Shake-Gels: Shear-Induced Gelation of Laponiteá/PEO Mixtures

Colloids and Surfaces A: Physicochem. Eng. Aspects 213 (2003) 189Á/197 www.elsevier.com/locate/colsurfa

Shake-gels: shear-induced gelation of laponiteÁ/PEO mixtures

J. Zebrowski a, V. Prasad a,*, W. Zhang b, L.M. Walker c, D.A. Weitz a,*

a Department of Physics and DEAS, Harvard University, 29 Oxford Street, Cambridge, MA 02138, USA b Department of Physics, James Franck Institute, University of Chicago, Chicago, IL 60637, USA c Department of Chemical Engineering, Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA

This paper is dedicated to our colleague and friend, Kees de Kruif, in celebration of his 60th birthday.

Abstract

Suspensions of clay particles (laponite), mixed with poly(ethylene oxide) (PEO) undergo a dramatic shear thickening when subjected to vigorous shaking, which transforms them from a low viscosity fluid into a ‘shake-gel’, a solid with elasticity sufficient enough to support its own weight. The shake-gel is reversible, relaxing back to a fluid with a relaxation time that is strongly dependent on PEO concentration. Shake-gels are observed for PEO concentrations slightly below the threshold for complete saturation of the laponite particles by the polymer. Light scattering measurements confirm that the PEO is adsorbed on the surface of the laponite particles, and suggests that shear induces a bridging between the colloidal particles, resulting in a gel network which spans the system. Desorption of the polymer reduces the bridging and thus relaxes the network. # 2002 Elsevier Science B.V. All rights reserved.

Keywords: Laponite; Poly(ethylene oxide); Adsorption; Gelation; Relaxation

1. Introduction The stability of colloidal suspensions is strongly influenced by solubilized polymer; it alters the Suspensions of colloids and polymers are widely interactions between the colloidal particles in encountered in many different applications, in- solution, and thus can be used to fine-tune both cluding biological fluids, drilling muds, cosmetics, the phase behavior and the rheology of the food and pharmaceuticals. In addition, many colloidal suspension. There are extensive studies manufacturing processes utilize colloidal suspen- elucidating the role of polymer in stabilization or sions, since liquid dispersions can be transported flocculation of colloidal suspensions [1Á/3]. much more easily than the bulk solids themselves. The primary reason for adding polymers to colloidal suspensions is to achieve desired rheological properties. Typically, polymers are used to

* Corresponding authors. Tel.: /1-617-496-8684; fax: /1- control the viscosity, often being added to induce 617-496-3088 (V.P.); tel.: /1-617-496-2842; fax: /1-617-495- shear thickening; sometimes the addition of poly- 2875 (D.A.W.). mers can even lead to shear-induced gelation, a E-mail addresses: [email protected] (V. Prasad), [email protected] (D.A. Weitz). highly non-Newtonian behavior. The most dra-

0927-7757/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 ( 0 2 ) 0 0 5 1 2 - 5 190 J. Zebrowski et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 213 (2003) 189Á/197 matic examples are solutions containing long- called ‘necklaces’ [6]; they correspond to multiplets chained polymers, such as ionomers [4], amphi- in the ionomer literature [4], or ‘flowers’ in the philic polymers [5] and mixtures of polymer and amphiphilic polymer literature [5]. For appropri- colloids [6]. In all these systems, the solution at rest ate polymer and laponite particle concentrations, and under low shear-rate deformation flows read- these bridges rapidly form a network that spans ily with a constant viscosity. Upon non-linear the entire solution, giving rise to a gel that persists levels of deformation, these solutions shear- while the shear is applied. However, once the shear thicken and form gels. The resultant gel is typically stops, the polymers desorb, reducing the bridging quite weak, and has been described as having the and attaining their original configuration; this consistency of ‘a half-cooled gelatin dessert [4].’ causes the gel to relax back to a fluid.

