Experimental Phase Diagram of Symmetric Binary ... - ACS Publications

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J. Phys. Chem. B 2006, 110, 13220-13226

Experimental Phase Diagram of Symmetric Binary Colloidal Mixtures with Opposite Charges Manuel S. Romero-Cano, Jose´ B. Caballero, and Antonio M. Puertas* Group of Complex Fluids Physics, Department of Applied Physics, UniVersity of Almerı´a, 04120 Almerı´a, Spain ReceiVed: February 2, 2006; In Final Form: April 7, 2006

The phase behavior of equimolar mixtures of oppositely charged colloidal systems with similar absolute charges is studied experimentally as a function of the salt concentration in the system and the colloid volume fraction. As the salt concentration increases, fluids of irreversible clusters, gels, liquid-gas coexistence, and finally, homogeneous fluids, are observed. Previous simulations of similar mixtures of Derjaguin-LandauVerwey-Overbeek (DLVO) particles indeed showed the transition from homogeneous fluids to liquid-gas separation, but also predicted a reentrant fluid phase at low salt concentrations, which is not found in the experiments. Possibly, the fluid of clusters could be caused by a nonergodicity transition responsible for the gel phase in the reentrant fluid phase. Liquid-gas separation takes a delay time after the sample is prepared, whereas gels collapse from the beginning. The density of the liquid in coexistence with a vapor phase depends linearly on the overall colloid density of the system. The vapor, on the other hand, is comprised of equilibrium clusters, as expected from the simulations.

I. Introduction Charge correlations drive many important physical, chemical, and biological processes. Such correlations were acknowledged in ionic fluids, modeled as a mixture of charged spheres interacting by Coulomb interactions by using the restricted primitive model (RPM).1 In this system, the phase behavior is dictated by charge correlations and the interplay between attractive and repulsive interactions.2 Charged colloids and their counterion clouds provide one of the first examples of charge correlations, as shown by Derjaguin and Landau3 and Verwey and Overbeek.4 These correlations add to the generally more complex behavior found in colloids with respect to atomic or molecular fluids.5 In particular, the existence of nonergodic states, where the system forms an amorphous solid at low density, so-called “gel”,6 caused by short-range attractions, has no analogue in the molecular systems. In this work, we study the phase diagram of 1:1 mixtures of charged colloids, with opposite sign of charge, but similar absolute charge, nature, and size. This symmetric system represents the colloidal analogue of ionic salts, but presents the advantage that the ionic strength in the solvent fulfills electroneutrality of the whole system and nonequimolar mixtures could be studied. On the other hand, the system is much more complicated than the ionic salts because it is a four-component mixture, with two ions and two colloidal species. Correlations between oppositely charged colloids, ion-colloid, and ion pairs can be present at the same time, resulting in an extremely complex phase behavior. The system can be also interpreted as a simplification of mixtures of polyelectrolites or proteins, which show a rich scenario of associating phenomena such as coacervation, phase separation, or precipitation.7,8 Previous studies with symmetrical mixtures of spherical particles have focused on the occurrence of crystallization at * Corresponding author. E-mail: [email protected].

Figure 1. Schematic representation of the phase behavior as a function the salt and colloid concentrations obtained in simulations.14 The actual location of the boundary depends on the temperature of the system.

high density.9-11 They reported different lattice structures depending on the ratio of the radii; in particular, bcc crystals were observed for similar sizes, which were also observed in simulations.11,12 Here, we concentrate on the liquid-gas transition. To our knowledge, the present work is the first attempt to rationalize the low-density phase behavior of such mixtures. Computer simulations on this system, appropriately simplified to model effective interactions between the colloidal particles, showed a liquid-gas transition in the low-density-low-temperature region.13,14 The critical temperature depends nonmonotonically on the interaction range due to the interplay of attractions and repulsions; as the range is decreased, the critical point first increases and then decreases. The critical density, on the other hand, continuously increases as the range is decreased. This implies a reentrant fluid phase as a function of the interaction range, set by the salt concentration, leaving an island of phase separation, which schematically is shown in Figure 1. We study a model system that allows us to probe these effects experimentally and compare qualitatively with the simulations. We thus restrict our study to low densities, where the liquidgas separation was predicted and keep the temperature, or the strength of the interaction, constant, whereas the range of the interaction is varied by adding salt to the medium. The phase

10.1021/jp0607162 CCC: $33.50 © 2006 American Chemical Society Published on Web 06/15/2006

