Langmuir 1997, 13, 2463-2470
2463
Colloidal Phase Transitions in Aqueous Nonionic Surfactant Solutions Richard D. Koehler† and Eric W. Kaler* Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Received June 5, 1996. In Final Form: January 31, 1997X Highly negatively charged polystyrene particles suspended in aqueous nonionic surfactant solutions undergo a phase transition when the solution is in close proximity to the cloud curve of the binary nonionic surfactant-water mixture. This transition is present only on the surfactant-rich side of the critical point of the binary mixture and is characterized by the presence of brilliant colors in the solution. These colors indicate the formation of polycrystalline aggregates of the polystyrene particles. This particle phase behavior is similar to the aggregation behavior observed for particles dispersed in aqueous solutions of 2,6-lutidine and its analogs. The observed behavior is best interpreted in terms of the appropriate ternary phase behavior and results from immiscibility between the particles and one of the liquid components. Although the details and origins of this unfavorable interaction vary from system to system, the same general pattern of phase behavior is observed in many mixed colloidal systems.
Introduction Useful colloidal dispersions depend on the control of interparticle interactions. Dispersions can either be made stable or be caused to flocculate by the addition of salts, polymers, or surfactants. In particular, the interactions between colloidal particles suspended in structured surfactant solutions can be adjusted by changing the size, shape, and interactions between the surfactant aggregates. There are also subtle effects on particle interactions near phase boundaries in suspensions of particles in binary liquid mixtures, as for example in mixtures of silica or polystyrene colloids in 2,6-lutidine and water.1-9 When the interactions between particles are of the order of the thermal energy kT, statistical thermodynamics can be used to describe the phase behavior of the colloidal particles. Experiment shows that when two phases are present, colloidal particles partition into the phase with less microstructure. Depletion attractions due to the presence of micelles or microemulsion droplets cause aggregation of particles or creaming of emulsions.10-15 More subtly, water soluble polymers can alter the phase behavior of * To whom correspondence should be addressed. † Current address: DuPont Central Research and Development, Experimental Station, P.O. Box 80174, Wilmington, DE 198800174. X Abstract published in Advance ACS Abstracts, April 1, 1997. (1) Beysens, D.; Este`ve, D. Phys. Rev. Lett. 1985, 54, 2123. (2) Gurfein, V.; Perrot, F.; Beysens, D. Prog. Colloid Polym. Sci. 1989, 79, 167. (3) Gurfein, V.; Beysens, D.; Perrot, F. Phys. Rev. A 1989, 40, 2543. (4) Duijneveldt, J. S. v.; Beysens, D. J. Chem. Phys. 1991, 94, 5222. (5) Narayanan, T.; Kumar, A.; Gopal, E. S. R.; Beysens, D.; Guenoun, P.; Zalczer, G. Phys. Rev. E 1993, 48, 1989. (6) Broide, M. L.; Garrabos, Y.; Beysens, D. Phys. Rev. E 1993, 47, 3768. (7) Gallagher, P. D.; Maher, J. V. Physica A 1991, 177, 489. (8) Gallagher, P. D.; Maher, J. V. In Structure and Dynamics of Strongly Interacting Colloids and Supramolecular Aggregates in Solution; Chen, S.-H., Ed.; Kluwer Academic Publishers: Holland, 1992; p 785. (9) Gallagher, P. D.; Kurnaz, M. L.; Maher, J. V. Phys. Rev. A 1992, 46, 7750. (10) Bibette, J.; Roux, D.; Pouligny, B. J. Phys. II 1992, 2, 401. (11) Kline, S. R.; Kaler, E. W. Langmuir 1996, 12, 2402. (12) Ma, C. Colloids Surf. 1987, 28, 1. (13) Piazza, R.; Pietro, G. D. Europhys. Lett. 1994, 28, 445. (14) Fillery-Travis, A. J.; Gunning, P. A.; Hibberd, D. J.; Robbins, M. M. J. Colloid Interface Sci. 1993, 159, 189. (15) Clegg, S. M.; Williams, P. A.; Warren, P.; Robb, I. D. Langmuir 1994, 10, 3390.
