. The dissipative energy per unit volume has been shown to depend on particle

ize, nature of the surface and suspending medium, volume fraction and shear strainmplitude. Despite these studies, the physical mechanism of the strain hardening in G� istill not fully understood.

In this article, we have investigated the influence of volume fraction, ionic strengthnd polymer concentration separately, to discriminate the contribution of excluded vol-me, electrostatic and steric interactions, respectively, to the linear and nonlinear vis-oelastic behavior. The main objective of the paper is to give some physical insight intohe microstructural origin of the G� hump.

I. MATERIALS AND EXPERIMENTAL METHODS

. Kaolinite

The clay particles used in this study are kaolinite particles, commercialized by Engel-ard Corporation �New Jersey� and referenced as Miragloss 91. Kaolinite particles con-ist of alumino silicate layers, responsible for their plate-shaped geometry. The averageiameter of kaolinite particles d�032 �m, obtained from the particle size distributionetermined with a particle size analyzer �laser Malvern Mastersizer 2000�, is consistentith the diameter value of 0.30 �m given by the supplier; the aspect ratio d /h is about0, h being the thickness of the plate.

The charge on the faces of the kaolin particles is negative and pH independent, whilehe charge on the edges changes from positive to negative values with increasing pH, dueo the coexistence of both positive and negative charges. Between pH 5 and 9, the edgeurface is expected to be negatively charged �Lee et al. �1991��. The kaolin powder wasispersed in an aqueous sodium phosphate buffer solution with an ionic strength I�410−3 M. A washing process, consisting of a centrifugation and redispersion sequence,as repeated until the pH ��7.3� and the ionic strength of the suspending medium were

he same as the original buffer solution �Jogun and Zukoski �1996��. As shown by Nicolnd Hunter �1970�, phosphate ions preferentially condense on the edges, leading to theeutralization of possible positive charges. Under these pH and ionic strength conditions,he negative charge of both the basal planes and the edges of the particles gives rise tolectrostatic repulsive interactions, minimizing particle aggregation. Measurements haveeen performed at ionic strength ranging from 3�10−3 M to 1.3�10−2 M and volumeraction � from 0.33 to 0.55 in order to study the influence of electrostatic and stericnteractions on viscoelastic behavior. All suspensions have a volume fraction much higherhan the critical volume fraction �*�0.1, corresponding to the onset of excluded volume
nteractions.

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. Polymer

The polymer used is a commercial �hydroxypropyl� guar, �HPG�, synthesized by Fra-elli Lamberti s.p.a. �Albizzate, Italy�. The weight average molecular weight is about 2

1016 corresponding to a degree of polymerization of about 3000, and the dispersityndex is close to 1.5. This polysaccharide contains an average of one hydrophilic sub-tituent �hydroxypropyl or hydroxybutyl group� per monomer. The intrinsic viscosity ofPG macromolecules is �1200 cm3/g corresponding to a radius of gyration of about0 mm.

. Adsorption measurements

Kaolinite suspensions in the presence of polymer have been prepared by dispersing theroper amount of clay particles into polymer solutions at ionic strength I=4�10−3 M.uspensions are stirred 24 h at room temperature before measurements. Samples contain-

ng polymer were first centrifuged at 18,000 rpm at 25 °C during 1 h in order to separateaolinite particle covered by polymer chains, located at the bottom, from the nonadsorbedhains located in the supernatant. A direct concentration measurement by the total organicarbon technique was used to determine the equilibrium concentration of the free chainoncentration Cequ in the supernatant. For this purpose, a small sample of supernatant waseated at 68 °C in an O2 atmosphere, so that all carbon atoms are to be found in CO2,hose concentration was determined by spectrometry; the free polymer concentrationas inferred from knowledge of the chemical structure of HPG.The polymer-adsorbed amount � was calculated from the difference between the ini-

ial polymer concentration and the equilibrium concentration.