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TABLE 1: Characteristics of Colloidal Systems latex functionality diameter (nm) PSPS+

sulphate amidine

185 ( 2 185 ( 7

PDI

surface charge (µC/cm2)

1.0060 1.0066

-3.9 ( 1.3 9.2 ( 2.4 at pH 4 4 ( 2 at pH 10

diagram is therefore constructed using the colloid volume fraction and the salt concentration as control parameters. Model polymer latexes with chemical charges are used to perform this study. Experiments are performed in water to enhance the electrostatic interaction, and irreversible aggregation is prevented by adsorbing a nonionic surfactant onto the surface of both latexes. We find fluid-fluid separation, as predicted, but also a solid noncrystalline phase, which is consistent with gels observed in other colloidal systems with attractions.15 At very low salt concentrations, we find fluids composed of (apparently irreversible) clusters. This fluid, however, cannot be connected straightaway with the reentrant fluid at low salt concentrations obtained in the simulations, although the general aspect of the phase diagram is similar to Figure 1. We discuss the interplay of the reentrant fluid predicted by the simulations and gelation as the possible origin of this “fluid of clusters”. The next section presents the experimental details of the work; in particular, we have made sure that both latexes have similar charges in absolute value. In this way, the system is indeed a symmetrical mixture. Next, we present the results: first we tackle the phase diagram, then we study the properties of the liquid-gas coexistence, and finally, we concentrate on the gels and low-salt fluids. II. Experimental Section All chemicals in this study were of analytical grade and were used without further purification. Ultrapure water with an electrical conductivity less than 1 µS/cm was used in all experiments. The positive latex (PS+) was synthesized in our laboratories, with N,N′-azo-bis(dimethyl-isobutylamide hydrochloride) as initiator, using the emulsifier-free method.16,17 This system has amidine chemical groups, which allows a control of the surface density charge by means of the pH.18 The negative latex (PS-) was supplied by Ikerlat Polymers (Spain). The latexes were cleaned by serum replacement until the conductivity of the supernatant was similar to that of the water. The particle diameters and the surface charge densities were determined by transmission electron microscopy and conductometric/potentiometric titration, respectively. Table 1 shows the main characteristics of both particles. To test the equivalence between both colloidal systems, the electrophoretic mobility was measured versus the electrolyte concentration. The effective charge can be obtained from the behavior at high salt concentrations. The electrophoretic mobility measurements were performed with a Zetasizer-Z, commercialized by Malvern Instruments (U.K.). The measuring technique is based on the principles of laser Doppler electrophoresis,19 consisting of analyzing the mixing of light scattered from a colloidal suspension and a reference beam of well-known frequency. We worked at a colloid concentration of ∼1010 particles/ cm3 (corresponding to a volume fraction of φc ∼ 4‚10-5), which guarantees simple-scattering conditions and constant electrophoretic mobility irrespective of small variations in particle volume fraction. The mobilities were taken as the average of at least 10 measurements, and the standard deviation of these measurements was considered to be the experimental error. Figure 2 shows the electrophoretic mobilities in absolute value of both colloidal systems as functions of the medium electrolyte concentration in a log-log scale for pH ) 6.21 Both systems

Figure 2. Electrophoretic mobility of the positive and negative latexes, black and red open circles, respectively, as a function of the salt concentration. The straight line represents the inverse square-root behavior according to Smoluchowski behavior (κ is the inverse Debye length).

