Thixotropic behavior of clay dispersions: Combinations of scattering and rheometric techniques

Thixotropic behavior of clay dispersions: Combinations of scattering and rheometrictechniquesFrédéric Pignon, Albert Magnin, and Jean-Michel Piau Citation: Journal of Rheology (1978-present) 42, 1349 (1998); doi: 10.1122/1.550964 View online: http://dx.doi.org/10.1122/1.550964 View Table of Contents: http://scitation.aip.org/content/sor/journal/jor2/42/6?ver=pdfcov Published by the The Society of Rheology

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Thixotropic behavior of clay dispersions: Combinationsof scattering and rheometric techniques

Frederic Pignon, Albert Magnin,a) and Jean-Michel PiauLaboratoire de Rheologie,b) B.P. 53, 38041 Grenoble cedex 9, France

(Received 3 December 1997; final revision received 11 August 1998)

Synopsis

The thixotropic behavior of a colloidal dispersion of clay consisting of disk-shaped particles wasstudied by means of a combination of rheometric measurements, static light scattering, andsmall-angle neutron scattering. At rest, the structure of the gel consists of dense micrometer-sizedaggregates assembled into a fractal mass of dimensionD. Under shear, in the case of volumefractions with (1< D < 1.2) at rest, a butterfly-type light scattering pattern is observed. This isattributed to the formation of rollers within the dispersion, which align themselves on averageperpendicular to the direction of shearing. This produces a fall in resistance to flow and in viscosity.The influence of shear rate on this disaggregation process was studied and linked to the rheometricmeasurements. Under shear flow conditions, the fall in viscosity is due to orientation anddisaggregation processes occurring at length scales on the order of 1mm. During recovery, the twotime scales identified correspond, respectively, to a rapid relaxation of the particle orientations anda slow aggregation process. Thixotropic behavior is identified as being mainly a reversibleaggregation process, for which large length scales on the order of a micrometer associated with afractal arrangement play a decisive role. ©1998 The Society of Rheology.@S0148-6055~98!01506-5#

I. INTRODUCTION

Of the various types of complex behavior encountered with colloidal dispersions,thixotropic behavior is very frequent. In these cases, the viscosimetric properties of thematerial are dependent upon both time and shear rate. A material is usually termedthixotropic @Mewis ~1979!# if, starting from a sufficiently long rest state, its viscositydecreases with time, when a constant shear is applied~breakdown!. If the shear ceases,the material gradually recovers its consistency and the structure that it had at rest~recov-ery!. Thixotropic behavior is thus a reversible phenomenon. Thixotropy can be defined asthe tendency of matter to exhibit a time-dependent change in its reference properties~reference viscosity, yield value, time scale, elasticity modulus, loss modulus, etc., orconductivity! when stresses are applied, and to recover these reference properties pro-gressively when stress is relieved@Piau~1997!#. This type of behavior is found in manydispersions formed from particles of various sizes and shapes~fibrous dispersions, crys-talline systems!, bubbles ~emulsions!, or macromolecules~polymer systems! @Cheng~1987!#.

Thixotropy has been observed for many years, but the physical mechanisms governingit are still poorly identified. Nevertheless, an understanding of the mechanisms that cause

a!Author to whom all correspondence should be addressed; electronic mail: [email protected]!UniversiteJoseph Fourier Grenoble I, Institut National Polytechnique de Grenoble, and CNRS~UMR 5520!.

© 1998 by The Society of Rheology, Inc.J. Rheol. 42~6!, November/December 1998 13490148-6055/98/42~6!/1349/25/$20.00


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this complex rheological behavior at mesoscopic scale is of vital importance when usingsuch materials and in controlling the industrial processes in which they are involved.Indeed, the entities dispersed in the matrix medium of such systems form aggregatesunder the effect of attraction and repulsion forces that may give rise to a continuousaggregated structure throughout the available bulk of the sample. These materials maythen possess yield stresses and/or time- and shear-dependent viscoelastic properties. Con-sequently, a combined study of the structure at mesoscopic scale and of the macroscopicmechanical behavior of these colloidal dispersions in flow conditions is of decisive im-portance for understanding the mechanisms governing their thixotropic behavior. Further-more, a knowledge of the length and time scales governing the mechanisms of thixotropyis essential for understanding such a property.

Laponite was chosen for this study of thixotropic behavior. This is a synthetic clay ofthe hectorite type, consisting of anisotropic particles of nanometric size. The disk-shapedparticles have marked anisotropy and a different surface polarity on their edges and sides.Consequently, the arrangement of the particles within the aqueous medium will bestrongly influenced by the particle volume fraction, by thepH, and by the ionic contentof the surrounding aqueous medium. Depending on these three parameters, the disper-sions can have different states: a stable colloidal solution, an elastic gel, a plastic paste oreven separate solid and liquid phases. The gel state is reached above a volume fractionfv* , for a given ionic strengthpH and gelation time. The existence of a yield stress isoften associated with the structure of a thixotropic material at rest, and this is why the gelphase is the principal field examined in this article.

The aims here are first to examine the influence of shear flow on structural changes inthe thixotropic dispersions at various length scales and to link these with their macro-scopic properties, and second to define the various pertinent time and length scales thatgovern the mechanisms occurring in the thixotropic process.

To do this, macroscopic rheometric measurements in the bulk of the sample werecombined with physical investigations of its structure, involving static light scattering andsmall-angle neutron scattering of the dispersions at rest and during flow.

In the case of thixotropic behavior, the mechanical properties and state of the structureare time and shear dependent. It was decided to dissociate the study of these two com-ponents~time and shear rate! in order to understand more clearly the mechanisms gov-erning the thixotropic behavior.

After describing the material and the experimental techniques used, this article willdiscuss the structure and mechanical behavior of the material under steady conditions.With an established shear, constant in time, the study will focus on the effect of shearintensity on the structural state of the material and its mechanical response, under steadyconditions. Second, transient conditions will be discussed: with shear of constant inten-sity, the study will focus on time-dependent changes in the structural and rheometricparameters.