. Rheometry

Viscoelastic measurements were performed on a controlled strain rheometer �ARES,heometric Scientific� equipped with either a cone-and-plate geometry �diameter�0 mm, cone angle�0.04 rad� or a parallel-plate geometry �diameter�25 mm, gap�mm�. The absence of a significant slip at the wall was verified by varying the gap from

.2 to 2 mm. Viscoelastic measurements are influenced by the stress history imposed onhe material before experiment, for example, during the loading of the sample in theheometer. So, a protocol was defined to assure the desired reproducibility: after loadingn the rheometer, the sample is kept at rest for a fixed time before starting the rheological

easurement. The resting time has been preliminary, determined from oscillatory mea-urements performed in the linear viscoelastic domain: immediately after loading theample, the time evolution of the elastic modulus G� at a frequency of 1 Hz is followednd the time needed to attain a G� constant value is determined. This time, which is aboutmin, can be considered as the time needed to recover an equilibrium structure. More-

ver, we have systematically verified that the nonzero normal force, which appears dur-ng the loading of the sample, has decayed to zero before starting a test. A thin layer ofow viscosity silicone oil was spread over the air/suspension interphase in order to pre-ent solvent evaporation. The presence of edge instabilities, such as edge fracture �Larson1992��, has never been detected by visual observation of the air/suspension interfaceuring measurement. Compared to other systems, such as polymer solutions or meltshich have large normal stresses, the absence of visible edge instabilities is probably due

o the low elasticity level of the suspensions studied. At all ionic strengths, volumeractions and polymer concentrations investigated, electrostatic repulsive interactions,
ombined with excluded volume interactions are strong enough to allow a good disper-

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ion and stability of the suspension over a long period of time �a few days� and preventhe samples from sedimentation during rheological tests �Bossard �2001��. All tests wereerformed at 25 °C.

II. RESULTS AND DISCUSSION

. Influence of volume fraction

Figure 1 shows the shear strain amplitude dependence of the storage modulus and theoss modulus measured at the frequency of 1 Hz for a suspension at �=0.55. The vis-oelastic behavior is representative of those obtained for any suspensions tested. As sheartrain amplitude increases, both moduli exhibit a constant value G0� and G0�, with G0�

G0�, until a critical shear strain amplitude �c, which defines the extent of the lineariscoelastic regime. Above �c, G� modulus decreases gradually with increasing sheartrain amplitude while G� modulus exhibits a strain hardening characterized by a humpith a maximum value, noted Gmax� , for a shear strain amplitude �max.Let us consider first the linear viscoelastic regime. Figures 2�a� and 2�b� show G0� and

0� moduli and critical shear strain amplitude �c as a function of volume fraction, respec-ively. In the narrow volume fraction range investigated, both moduli in the linear regimencrease sharply with �. The volume fraction dependence of G0� and G0� moduli is prop-rly described by a power law, with an exponent of about 17 and 11, respectively. Similarolume fraction dependence of G0�, with an exponent lying from 10 to 20, has beenentioned for sterically interacting hard sphere suspensions �Rabaioli et al. �1993�; Rao

t al. �2006��. Due to the anisometric character of kaolinite particles, volume fractionffects will be discussed in terms of excluded volume interactions rather than stericnteractions. Such volume fraction dependence of the material parameters G0� and G0�uggests that excluded volume interactions play an important role in the elasticity andiscosity enhancement of kaolinite suspensions.

The linear viscoelastic behavior can be analyzed in terms of cohesive energy density

IG. 1. Storage modulus G� and loss modulus G�, at frequency of 1 Hz, as a function of shear strain amplitude,=0.55.

c corresponding to the work needed to break the structure

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IG. 2. �a� Storage modulus G0� and loss modulus G0� in the linear regime; �b� critical shear strain amplitude �c

nd �c� cohesive energy density Ec as a function of volume fraction, =1 Hz.

he cohesive energy density is then

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As depicted in Fig. 2�c�, the cohesive energy density of kaolinite suspensions scales as7. Such power law dependence of Ec has been observed for montmorillonite �Sohm andadros �1989�; Aubry and Moan �1997�� and Laponite �Ramsay �1986�� suspensions withmaller exponents, 3 and 1.8, respectively. From a phenomenological point of view, thencrease of the cohesive energy density with increasing volume fraction is a direct con-equence of the enhancement of excluded volume interactions between plate-like par-icles, due to the reduction of the average inter-particle distance.