present equal mobilities at all salt concentrations, indicating that they have exactly the same effective charges (but with opposite sign). The maximum at intermediate ionic strength has been reported in other mobility studies for hard particles, and its origin has been widely discussed.20,22 At high salt concentrations, the particles show the behavior ∼[NaCl]-1/2 predicted by the Smoluchowski approximation for charged hard spheres (for κσ . 1, where κ is the inverse Debye length),23 which permits us to obtain an effective charge (in absolute value) of Q ) (100.0 ( 1.9)‚102e-. Using this value for the particle charge, the potential energy at contact in water is of the order of hundreds kBT for κσ ∼ 1, although the range of the interaction potential is only ∼0.01 diameters. Additionally, the heteroaggregation kinetics was studied to check the similarity of both systems. A Malvern 4700 light scattering instrument was used to study the initial heteroaggregation stages by static light scattering. The light source was a He-Ne laser, with a wavelength 633 nm. The scattering angle was set to 20°, and the particle concentration was 2‚109 parts/ cm3 (φc ) 7.4‚10-6) and pH ) 6. The concentration of positive and negative particles was varied, keeping the total concentration at the value indicated above in all cases. The electrolyte (NaCl) concentration was kept at 0.33 mM, a value at which the particle electrical double layer was weakly screened, and attraction between oppositely charged particles drove the reaction.24 The initial aggregation velocity was obtained from the initial slope of the intensity vs time curve. Because the aggregation is driven by electrostatic attractions, it is very fast, and the initial stages (up to one aggregation time) not only contained formation of doublets, but also of larger aggregates (trimers).24 In Figure 3, the heteroaggregation velocities are presented as a function of the negative particle fraction. Note the symmetry of the curve, which can be fitted to a parabola. This fact confirms that both systems present similar effective surface potentials (in absolute value).24 In the experiments for the phase diagram, however, colloidal aggregation must be prevented. For this purpose, a nonionic stabilizer Triton X-100 was adsorbed onto the particle surface.25 To gain more information of the surfactant purity, a mass spectroscopy spectrum was obtained (Centre of Scientific Instrumentation, University of Granada). The results showed that the surfactant is of good purity, with a polydispersity index (〈Mw〉/〈Mn〉) of 1.031,26 where 〈Mw〉 and 〈Mn〉 are the numberaverage molecular weight and the weight-average molecular weight, respectively. Surfactant adsorption was performed in batteries for 24 h at 25.0 ( 0.1 °C; during the adsorption, the systems were gently

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Figure 3. Aggregation velocity, measured by static light scattering, as a function of the fraction of negative particles. The line shows a parabolic fitting with maximum at x- ) 0.5.

shaken. At this temperature, the adsorption plateau was found for surfactant concentrations lower than the critical micelle one. Thus, the adsorption was performed in the plateau conditions to guarantee maximal coverage for all the latex concentrations to be used. More details on the adsorption process and preparation of the complexes (colloidal particle with surfactant adsorbed) have been previously published.27,28 The surfactant prevents colloidal aggregation by increasing the minimum surface-to-surface distance, lying outside the range of the van der Waals attraction. However, the increase of this distance also causes a significant weakening of the electrostatic attraction, which nevertheless is strong enough to induce bonding and phase separations. In conclusion, as shown by electrophoretic mobility and heteroaggregation, the mixture of both latexes is completely symmetric at pH ) 6.21 On the other hand, the surfactant, physically adsorbed onto the particles, inhibits irreversible aggregation and allows the experimental study of the phase diagram of the colloidal analoge of simple ionic fluids. We prepared aqueous suspensions of 1:1 mixtures of negative and positive polystyrene particles, previously sterically stabilized, at different weight fractions (between 0 and 10%) and electrolyte concentrations (NaCl). Water was chosen as the solvent to enhance the electrostic interaction due to the high degree of ionization of the chemical surface groups in water. The complexes were mixed without dilution from the adsorption battery to avoid desorption of the surfactant.28 The ordering of mixing was: one complex, salt, and finally, the second complex. In this way, both complexes never were in contact before the salt was added. After preparation, the mixtures were shaken in a vortex stirrer for 30 s. Different cells were used for different purposes: cylindrical cells for the determination of the phase diagram (with a total volume of 1 ml), rectangular narrow cells for the kinetics of phase separation (with a total volume of 1 ml), and rectagular wide cells for the experiments with a step in the bottom of the cell (with a total volume of 3 ml). No difference in the final state of the sample was observed for different cells. The phase diagram is reported using the colloid volume fraction, φc, and the salt concentration, [NaCl], or the inverse Debye length, κ, as control parameters. III. Results and Discussion The system was prepared by mixing the components, as described in the Experimental Section, and the phase in every state was determined by visual inspection. Figure 4 presents pictures for different states, prepared by adding salt to a sample at φc ) 0.10. As shown in the figure, the samples were also tilted to identify fluid or solid phases.

Figure 4. Pictures of the system along the isochore φc ) 0.10. From top to bottom, the salt concentration is 2.44 mM (κ ) 0.162 nm-1), 25.57 mM (κ ) 0.526 nm-1), and 50.67 mM (κ ) 0.740 nm-1) (the arrows mark the liquid-gas boundary) and 88.31 mM. The right column shows the same systems tilted, showing its fluidity.