S0743-7463(96)00552-5 CCC: $14.00
microemulsions if they are larger than the water pools available to them; this leads to their exclusion from the microstructured microemulsion phase.16,17 While the detailed nature of the interactions between the particles and microstructured fluids may be unknown and will be different for different solutions, the microstructure controls the interactions between the particles and will result in a general recognizable pattern of phase behavior. There is an analogy between the behavior of colloidal particles in binary solutions that have upper miscibility gaps,1-9,18-21 as for example 2,6-lutidine and water, and the way particles behave in aqueous solutions of a variety of nonionic surfactants. Silica particles suspended in the 2,6-lutidine-water binary system aggregate near the phase boundary of the lutidine-water phase diagram on only one side of the lower consolute critical point.1-9 The side of the miscibility gap where aggregation occurs depends on the surface properties of the colloidal silica.2-4,7,8,22 These results have been interpreted in terms of preferential adsorption on the colloids of the mixture component on the opposite side of the phase diagram from the aggregation region. For example, preferential adsorption (wetting) of water would lead to aggregation on the lutidine-rich side of the miscibility gap. Subsequently this adsorbed layer grows from a thin layer to a thick wetting film at the wetting temperature, and these wetting films are supposed to cause the particles to aggregate. There is conflicting experimental support for the presence of this film, and there are limits in the light-scattering methods used.23 Polystyrene colloids also aggregate similarly7-9 and partition in the liquid-liquid two-phase region in different ways depending on their surface properties.18 This partitioning suggests that the surface of the particles prefers the majority component of the particle-rich phase. (16) Kabalnov, A.; Olsson, U.; Wennerstro¨m, H. Langmuir 1994, 10, 2159. (17) Kabalnov, A.; Olsson, U.; Thuresson, K.; Wennerstro¨m, H. Langmuir 1994, 10, 4509. (18) Gallagher, P. D.; Maher, J. V. Phys. Rev. A 1992, 46, 2012. (19) Kline, S. R.; Kaler, E. W. Langmuir 1994, 10, 412. (20) Jayalakshmi, Y.; Kaler, E. W. Phys. Rev. Lett. 1997, 78, 1379. (21) Nikas, Y. J.; Liu, C.-L.; Srivastava, T.; Abbott, N. L.; Blankschtein, D. Macromolecules 1992, 25, 4797. (22) Gurfein, V.; Perrot, F.; Beysens, D. J. Colloid Interface Sci. 1992, 149, 373. (23) Beysens, D.; Houessou, C.; Perrot, F. In On Growth and Form; Stanley, H. E., Ostrowsky, N., Eds.; Martinus Nijhoff Publishers: Boston, 1986; p 211.
© 1997 American Chemical Society
2464 Langmuir, Vol. 13, No. 9, 1997
Koehler and Kaler
Table 1. Particle Size and Charge Reported by Manufacturer Å2
charge
particle diameter (Å)
charge
particle
2640 2240 1900 1560 1200 980
1518 1083 2167 1482 1034 1378
14400 14600 5200 5200 4400 2200
To explore this phenomenon in a broader range of solutions with upper miscibility gaps, we have investigated the behavior of silica and polystyrene colloids of various sizes in aqueous solutions of n-alkyl polyglycol ethers (H(CH2)i(OCH2CH2)jOH), denoted as CiEj.24 Members of this family of surfactants also form aggregates in solution, although the coherence of the microstructure depends on the strength of the amphiphile. This paper reports the study of surfactants at both ends of this homologous series, namely C4E1, a weak amphiphile,25 and C12E5, a micelleforming surfactant.26 Using CiEj surfactants also allows systematic changes in solution properties while holding all else, such as the surface properties of the colloids, constant. Experimental Section Polystyrene particles (Interfacial Dynamics Corporation, Portland, OR) in deionized water were used as received. The particles have sulfate groups on the surface and are negatively charged. Particle sizes measured from dynamic light scattering agree with the size reported by the manufacturer. Table 1 gives the reported particle diameter and surface charge. C12E5 (Nikko Surfactants, 99+% purity), 2-butoxyethanol or C4E1 (Aldrich, 99+% pure, 160°). The particle size determines the color that appears at a particular angle, and the order of colors is the same for all particle sizes.