However, it is also possible to obtain significantly This mechanism requires that the monomerÁ/ greater shear thickening, leading to much more clay bond is weak and the energy associated with elastic gels. In this paper, we present a study of a adsorption is much less than that associated with new system where the resultant gel is surprisingly the entropy of the polymer coil. In this limit, strong. It is a solution of nanometer-sized clay moderate shear can increase the number of bonds particles mixed with a long-chained, linear poly- between the polymerÁ/clay without significantly mer. If a jar containing a sample of this mixture is altering the configuration of the polymer. This is shaken vigorously, a highly elastic gel is formed; the opposite limit from that of shear-thickening in which is rigid enough that when the jar is inverted, ionomers and telechelic polymer solutions, where the gel supports its own weight. The abrupt change the bonds formed between ‘stickers’ [4], ionic side in stiffness is reminiscent of electrorhelogical fluids groups or hydrophobic heads which play a role rather than the shear-thickening typically observed analogous to clay particles for our solution, are in polymer solutions. More surprisingly, this flow- strong and form the dominant contribution to the induced gelation is reversible; if the sample is left free energy of the aggregate. In these systems, at rest for some time, ranging from minutes to moderate shear will significantly alter the polymer days, the gel relaxes back into a slightly viscous chain configuration without altering the number liquid. of bonds between sticker particles. A similar behavior has been reported for In this paper, we report measurements of the mixtures of nanometer-sized silica spheres and phase behavior of laponiteÁ/PEO mixtures subject polyethylene oxide (PEO); however, the silicaÁ/ to flow, and we determine the range of concentra-

PEO gels were not observed to be as rigid as those tions of polymerÁ/colloid mixtures that exhibit studied here, nor were the relaxation times re- shake-gel behavior. Static and dynamic light ported [6].Nevertheless, the silica studies provide scattering measurements on the mixtures at rest important insight into the basic mechanism lead- are used to characterize the adsorption of PEO ing to gelation: at rest, the PEO is weakly adsorbed polymer on the clay particles. Relaxation times of to the clay particles, forming small aggregates the shake-gels are measured to gain insight into comprised of several clay particles. When a adsorption energies. We use these data to char- sufficiently strong shear is applied, the polymer acterize the behavior of the shake-gels, and to chain segments near the clay disk deform exposing develop a physical picture of the underlying additional clay surfaces to the bulk solution, thus mechanism that causes their formation. making it possible for additional polymer mono- mers to adsorb onto the clay disk. As the shear proceeds, an increasing number of polymerÁ/clay 2. Experimental procedures adsorption sites are created, a fraction of which involve adsorption of a polymer chain onto clay 2.1. Materials particles belonging to different aggregates, thus forming polymer bridges between the particles. In The clay used in this study was Laponite-XLG the case of silica, the larger aggregates havebeen (Southern Clay Products, Inc., Gonzales, TX). The J. Zebrowski et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 213 (2003) 189Á/197 191 laponite particles are synthetic disc-shaped crys- sets the individual concentrations of laponite and tals, 25 nm in diameter and 0.92 nm in width, with PEO in the final mixture, enabling the phase space an empirical formula given by: to be explored. All measurements are