At very low salt concentrations (Figure 4, top row of panels, A), the system appears to be a homogeneous fluid, although slightly heterogeneous, as observed by eye. By increasing the salt concentration, a solid phase forms that contains all of the particles, row B in Figure 4. The solid, however, has a very low colloid concentration (in the picture the solid has a volume fraction of less than 15%) and does not show iridiscence; i.e., it is an amorphous phase. We identify this solid as a “gel”, analogous to similar findings in monocomponent systems, in e.g., colloids with attractions induced by nonadsorbing polymers.6 By increasing the salt concentration (around 50 mM) for all volume fractions, two fluids with different density are observed because both of them flow when the bottle is tilted (row C in Figure 4). Accordingly, the fluid-fluid interface is always horizontal, as shown in the figure by the arrows. This two-fluid coexistence resembles liquid-gas coexistence in atomic systems and has been observed previously in monocomponent colloidal systems.6 In our case, the colloid concentration of the denser phase (liquid) depends on the salt concentration but can be rather low; the liquid in Figure 3 has φl ≈ 0.16. At even higher salt concentrations (above ∼70 mM, for this volume fraction), the system is completely homogeneous (Figure

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Figure 5. Phase diagram of the binary mixture of oppositely charged colloids in κ vs φc. By increasing the salt concentration, a fluid phase is observed at low κ (black circles), followed by a gel phase (red circles), liquid-gas separation (green crosses), and a homogeneous fluid (blue diamonds). The letters and the black bullets correspond to the states shown in Figure 3. Several salt concentrations are shown in the right y-axis.

4, lower picture, labeled D). At these high salt concentrations, the particle charges have been fully screened. Therefore, the range and strength of the interactions are not large enough to induce any phase transitions, although they may still cause reversible bonding between individual particles. Interestingly, this fluid phase is macroscopically different from the fluid phase observed at very low salt concentrations; whereas the low-salt one looks grainy shortly after preparation, this one is completely homogeneous, indicating that it is composed of individual particles, or very small clusters. The appearance of a gel phase, followed by a liquid-gas transition when the salt concentration is increased and the fluid phase is at very high ionic strength, is observed at all the (low) volume fractions studied here, with slight differences only in the actual values where the transitions from one to another are found. The fluid phase at low salt concentrations, on the other hand, depends strongly on the colloid concentration, and below φc ) 0.02, it is observed only when no salt is added to the mixture (a residual ionic strength of less than 0.1 mM is present, though). All of these findings are summarized in Figure 5. This plot represents the major result of this paper: the phase diagram of the 1:1 binary mixture of oppositely charged colloids below φc ) 0.10. Note that κ controls mainly the interaction range, but also its strength. To make direct contact with the experiments, corresponding values of the salt concentrations are given in the right y-axis. The apparent fluid phase found at low salt concentrations is indeed composed of irreversible clusters, as observed by optical microscopy (see Figure 11). It is, thus, not an equilibrium colloidal fluid and, therefore, different from the fluid at high salt concentrations. This “fluid of clusters” is possibly caused by the interplay of the fluid phase with a nonergodicity transition, as we discuss below. The agreement between the experimental phase diagram in Figure 5 and that expected from simulations (Figure 1) at low salt concentrations is good in a macroscopic sense. However, if the fluid of clusters reflects an underlying fluid phase, the lines and phases in both diagrams can still be compared, showing excellent qualitative agreement, although the lines delineate boundaries between different kinds of phases. In the following, we analyze the properties of the system in the different regions observed. First, we study the samples in the liquid-gas separated region; next, we concentrate on the nonergodic samples, i.e., gels and low-salt fluids.

Figure 6. Evolution of the height of the liquid-gas interface for different colloid concentrations (upper panel) and ionic strength (lower panel). Upper panel: from bottom to top, φc ) 0.01, 0.03, 0.05, and 0.07, with [NaCl] ) 63.07 mM. Lower panel: from top to bottom, [NaCl] ) 63.07 mM, 66.61 mM, and 70.14 mM, with φc ) 0.03.

A. Liquid-Gas Coexistence. After preparing a sample in the appropriate range of salt concentration, an interface separating two fluids forms and drops as the liquid and vapor phases separate. The height of the interface is presented in Figure 6 as a function of the time elapsed since the mixing. In the upper panel, different colloid concentrations at constant κ are studied, whereas varying salt concentrations at constant φc is tackled in the lower one. In all cases, a fast initial decay of less than 10% is observed, followed by a much slower one. The interface finally decays after a delay time that depends strongly on the conditions, and a steady state is reached at much longer times (in all cases several days, outside the time window presented here). Similar results are obtained at other salt concentrations or colloid concentrations. As observed in simulations13,14 and in confocal microscopy experiments,9 the liquid is locally highly structured due to the interplay of attractions and repulsions. Every particle is surrounded of shells of particles with an opposite sign of charge, minimizing the energy of the system. The formation of this structure can be responsible for the delay time between the formation of pairs or groups of particles and their growing to form a macrophase. Increasing the colloid concentration makes the separation between these two decays longer, until the final decay is outside our time window, possibly indicating that the local structuring is complicated by crowding. On the other hand, increasing the salt concentration slightly decreases the delay time, but makes the final decay faster because the drops formed are denser. We thus hypothesize that the delay time is controlled by crowding inside the liquid drops, and the final decay by the density of the final liquid phase (drops). Accordingly, in monocomponent systems, the liquid needs no structuring, and there is no such latency time.29 The final height of the liquid phase is presented in the inset to Figure 7 as a function of the colloid concentration at constant ionic strength. Assuming that the concentration in the liquid is