II. MATERIALS AND EXPERIMENTAL TECHNIQUES

A. Materials

The synthetic clay used for the experiments, Laponite XLG, is manufactured byLaporte Industrie. Its chemical composition is as follows: 66.2% SiO2, 30.2% MgO,2.9% Na2O, and 0.7% Li2O, which corresponds to the chemical formula:

[email protected]#0.72Na0.7

0.71.

1350 PIGNON, MAGNIN, AND PIAU


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The suspension is prepared as follows: the clay powder is mixed in a solution ofdistilled water and NaCl at a concentration of 1023 M. This is then stirred for 30 min ata temperature of about (2062) °C by means of a deflocculating vane rotating at 1500rpm. A few hours after stirring, a transparent gel is formed.

Interparticle reactions take place as the clay swells following preparation. The sus-pended particles are thus subject to electrostatic repulsion and attraction, which are incompetition with the Van der Waals attraction, polar repulsion between water moleculesadsorbed at the surface, interparticle excluded bulk effects, and Brownian motion. De-pending on the particle concentration, the ion content of the water, and thepH value,these states may give rise to a stable colloidal solution, an elastic gel, plastic paste, oreven separate solid and liquid phases@Mourchid et al., ~1995!#.

This clay is of high purity and has a small and remarkably uniform crystallite size. Itwas thus possible to use radiation~x-rays, neutrons, and light! scattering techniques inorder to examine the structure over extensive length scales ranging from a few nanom-eters to a few micrometers. Because of the transparency of the dispersions, it was pos-sible to visualize the strain field in the bulk of the sample at the same time as therheometric measurements.

ThepH value of all the preparations studied in this article was adjusted to 9.5 in orderto avoid any later dissolution of the material. Thomson and Butterworth~1992! showedthat there is significant dissolution of magnesium silicate withpH values of less than 7and the disappearance of such dissolution atpH values above 9.

The study domain corresponds to that in which a thixotropic gel is obtained. With aweak ionic strength~@NaCl# 5 1023 M), at apH of 9.5, this domain extends in concen-tration from 0.931022 to 531022 g m21, corresponding to a volume fractionfv of0.35 to 2 vol %.

The density of the particles is 2.53 g cm23 @Rosta and Von Gunten~1990!#. At thisionic strength, the sol–gel transition is marked by the volume fractionfv*' 0.35 vol % @Mourchid et al. ~1995!#.

The ageing or gelation timetp takes into account the change occurring in the clay gelsduring the time that elapses from the end of sample preparation. This time-dependentchange in the gels corresponds on the one hand to the osmotic swelling caused byrepulsion between the double layers and on the other hand to a slow aggregation process,the kinetics of which are strongly dependent upon the particle volume fraction. With anincreasing volume fraction, the kinetics of gelation are increasingly rapid. This aggrega-tion process was studied by static light scattering@Pignonet al. ~1997a!#.

In the concentration domain studied here, the gels display marked thixotropy. Simplyshaking the flask by hand is enough to liquefy the suspension, and this returns to its initialconsistency as soon as it is left to rest.

B. Rheometric techniques

The rheometric measurements were performed on Weissenberg–Carrimed and Rheo-metrics RMS 805 controlled-shear rheometers at a temperature of (2061) °C. The RMS805 rheometer gave short-period stress responses during transient conditions, the re-sponse time of the torque sensor being less than 1022 s. Two types of setup were used:

~i! a cone-plate setup~angle 0.076 rad and radius 24.5 mm!. The instruments weremade of steel, covered with glass paper with a roughness of 200mm @Magnin andPiau ~1990!#.

~ii ! a plate-plate setup, consisting of two quartz disks of 20 mm radius. The surface

1351THIXOTROPIC BEHAVIOR OF CLAY DISPERSIONS


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roughness was on the order of 50 nm. The gap was fixed at 0.4 mm in order toreproduce the shearing conditions applied during static light scattering.

During preliminary work@Pignonet al. ~1996b!#, it was shown that instabilities occurin flowing thixotropic yield-stress fluids. However, by carefully monitoring the kinematicfield, it was possible to identify the volume fraction and shear rate domains where correctstrain is achieved throughout the bulk of the sample. Measurements in the two setups~smooth and rough! were compared, and combined with visualization of the strain field.It was thus possible to identify the volume fraction and shear rate domains where homo-geneous strain of the sample occurs with no slip at the wall–sample interfaces.

During the recovery tests, which involve long times, the atmosphere around thesample was saturated with water to prevent evaporation@Magnin and Piau~1990!#.

C. Breakdown using ultrasonic waves

Tests were carried out to break down the structure of the material using ultrasonicwaves. The apparatus consisted of a Labsonic U ultrasonic rod. This transmits waves at20 kHz frequency into the sample between 30 and 350 W, with impulse times varyingfrom 0.1 s to a continuous impulse. For the long recovery tests, the buildup dispersionwas kept in a water-tight bottle to avoid evaporation. Every 24 h, a part of the dispersionin the bottle was taken and changed in the cone-plate setup for measurements. Hence themeasurements ofG8 andG9 correspond to different samples of the same builtup disper-sion.

D. Static light scattering „SLS… under shear flow conditions

The laser test facility used for the experiment was developed and built at the Labora-toire de Rhe´ologie in Grenoble@Dorget~1995!; Piauet al. ~1998!#. It consists of a 2 mWlaser beam~He–Ne! with a wavelengthl 5 6328 Å, and a Fresnel lens acting as ascattering screen. The detector is a video camera with a charge coupled device~CCD!7523582 pixel sensor. The analysis is performed by image processing a video systemand a specific software to carry out the conventional integration operations. The scatter-ing patterns are recorded by the camera and video system throughout the test. Themodulus of the scattering vector is defined byQ 5 (4pn/l)sin(u/2), wheren is therefractive index of the suspending medium,l is the wavelength of the radiation, andu isthe scattering angle. The light scattering measurements cover aQ domain, ranging from231025 to 431024 Å 21.