performed at 0.7 Na0.7[(Si8Mg5.5Li0.3)O20(OH)4] . The unit cell room temperature, T/22 8C. of the crystal is comprised of six octahedral magnesium ions sandwiched between two layers of tetrahedral silicon atoms, with these groups 2.3. Light scattering measurements balanced by 20 oxygen atoms and four hydroxyl groups. When laponite is dispersed in water, the Na ions are released into solution, creating a Static and dynamic light scattering measure- double layer that causes the particles to repel each ments are performed on laponite solutions, PEO other, initially stabilizing the particles. The solutions and unshaken laponiteÁ/PEO mixtures suspensions are stable up to concentrations of using a laser light scattering instrument (ALV- Laser GmbH, Langen, Germany), at a wavelength 2.5Á/3% by weight, above which they form an irreversible gel. However, even at low concentra- of l/514.5 nm in vacuuo. Static light scattering tions, these solutions age slowly in time, ultimately measurements are performed at angles ranging forming gels; this suggests a weak driving force from u/15 to 1508. Dynamic light scattering for the formation of the gel structure. The polymer measurements are also performed on laponite used in the study is PEO, a linear chain polymer, solutions, PEO polymer solutions, and unshaken (Sigma-Aldrich Co., Milwaukee, WI) with mixtures of the two components at u/908. a molecular formula,Ã/[CH2Ã/CH2 Ã/O]Ã/n. The molecular weight of the polymer used is Mw / 1 300 000 g mol , with an approximate radius 2.4. Phase diagram and relaxation times of gyration Rg/32 nm [7], so the polymer in solution is comparable in dimension to the clay Measurements for the phase diagram and re- particles. laxation times are performed by observation. The laponite and PEO stock solutions are mixed in 2.2. Sample preparation varying ratios and total concentrations, enabling a wide section of the phase space to be explored. The laponite powder is added to deionized water Initially, the samples have viscosities that are not and mixed at high speeds with a magnetic stirrer. significantly different from pure water, as expected The solution is initially turbid, but becomes clear for a suspension of dilute colloidal particles [9]. in 15Á/20 min, indicating that the particles are fully hydrated. The laponite concentrations used for the The samples are shaken vigorously, several times stock solutions are typically 2.5 wt.%, and the pH per second for 15Á/20 s, and inspected visually for 10.0. Since laponite at such high concentrations increased viscosity, increased turbidity, and the demonstrates aging characteristics [8], all samples appearance of bubbles suspended within the are prepared within a few hours of use, and the sample. If the samples become elastic, and bubbles measurements are performed before any signifi- remain suspended in the solution, we consider cant aging of the stock Laponite solution occurs. them to have gelled. Measurement of the The stock solutions of polymer are prepared by relaxation time begins immediately upon comple- adding PEO to water and allowing it to dissolve tion of shaking, and ends when the sample for a few days; typical polymer concentrations are has totally relaxed, and becomes clear with all 1.5 wt.%. Prior to our experiments, the laponite of the bubbles suspended in the sample and polymer stock solutions are mixed together by having risen to the top. Samples that ‘relax’ adding the polymer stock to the laponite stock according to these criteria have final viscosities with a pipette and then gently tilting the mixture not significantly different from their initial back and forth to ensure complete mixing. This values. 192 J. Zebrowski et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 213 (2003) 189Á/197