Let us consider now the nonlinear viscoelastic regime. In order to compare qualitativeffects of volume fraction on viscoelastic behavior, G� and G� moduli have been normal-zed by their respective values in the linear regime G0� and G0�. Figure 3 represents theeduced storage modulus G� /G0� as a function of reduced shear strain amplitude �0 /�c atarious volume fractions. All reduced storage moduli can be plotted on a master curve.o have a rheo-physical insight into the viscoelastic behavior of concentrated suspen-ions, measurements have been carried out at various frequencies. As shown in the insetor a suspension at �=0.55, the elastic behavior is frequency independent. These resultsoint out that the elastic response of kaolinite suspensions is not related to the time scalef the mechanical stress but depends mainly on the shear strain amplitude. Figure 4hows the reduced loss modulus G� /G0� as a function of shear strain amplitude �0 atifferent volume fractions. At �=0.40, the loss modulus decreases with increasing sheartrain amplitude whereas the strain hardening in G� appears at intermediate shear strainmplitudes for ��0.40 and its intensity increases with �, i.e., with decreasing inter-

IG. 3. Reduced storage modulus G� /G0� as a function of reduced shear strain amplitude �0 /�c at volumeractions �=0.40 ��, 0.45 ��, 0.50 ��, and 0.55 ��, =1 Hz. Inset: reduced storage modulus G� /G0� ofhe suspension at �=0.55 as a function of reduced shear strain amplitude �0 /�c at different frequencies.

article distance. As observed for the storage modulus, the inset shows that the loss

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odulus profile is frequency independent. It has to be noticed that such strain hardeningn G� has been already observed for kaolinite �Jogun and Zukoski �1999, 1996�; Yziquelt al. �1999a, 1999c��, Laponite �Avery and Ramsay �1986�� and montmorillonite sus-ensions �Marchal et al. �1996��. However, this nonlinear G� feature at intermediate sheartrain amplitudes has been scarcely discussed and interpreted �Avery and Ramsay1986��. The strain hardening in G� is expected to depend on inter-particle interactions,hat is, on inter-particle distance. As volume fraction lies from 0.4 to 0.55, the inter-article distance, noted e and estimated from a packed organization of piled clay particlessing Eq. �4�, ranges approximately from 50 to 20 nm, which is small compared to theverage plate diameter d�320 nm.

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At such dense packing, an oscillatory shear induces complex relative motions of twoery close neighboring particles. The relative displacement has been evaluated, consid-ring the simple case of two parallel particles with an inter-particle distance e, orientedith an angle relative to the velocity field, as presented in Fig. 5. For this purpose, theisplacement gradient tensor �� has been determined using Eq. �5�. Details are reportedn the Appendix:

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�0 sin2 �0 sin 2 . �5�

IG. 4. Reduced loss modulus G� /G0� as a function of shear strain amplitude �0 at volume fractions �=0.40��, 0.45 ��, 0.50 ��, and 0.55 ��, =1 Hz. Inset: reduced loss modulus G� /G0� of the suspension at �0.55 as a function of reduced shear strain amplitude �0 /�c at different frequencies.

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Thus the relative displacements along directions parallel and orthogonal to the basallane are given by the following relations:

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These equations show that kaolinite particles have a complex motion: the displace-ent, �d, along the basal plane corresponds to a sliding motion and the displacement,e, along the orthogonal direction to the basal plane, corresponds to alternative pushingnd pulling apart basal surfaces of neighboring particles.

For =0, the relative displacement is a slipping motion only and for =45°, �e isaximum. These two relative displacements have been estimated for clay suspensions at=0.55 in the arbitrary case =30° at shear strain amplitude �c=2% and �max=30%. At

hear strain amplitude �c, �d /d and �e /e are small: �0.1% and 0.6%, respectively.herefore, under shear strain amplitude �0 �c, the relative displacement of clay par-

