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Mixtures of Colloids and Wormlike Micelles: Phase Behavior and Kinetics G. Petekidis,*,† L. A. Galloway, S. U. Egelhaaf,* M. E. Cates, and W. C. K. Poon Department of Physics and Astronomy, The University of Edinburgh, JCMB, The Kings Buildings, Edinburgh, EH9 3JZ U.K. Received December 7, 2001. In Final Form: February 20, 2002 We have studied equilibrium phase behavior and nonequilibrium particle aggregation in a mixture of charged colloids and ionic wormlike micelles. At high enough concentration of micelles but below the overlap concentration (c*), separation into coexisting colloidal gas and liquid phases occurred. Beyond c*, we observed rapid, nonequilibrium aggregation of the particles to form “transient gels”. These space-filling structures can show rapid gravitational collapse after an initial “latency period”, a behavior also found in model colloid-polymer mixtures at high polymer concentrations. The depletion mechanism was found to play an important role in phase separation. Diffusing wave spectroscopy (DWS) was used to study the dynamics of a transient gel. After about one-half of the latency period, the fluctuations in the scattered intensity increased significantly. The particle dynamics slowed during the whole latency period, consistent with the aging of the gel structure. After gravitational collapse, a very broad, logarithmic decay of the correlation function was detected for the sediment.
I. Introduction Colloids, polymers, and surfactants usually occur as mixtures both in nature and in industrial applications. As novel many-body mesoscopic systems, such mixtures are also of fundamental academic interest. In particular, mixtures containing a colloid and a second components another colloid, a polymer, or surfactant micellesshave received considerable attention in recent years.1 In the simplest model systems of this kind, the second component is smaller than the particles with which they are mixed, and the interactions between any of the components are purely repulsive. A rich variety of phase behavior and nonequilibrium phenomena have both been observed. The basic physical mechanism was long ago elucidated by Asakura and Oosawa2 in terms of the “depletion” model. The second species, known as the “depletant”, is excluded from the space between the surfaces of two nearby particles. This results in a net osmotic force pushing the particles together, which can be modeled as an effective interparticle attraction, the “depletion potential”, Udep. The depth and range of Udep are controlled by the depletant concentration and size, respectively. In the case of ideal polymer coils below the overlap concentration (c*), the depth of Udep is proportional to the activity of the polymer solution, while its range scales as the polymer’s radius of gyration, rg. In such a colloid-polymer mixture, it is well-known that the topology of the equilibrium phase diagram is sensitively dependent on rg, conveniently expressed as a dimensionless ratio to the colloid radius R: ξ ) rg/R. There exists a crossover size ratio, ξc, below which the polymer can cause only the crystallization of the colloids; in other words, the phase diagram includes fluid, crystal, and fluid-crystal coexistence regions. Above ξc, however, two fluid phases of different densities become possible, usually called “gas” and “liquid” in analogy to the phase behavior of simple atomic and molecular materials. Theory predicts, for a mixture of hard spheres and ideal linear polymers, * To whom correspondence should be addressed. † Present address: Institute of Electronic Structure and LaserFORTH, P.O. Box 1527, Heraklion, 71110, Crete, Greece. (1) Poon, W. C. K. Curr. Opin. Colloid Interface Sci. 1998, 3, 593. (2) Asakura, S.; Oosawa, F. J. Chem. Phys. 1954, 22, 1255.