3. Results and discussions

3.1. ‘Phase behavior’ of laponiteÁ/PEO mixtures

Laponite particles dispersed in an aqueous medium form many different phases such as gels, viscous fluids or phase separated flocs [10,11]. Well-defined phase diagrams exist for these dispersions, where the phases are determined as a function of the laponite concentration and the concentration of added counterions. Our experiments are performed in the absence of added counterions. However, when a non-associative, linear chain polymer such as PEO is added to the suspension of laponite discs, the situation is more Fig. 1. Phase behavior of laponiteÁ/PEO ‘shake-gels’, formed complicated. PEO is known to adsorb on clay by vigorous shaking. The open triangles represent mixtures that particles [12Á/14], with the amount of adsorbed form shake-gels upon application of shear; the circles represent polymer depending on the equilibrium concentra- mixtures that shear-thicken and show an increase in viscosity tion of polymer added. We present results on but do not gel; and the solid squares represent mixtures that do not gel even when subjected to large shear. The molecular mixtures of PEO and laponite, where the concen- 1 weight of PEO used is Mw /300 000 g mol , with a radius of trations of both components have been varied. At gyration Rg /32 nm. rest, all suspensions are clear and show low viscosity Newtonian-fluid-like behavior, where history. Three distinct phases are observed, as the viscosity is not a function of applied shear characterized visually: (1) the shake-gel phase rate. However, when shaken vigorously by hand, (triangles), where the samples show bulk elasticity. some of the samples exhibit an intriguing behavior. This phase is characterized by increased opacity of The non-linear shear created by shaking the the sample, and macroscopic heterogeneities re- samples causes some of the mixtures to form sulting in a ‘lumpy’ gel. (2) The shear-thickening macroscopic, heterogeneous gels. In fact, these phase (circles), where the suspensions show a gels are so elastic that even upon inverting the vials substantial increase in viscosity, but no visible 1 the samples remain stationary . If left undisturbed, elasticity, as the suspensions can still flow. This the gels relax back to the fluid state in time scales phase is also more turbid than the unshaken that range from a few seconds to many hours, and mixture. (3) The liquid phase (squares), where sometimes even days. Once the gels return to the even the most vigorous shaking causes no visible fluid state, gelation can be caused by shaking gelation or shear thickening. This phase is char- again. All samples that form shake-gels are acterized by the absence of any apparent rise in the reversible. viscosity of the sample, although a foam forms at To explore this phenomenon, we vary the the surface of the samples. The turbidity of this relative concentrations of PEO and laponite in phase also remains unchanged from the fluid state the mixture, and determine when the shake-gels at rest. The observation of foam suggests the are formed. The results are summarized in Fig. 1, presence of free PEO in solution, since PEO is where we show the phase behavior of the samples somewhat surface active while laponite is not. that have been prepared using the same flow As seen in the phase diagram shown in Fig. 1, for very low concentrations of polymer, no shake- 1 Images of the shake-gel can be viewed at http:// gels are formed, irrespective of the laponite con- www.deas.harvard.edu/projects/weitzlab/research/lappix/ centration. For a fixed laponite concentration, we index.html. observe shake-gel like behavior for a finite range J. Zebrowski et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 213 (2003) 189Á/197 193 of polymer concentrations. This range seems to laponite surfaces, in the absence of shear. In the increase as we increase the laponite concentration. absence of polymer, Fig. 2(a), the laponite discs However, beyond a certain polymer concentration, are stable in solution due to the charge on their shake-gels no longer form. To account for the surfaces. As the PEO concentration is increased, behavior of the phase diagram, we use the physical polymer adsorbs on the laponite surfaces. The picture developed to explain shear thickening in most likely explanation for this adsorption lies in mixtures of silica and PEO [6]. The surface the displacement of water molecules immediately chemistry of the silica and laponite are similar; adjacent to the clay surfaces by the ethylene oxide when clay particles are dispersed in water, sodium segments on the PEO backbone [14]; the ether ions are released into solution, leaving many bare oxygens of PEO act as Lewis bases and have a high silica sites on the surface of the discs. The main affinity for the silica on the clay surface, which act difference in the two systems is the geometry of the like Bro¨nsted acids. Since the pH of the laponite particles; however, this does not make a significant suspension is quite high (pH/10.0), there is difference in the general phase behavior. The competition between the hydroxyls and the poly- essence of this physical picture is illustrated mer for the silica on the surface of the clay particle. schematically in Fig. 2, which shows different This suggests that the adsorption energy is of the configurations of polymer adsorption on the order a few kBT [14], with a finite probability for desorption (for silicaÁ/PEO, the adsorption energy 1 is about 1.2 kBTmol of segment [6]). At low PEO concentrations, the surface coverage is in- complete, as illustrated schematically in Fig. 2(b);