A plate–plate shear cell was built to observe the structure during flow~Fig. 1!. Thesample, which has a fixed thicknesse0 5 0.4 mm, is sheared between two parallel quartzdisks, one of which rotates at an angular rotation speedv around the axisOx. The lightbeam is directed alongOx, perpendicular to the disks lying in the planeOyz, at a pointalong the horizontal axisOz, located at a distanceRc from the axis of rotationOx. Thevelocity V 5 2vy is collinear to the axisOy. The intensity of light scattered by thesample is recorded by the detector in the planeOyz. Consequently, the plane of obser-vation corresponds to the plane (y,z) 5 (v,z). The local shear rate at a given distanceRc with a modulusg 5 Rcv/e0 , belongs to the planeOxy. This system can be used toapply jumps in shear rate between 0 and 500 s21 and sudden interruptions over very shortperiods~ ' 0.15 s!. After shearing has stopped, it is possible to monitor the changesoccurring as the sample recovers its structure. This cell is airtight, which prevented thesamples from evaporating as their recovery was being monitored.



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E. Small-angle neutron scattering „SANS…

The measurements were made at the Laue–Langevin Institute in Grenoble, usingmulti-detector D11, with a wavelength of 6Å. The samples were placed at distances of 10and 35.7 m from the detector, with beam collimations of, respectively, 20.5 and 40.5 m.The SANS measurements cover aQ domain, ranging from 231023 to 231021 Å 21. ACouette shear cell developed by Lindner and Oberthu¨r ~1984! was used for the measure-ments under shear conditions. This quartz cell consists of a fixed inner cylinder~stator!and a rotating outer cylinder~rotor! ~Fig. 2!. Radiation is directed along the main axis ofthe shear cell, and the observation plane is (y,z) 5 (y,v). The stator is 46 mm in

FIG. 1. SLS under shear. Plate-plate shear cell and coordinate system for the optical setup.

FIG. 2. SANS under shear. Schematic illustration of the quartz Couette cell used for scattering measurements.



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diameter and the gap is 0.5 mm wide, so that the sample crossed by radiation is 1 mmthick in total. The detector consists of a set of 64364 elements measuring 1 cm31 cm.The data were analyzed with standard programs in order to eliminate background incon-sistencies. The radial mean of the total scattering intensity was then calculated, usingclassic integration software.

F. Procedures for characterizing thixotropic behavior

The established procedures for characterizing thixotropic behavior@Mewis ~1979!;Cheng~1987!; Coussot~1992!; Coussotet al. ~1993!; Mas and Magnin~1994!; Ducerf~1995!; Pignonet al. ~1996b!# employed in this work are shown schematically in Fig. 3.

In the study of breakdown, the procedure involves applying a jump in shear rate froman initial value (g i ) to a final value (g) with (g i , g) ~the initial shear may be nil,

FIG. 3. Procedures for characterizing thixotropic behavior.



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characterizing the rest state!. During this test, the material passes from an aggregatedstructure with a certain ‘‘high’’initial consistency to a less aggregated structural state, i.e.,with a lower level of consistency.

In the study of recovery, the procedure involves passing from a high initial shear rate(g i ) to a lower final shear rateg with (g , g i ). During this procedure, the materialgoes from an initial consistency with a structure at a certain level of disaggregation to ahigher consistency, i.e., a more aggregated structure. When the intrinsic recovery of thematerial is to be measured at the end of the initial shearing without destroying thestructure, a harmonic shear at low strain amplitude is applied.

In order to define the viscoelastic linear domain in these materials with time-dependent rheological properties, it is necessary to take into account the state of recoveryof the sample. To do this, two types of tests were performed to evaluate the extent of theviscoelastic linear domain for various ranges of frequency and strain@Pignon et al.~1997a!#.

In the first test, at a fixed frequency and at various recovery times, the sample wassubjected to a strain sweep.

In the second test, with a fixed strain amplitude corresponding to the linear straindomain defined by the first test, the recovery of the sample after breakdown is monitoredfor various oscillation frequency values.

These two tests defined the minimum recovery time for which a viscoelastic lineardomain is achieved. It is thus possible to monitor the kinetics of recovery by measuringthe viscoelastic moduli in time after this minimum recovery time.

III. STRUCTURE AND MECHANICAL BEHAVIOR IN STEADY CONDITIONS

The purpose of this section is to study the influence of shear intensity on the state ofaggregation of the structure and the relations that exist with the macroscopic mechanicalbehavior. The processes of disaggregation during shear flow are examined over the wid-est possible range of length scales~from a few nanometers to a few micrometers! in orderto determine the pertinent length scales that govern thixotropic behavior at the differentparticle volume fractions. The structural state and stresses will be characterized for agiven shear intensity under steady conditions. These steady states represent the initial andfinal conditions for studying the transition between recovery and breakdown discussed inSec. IV. It is first of all necessary to recall the state of the structure at rest, where theintensity of shearing is nil.

A. At rest

The structure at rest was studied by combining scattering measurements for varioustypes of radiation~x-rays, neutrons, and light! with rheometric measurements@Pignonet al. ~1996a! and~1997a!#. Two characteristic length scales were detected in these yieldstress suspensions. The first, measuring several tens of nanometers, and the second, onthe order of a micrometer, are linked to a fractal behavior of dimensionD that increaseswith the particle volume fraction. Consequently, it is suggested that the structure of thedispersions at rest is composed of subunits measuring a few tens of nanometers thatcombine to form dense aggregates measuring about 1mm. At larger length scales, thesemicrometer-sized aggregates are rearranged to form a continuous three-dimensional iso-tropic structure that has a fractal behavior of dimensionD, which gives the gels theirtexture. This fractal dimension is a function of the gelation time, particle volume fraction,and ionic content. With an increasing volume fraction, the kinetics of gelation are in-creasingly rapid. However, for a given ionic strength@NaCl# 5 1023 M, a pH ' 9.5,



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and gelation timetp > 250 days, it was possible to demonstrate three volume fractionzones that tend towards a well-defined fractal behavior.