a value of ξ ≈ 0.32.3,4 The most extensively studied model colloid-polymer mixture to date5 contains sterically stabilized poly(methyl methacrylate) (PMMA) particles, which behave as nearly perfect hard spheres, and linear coils of polystyrene dispersed in slightly better-than-theta solvents (e.g., cis-decalin). In this system at room temperature, ξc ≈ 0.25.5 The observed equilibrium phase behavior below and above ξc confirms the predictions of theory. At all size ratios studied to date, nonequilibrium aggregation has also been observed at the highest polymer concentrations, giving rise to space-spanning, ramified gel structures. The formation and initial structure of these gels can be modeled, in the limit of very high polymer concentrations (and hence very deep Udep), as diffusionlimited cluster aggregation (DLCA).6,7 The gels found in experiments, however, have a finite lifetime, and when contained in large enough vessels, they are observed to undergo rapid sedimentation after an initial “latency period”.8 Two-color dynamic light scattering (TCDLS) has been used to study the particle dynamics in these somewhat turbid gels during the latency period.8 Very high values of the nonergodicity parameter, f (q,∞), were found near the particle-particle peak of the static structure factor, suggesting the existence of very compact structures on the length scale of a few particles. The understanding gained from studying such a simple model colloid-polymer mixture can form the basis for exploring more complex systems. Thus, in a recent investigation, we replaced the linear polymer coils with star polymers of various functionalities.9 In another study, the polymer was replaced by uncharged wormlike mi(3) Gast, A. P.; Hall, C. K.; Russel, W. B. J. Colloid Interface Sci. 1983, 96 (1), 251. (4) Lekkerkerker, H. N. W.; Poon, W. C. K.; Pusey, P. N.; Stroobants, A.; Warren, P. B. Europhys. Lett. 1992, 20, 559. (5) Ilett, S. M.; Orrock, A.; Poon, W. C. K.; Pusey, P. N. Phys. Rev. E 1995, 51, 1344. (6) Poon, W. C. K.; Pirie, A. D.; Haw, M. D.; Pusey, P. N. Physica A 1997, 235, 110. (7) Haw, M. D.; Poon, W. C. K.; Pusey, P. N. Phys. Rev. E 1997, 56, 1918. (8) Poon, W. C. K.; Starrs, L.; Meeker, S. P.; Moussaid, A.; Evans, R. M. L.; Pusey, P. N.; Robins, M. M. Faraday Discuss. 1999, 112, 143. (9) Poon, W. C. K.; Egelhaaf, S. U.; Stellbrink, J.; Allgaier, J.; Schofield, A. B.; Pusey, P. N. Philos. Trans. R. Soc. London A 2001, 359, 897.
10.1021/la011751x CCC: $22.00 © 2002 American Chemical Society Published on Web 04/23/2002
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celles.10 In both cases, a judicious application of the depletion picture still threw considerable light on the observed equilibrium phase behavior. In this paper, we present a study in which we make both components of the model colloid-polymer mixture more complex. The hardsphere colloids are replaced by charged particles, and wormlike micelles self-assembled from ionic surfactants are used as the second component. Our motivation for using charged components was largely practicalswaterbased complex fluids, which are ubiquitous in a range of industrial products, frequently contain charged species. Our motivation for studying wormlike micelles mixed with particles is, however, both practical and fundamental. The surfactants in some industrial products do exist as wormlike micelles, often to exploit their unique flow properties.11 More fundamentally, it is of interest to ask how efficiently such micelles can function as depletants compared to polymer coils. The bonds between monomers in the latter are permanent. In contrast, wormlike micelles can break and reform. Because depletion is fundamentally about the depletant being excluded from the vicinity of particle surfaces, we might expect a depletant that can break apart to be less effective. Moreover, wormlike micelles, being equilibrium self-assembled structures, have a very broad, exponential size distribution.11 Even more interestingly, this size distribution is strongly concentration dependent. The average length L h is expected h ∼ φsR to grow with surfactant volume fraction φs as L exp(E/2kBT), where E is an end-cap energy. For the growth exponent R, theory predicts R ) 0.5,11 whereas experimentally this value as well as others have been found.12-14 The growth of worms can also be promoted by the addition of salt15 or suitable cosurfactants.14 These unique features of wormlike micelles might have nontrivial effects on their behavior as depletants. Below, we present a study of the phase behavior and gelation of charged polystyrene particles dispersed in a solution of wormlike micelles formed in brine by the anionic surfactant sodium lauryl ether sulfate (SLES) and the zwitterionic cosurfactant cocoamidopropylbetaine (CAPB). To a 1% volume fraction suspension of particles, we systematically added surfactant (SLES and CAPB at a fixed ratio) and salt. The surfactant self-assembled into spherical micelles, which grew into cylinders; these lengthened into semiflexible worms, which then entangled. We observed first phase separation and then gelation of the particles. This might be caused in part by the depletion effect due to the evolving micellar structures. On the other hand, adding