this allows for the formation of PEOÁ/laponite complexes or aggregates, with a single PEO macromolecule bridging more than one laponite disc. The aggregates themselves remain stable, and equilibrated. As the PEO concentration is increased still further, the polymer completely satu- rates the clay surface, resulting in a steric stabilizing layer around the particles, as illustrated schematically in Fig. 2(c). In this case, a single PEO macromolecule absorbs on a single laponite disc on average. For a laponite concentration of 0.75 wt.%, and a polymer concentration of 0.25 wt.% (near the phase boundary), the molar ratio of polymer to disc is 0.9:1. This indicates that there is enough polymer to completely cover the discs at Fig. 2. Schematic representation of different confirmations seen concentrations of polymer above the phase bound- in laponiteÁ/PEO mixtures in the absence of shear, for increas- ary, consistent with the picture proposed in Fig. ing PEO concentration (a) when there is no polymer, the 2(c). laponite discs are stable in solution due to the charges on their The configurations of PEOÁ/laponite complexes surfaces; (b) with increasing amounts of PEO, the laponite surfaces are unsaturated, and the polymer can bridge different depicted in Fig. 2 are for solutions at rest; upon discs to form small aggregates; (c) as the PEO concentration application of shear, the situation changes drama- increases still further, the laponite surfaces become saturated tically. When the laponite surfaces are not fully with polymer, which forms a steric stabilization layer that saturated by PEO, the effect of shear is to lower prevents discs from aggregating. Only when the surfaces are not the coverage of some surfaces by breaking the completely saturated can shear cause desorption of the polymer and readsorption onto neighboring particles, increasing the bonds between the polymer and the clay [6]. At the bridging and hence increasing the size of the aggregates, and same time, new bonds are formed between the ultimately leading to the formation of the shake-gel. polymer and clay particles belonging to other 194 J. Zebrowski et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 213 (2003) 189Á/197 aggregates. As the size of these new aggregates no gelation is observed. This suggests that exten- grows, it becomes even easier to stretch them out sional flow is important in the aggregate growth. by shear. One way of characterizing this is by The flow pattern in the shaken sample comprises means of the Peclet number of the aggregates, recirculating eddies which change their size and Peg˙a2=D whereg ˙ is the shear rate, a is the orientations rapidly in time, so the shear rate is aggregate size and D is the aggregate diffusion spatially non-uniform. A fluid parcel is rapidly coefficient. The Peclet number characterizes the accelerated and decelerated. We also generate ratio of shear to diffusion, and is a measure of the instantaneous stagnation points, so there will be importance of the shear rate compared with the local regions of large extension. A complete relaxation rate due to diffusion. As the Peclet understanding of the nature of the flow that causes number increases, the effect of the shear rate gelation requires additional experiments; however, 3 becomes greater, and since Pe /a , it increases since the behavior observed with shaking is rapidly with the aggregate size. Eventually, these reproducible, we use this to induce gelation for large aggregates span the entire sample, forming our studies. the ‘shake-gel.’ Since the adsorption energy of PEO on laponite is a few kBT, thermal fluctua- 3.2. Static light scattering measurements tions are sufficient to cause the shake-gels to relax and revert back to their original fluid state. As the The physical picture described in the previous polymer concentration increases, the laponite section to explain the shake-gel behavior relies on particles become completely saturated with PEO, the assumption that PEO adsorbs on laponite. To and the polymer segments on the surface of the test the validity of this assumption, we perform laponite repel each other. Then, no reasonable static light scattering measurements on the un- level of shear is able to cause bridging of the shaken laponiteÁ/PEO mixtures and compare to particles by the PEO because of the stabilization scattering from solutions of laponite and PEO. due to the polymer coating; thus, for high PEO The measurements are performed at several angles, concentrations, the liquid phase persists, as shown ranging from u/15 to 1508; however, there is little in the phase diagram in Fig. 1. Therefore, the variation with angle, except for a slight increase at phase boundary between a shake-gel and a liquid the lowest angle. This behavior is reasonable since defines the limit of complete coverage of the we are probing length scales large compared with laponite surfaces by the adsorbed PEO for a fixed those typical of the laponiteÁ/PEO aggregates. laponite concentration. Since the phase boundary Therefore, we focus on the scattering at 908.We is linear in shape, we obtain a value of the find that the mixture scatters more than the sum of saturation coverage from the slope of the line, the individual components, which is an indication which is 0.455 mg m2. We are unaware of any of adsorption [12,13]. As a simple estimate of the measurements of this saturation value for effect of the adsorption, we assume that a single laponiteÁ/PEO mixtures; however, by comparison, PEO adsorbs on each laponite particle. The from adsorption isotherms for silicaÁ/PEO mix- scattering intensity from each coated particle is tures, the saturation value is 1.0 mg m2 for PEO the coherent sum of the scattering from the 1 with Mw /2 000 000 g mol [15,16]. This is in individual laponite particle and PEO polymer; reasonable agreement with the value for laponite, therefore, the scattered fields add, rather than the particularly considering the difference in particle intensities. The scattering intensity per laponite shapes and molecular weights of the PEO. particle is ILAP/NLAP, where ILAP is the measured The nature of the shear that causes gelation is scattering intensity from the pure laponite solu- not simple. The shaking rate used is about 200 tion, and NLAP is the number concentration of rpm, and in the geometry of the cell, this corre- laponite particles. Similarly, the scattering inten- 1 sponds to a linear shear rate ofg ˙/ :/20 s . This is sity per PEO polymer is IPEO/NPEO, where IPEO is not a large shear; indeed if a similar shear rate is the measured scattering intensity from the pure applied in a controlled geometry in a rheometer, polymer solution, and NPEO the number concen- J. Zebrowski et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 213 (2003) 189Á/197 195 tration of PEO polymers. To parameterize the 3.3. Dynamic light scattering measurements adsorption, we define a normalized scattering intensity: Dynamic light scattering gives additional infor- mation about the configuration of the adsorbed polymer on the laponite [15,16] prior to the pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 N ( I =N I =N ) formation of the shake-gel. We again fix the I˜ PEO LAP LAP PEO PEO (1) I concentration of laponite at 1.25 wt.%, and vary MIX the concentration of polymer. We measure the