Figure 3. Samples from Figure 2 after settling for 23 days, observed at 90° and in backscatter, with particle sizes (a) 0.264 µm, (b) 0.224 µm, and (c) 0.156 µm. The colloidal crystals settle to a polycrystalline film. (d) At 32.0 °C, outside of the colored region, the sample with 6.0 × 10-3 wt %, 0.224 µm particles in 4.0 wt % C12E5 in water does not show brilliant colors with increasing angle. (e) Without particles only weak scattering from micelles is visible for 4.0 wt % C12E5 at 32.50 °C.
The colors from the ordered colloidal structures are reminiscent of those from colloidal crystals. The particle size determines the color that appears at a particular angle, but the order of colors is the same for all particle sizes. These colloidal crystals eventually settle over a period from days to weeks depending on the concentration of particles (see Figure 3a-c). The rate of appearance of the colors, and hence the rate of formation of the crystalline phase, increases with increasing particle concentration. More concentrated dispersions have brighter colors, and the crystalline phase settles faster. Figure 3d is a picture of a sample containing 6.0 × 10-3 wt %, 0.224 µm diameter
polystyrene particles in 4.0 wt % C12E5 in water at 32.00 °C. This sample is outside of the region where ordered structures form and hence shows no colors. Samples without particles show only weak and colorless scattering from micelles, and no colors are observed (Figure 3e). The diffraction of colors from these samples suggests static light scattering would yield useful information about the colloidal order within the sample. Figure 4 shows light-scattering spectra for 1.0 × 10-2 wt %, 0.098 µm polystyrene particles in 4.0 wt % C12E5 aqueous solution at 32.55 °C. The spectra are recorded as a function of time at 32.55 °C. This sample is well into the colored region, and the colors take about a day to become visible.
2466 Langmuir, Vol. 13, No. 9, 1997
Koehler and Kaler
Figure 4. Light-scattering spectra for 1.0 × 10-2 wt %, 0.098 µm diameter polystyrene particles in 4.0 wt % C12E5 at 32.55 °C as a function of time. Intensity is plotted in arbitrary units on a log scale vs scattering vector q on a linear scale. The data are shifted by factors of two for clarity. Note that the peak height grows with time until it reaches an equilibrium value, while the peak position does not change.
The lowest curve in Figure 4 was collected after 1.5 h at 32.55 °C, which is before colors are visible. As colors appear, the intensity and sharpness of the scattering peak both evolve with time, while the position of the peak remains the same. The spectra stop evolving after 34 h. Spectra for the samples discussed below were measured after the scattering peak had reached its equilibrium value but before the crystalline phase settled. The position of the peak depends only slightly on particle concentration. Figure 5 displays scattering spectra scaled for clarity and in arbitrary units for samples containing 0.156, 0.224, and 0.264 µm particles at two different concentrations in 4.0 wt % C12E5 at 32.55 °C. Increasing the particle concentration by an order of magnitude shifts the peak position weakly to higher q. Increasing particle concentration also increases the intensity and rate of formation of the colors, which implies more colloidal crystals are formed at higher particle concentration. Particle size has an important effect on the position of the peak in the scattering spectra. Figure 6 shows spectra for samples containing particles of various sizes in 4.0 wt % C12E5 at 32.55 °C. The position of the peak shifts to higher q with decreasing particle size. Variation in particle concentration (see Table 2) again has only a secondary effect on the peak position. The positions of the scattering peaks in Figure 6 are inversely related to the spacing of the particles in the colloidal crystal. Table 2 lists estimated particle centerto-center distances (2π/qmax) calculated using Bragg’s law and the position of the scattering peak (qmax). 