salt also decreases the electrostatic repulsion between the charged colloids, which itself can also cause phase separation and gelation. To distinguish between depletion and charge effects, at least qualitatively, we also performed experiments at fixed ion concentration; micellar growth was instead promoted by varying the concentration of the second zwitterionic surfactant (CAPB) or by adding a cosurfactant (octanol). (CAPB is a betaine, and thus, an inner salt is formed upon intramolecular transfer of hydrogen ion.) We concluded that the dominant (10) Galloway, L. A.; Warren, P. B.; Fuchs, M.; Poon, W. C. K.; Cates, M. E.; Egelhaaf, S. U., manuscript in preparation. (11) Cates, M. E.; Candau, S. J. J. Phys: Condens. Matter 1990, 2, 6869. (12) Jerke, G.; Pedersen, J. S.; Egelhaaf, S. U.; Schurtenberger, P. Phys. Rev. E 1997, 56, 5772. (13) Schurtenberger, P.; Cavaco, C.; Tiberg, F.; Regev, O. Langmuir 1996, 12, 2894. (14) Stradner, A.; Glatter, O.; Schurtenberger, P. Langmuir 2000, 16, 5354. (15) Magid, L. J.; Han, Z.; Li, Z.; Butler, P. D. J. Phys. Chem. B, 2000, 104, 6717.
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effect causing phase separation and gelation in our system was indeed depletion. To quantify the particle dynamics in the gel, we performed diffusing wave spectroscopy (DWS) measurements, the use of this technique being necessitated by the large refractive index mismatch between polystyrene and water (which renders suspensions even at 1% volume fraction opaque). Time-resolved DWS measurements were done for a typical period of 2 days to follow the evolution of local dynamics while the gel aged and finally collapsed. The rest of this paper is organized as follows. In section II, we present background on materials and experimental methods. Ternary phase diagrams and DWS data are presented and discussed in section III. Finally, the main conclusions are summarized in section IV. II. Materials and Methods A. Materials. Surfactant-free polystyrene particles were obtained from Interfacial Dynamics Corporation (IDC). The manufacturer’s data sheet quotes: particle radius R ) 190 nm, polydispersity σ ) 3.5%, and surface charge Q ) -4.1 × 104e. The critical coagulation concentration (ccc), i.e., the salt concentration at which macroscopic aggregation can be observed in seconds,16 was determined to be ∼1.3% w/w of NaCl at a particle volume fraction of 1%. Wormlike micelles were formed from an aqueous mixture of the anionic surfactant sodium lauryl ether sulfate C12H25(OCH2CH2)2-OSO3Na (SLES) and the zwitterionic surfactant cocoamidopropylbetaine (CAPB). Stock solutions of industrial-grade SLES (26.4% w/w) and CAPB (30% w/w) were provided by Unilever PLC and used without further treatment (except for the addition of trace amounts of sodium azide as a preservative). A small number of samples were also prepared using pure SLES (purity 97.7%) obtained from Henkel, Germany, to check the effect of impurities in the industrial-grade anionic surfactant. The phase diagram was found to be essentially unchanged when pure SLES was used instead of industrial-grade SLES. A cosurfactant, n-octanol (Sigma-Aldrich, U.K.), was added in some experiments. In all cases, sodium chloride with a purity of 99.5% and deionized water (Millipore) were used. We quote the sodium chloride concentration in units of % w/w, where 1% w/w corresponds to about 170 mM. Particle-surfactant mixtures were prepared by weighing and mixing SLES, CAPB, deionized water, particles, and salt (in this order) and subsequently tumbling the mixture for several minutes. It was important to add the salt lastsit promotes the growth of wormlike micelles and therefore increases the viscosity of the sample dramatically, which could jeopardize homogenization. Samples were stored at 20 ( 1 °C and left undisturbed for visual observation for several months. All samples used for the studies of transient gelation were freshly prepared for each observation or DWS experiment. B. Rheology. The surfactant solutions without particles were characterized using oscillatory shear measurements in a TA Carrimed CSL2100 controlled-stress rheometer with cone-andplate geometry. A pre-shear at a constant stress of 2 Pa for 30 s was applied to remove history effects caused by loading. A frequency sweep (from 0.01 to 40 Hz) at 5% strain was then applied to determine the storage and loss moduli, G′ and G′′, respectively. Entangled wormlike micelles exhibit a singleexponential stress decay following a Maxwell model.11 The characteristic Maxwellian rheological behavior of G′ and G′′ therefore indicates the crossover to the entangled regime. This is particularly apparent in the Cole-Cole representation, where G′′ is plotted against G′, giving a semicircle for a Maxwell fluid. C. Direct Observation. Phase separation in these mixtures was observed by visual inspection in cells of inner diameter 25 mm. Because of the large refractive index mismatch between the polystyrene particles (n ) 1.591 at 20 °C) and the aqueous micellar solution (n ) 1.33 at 20 °C), a particle-rich phase appears opaque. In some cases, especially in gel-like samples that showed (16) Shaw, D. J. Introduction to Colloid and Surface Chemistry, 4th ed; Butterworth Heinemann: Oxford, U.K., 1992.