In a volume fraction domain close to the sol–gel transition (0.35 vol %< fv< 0.56 vol %), the micrometer-sized aggregates form bundles (D 5 160.05), giving

the gels a fibrous texture. In a high volume fraction domain (1.20 vol %< fv< 2 vol %), the structure is more heterogeneous, with zones of dense and less dense

particle concentrations (D 5 1.860.01). Between these two volume fraction domains,there is a transition zone~with the fractal dimension rising from 1 to 1.8!, where themicrometer-sized aggregate fibers become entangled to produce an increasingly densestructure. The structure is shown schematically in Fig. 4.

The influence of volume fraction on structure was linked to the yield stress of thedispersions by means of a scaling law. It was demonstrated that the fractal dimension ofthe structure governs the change in yield stress with volume fraction@Pignon et al.~1996a!#. In addition, studying the influence of ionic strength and equilibrium gelationtime on the structure of the dispersions revealed that changes in fractal dimensionsgovern changes in mechanical properties@Pignonet al. ~1997a!#.

It is therefore essential to check the kinetics of aggregation found in these clay dis-persions in order to understand the structural and rheological mechanisms governing theirmacroscopic behavior at equilibrium.

The remainder of this article will discuss only results concerning the case of disper-sions with a fractal dimension at rest such that (1< D < 1.2), i.e., for a volume fractiondomain extended from 0.35 to 0.80 vol % at a weak ionic strength of 1023 M and pH

FIG. 4. Schematic representation of structure of Laponite suspension at rest. The network is made of two typesof characteristic aggregates:~a! subunits of oriented clay particles, which define a first length scale of about afew nanometers;~b! aggregates of tight isotropic distributions of subunits, which define a second length scaleof about one micrometer;~c! the loose connection of these micrometer-sized aggregates gives rise to anisotropic equilibrium structure.



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5 9.5. In these dispersions, which have a strong thixotropic character, measurementsshow that the kinematic fields are homogeneous, which meant that it was possible toconcentrate on the bulk properties of the samples. This is an important point, as in orderto study thixotropic behavior correctly, it is necessary to look at the bulk properties of thematerial.

The case of dispersions with fractal dimensions of more than 1.2, which is reached forvolume fraction domain extended from 1.2 to 2 vol % at a weak ionic strength of1023 M and pH 5 9.5, will not be discussed here as localized shear within the sample@Pignonet al. 1996b# has been demonstrated, preventing the bulk properties of the ma-terials from being determined.

B. Under shear flow conditions

Starting with a rest state, characterized by a fractal dimension that is constant in timeand an isotropic scattering pattern, the sample is subjected to a breakdown process at agiven shear rate. The equilibrium state of the structure under steady conditions is shownin Fig. 5 and the corresponding stress level in Fig. 6.

The dispersions observed by SLS during shear flow display anisotropic butterfly-shaped scattering patterns at low shear rates is shown in@Figs. 5~a2! and ~a3!#. With anincreasing shear rate, the dark streak perpendicular to the direction of shearing decreasesuntil it is completely filled by the scattering intensity in the direction of flow@Fig. 5~a4!#.Above a critical shear rate, the butterfly-like scattering pattern is replaced by an aniso-tropic scattering pattern with no extinction of the scattering intensity perpendicular to thedirection of flow @Fig. 5~a5!#.

Figure 7 shows the scattering intensityI v parallel to the velocity direction andI zperpendicular to it.I v and I z are obtained by integration of patterns on a strip ofQ5 0.53mm21 width, centered on the beam stop. At rest, the scattering is directionally

independent, characteristic of scattering from homogeneous isotropic [email protected]~a!#. At increasing shear rate and below the critical shear rate, scattering is enhancedalong the velocity direction, and the scattering intensity normal to it is reduced@Figs. 7~a!and 7~b!#. At 40 s21, I v /I z increases from about 2 to 5 for theQ domain extending from631025 to 331024 Å 21 @Fig. 7~b!#. Approaching the critical shear rate, the anisotropytends to decrease@Fig. 7~b!# and above the critical shear rate of 130 s21, the scatteringbecomes more and more isotropic with a further increase of the shear rate@Fig. 7~c!#.When shear ceases, the anisotropy is greatly reduced@Fig. 7~d!#.

In order to quantify the anisotropy of the scattering pattern more precisely, the inten-sity I (c) on a crown ~Fig. 8! was integrated over aQ domain from 731025 to1024 Å 21, such that

I~c! 5 ErQ1

rQ2I~rQ ,c!

rQ22rQ1

drQ

with Qi 5 2pdf r Qi/l, in which df is the distance between the sample and the Fresnel

lens@Dorget~1995!; Piauet al. ~1998!#. At rest the intensityI (c) is flat, confirming thatthe system is isotropic. During flow, maximum anisotropy occurs with the lowest shearrate~10 s21!. When the shear rate increases, the anisotropy decreases. Beyond a criticalshear rate, the anisotropy is severely reduced but remains significant.

The flow curve under steady conditions~Fig. 6! shows that the change in structurewith increasing shear rate is characterized by an increase in stress~a decrease in theviscosity of the dispersion!. Near the critical shear rate, which is 130 s21 in this case, the



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curve showing stress versus shear rate changes slope. Beyond the critical shear rate,stress increases more quickly with shear rate, which corresponds to the disappearance ofthe butterfly-like scattering pattern. Measurements performed in the two types of setup~smooth and rough! show the same behavior on either side of the critical shear rate. Stresslevels measured with the two types of surface state concur, attesting to the fact that thesample is correctly entrained and deformed throughout the gap separating the two plates,in a shear rate domain ranging from 10 to 3500 s21.

FIG. 5. SLS of Laponite dispersion under steadily increasing shear rate:fv 5 0.56 vol %,@NaCl# 5 1023 M,pH 5 9.5, tp 5 150 days.