icles is too weak to disrupt the microstructure. As shear strain amplitude increases,elative displacements �d /d and �e /e increase and reach 1.6% and 9.6%, respectively, athear strain amplitude �max=30%. Thus, along the basal plane, displacement �d of ka-linite plates is small compared to their average diameter but displacement �e is non-egligible compared to the inter-particle distance. To get a physical insight into the originf the strain hardening in G�, let us consider the repulsive electrostatic interactions andxcluded volume interactions. The fluctuation of the inter-particle distance induced byscillatory shear measurement is responsible for the variation of both electro-viscousissipation, through the deformation of the diffuse charge clouds surrounding particles,nd steric interactions between neighboring particles. The two contributions are com-ined: excluded volume interactions force close-packed plate-like particles to align,hich enhances electrostatic interactions. On increasing volume fraction, inter-particleistance decreases, leading to strengthen the electro-viscous dissipation and steric inter-ctions. Consequently, the increase of the strain hardening intensity in G� with increasing

originates from the increase of both excluded volume and electrostatic interactions,overned by the fluctuation of the inter-particle distance during oscillatory shear mea-urement. This physical interpretation will be confirmed in the following section devoted

FIG. 5. Schematic illustration of two neighboring plate-like particles under oscillatory shear.

o the influence of ionic strength.

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. Influence of ionic strength

Figures 6�a� and 6�b� show the plateau storage modulus G0� and the critical shear strainmplitude �c, respectively, measured at =1 Hz, as a function of ionic strength, atolume fractions �=0.40, 0.45, 0.50, and 0.55. For all volume fractions investigated, thelateau storage modulus decreases and the critical shear strain amplitude increases withncreasing ionic strength. The ionic strength dependence of G0� and �c induces a decreasef the cohesive energy density with increasing ionic strength, as depicted by Fig. 6�c�. It

IG. 6. �a� Storage modulus in the linear regime, �b� critical shear strain amplitude �0 and �c� cohesive energyensity Ec as a function of ionic strength at volume fractions �=0.40 ��, 0.45 ��, 0.50 ��, and 0.55 ��,=1 Hz.

as to be noticed that the decay of Ec is more and more pronounced as volume fraction

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ncreases. At ionic strength I=4�10−3 M, the Debye length �−1 is close to 4 nm, that is20% of the inter-particle distance e at �=0.55. Consequently, basal surfaces bearing

egative charges undergo strong repulsive interactions at low ionic strength. As ionictrength increases, repulsive interactions are gradually screened, leading to a decrease ofhe cohesive energy density. Such effect is enhanced when the inter-particle distanceecreases, i.e.,when the volume fraction increases.

The ionic strength also modifies qualitatively the viscoelastic behavior in the nonlinearegime. Figures 7�a� and 7�b� show the reduced storage modulus G� /G0� and the reducedoss modulus G� /G0� as a function of reduced shear strain amplitude �0 /�c, measured at=1 Hz, for a suspension at �=0.55 at different ionic strengths, from I=3�10−3 M to

.3�10−2 M. The reduced storage modulus G� /G0� is well described by a master curveor all ionic strengths investigated, whereas the G� /G0� hump is progressively reduced asonic strength is increased. As shown in Fig. 8, the decay of the intensity of strain

IG. 7. �a� Reduced storage modulus G� /G0�, �b� reduced loss modulus G� /G0� as a function of reduced sheartrain amplitude �0 /�c at ionic strengths I=3�10−3 M ��, 4�10−3 M ��, 6.8�10−3 M ��, 10−2 M ��nd 1.3�10−2 M ��, �=0.55 and =1 Hz.

ardening in G� with increasing ionic strength comes out for all volume fractions inves-

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igated, and it is more pronounced as volume fraction increases. The ionic strengthependence of the intensity of the strain hardening in G� is attributed to the decrease ofhe Debye length �−1 that weakens electro-viscous effects.