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a latency period, time-lapse video recording was performed. Samples were illuminated either from behind, to see details of separated phases, or from the front, which enabled the determination of the position of a phase boundary or meniscus to within (1 mm. The ratio of the height of the bottom phase to the total sample height in the cell was used to determine the sedimentation profile. D. Diffusing Wave Spectroscopy (DWS). An argon ion laser operating at a wavelength of λ ) 514.5 nm and a power of typically 100 mW was used to illuminate the sample. The transmitted intensity was collected by a single-mode optical fiber, and the intensity autocorrelation function was obtained utilizing an ALV5000E multitau correlator. The normalized intensity correlation function, g(2)(τ) ) 〈I(0) I(τ)〉/〈I(0)〉2, was measured, and because of the Gaussian statistics of the scattered intensity, it could be related to the normalized electric field autocorrelation function, g(1)(τ) ) 〈E(0) E*(τ)〉/〈| E(0)|2〉 by the Siegert relation17
g(2)(τ) ) 1 + [g(1)(τ)]2
(1)
The normalized electric field autocorrelation function in the diffusing wave approximation for noninteracting scatterers is17-19
g(1)(τ) )
∫ P(s) exp{- 31k ∞
0
}
〈∆r2(τ)〉s/l* ds
2
0
(2)
where 〈∆r2(τ)〉 is the mean square displacement of the scatterer after time τ, P(s) is the fraction of paths with length s, and k0 ) 2πn/λ. P(s) depends mainly on the geometry of the sample, the characteristics of the incident beam (focused or extended), and the geometry of the detection system (transmission or backscattering). The relaxation times observed in a DWS experiment depend not only on the intrinsic dynamics of the sample but also on the scattering geometry (transmission or backscattering) and the number of scattering events (or the transport mean free path, l*). It is, however, unlike single scattering measurements, independent of the scattering angle. For the transmission geometry and a planar source, standard DWS theory in a thick sample (L . l*) yields17-19
g(1)(τ) = (L/l*)x6τ/τ0/sinh[(L/l*)x6τ/τ0] ≈ exp[-(L/l*)2τ/τ0] (3) where τ0 ) 1/(k02D) is the characteristic decay time of the relaxation with mean square displacement 〈∆r2(τ)〉 ) 6Dτ and D is the diffusion coefficient for diffusing particles. The transport mean free path, l*, can be calculated from the total amount of light transmitted through the sample, T, using T ) (5l*/L)/(1 + 4l*/3L).17 In practice, to overcome technical problems such as reflectivity and measurement of the full transmission, a reference sample of known l/0 is used to determine the unknown l* from the ratio T0/T, where T0 is the transmission of the reference sample.20 In the transmission geometry, the average number of scattering events is N ) (L/l*)2, so that, according to eq 3, the characteristic length scale probed by DWS is lDWS ≈ λ/xN. For the DWS measurements, samples were kept in a cylindrical cell with an inner diameter of 8 mm. The measurements were performed at a temperature of 19 ( 1 °C. Single measurements of 15-30 min were repeated over a period of several days to follow the evolution of the sample. Simultaneously with the DWS measurements, the samples were visually observed using a CCD camera attached to a time-lapse video recorder.