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At the small length scales~1–100 nm! investigated by SANS, no anisotropy of thescattering pattern in the plane (y,v) was observed under shear for shear rate extendedfrom 50 to 104 s21 ~Fig. 9!. Such a result had already been obtained by Ramsay andLindher~1993!. This is probably due to the fact that, even at the high shear rates achievedin this study, the hydrodynamic forces are not sufficiently high in comparison with theBrownian motion. The elementary particles are too small to be oriented. The isotropicmean of the scattering intensity does not reveal any change for the different shear rates.This means that interparticle correlations are not affected by shear at these smallestlength scales.

C. Interpretation of breakdown

The various results obtained by SLS, SANS, and rheometric measurements suggest apossible interpretation of the change in structure of Laponite dispersions during shearflow under steady conditions. This interpretation is based on the one hand on analysis ofthe butterfly-like scattering pattern@Pignonet al. ~1997b!# and on the other on the worksof Potanin ~1991!, ~1993! and Potaninet al. ~1995! concerning disaggregation duringflow.

A butterfly-like scattering pattern has already been observed using silica–silicon com-posites@De Grootet al. ~1994!; Dorget ~1995!; Piauet al. ~1998!# or semi-diluted solu-tions of entangled polymers@Hashimoto and Kume~1992!; Moses, Kume and Hashimoto~1994!# or yet again semi-diluted aqueous solutions of micelles@Wheeleret al. ~1996!;Kadoma and van Egmond~1996!#.

The butterfly-like scattering patterns observed by Hashimoto and Kume~1992! are

FIG. 6. Shear stress level in steady regime, as a function of shear rate:fv 5 0.56 vol %, @NaCl# 5 1023 M,pH 5 9.5, tp 5 150 days. The labels~ai! correspond to the scattering pattern~a1–a5! in Fig. 5.



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attributed to fluctuations in the particle or aggregate concentrations in the direction offlow, while no heterogeneity is detected perpendicular to it. These fluctuations in con-centration imply an increase in scattering intensity parallel to the flow and its disappear-ance perpendicular to it. De Grootet al. ~1994! suggested that shear makes the largest

FIG. 7. Intensity distributions along the velocity direction (I v) and normal to it (I z) obtained by integration ofpatterns of Fig. 5 on a strip ofQ 5 0.53mm21 wide: fv 5 0.56%, @NaCl# 5 1023 M, pH 5 9.5, tp5 150 days.



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FIG. 8. Integral of scattering intensity on a crown, for aQ domain from 731025– 1024 Å 21 as a function ofanglec, for the various shear rates shown in Fig. 5;fv 5 0.56%, @NaCl# 5 1023 M, pH 5 9.5, tp 5 150days.

FIG. 9. SANS of Laponite dispersion under steady shear rate of 53103 s21: fv 5 0.48 vol %,@NaCl# 5 1023 M, pH 5 9.5, tp 5 345 days.



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flocs contract in the direction of flow by rolling themselves up and turning their main axisperpendicular to the shear, thus forming a roller-type structure. According to them, thisdeformation and stretching of the aggregates causes the development of a butterfly-likescattering pattern. According to De Grootet al. ~1994!, in order for a butterfly-likescattering pattern to appear, it must be possible to detect fluctuations in concentration~i.e., a mean interaggregate distance! at an observation length scale~the reverse of ascattering vector! that is at least an order of magnitude greater than the size of theaggregates. In the case of Laponite dispersions, as in that of the silica–silicon compositesstudied by De Grootet al. ~1994!, this length scale of fluctuations in concentration is ofthe order of 5mm (1/Q ' 231025 Å) for an aggregate size on the order of a microme-ter (1/Q ' 131024 Å).

A theoretical study@Potanin~1991!# and numerical simulations@Potanin~1993!# ex-amined the deformation and breakup of colloidal aggregates under shear flow conditions.These studies proposed that the aggregate radiusR depends on the shear rate, as ex-pressed by the power law:R } g2m. These studies also demonstrated the existence of acritical shear rate. The mechanism whereby aggregates are broken up or deformed hastwo possible forms:~i! The aggregate is defined as being compressible or soft and able tocontract, in which case the fractal dimension of the aggregate increases with increasingshear rate, and the number of aggregates in the dispersion remains constant, or else~ii !the aggregate is said to be rigid, and the breakdown mechanism corresponds to a decreasein the number of particles per aggregate and to a constant fractal dimension. Thesetheoretical studies@Potanin ~1991!# clearly show, using compressible aggregates, thatthere is a critical fractal dimension, corresponding to a critical shear rate, beyond whichany additional contraction of the aggregate is impossible~the aggregate becomes rigid!and breakup may be attributed to mechanical stresses.

FIG. 10. Schematic representation of the structure of a suspension of Laponite at rest and under shear. Belowthe critical shear rate, the aggregates form elongated rollers lying perpendicular to the direction of shearing. Thestructure is anisotropic. Above the critical shear rate, the aggregates break up into smaller subunits and thestructure becomes less and less anisotropic at large length scales.



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In the light of various results obtained by SLS, SANS, and rheometric measurements,a possible interpretation may be proposed for the change in structure of Laponite suspen-sions under shear flow in steady conditions~Fig. 10!. This is as follows in the case ofdispersions with a fibrous texture at rest. At low shear rates, under the effect of hydro-dynamic forces, the micrometer-sized aggregates contract and roll up on themselves.They form more concentrated rollers than in the remainder of the suspension. Theserollers are aligned in a direction perpendicular to the velocityV ~in a plane that containsthe GradV direction and direction perpendicular toV!. The formation of these rollersimplies that particle concentrations vary in the direction of shearing. These observationsshow that structural changes occur essentially at large length scales of 0.2–5mm.

As shear rate increases, fluctuations in concentration in the direction of shearing de-crease. Beyond a critical shear rate, the butterfly-like scattering pattern gives way to ananisotropic one, with no extinction of the scattering intensity perpendicular to the direc-tion of flow. When the critical shear rate is reached, the roller-shaped aggregates can nolonger contract and are therefore fragmented. The scattering figure then becomes increas-ingly isotropic and less and less intense~Figs. 7 and 8!. This suggests that smaller andsmaller objects are being scattered at the length scale observed here~Fig. 10!.