2π/qmax depends linearly on the particle diameter (Figure 7). The range of the peak positions reported for a given particle size (Figure 7) shows the effect of variations of particle or surfactant concentration. These changes in 2π/qmax are small compared to the change due to particle size (see Figure 5). The q value of the scattering peak also does not depend strongly on the surfactant concentration. Figure 8 is the scattering from 6.0 × 10-3 wt %, 0.264 µm polystyrene particles at three different concentrations of C12E5 at 32.50 °C. The peak position shifts to higher q with increasing surfactant concentration, and the top curve in Figure 8 may display a second-order scattering peak. As expected, scattering peaks are also observed in the colored region for C4E1. Figure 9 shows the progress of the peak for a 0.264 µm particle concentration of 6.0 ×
Figure 5. Light-scattering spectra for (a) 0.156 µm, (b) 0.224 µm, and (c) 0.264 µm diameter polystyrene particles in 4.0 wt % C12E5 in water at 32.55 °C for low particle concentration (bottom curve in each frame) and high particle concentration (top curve in each frame). Intensity is plotted in arbitrary units on a log scale vs scattering vector q on a linear scale. The data are shifted for clarity. The peak position moves weakly toward higher scattering vector with increasing particle concentration.
Figure 6. Light-scattering spectra for different sized polystyrene particles in 4.0 wt % C12E5 in water at 32.55 °C. Intensity is plotted in arbitrary units on a log scale vs scattering vector q on a linear scale. The data are shifted for clarity. The position of the scattering peak shifts to higher scattering vector with decreasing particle size. Particle concentrations are given in Table 2.
10-3 wt % in 37 wt % C4E1 at 48.9 °C and in 40 wt % C4E1 at 49.3 °C. The peaks shift to higher q values with increasing surfactant concentration, just as is observed with C12E5.
Aqueous Nonionic Surfactant Solutions
Langmuir, Vol. 13, No. 9, 1997 2467
Table 2. Distance between Particles in the Polycrystalline Phase Calculated Using Bragg’s Law, as a Function of Particle Diameter, Particle Concentration, and Surfactant Concentration particle diameter (Å)
wt % particles × 103
wt % C12E5
d ) 2π/qmax (Å)
980 1200 1560
10.0 6.1 1.2 6.2 1.2 0.6 6.0
4.0 4.0 4.0 4.0 4.0 4.0 4.0
2000a,c 2400c 2600b,c 2500b 3000c 3400b,c 3300b
6.0 0.6 6.0 6.0 6.0
3.6 4.0 4.0 4.0 4.4
3900d 3700b,c 3600b 3600d 3400d
1900 2240 2640
aSpectra plotted in Figure 4. bSpectra plotted in Figure 5. cSpectra plotted in Figure 6. dSpectra plotted in Figure 8.
Figure 7. Particle center-to-center distance as calculated from Bragg’s law. The best fit line through the data is d (Å) ) 1110 + 0.964 × particle diameter (Å). The range of the peak position for a given particle diameter shows the effect of surfactant concentration. These changes are small compared to the effect due to particle size.
Figure 8. Light-scattering spectra for 6.0 × 10-3 wt %, 0.264 µm polystyrene in 3.6 wt % (top curve), 4.0 wt % (middle curve), and 4.4 wt % (bottom curve) C12E5 in water at 32.50 °C. Intensity is plotted in arbitrary units on a log scale vs scattering vector q on a linear scale. The data are shifted for clarity. The peak position shifts to higher scattering vector with increasing surfactant concentration. The top curve (3.6 wt %) also has a shoulder indicating a second-order scattering peak.