III. Results and Discussion A. Pure Micellar Solutions. The effect of the composition of the micellar solution on the rheological behavior (17) Weitz, D. A.; Pine, D. J. In Dynamic Light Scattering: The Method and Some Applications; Brown, W., Ed.; Oxford Science Publications: Oxford, U.K., 1993; Chapter 16, p 653. (18) Maret, G.; Wolf, P. E. Z. Phys. B: Condens. Matter 1987, 65, 409. (19) Pine, D. J.; Weitz, D. A.; Chaikin, P. M.; Herbolzheimer, E. Phys. Rev. Lett. 1988, 60, 1134. (20) Kaplan, P. D.; Dinsmore, A. D.; Yodh, A. G.; Pine, D. J. Phys. Rev. E 1994, 50, 4827.
Figure 1. Cole-Cole plots for (A) 7% SLES, 1% CAPB, and varying NaCl concentrations as indicated and for (B) 7% SLES, 1% CAPB, 1% NaCl, and varying concentrations of octanol as indicated.
was investigated. Figure 1A shows Cole-Cole plots for 7% SLES, 1% CAPB, and varying amounts of NaCl. At low salt concentration (below 2%), the micelles are sufficiently small that they do not overlap, as suggested by a non-Maxwellian behavior. As the salt concentration is increased above 2%, the wormlike micelles become longer, and around the overlap concentration, the sample exhibits viscoelastic behavior, as indicated by a partial semicircle in the Cole-Cole plot. At salt concentrations above 5%, a full semicircle could be observed, indicating Maxwellian behavior with a reptation time much longer than the scission time.11 At higher surfactant concentrations (14% SLES and 2% CAPB), a semicircle in the ColeCole plot that could be fitted by a Maxwell model was observed at a concentration of about 2.5% NaCl (data not shown). Furthermore, upon addition of octanol, which does not affect electrostatic interactions, Maxwellian behavior was found for 7% SLES, 1% CAPB, 1% NaCl, and 0.8% octanol (Figure 1B). In general the behavior with increasing octanol was found to be similar to that with increasing NaCl concentration. Note that the value for the salt or octanol concentration is an upper limit for the onset of Maxwellian behavior as the limited frequency range in the rheological measurements might exclude the righthand side of any semicircular Cole-Cole plot at lower salt or octanol concentration. B. Phase Behavior of Particle-Surfactant Mixtures. The phase diagram of aqueous mixtures of colloid, surfactant (mixture of SLES and CAPB), and salt (NaCl) is shown in Figures 2 and 3. We first varied the concentrations of surfactant and salt while keeping the particle volume fraction constant at 1% and also the SLESto-CPAB weight ratio fixed at 7. The phase behavior can
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Figure 3. Ternary phase diagram of the SLES/CAPB/water system. The types of behavior are fluid (b), gas-liquid coexistence (0), collapsing gel (1), and slow gel (3). The dashed line marks the ionic strength corresponding to the ccc. An estimate of c* is given by the dot-dashed line, and the onset of Maxwellian behavior is indicated by the solid line.
Figure 2. (A) Ternary phase diagram of the SLES-CAPB(7:1)/NaCl/water system with fixed particle concentration of 1%. The types of behavior are fluid (b), gas-liquid coexistence (0), collapsing gel (1), and slow gel (3). The dashed line marks the ionic strength corresponding to the ccc. An estimate of c* is given by the dot-dashed line, and the onset of Maxwellian behavior is indicated by the solid line. (B) Photographs of samples with 7% SLES, 1% CAPB, and varying NaCl concentration. From left to right: equilibrium gas-liquid (0 and 1.5% NaCl), collapsed gels (3% NaCl), and slow gel (5% NaCl) where inhomogeneities have appeared over a period of a few months.