This interpretation is consistent with the studies by Potanin~1991!, ~1993! concerningdisaggregation during flow. The micrometer-sized aggregates may undergo some com-pression under the effect of hydrodynamic forces. Moreover, it is this compressibility thatenables the formation of rollers and the occurrence of fluctuations in concentration in thedirection of shearing. Beyond the critical shear rate, the micrometer-sized aggregates canno longer tolerate further compression and they fragment into smaller units under theeffect of mechanical stresses.

IV. STRUCTURE AND MECHANICAL BEHAVIOR IN UNSTEADYCONDITIONS

This section examines the time dependency of the mechanical properties and structuralstate of a thixotropic material. The order of magnitude of the time scales encountered inthe breakdown and recovery processes specific to thixotropic Laponite dispersions willnow be characterized. An interpretation is put forward concerning the origin of these timescales as a function of the observed structural changes~orientation–disorientation andaggregation–disaggregation!. All the rheometric measurements presented in this sectionwere obtained using a rough cone-plate setup.

A. Time scales of breakdown

Figure 11 shows the time-dependent structural and mechanical changes occurring in agel subjected to a jump in shear rate after a period of rest defining the initial state, andthen to an interruption of the shear. During the unsteady conditions following applicationof the jump in shear rate, the scattering pattern changes from the initial isotropic shape~atrest! to an elongated one and then a butterfly-like one near the critical strain, correspond-ing to maximum stress. Beyond the critical strain, and as the stresses are relaxed in theperiod leading back to steady conditions, the butterfly-like scattering pattern remainsstable but its intensity is reduced. When the sample is suddenly released, the butterfly-like scattering pattern is replaced by a slightly anisotropic one.

The intensity I (c) on a crown @Fig. 12~a!# was integrated over aQ domain (731025 < Q < 1024 Å 21). At rest the intensityI (c) corresponding to the scatteringpattern@Figs.~12a!–~12b1!# is flat, confirming that the system is isotropic prior to shear-ing. During unsteady conditions@Figs. ~12a!–~12b2!#, maximum anisotropy occurs atangles ofc 5 90° and 270°, corresponding to elongation of the scattering pattern in the



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FIG. 12. ~a! Integral of light scattering intensity on a crown of the scattering patterns of Fig. 11, for aQ domainfrom 731025– 1024 Å 21 as a function of anglec. ~b! Transient stress response at start of shearing. Influenceof shear rate on characteristic times of breakdown:fv 5 0.56 vol %, @NaCl# 5 1023 M, tp 5 150 days.

FIG. 11. SLS and transient stress response of Laponite dispersion under steady shear rate of 10 s21: fv5 0.56 vol %, pH 5 9.5, @NaCl# 5 1023 M, tp 5 150 days.



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direction of shearing. Then, as steady conditions are established, the anisotropy decreasesand stabilizes@Figs. ~12a!–~12b4!#.

The increase in linear stress with time corresponds to elastic strain of the material@Pignonet al. ~1996b!#. During this elastic strain, the stresses in the material are belowthe yield stress. The strain must correspond to a connected structure, in which shearingrearranges the constituent objects without separating them. The anisotropy of the scatter-ing pattern observed during this elastic strain shows that these connected objects areoriented. The length scale at which this orientation occurs is on the order of 1mm.

Beyond the critical strain, shearing exceeds the level of energy required to break theaggregate network and enable the dispersion to flow. As the stress falls from maximumdown to steady conditions, the breakdown of the material’s structure is accompanied bya decrease in the anisotropy of the scattering pattern.

The time-dependent changes in stresses and structure described above reveal twoperiods with distinct time scales in the breakdown process, situated on either side of themaximum stress and corresponding critical strain. The first period corresponds to elasticstrain of the material and orientation of the structure, which remains connected. Thesecond corresponds to flow and disaggregation of the structure. The order of magnitudeof the time scale in the first period is shorter than that in the second. In the test presentedhere~Fig. 11!, the first period lasts for about 0.1 s and the second about 100 s, giving atime scale ratio of 1/1000. In order to allow for the influence of shear rate on thecharacteristic times of breakdown, the time-dependent changes in stress were plotted forvarious shear rates@Fig. 12~b!#. It is interesting to note that the kinetics of breakdowndiffer depending on the shear rate applied, but the ratio of the time scales remains of theorder of 1/1000.

FIG. 13. Kinetics of recovery (f 5 0.1 Hz, g0 5 0.05! in a Laponite dispersion as a function of preshearingintensity:fv 5 0.48 vol %, @NaCl# 5 1023 M, pH 5 9.5, tp 5 425 days.



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B. Time scales of recovery

The dispersions studied here belong to the domain in which there is homogeneousstrain of the sample occuring during the shearing process, and the entire bulk of thesample is disaggregated. Recovery is therefore a bulk property of the sample rather thana kind of healing process following localized fracturing of the sample in a single place@Pignonet al. ~1996b!#.

The material is brought initially to a state of disaggregation, in which its consistencyis lower than that towards which it will tend to evolve as it recovers its structure~Fig. 3!.In Sec. III, it was shown that each stress intensity corresponds to a given structural state.Here, two types of conditioning were used to obtain an initial structural state:

~i! simple shearing, creating a principal direction of shearing within the sample,~ii ! ultrasonic conditioning, the effect of which is greater than simple shearing.

The ultrasonic waves produce isotropic breakdown spread over a wider range of lengthscales within the sample.Recovery is monitored in time:

~i! by measuring the elastic moduliG8 and viscous moduliG9,~ii ! by measuring the scattering intensity and fractal dimension of the structure.

1. Recovery after simple shearing

First, in a rheometric test, a sample initially at rest is presheared at a given shear rateto breakdown its structure and is then subjected to low-strain harmonic shearing in orderto monitor the kinetics of recovery. Figure 13 shows that the more the structure is brokendown by preshearing, the longer it takes for it to be recovered. In addition, the greater theintensity of preshearing, the lower the values of the elastic moduli after preshearing hasceased.