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Figure 8. Scattered intensity for vapors in coexistence with liquids for total volume fractions of φc ) 0.005 (black points) and φc ) 0.01 (red points) and [NaCl] ) 62.23 mM, compared with the intensity of single particles (open circles). The curves have been scaled vertically to overlap in the high-q regions. The lines are power-law fits to the intensity, with the exponents indicated in the figure.

Figure 7. Volume fraction of the liquid phase as a function of the overall colloid volume fraction, φc, for [NaCl] ) 61.28 mM (upper panel) and for different salt concentrations in the lower panel (as labeled). The inset in the upper panel shows the final height of the liquid-vapor interface for [NaCl] ) 61.28 mM. The data at high φliq have large error bars, not presented for clarity.

much bigger than in the gas, and neglecting the latter, the calculated liquid concentrations are presented in the main panels. Because the final height of the liquid is not linear with φc, the liquid volume fraction depends on the overall colloid concentration, indicating that the tie-lines are not iso-κ lines. We have checked the salt concentration in the vapor, which should vary as it changes in the liquid phase, by conductometric measurements (colloidal particles removed). Three samples were prepared for the same state, giving three values scattered around the overall salt concentration. Thus, within the accuracy of the method ((2 mM), we could not identify any variation of the salt concentration in the vapor. This finding, however, does not rule out slight variations that could cause the differences in the liquid volume fraction due to the flatness of the boundary lines in the phase diagram. Interestingly, the volume fraction in the liquid shows a linear dependence with φc, at all salt concentrations, with the slope increasing with κ (lower panel of Figure 7). Also, all of them yield a y-intercept close to φliq ) 0.05. The origin of this behavior is as yet unclear. The liquid concentrations at the highest φc and salt concentrations are extremely high (see Figure 7), with large uncertainty, and lie close to the glass transition, driven by crowding. In addition, because the tie-lines are not flat, these liquids could be inside the gel phase at lower salt concentrations. Thus, we have tested the fluidity of some of these samples by using a cell with a step in the bottom.30 Indeed, the denser liquids show the typical behavior of nonergodic samples, or at least of very viscous liquids. This behavior is also observed in more dilute liquids, with volume fractions as low as 10 or 20%, probably because the liquid has entered the nonergodic region at low salt concentrations, or it is very close to the boundary. It should be noted, however, that in all cases, when the bottles are tilted, the liquid flows, indicating that the gel formed can be shear melted by applying moderate stresses.

We now move our attention to the vapor phase. In simulations, the vapor was found to be composed of (equilibrium) clusters of particles, with larger clusters closer to the liquidgas boundary.31 To check this prediction, we have performed static light scattering on samples showing liquid-gas coexistence. The laser beam was directed to the vapor phase (in equilibrium with the liquid in the lower part of the cell) in cases where its concentration was low enough to guarantee simple scattering. The results are presented in Figure 8 as a function of the wavevector, q. The static light scattering of vapor in samples with φc ) 0.005 and φc ) 0.01 are compared with the intensity scattered by single particles (the curves have been arbitrarily scaled to collapse in the high-q region). The figure shows increasing scattered intensity for low wave vectors, but a collapse of the high-q region. These features imply the existence of structures in scales larger than the particle size, namely, clusters. Although the q-range is quite small, a power law can be fitted to the intensity, with exponents close to 3 in both cases, indicating that the clusters are quite compact. It is also interesting to compare these exponents with those obtained in irreversible charge heterocoagulation, which were as low as 1.2.34,35 The equilibrium clusters are denser than those due to the finite strength of the bonds, which allows reestructuration. Notably, the overlap at high-q indicates that the structure factor, S(q), goes to one, corresponding to a gas with just a few bonds between particles and clusters. We also studied dilute systems corresponding to homogeneous vapors, i.e., outside the liquid-gas binodal. According to the simulations, these systems should also be composed of clusters, smaller the further away from the boundary.31 We prepared systems with φc ) 1.6‚10-4 (which is the estimated density of the vapor at φc ) 0.005) and measured the scattered intensity at different salt concentrations, higher than the concentration of the vapor (62.23 mM). At all the salt concentrations studied, the system was homogeneous, i.e., it did not phase separate. The results are presented in Figure 9, scaled to overlap in the high-q region. No evolution of the scattered intensity was noticed after equilibration of the samples (which took 3 h for the lowest salt concentration, and less than 1 h for the rest of samples). Again, the vapor is found to be composed of clusters, as shown by the rise of the scattered intensity for low wave vectors. By increasing the salt concentrations, the clusters disappear until the single particle behavior is recovered at high salt concentrations. Because the concentration of clusters is