thus be represented in a quasi-ternary phase diagram considering the fractions of (total) surfactant, NaCl, and water (Figure 2A). At low surfactant and salt concentrations, the solutions are colloidal fluids. As the surfactant and/or salt concentrations are increased, the mixtures separate into coexisting colloid-rich and colloid-poor regions (Figure 2B). Interfaces and surfaces remain horizontal upon tilting as expected for fluids. Judging from the DLVO potential only, one would anticipate that the repulsive electrostatic interactions are screened by the added salt and the counterions of SLES. Furthermore, for ionic strengths above a value corresponding to the ccc of the surfactant-free solution (dashed line in Figure 2A), phase separation is expected to occur, whereas samples with a lower ionic strength should show only a single phase. However, by analogy with simple colloid-polymer mixtures, we believe that we are observing an incomplete “gas-liquid” phase separation (with the incompleteness being due to gelation intervening in the developing dense “liquid” phase).21 Phase separation is, however, also observed at lower ionic strengths, particularly for no added salt and (total) surfactant concentrations above about 3%. This indicates that, for gas-liquid phase separation to occur in these samples, a significant role must be played by the depletion induced by the micelles. (21) Sedwick, H.; Egelhaaf, S. U.; Poon, W. C. K., manuscript in prepearation. In a sticky hard-sphere colloid, similar observations have also been discussed in “gas-liquid” phase separation terms: Verduin, H.; Dhont, J. K. G. J. Colloid Interface Sci. 1995, 172, 425.
On the other hand, at very low (total) surfactant concentrations (720 h.
Figure 11. Time evolution of (A) the transmitted intensity, I, and (B) the relaxation time, τ2, at the bottom of the sample.
to be essential for the ability of the gel to self-heal.8,27 Coarsening of tenuous structures in colloid-polymer gels is thought to be caused by particles at the surface of the aggregate that tend to diffuse in the direction of concave regions.8,33 The progressive incorporation of free and more mobile tendrils into the network might lead to the observed slower dynamics but might also lead to a lower ability to self-heal and thus finally to the collapse of the gel under its own weight. The slowing of the dynamics might thus reflect the aging prior to the collapse and the oncoming gel collapse. While the gel collapses, the intensity shows a large peak (Figures 9A, 11A) because of the light scattered by the interfaces while they pass through the laser beams. (As mentioned above, the time when this happens depends on the precise position of the two beams.) After the interfaces have passed through the beams, the transmitted intensity is found to have increased at the top of the sample (Figure 9A). This is attributed to the sharp decrease of the particle density in the supernatant when compared to the initial gel. This leads to a dramatic change in the scattering conditions, with a pronounced decrease in the number of scattering events, N, leading to a slowing of the observed dynamics. It is thus not possible to relate the measured rapid increase in relaxation time at the top of the sample (Figure 9B) to the intrinsic dynamics. At the bottom of the sample, the correlation functions are observed to change shape (Figure 10B). They become broader (Figure 10B) and faster (Figure 11B) until (after about 24 h) the sediment fills all of the space probed by the laser beam. As the sediment accumulates, the increasing particle density leads to significantly more scattering events. This is expected to be the decisive factor for the observed decrease of the relaxation time. The increasing particle density is also consistent with the (33) Olivi-Tran, N.; Thony, R.; Jullien, R. J. Phys. I (Fr.) 1996, 6, 557.