decay time of the normalized fieldÁ/field autocor-

relation function, g1 at a scattering angle of u/ where IMIX is the scattering intensity from the 908; a separate set of measurements confirms that laponiteÁ/PEO mixture. This expression implicitly assumes that only a single polymer adsorbs per there is no anomalous dependence on scattering laponite particle, and that the concentration of angle, other than that expected for single particle each is sufficiently low that there is no interaction diffusion [17]. We find a nearly exponential decay between the particles. We plot the variation of I˜ as of g1 indicating a reasonably monodisperse dis- a function of PEO concentration in Fig. 3 using a tribution of scatterers. This allows us to character- fixed laponite concentration of 1.25 wt.%. When ize the scatterers with their characteristic decay the laponite coverage is saturated, we expect I˜/ /1. time t, the larger the scatterers, the more slowly By contrast, for PEO concentrations below satura- they diffuse, and the larger is their decay time. tion, there is less than one laponite particle per Thus, we define a dimensionless time constantt ˜ polymer, and we expect I˜/ B/1; by contrast, for t=t0; where t0 /0.24 ms, the decay time measured PEO concentrations above saturation, there are for the bare laponite particles in solution. This fewer laponite particles, and an excess of PEO decay time is consistent with the diffusion time of polymers, and we expect I˜/ /1. As seen in the Fig. individual laponite discs that are 25 nm in

3, I˜/ /1 at a PEO concentration of about 0.5 wt.%, diameter. Surprisingly, as shown in Fig. 4, at low which is in good agreement with the saturation PEO concentrations,t ˜ is greater than one; more- value determined from the phase behavior. overt ˜ decreases with increasing PEO concentration, reachingt ˜:1 when the concentration of

Fig. 3. The reduced intensity I˜ as a function of polymer concentration, for fixed laponite concentration of 1.25 wt.%. Fig. 4. The dimensionless time scalet ˜ as a function of PEO We define the phase transition when I˜1; found to be C/0.5 concentration, for a fixed laponite concentration of 1.25 wt.%. wt.%, in reasonable agreement with the observed macroscopic The upper phase boundary at C/0.45 wt.% is consistent with a upper phase boundary. change int ˜ from 2 to 1. 196 J. Zebrowski et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 213 (2003) 189Á/197