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Figure 9. Scattered intensity from dilute systems (φc ) 1.6‚10-4) for different salt concentrations: 62.3 mM (black points), 84.9 mM (red open circles), 119 mM (green diamonds), and 186 mM (black crosses).

Figure 10. Evolution of the height of the interface for different salt concentrations at φc ≈ 0.02. From top to bottom at long times, [NaCl] ) 0.99 mM, 4.95 mM, 17.65 mM, 29.41 mM, 61.28 mM, and 71.90 mM, corresponding to a fluid of clusters, three gels, and two systems showing liquid-gas coexistence, respectively. The thin black lines are fittings according to the model of gel collapse in ref 30.

smaller than that in the saturated vapors above, the structure of the clusters cannot be analyzed for this low concentration. B. Nonergodic Samples: Gels and “Fluids of Clusters”. At low salt concentrations, the interactions are long and intense enough to induce strong bonding between particles, which end up forming irreversible clusters. Figure 10 presents the position of the interface as a function of time for different states with φc ) 0.02. The state with the lowest salt concentration shown in the figure, 1 mM, is in the boundary between the low-salt fluid and gels. It has decayed a little, leaving a layer of clear solvent, but flows when the sample is tilted. At lower salt concentrations, the interface decays less, and only at extremely low salt concentrations it does not decay. By increasing the salt concentration, a clear interface forms (between gel and solvent) at very short times after preparation, which decays from the beginning, reaching a minimum steady value at long times. The evolution of three gels is shown in Figure 10, with two states undergoing liquid-gas separation for comparison. It can be seen in the figure that the collapse of the gel is faster the lower the salt concentration, but the final volume fraction of the gel is lower for higher salt concentrations. Contrary to the systems showing liquid-gas demixing, there is no delay time for gels, but the collapse starts from the initial time. This difference probably arise from the structuring of the liquid, which is not compulsory for gels. The collapse of the gel can be described using a theoretical model where the gravitational stress is balanced by stresses due to fluid flow and the network elasticity, producing an exponential decay of the

Figure 11. Optical microscopy photographs of a fluid at low salt concentrations, [NaCl] ) 0.26 mM (upper panel) and a gel, [NaCl] ) 24.75 mM (lower panel), both of them with φc ≈ 0.05. Photographs were taken using a 40× objective, without cover slip, close to the drop border. The samples were taken with a Pasteur pipet from a sample where the systems were prepared and steady states reached. The photographs were taken after some time. The bar in the lower left corner shows the scale.

interface.30 The agreement, however, is not as impressive as for monocomponent gels.30 It is noteworthy that this model cannot describe the decay of the liquid-vapor interface (compare Figures 6 and 10). Both gels and low-salt fluids are much too concentrated to allow light scattering studies such as those performed on vapors. Instead, we have observed the structure of both systems using optical microscopy. Figure 11 shows photographs of two examples of a gel and a low-salt fluid, where important differences can be appreciated. Whereas the gel is homogeneous above the scale of microns, the low-salt fluid is composed of large clusters, irregular in shape. These clusters were observed to be indeed independent of each other or very weakly bonded; their Brownian motion is negligible, but they are dragged by the solvent. Additionally, they do not restructure or dissolve over hours, i.e., the bonds are permanent. Therefore, the lowsalt fluid must be described as a fluid of irreversible clusters and, thus, nonergodic. These clusters resemble other clustering phenomena found in simpler systems such as proteins32,33 or colloid-polymer mixtures.36-38 In these cases, the clustering is attributed to an interplay between attractive and repulsive parts in the total interaction potential and thus can be an equilibrium feature of the system. In our case, the clusters are much larger than those; they are irreversible, as observed by visual inspection, and the position in the phase diagram lead us to point to a nonergodic transition as their origin. In systems where gelation competes with phase separation, the former is interpreted as a nonergodicity transition that arrests the liquid-gas demixing, and the system ends up in an intricate