observed decrease in transmitted intensity (Figure 9A). We thus anticipate that the changes in the (multiple) scattering conditions dominate the changes in the observed dynamics at both the top and bottom of the sample and completely conceal the evolution of the intrinsic dynamics during this transient period. After the collapse, almost-single-scattering conditions prevail at the top of the sample. This leads to the relatively high transmitted intensity (Figure 9A) and the observed large relaxation time, which seems to reach a plateau (Figure 9B). It represents the dynamics of a small number of aggregates left in the less cloudy top of the sample. A very different behavior is observed at the bottom of the sample, where we follow the compactification of the sediment. We thus expect, as mentioned above, the density of particles to increase and, hence, the number of scattering events N to increase and l* to decrease. This is reflected by the level of transmitted intensity being lower than it was before the collapse (Figure 11A) and by the initial decrease of the relaxation time (Figure 11B). Once the scattering conditions have stabilized at the late stage of sediment compactification (after about a day), a further slowing of the dynamics is observed, along with a broadening of g(1)(τ) (Figure 10C). Remarkably, measurements after a month reveal a broad, logarithmic decay of the correlation function that spans about eight decades. Because g(1)(0) < 1, there are additional fast dynamics of the system that are outside the time window of the correlator. It is surprising that, at the small length scales probed, lDWS = 3 nm, a logarithmic relaxation of density fluctuations is observed. The origin of this relaxation is not clear. To gain additional insight into the underlaying intrinsic dynamics at the bottom of the sample, we calculated the square root of the mean square displacement x〈∆r2(τ)〉 (Figure 12), which can be deduced from g(1)(τ) under the assumption that it is accurately described by eq 3. During the latency time, the two-stage relaxation observed in g(1)(τ) is recovered in the two regimes visible in x〈∆r2(τ)〉. The fast motion of the particles at short τ essentially does not change, as already indicated by the constant τ1 (eq 5). On the other hand, the dominating long-time motion becomes slower (Figure 12), in agreement with the time dependence of τ2 (Figure 11B), and seems to disappear after a very long period, at least a week, after the collapse. At this late stage, the correlation function g(1)(τ) is found to be very broad (Figure 7B). It corresponds to a weak, power-law
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dependence of x〈∆r2(τ)〉 ∝ τν with ν = 0.05 (Figure 12). The displacements probed are very local, on the order of 1 nm, which is much shorter than those probed during the latency period when l* is larger. On this very short length scale, only 20% of the density fluctuations appear to be frozen (Figure 7B). We can only speculate about the origin of the two relaxations. The fast relaxation might be related to the cooperative motion of the particles in the aggregates, which includes both particles restricted within the clusters and others moving more freely at the surface of the clusters. Under the present conditions, the electrostatic interactions are essentially screened, and the particles are thus expected to only wiggle in a short-ranged, very deep potential. Because the average density inside the clusters is expected to remain constant during coarsening, τ1 should also not change. This is, in fact, observed. The slow relaxation, τ2, might represent the diffusion of the clusters as a whole; such a motion is progressively more restricted during the latency period because of the coarsening mechanism. Furthermore, at the late stage of sediment compactification after a long period of about a week, this relaxation seems to disappear (Figure 12). At this stage, the particles are essentially restricted inside the deep, short-range potential, and therefore x〈∆r2(τf∞)〉 is bound to about 1 nm (Figure 12). Moreover, we can speculate that the broad range of local packing conditions and related dynamic heterogeneities in the collapsed dense sediment give rise to such a broad range of relaxation times. The fact that the dense sediment appears lumpy (Figures 4B and 6C) supports the idea of a locally heterogeneous sample. Such a slow,
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logarithmic decay of g(1)(τ) has been predicted by mode coupling theory for gels with high particle volume fraction.34 IV. Conclusions In this paper, we present the phase behavior of a multicomponent system consisting of charged colloids and ionic wormlike micelles. We monitor the process of gel collapse by direct observation and diffusing wave spectroscopy. The phase behavior can be rationalized by the depletion mechanism. This is supported by the observation of liquid-gas coexistence for relatively small concentrations. At surfactant concentrations above about c*, gels were found with behavior similar to that observed for colloid-polymer mixtures but with longer latency times. The dynamics during the aging of a gel was investigated in detail by DWS experiments. Most correlation functions exhibited a two-stage decay. A slowing of the dynamics was observed during the latency period and a significant increase of the fluctuations in the transmitted intensity after about one-half of the latency time. At the late stage, long after the gel collapse, DWS measurements of the compactified sediment revealed very broad dynamics spanning several decades in time. Acknowledgment. G.P. was funded by a Marie Curie Fellowship of the European Community program under Contract ERBFMBICT983380, and S.U.E. is supported by Unilever Research. L.A.G. thanks EPSRC and Unilever Research for a CASE studentship. LA011751X (34) Dawson, K.; Foffi, G.; Fuchs, M.; Gotze, W.; Sciortino, F.; Sperl, M.; Tartaglia, P.; Vigtmann, T.; Zaccarelli, E. Phys. Rev. E 2001, 63, 011401.