FIG. 14. Recovery for different preshear rate in a Laponite dispersion as a function of preshearing intensity:f 5 0.1 Hz, g0 5 0.05,fv 5 0.48 vol %, @NaCl# 5 1023 M, pH 5 9.5, tp 5 210 days.



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In order to evaluate the influence of preshear history, two different samples of thesame volume fraction were presheared at 10 and 100 s21 during 300 s. It is observed thatthe kinetics of recovery are faster for the lowest intensity of preshear. The levels reachedfor G8 and G9 are different in Figs. 13 and 14, because of the gelation time of thesamples used in these two experiments. Clearly, older samples have higherG8 andG9levels, which correspond to a more rigid structure at rest.

Second, a light scattering test was carried beginning with a sample at rest. The fol-lowing shear rates were then applied in succession: 10, 180, and 10 s21 ~Fig. 15!. Whenthe first shear rate of 10 s21 was applied, a butterfly-like scattering pattern [email protected]~c1!#. Increasing to a shear rate of 180 s21 broke down the sample so that the scatter-ing pattern became slightly anisotropic@Fig. 15~c2!#. Finally, 1 min after the end of thishigh shear rate, an identical shear rate to the first was again applied. The scatteringpattern remained slightly anisotropic@Fig. 15~c3!#. This shows that, after the high shear-ing at 180 s21, the dispersion reaches a sufficient level of breakdown for it to no longerconsist of micrometer-sized objects that are able to contract and roll themselves up toform rollers. In contrast, if after shearing at 180 s21 the sample is left to rest for 90 minsbefore a low shear rate of 10 s21 is again applied, the scattering pattern is more aniso-tropic but not really butterfly-like@Fig. 15~c4!#.

Figure 16 shows the scattering intensityI v parallel to the velocity direction andI zperpendicular to it.I v and I z are obtained by integration of patterns on a strip ofQ5 0.53mm21 width, centered on the beam stop. All these data are obtained for the same

shear rate of 10 s21, but with different sample shearing histories. Starting from the reststate and during shear at 10 s21, the anisotropy is high@Fig. 16~c1!#. But after a severebreakdown of the structure by applying the shear rate of 180 s21, the anisotropy duringshear at 10 s21 is highly reduced@Fig. 16~c3!#. After a high shear of 180 s21 followed bya rest time of 90 min, the anisotropy during shear at 10 s21, is again [email protected]~c4!#. These observations show that the high shear rate of 180 s21 has broken down thestructure of the sample to such an extent that it requires several hours to reach a suffi-ciently high level of recovery to exhibit anisotropic scattering when a low shear rate isapplied.

2. Recovery after ultrasonic conditioning

Rheometric measurements were combined with static light scattering to monitor therecovery of a sample atfv 5 0.80 vol %, after it has been broken down by ultrasonicwaves. The sample at rest has a fractal dimension of 1.2 and the slopeI (Q) at the largestQ is of Q23 type. The characteristic dimensiond separating these two types ofQ powerlaw behavior is situated at 1.231024 Å 21, i.e., at a length scale' 0.85mm ~Fig. 17!.After 20 kHz ultrasonic waves have been applied at 350 W for 10 min in 0.3 s intervals,the material’s structure has broken down, and it flows under its own weight. At the endof the breakdown period~assumed to be the initial instant in what follows!, it wasnecessary to wait 50 min before making a correct measurement with the rheometer, i.e.,obtaining a sufficiently strong signal for the apparatus to detect. The recovery of thesample’s structure was monitored by measuring both the viscoelastic moduli~recovery ofconsistency! and the appearance of a fractal character~aggregation process at the scale ofa few micrometers!.

Curve G8(t) ~Fig. 18! clearly shows two periods, the first lasting about 4 h, duringwhich the kinetics of recovery are 3–4 times faster than during the second, lasting from4 to 52 h.

At time t 5 1500 s after the structure of the sample has been broken down, the



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FIG. 15. SLS of Laponite dispersion under shear. Influence of past shearing on structure:fv 5 0.56 vol %,@NaCl# 5 1023 M, pH 5 9.5, tp 5 150 days.

FIG. 16. Change in light scattering intensity distributions along the velocity direction (I v) and normal to it(I z), as a function of past shearing for a Laponite dispersion:fv 5 0.56 vol %, @NaCl# 5 1023 M, pH5 9.5, tp 5 150 days.



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scattering pattern is isotropic. Integrating this pattern~Fig. 17! shows that there is nolinear correlation of the intensity in theQ domain 231024– 431025 Å 21, whereas theQ23 slope at rest at higherQ is slightly less. The characteristic dimensiond separatingtheseQ23 power law and the intensity at lowerQ vector is situated at 231024 Å 21,corresponding to a length scaled ' 0.48mm. The structure of the material after ultra-sonic treatment probably consists of aggregates of smaller average size than at rest,separated from one another and arranged without any particular orientation or organiza-tion of fractal type at this length scale.

SLS measurements~Fig. 17! show that the fractal character of the structure appearsonly after a period of about 67 h. Measurements show that the fractal behavior of thestructure has still not been established after 23 h of recovery, but the structure would bea connected one because of the high level ofG8 compared toG9 at this time of recovery.These observations demonstrate that the Laponite dispersions take about 2–3 days toreach a fractal behavior, which should correspond to a slow aggregation process.

V. NATURE OF MECHANISMS BEHIND BREAKDOWN AND RECOVERY

The mechanisms behind breakdown and recovery in thixotropic Laponite dispersionsinvolve the notion of organization and orientation of the constituent particles, and that ofthe time for these organizations and orientations to change. More generally, these notionsare at the basis of studies on colloidal systems under shear flow conditions. The exampleof clay dispersions studied here has many similarities with other colloidal dispersions,such as silica–silicon composites@De Groot et al. ~1994!; Dorget ~1995!; Piau et al.~1998!#, semi-diluted solutions of high molecular weight polystyrene, polymer gels, andpolymer melt mixtures@Moses, Kume and Hashimoto~1994!# or even semi-diluted aque-ous solutions of micelles@Wheeleret al. ~1996!; Kadoma and van Egmond~1996!#.