13226 J. Phys. Chem. B, Vol. 110, No. 26, 2006 structure (frozen spinodal decomposition), which finally collapses.32,36,39,40 A similar interpretation of our data is possible: a nonergodic transition inhibits liquid-gas separation, and demixing is not observed for lower values of κ. However, at low salt concentrations, repulsions between similarly charged particles stabilizes the fluid with respect to liquid-gas separation, and nonergodic states are obtained in homogeneous “fluids”. Clustering of particles occurs, but macrophase separation does not take place. However, we have yet to understand why electrostatic repulsions stabilize the system with respect to liquid-gas separation, but not with respect to gelation, because both process are driven by the attractions in the system. Computer simulations are underway to clarify this point. IV. Conclusions We have studied the phase diagram of aqueous suspensions of 1:1 binary mixtures of oppositely charged colloids, in the low density region, using the salt concentration and colloid density as control parameters. At very low salt concentrations, where the colloid charges are hardly screened, we have found a fluid of micron-sized irreversible clusters. The clusters are independent from each other, or form weak bonds, and when the sample is tilted, the system flows, i.e., it behaves macroscopically as a fluid. Upon adding salt, the colloids form a solid amorphous phase, which compacts by further increasing the ionic strength. This phase is similar to colloidal gels reported in other systems. At even higher salt concentrations, the electrostatic interactions induce a separation between two fluid phases with different density, identified as liquid-gas separation, until a fluid system is found at high enough ionic strength, when the surface charges are completely screened. The liquid-gas separation takes a delay time, as observed by the evolution of the interface, which does not appear in gels, contrary to the observations in other systems. This delay time increases with the colloid density, but decreases as the charges are more screened. The density of the liquid in coexistence with vapor shows a linear dependence on the total volume fraction, and increases with the ionic strength in the system. The vapor, on the other hand, is composed of equilibrium compact clusters, as observed by static light scattering, in agreement with simulations. The existence of a liquid-gas transition agrees with computer simulations in a 1:1 mixture of positive and negative DerjaguinLandau-Verwey-Overbeek (DLVO) particles (ions are not considered in the simulation). However, the simulations predict a reentrant liquid at low salt concentrations, which is not found experimentally. Instead, a transition from a gel phase to a fluid of clusters is observed as the ionic strength decreases. Because the gel transition is caused by a nonergodicity transition, we speculate that the fluid of clusters is the result of this nonergodicity transition in the fluid phase. Some of the results presented here remain as yet unexplained. The complexity of the system, composed of four species (two colloids and two ions) and the solvent, with strong electrostatic correlations between some species, makes fundamental studies extremely complicated. The present work is the first attempt to rationalize the phase behavior of this interesting system. Acknowledgment. The financial support was provided by the Ministerio de Educacio´n y Ciencia, under project MAT200403581. We thank Prof. W. Poon and Dr. H. Sedgwick for many clarifying discussions, and Dr. Joxe Sarobe for supplying the negative latex.