PEO reaches about 0.45 wt.%, the saturation value. At the highest polymer concentrations, the dynamics are indistinguishable from that of bare laponite in solution andt ˜1: These data are, in fact, consistent with our physical picture. At low PEO concentrations, the polymer bridges several laponite discs, and sot ˜2; reflecting the larger particles. As the concentration of polymer is increased, the polymer completely coats the laponite disc. However, the polymer used has a radius of gyration Rg/32 nm, which is comparable to the diameter of the laponite discs. Since the polymer adsorbs on the face of the discs rather than the edges, there is no increase in the longest dimension of the discs, and there is no change in the translational diffusion coefficient, so that the Fig. 5. Relaxation times of 1.25 wt.% laponite shake-gels as a decay time for the fully saturated laponite particles function of PEO concentration. The relaxation time scales vary is the same as for the bare laponite particles, and over nearly four orders of magnitude, for a very small change in PEO concentration. t˜1: The transition occurs at a PEO concentration of approximately 0.5 wt.%, in good agreement Furthermore, for polymer concentrations near with the value observed in the phase diagram. the transition in the phase diagram, for 0.45 wt.%, the time scale for relaxation was only a 3.4. Relaxation times of shake-gels few seconds. An intriguing observation is that the time scales for the relaxation appear to be The mechanism for the formation of shake-gels exponential in polymer concentration, suggestive involves formation of new bonds between PEO of an activated process. and laponite, creating larger aggregates. The Further refinement of the physical picture pre- energies of the new bonds formed are of order a sented here requires quantitative knowledge of the few k T, and thermal fluctuations are enough to B polymer adsorption and details of the polymer cause the polymer to revert to its stable config- conformation before and during shear. Techniques uration prior to the application of shear. The such as neutron scattering [12,13] may be useful equilibrium polymer concentrations we use are for this, especially in the unsaturated regime where near the overlap concentration, C*:/0.36 wt.%, the laponite surfaces have low polymer density and the polymer disentanglement time plays no sig- shake-gel behavior is observed. Theoretical ap- nificant role in the relaxation process; instead, the proaches that look at structure and entropy of time scale of relaxation must depend solely on the polymer chains in the presence of colloidal parti- number of new bonds that have been created due cles [18] may also aid in the understanding of the to shear. As the polymer concentration increases, relaxation times. the laponite surfaces approach complete coverage, and fewer new bonds are created by shear. This implies that the relaxation time must decrease with increasing polymer concentration. This is sup- 4. Conclusions ported by the results shown in Fig. 5, where the relaxation times, tr, of the shake-gels are plotted as A shear-induced transition from fluid to solid is a function of polymer concentration, at a fixed observed in mixtures of clay and polymer, for laponite concentration (1.25 wt.%). The time scales certain concentrations of laponite and PEO. The vary over nearly four orders of magnitude, for a phase behavior as a function of both laponite and very small change in polymer concentration. PEO concentration is determined by visual ob- J. Zebrowski et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 213 (2003) 189Á/197 197 servation. The PEO adsorbs on the laponite effectively measure the macroscopic behavior and particles; when the adsorption is not fully satu- gel properties. rated, the PEO can bridge laponite particles, causing aggregates to be formed. Application of strong shear can desorb some bonds of the PEO, Acknowledgements and readsorb them onto other laponite particles, causing the aggregates to grow substantially, and a We thank Southern Clay Products for the clay gel to form. These shake-gels can be rigid enough particles used in this paper. We also thank G. to support their own weight. As the PEO coverage McKinley, T.A. Witten, T. Kohl, D. Pozzo, S.-Y. increases, each laponite particle becomes satu- Tee and S. Pautot for stimulating discussions. This rated, and shake-gels no longer form. The adsorp- work was supported by the NSF (DMR-9971432). tion behavior of the PEO on the laponite is measured with both static and dynamic light scattering, and confirms the coverage assumed in References our picture of the phase behavior. The behavior observed for the laponiteÁ/PEO mixtures is con- [1] P.G. de Gennes, Adv. Colloid Interf. Sci. 27 (1987) 189. [2] S.M. Ilett, A. Orrock, W.C.K. Poon, P.N. Pusey, Phys. sistent with that observed for silicaÁ/PEO mix- Rev. E 51 (1995) 1344. tures, although the shake-gels formed with [3] D.H. Napper, Polymeric stabilization of colloidal disper- laponite are more rigid than those reported with sions, Academic, New York, 1983. silica. The mechanism of shear-induced gelation in [4] T.A. Witten, J. Phys. France 49 (1988) 1055. colloidÁ/polymer mixtures is qualitatively different [5] A.N. 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