. Influence of polymer concentration

In this third section, HPG at various concentrations is added to concentrated suspen-ions at �=0.45 and I=4�10−3 M in order to modify the nature of the inter-particlenteractions that govern the rheological behavior. Preliminary adsorption measurementsave been carried out to define the saturation concentration, corresponding to the totaloverage of kaolinite particles by polymer chains. Measurements that request the cen-rifugation of suspensions cannot be performed at �=0.45 for which a sufficient volumef supernatant cannot be obtained. Consequently, adsorption measurements have beenerformed at solid/liquid ratios S /L ranging from 0.46% to 20%, corresponding to vol-me fractions from 0.0018 to 0.0714, respectively. Figure 9 shows the adsorption iso-herm of HPG at various solid/liquid ratios. As equilibrium concentration increases, alldsorption isotherms are characterized by a sharp increase of the adsorbed amount, fol-owed by an adsorption plateau marking the saturation of kaolinite surfaces. Adsorptionsotherms can be correctly fitted to Langmuir equation

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1 + K . Cequ, �8�

here �m is the saturated adsorption and K is the equilibrium constant, in the very diluteimit. This model has been applied successfully to describe the adsorption isotherm ofPG on Laponite particles �Aubry et al. �2002��. Equation �8� is used as a fit equation toetermine the saturated adsorption at different S /L ratios. Adsorption at saturation �m,eported as a function of S /L ratios in inset of Fig. 9, decreases upon increasing volumeraction. Such decay is due to the decrease of accessible particle surfaces for polymerhains as inter-particle distance decreases �Lee et al. �1991�; Argillier et al. �1996�;

IG. 8. Reduced intensity of the G� peak as a function of ionic strength, at volume fractions �=0.40 ��, 0.45��, 0.50 ��, and 0.55 ��, =1 Hz.

abzar et al. �1986��. In the S /L ratio range investigated, the saturated adsorption decay

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s correctly fitted by a power law. Assuming that the adsorption mechanism is not modi-ed at high S /L ratios, the adsorption at saturation at S /L=210% �corresponding to �0.45� can be estimated through data extrapolation. The extrapolated �m value is aboutmg/g, which corresponds to a polymer concentration at saturation of about 2000 ppm.Figure 10 shows the shear strain amplitude dependence of storage and loss moduli of

=0.45 kaolinite suspensions �i� without polymer �ii� with 2000 ppm of HPG, corre-ponding to the estimated polymer concentration at saturations �iii� with 6250 ppm ofPG, i.e., with polymer in excess. From a qualitative point of view, the shear strain

mplitude dependence of viscoelastic moduli of suspensions in the presence of polymer is

IG. 9. Adsorption isotherms of HPG on kaolinite particles at solid/liquid ratio S /L=0.46% ��, 1% ��, 2%��, 4% ��, 10% ��, and 20% ��. Inset: adsorption at saturation, �m, as a function of S /L.

IG. 10. Shear strain amplitude dependence of storage modulus �open symbol� and loss modulus �full symbol�f kaolinite suspensions at �=0.45 without polymer �� , � �, with 2000 ppm �� , � � and 6250 ppm �� , � � of
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imilar to that observed without polymer. It is worth mentioning that shear strain ampli-ude �max increases drastically with increasing polymer concentration, especially above000 ppm. Linear viscoelastic parameters G0�, G0� and �c are plotted as a function ofolymer concentration in Fig. 11. As polymer concentration increases up to 2000 ppm,oth G0� and G0� moduli increase sharply and the critical shear strain amplitude remainsearly constant. Above 2000 ppm, both G0� and G0� moduli decrease and �c increasesrastically. The dependence of rheological parameters with polymer concentration in theinear viscoelastic domain is shown in Fig. 12. The cohesive energy density curve �Fig.2�a�� displays an intermediate concentration regime, from 2000 to 4000 ppm, where it isonstant, separating two regimes at low and high concentrations, characterized by aubstantial increase of cohesion energy density with increasing polymer concentration.herefore, the concentration of �2000 ppm, corresponding to the polymer concentrationt saturation, appears as a transition concentration in the rheological behavior of concen-rated suspensions. The description in three concentration regimes is also relevant regard-ng the reduced intensity of the G� peak, presented in Fig. 12�b�. In the lowest concen-ration regime, that is up to 2000 ppm, the intensity of the strain hardening in G�ncreases sharply upon increasing polymer concentration. The intermediate concentrationegime is characterized by a significant reduction of the rate of increase of the Gmax� /G�atio, up to 4000 ppm. Above 4000 ppm, Gmax� /G� decreases extensively, and finallyends to a nearly constant value at high polymer concentrations.