Romero-Cano et al. References and Notes (1) McQuarrie, D. A. Statistical Mechanics; Harper & Row: New York, 1976. (2) Levin, Y. Rep. Prog. Phys. 2002, 65, 1577. (3) Derjaguin, B. V.; Landau, L. Acta Physicochim. (URSS) 1941, 14, 633. (4) Verwey, E. J. W.; Overbeek, J. T. G. Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948. (5) Anderson, V. J.; Lekerkerker, H. N. W. Nature 2002, 416, 811. (6) Poon, W. C. K.; Pirie, A. D.; Pusey, P. N. Faraday Discuss. 1995, 101, 65. (7) de Kruif, C. G.; Weinbreck, F.; de Vries, R. Curr. Opin. Colloid Interface Sci. 2004, 9, 340. (8) Biesheuvel, P. M.; Lindhoud, S.; de Vries, R.; Cohen Stuart, M. A. Langmuir 2006, 22, 1291. (9) Bartlett, P.; Campbell, A. I. Phys. ReV. lett. 2005, 95, 128302. (10) Leunissen, M. E.; Christova, C. G.; Hynninen, A.-P.; Royall, C. P.; Campbell, A. I.; Imhof, A.; Dijkstra, M.; van Roij, R.; van Blaaderen, A. Nature 2005, 437, 235. (11) Hynninen, A.-P.; Leunissen, M. E.; van Blaaderen, A.; Dijkstra, M. Phys. ReV. Lett. 2006, 96, 018303. (12) Caballero, J. B.; Puertas, A. M. J. Mol. Struct. (THEOCHEM), 2006, cond-mat/0511666. (13) Caballero, J. B.; Puertas, A. M.; Ferna´ndez-Barbero, A.; de las Nieves, F. J. J. Chem. Phys. 2004, 121, 2428. (14) Caballero, J. B.; Puertas, A. M.; Ferna´ndez-Barbero, A.; Javier de las Nieves, F.; Romero-Enrique, J. M.; Rull, L. F. J. Chem. Phys. 2006, 124, 054909. (15) Starrs, L.; Poon, W. C. K.; Hibberd, D. J.; Robins, M. M. J. Phys.: Condens. Matter 2002, 14, 248. (16) Guthrie, W. H. PhD Dissertation, Lehigh University, Bethlehem, PA, 1985. (17) Hidalgo-A Ä lvarez, R.; de las Nieves, F. J.; van der Linde, A. J.; Bijsterbosch, B. H. Colloids Surf. 1986, 21, 259. (18) Puertas, A. M.; de las Nieves, F. J. J. Colloid Interface Sci. 1999, 216, 221. (19) Hunter, R. J. Zeta Potential in Colloid Science; Academic Press: New York, 1989. (20) Hidalgo-A Ä lvarez, R. AdV. Colloid Interface Sci. 1991, 34, 217. (21) The distilled water used in this work has pH ) 6, and it was observed to be constant in several experiments. We did not, thus, buffer solutions to keep pH fixed. (22) Borkovec, M. Behrens, S. H.; Semmler, M. Langmuir 2000, 16, 5209. (23) Ohshima, H.; Healy, T. W.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1983, 79, 1613. (24) Puertas, A. M.; Ferna´ndez-Barbero, A.; de las Nieves, F. J. J. Chem. Phys. 2001, 114, 591. (25) Romero-Cano, M. S.; Puertas, A. M.; de las Nieves, F. J. J. Chem. Phys. 2000, 112, 8654. (26) Napper, D. H. Polymeric Stabilization of Colloidal Disersion; Academic Press: London, 1983. (27) Romero-Cano, M. S.; Martı´n-Rodrı´guez, A.; de las Nieves, F. J. J. Colloid Interface Sci. 2000, 227, 322. (28) Romero-Cano, M. S.; Martı´n-Rodrı´guez A.; de las Nieves, F. J. J. Colloid Interface Sci. 2000 227, 329. (29) Petekidis, G.; Galloway, L. A.; Egelhaaf, S. U.; Cates, M. E.; Poon, W. C. K. Langmuir 2002, 18, 4248. (30) Manley, S.; Skotheim, J. M.; Mahadevan, L.; Weitz, D. A. Phys. ReV. Lett. 2005, 94, 218302. (31) Caballero, J. B.; Puertas, A. M.; Ferna´ndez-Barbero, A.; de las Nieves, F. J. Colloids Surf. A 2005, 270, 285. (32) Sedgwick, H.; Kroy, K.; Salonen, A.; Robertson, M. B.; Egelhaaf, S. U.; Poon, W. C. K. Eur. Phys. J. E 2005, 16, 77. (33) Stradner, A.; Sedgwick, H.; Cardinaux, F.; Poon, W. C. K.; Egelhaaf, S. U.; Schurtenberger, P. Nature 2004, 432, 492. (34) Puertas, A. M.; Ferna´ndez-Barbero, A.; de las Nieves, F. J. 2001, 115, 5662. (35) Kim, A. Y.; Hauch, K. D.; Berg, J. C.; Martin, J. E.; Anderson, R. A. J. Colloid Interface Sci. 2003, 260, 149. (36) Sedgwick, H.; Egelhaaf, S. U.; Poon, W. C. K.; J. Phys.: Condens. Matter 2004, 16, S4913. (37) Lu, P. J.; Conrad, J. C.; Wyss, H. M.; Schofield, A. B.; Weitz, D. A. Phys. ReV. Lett. 2006, 96, 028306. (38) Campbell, A. I.; Anderson, V. J.; van Duijneveldt, J. S.; Bartlett, P. Phys. ReV. Lett. 2005, 94, 208301. (39) Kroy, K.; Poon, W. C. K.; Cates, M. E. Phys. ReV. Lett. 2004, 92, 148302. (40) Manley, S.; Wyss, H. M.; Miyazaki, K.; Conrad, J. C.; Trappe, V.; Kaufman, L. J. Phys. ReV. Lett. 2005, 95, 238302.