FIG. 17. Time-dependent aggregation after ultrasonic breakdown. Measurement of scattering intensity of aLaponite dispersion:fv 5 0.80 vol %, @NaCl# 5 1023 M, pH 5 9.5, tp 5 280 days.



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However, what is of prime interest here is the notion of time, which is one of thecomponents of thixotropic behavior.

A. Mechanisms and time scales of breakdown

When the structure of the material is broken down by means ofsimple shearing,measurements showed that the mechanisms producing a lower consistency in the materialare those of orientation and disaggregation, taking place over two distinct periods thathave different time scales.

Orientation of the structure takes place mainly in the first few moments following theapplication of shear. A first period of breakdown is thus defined for which the charac-teristic time scale is three orders of magnitude less than that involved in the secondperiod. It is thus possible to define a short time scale and long time scale, corresponding,respectively, to the first and second periods. The terms short and long used here are to beunderstood in a comparative rather than quantitative sense. The values of these two timescales are of course governed by the intensity and the nature of the shear applied duringbreakdown and also depend on the particle volume fraction.

The short time scale is evidenced by~i! the formation of a butterfly-like scatteringpattern and~ii ! elastic strain of the material until a critical strain is reached, correspond-ing to the moment when peak stress in the mechanical response is exceeded.

The long time scale begins when the critical strain is exceeded. This is evidenced by~i! a decrease in stress, from the peak down to the level of steady conditions,~ii ! the lossof linear correlation at the lowestQ vector, and~iii ! a decrease in structure orientationduring flow. During this second period, the already oriented structure is affected mainlyby a disaggregation mechanism, involving a disappearance of the fractal character and adecrease in scattering intensity at the largest length scales. In the case of breakdown byultrasonic waves, only disaggregation and loss of fractal behavior were observed. This

FIG. 18. Kinetics of recovery (f 5 0.1 Hz, g0 5 0.05! in a Laponite dispersion after ultrasonic breakdown:fv 5 0.80 vol %, @NaCl# 5 1023 M, pH 5 9.5, tp 5 280 days.



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type of conditioning produces isotropic breakdown over a wider range of length scales, sothat no preferential orientation of the structure could be observed.

B. Mechanisms and time scales of recovery

During recovery, after preshearing has ceased, two characteristic time scales can bedetermined. During recovery, the disorientation and aggregation mechanisms combinebut observations tend to prove that one or the other of these mechanisms prevails over thetwo characteristic time scales defined below.

A first, short time scale during which structure disorientation prevails. This short timeis characterized first by the transition from a butterfly-like scattering pattern below thecritical shear rate or from an anisotropic scattering pattern above the critical shear rate toa slightly anisotropic one, and second by a rapid recovery of consistency in the sample.This time scale appears to correspond to the transition from a structure in which theseparate aggregates are oriented and deformed, to one of deformed aggregates, dispersedisotropically but once again connected to one another.

A second, long, time scale ranges from a few hours to several days depending on theintensity and nature of the previous breakdown and on the physico-chemical conditions(fv , pH, ionic strength!. This second time scale distinctly corresponds to the prevalenceof aggregate connection and rearrangement, i.e., an aggregation mechanism leading to theformation of a fractal structure. During this long time scale, a minor disorientation of thestructure takes place in the case of simple shearing. This long time is characterizedsimultaneously by an increase in the viscoelastic moduli in time and by a slow aggrega-tion process which gives rise at the end to a fractal behavior equal to the one at rest.

VI. CONCLUSION

The main mechanisms involved in the thixotropic behavior of clay dispersions werestudied by means of a combination of rheometric measurements, light scattering, andsmall-angle neutron scattering measurements.

In the case of volume fractions (0.35 vol %< fv < 0.80 vol %) with a texture atrest of fractal dimensionD, with (1 < D < 1.2) and in fixed physico-chemical condi-tions (pH and ionic strength!, structural changes~organization and orientation! could belinked to the characteristic time and length scales of the thixotropic behavior.

In shear flow, the fall in viscosity measured in the study was due to the disaggregationand orientation of aggregates at length scales on the order of 1mm.

The butterfly-like scattering patterns observed under simple shear conditions corre-spond to the formation of elongated rollers of aggregates arranged perpendicularly to thedirection of shearing. The existence of a critical shear rate beyond which this orientedstructure is broken into smaller aggregates was clearly demonstrated.

The process of breakdown generated by simple shearing follows a process of structureorientation, mainly at large length scales, associated with a slower process of disaggre-gation at length scales ranging from 1mm downwards. The characteristic time of orien-tation is three orders of magnitude less than that of disaggregation.

The process of recovery, which takes place when the system is left to rest afterbreakdown, occurs over two distinct time scales: a short one—after shearing is inter-rupted, corresponding to relaxation of the alignment produced by the shearing, and a longone—corresponding to a slow aggregation process which gives rise to a fractal behaviorat length scales on the order of 1mm. It is during this second stage that the continuousaggregate network is established, giving the dispersion its yield stress fluid character.



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The nature of the thixotropic behavior was thus identified as being mainly a reversibleaggregation process, where the fractal character of the structure at a length scale on theorder of 1mm plays a decisive role.

This study demonstrates the enormous advantage of combining physical investigationsof the fluid’s structure with rheometric measurements, in order to understand the complexrheological behavior of this type of colloidal suspension.

ACKNOWLEDGMENTS

The small-angle neutron scattering measurements were carried out in association withPeter Lindner, responsible for beam line D11 at the Institut Max von Laue–Paul Lange-vin, Grenoble, and Bernard Cabane, Director of the Unite´ Mixte Rhone-Poulenc/CEA,Aubervilliers. The authors wish to express their deepest thanks for their help.

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Thixotropic behavior of clay dispersions: Combinations of scattering and rheometric techniques

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