From a molecular point of view, adsorbed polymer chains are known to form a poly-er layer with a thickness close to the radius of gyration, Rg, of free chains �Semenov et

l. �1996, 1997��. Assuming that kaolinite particles are uniformly dispersed, the averagenter-particle distance is about 40 nm at �=0.45, which is much smaller than 2Rg

180 nm, meaning that adsorbed polymer chains are most likely confined within thisarrow inter-particle region. As a consequence, in the low concentration regime, theontribution of polymer chains to the enhancement of both cohesive energy density andtrain hardening in G� can be attributed to both polymer bridges between clay particlesnd steric interactions of confined adsorbed polymer. However, at high polymer concen-rations, above 4000 ppm, the enhancement of cohesive energy density is mostly due to

IG. 11. Storage modulus in the linear regime, loss modulus in the linear regime and critical shear strainmplitude �c of kaolinite suspensions at �=0.45 as a function of polymer concentration, =1 Hz.

teric interactions induced by free polymer chains, which make particle bridges less

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ikely. The rate of increase of Ec, which is more important in the lower concentrationegime than that in the higher one, suggests that the contribution of bridging polymerhains to cohesive energy density is more important than that induced by steric interac-ions between polymer chains, which makes sense. Concurrently, free chains induceubrication effects between kaolinite particles covered by adsorbed polymer chains,hich may be responsible for the sharp decay of the strain hardening in G� above000 ppm, and could also explain the high value of the shear strain amplitude, �max,orresponding to the maximum of the strain hardening in G�. In the intermediate con-entration regime, steric interactions between adsorbed polymer layers overcome contri-utions to cohesive energy density from particle bridging, finally leading to a leveling offf Ec.

V. CONCLUDING REMARKS

Linear and nonlinear viscoelastic behaviors of concentrated suspensions of kaolinitelate-like particles have been investigated as a function of volume fraction, ionictrength, and polymer concentration. These three adjustable parameters have been used toune the influence of inter-particle interactions: excluded volume interactions betweenlay particles, long range electrostatic repulsive interactions and steric interactions me-

IG. 12. �a� Cohesive energy density Ec and �b� reduced intensity of the G� peak of kaolinite suspensions at=0.45 versus polymer concentration, =1 Hz.

iated by adsorbed polymer chains.

pc

Gcit

fap

A

It

.

i

c

w

R

A


As repulsive interactions increase, by either increasing volume fraction or increasingolymer concentration or decreasing ionic strength, the cohesive energy density of con-entrated suspensions increases.

The nonlinear viscoelastic behavior has been thoroughly investigated. In particular, the� vs. strain amplitude curve exhibits a hump, characterized by a relative intensity which

an be tuned by repulsive interactions. This strain hardening in G� is mostly enhanced byncreasing repulsive interactions, except at high polymer concentrations, due to lubrica-ion effects mediated by free polymer chains.

The whole set of rheological data suggests that the strain hardening in G� originatesrom extra electro-viscous dissipation, due to the coupled increase of excluded volumend electrostatic interactions, which are both modulated by the fluctuation of the inter-article distance during oscillatory shear measurement.

ppendix

Under oscillatory shear, any vector du�dx0 ,dy0� is transformed into du��dx0� ,dy0��:

�du�� = �F0��du� or �dx0�

dy0�� = �dx0 + �0 · dy0

dy0� .

n the coordinate system of the laboratory, �x0 ,y0�, the gradient tensor of the transforma-ion is given by

�F0� = �1 �0

0 1�

In the coordinate system of the particle �x ,y�, the gradient tensor of the transformations given by �F�= �R�,z0�

−1 ��F0��R�,z0��.With

�R�,z0�� = � cos sin

− sin cos �,

onsequently:

�F� =1 −�0

2sin 2 �0 cos2

�0 sin2 1 +�0

2sin 2 = �1d� + �� ,

ith �Id� the identity matrix and ��, the displacement gradient tensor

�� =−�0

2sin 2 �0 cos2

�0 sin2�0

2sin 2 .

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LINEAR AND NONLINEAR VISCOELASTIC BEHAVIOR OF OIL-IN-WATER EMULSIONS STABILIZED WITH POLYSACCHARIDES

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