Discussion Polystyrene particles form ordered structures near the liquid-liquid phase boundary of aqueous solutions of C12E5 and C4E1. This ordering occurs on the surfactant-rich
Figure 9. Light-scattering spectra for 6.0 × 10-3 wt %, 0.264 µm polystyrene in 37 wt % C4E1-water at 48.9 °C (top curve) and 4.0 wt % C4E1-water at 49.3 °C (bottom curve). Intensity is plotted in arbitrary units on a log scale vs scattering vector q on a linear scale. The data are shifted for clarity. The peak position shifts to higher scattering vector with increasing surfactant concentration.
side of the liquid-liquid critical point, and the ordered phases give rise to brilliant colors. Light-scattering spectra of these solutions reveal well defined peaks, the locations of which depend strongly on the particle size but only weakly on the particle or surfactant concentration. The appearance of the colors in these solutions (Figure 2) is a consequence of scattering from the colloidal crystalline phase that forms near the upper miscibility gap between the nonionic surfactant and water. The progression of colors with observation angle from 45° to 135° is consistent with diffraction of a crystal and is not due to Tyndall scattering.27 These colloidal crystalline aggregates, which eventually settle, are droplets of a second particle-rich phase that remains suspended during the scattering experiments. Because of the variation of orientation from droplet to droplet, the scattering experiment records the powder diffraction pattern from these crystallites. Either face-centered cubic (FCC) or body-centered cubic (BCC) structures could exist in these solutions. The ratio between the first and second peak for an FCC crystal is 2/x3, while for a BCC crystal it is larger, 2/x2.28 In Figure 10 the top curves of Figures 5c and 8 are replotted, with the arrows on the q-axis indicating the position of the first peak and the appropriate position of the second peak for both an FCC and a BCC crystal. Clearly the shoulder in the curves at q ≈ 0.0027 Å-1, which is suggestive of a second peak in the scattering spectra, is inconsistent with either a BCC or FCC crystal, although the presence of the second peak does indicate long range, possibly crystalline, structure in the solution. Unfortunately, the minimum in the particle form factor coincides with the second maximum in the crystal structure factor (the empty circles of Figure 10b). The observed scattering is the product of the form and structure factors, so the form factor minima smears and diminishes any second peak in the spectra. The flatness in the spectra observed around q ≈ 0.0027 Å-1 reflects the product of these two functions, but it is not possible to separate the two effects quantitatively. Within the crystallites, the particle spacing is relatively unaffected by any variable except particle size. The smaller interparticle spacing observed with smaller particles shows that the crystalline structure scales with (27) Hunter, R. J. Foundations of Colloid Science; Clarendon Press: Oxford, 1987. (28) Shackelford, J. F. Introduction to Materials Science for Engineers; Macmillan Publishing Company: New York, 1985.
2468 Langmuir, Vol. 13, No. 9, 1997
Koehler and Kaler
Figure 11. Schematic phase prism representation of the ternary phase behavior with temperature for surfactantwater-particle solutions. The boundary of the colored region (Y) is projected onto the water-surfactant side of the phase prism, which shows the upper miscibility gap (X) between the surfactant and water. The particle-surfactant side of the phase prism shows the postulated miscibility gap between particles and surfactant. The particles undergo a transition from liquidlike colloidal structures to crystal-like colloidal structures with increasing particle concentration on the water-particle side. For further discussion see text. Figure 10. Filled circles are the light-scattering spectra for 6.0 × 10-3 wt %, 0.264 µm polystyrene in (a) 3.6 wt % (top curve of Figure 5c) and (b) 4.0 wt % (top curve of Figure 8) C12E5 in water at 32.50 °C. Intensity is plotted in arbitrary units on a log scale vs scattering vector q on a linear scale. Arrows on the q-axis indicate the position of the first peak and the appropriate position of the second peak for an FCC or a BCC crystal. The empty circles of part b show the form factor for the polystyrene particles measured for 6.0 × 10-4 wt %, 0.264 µm polystyrene particles in 4.0 wt % C12E5 at 25.00 °C. Note the minimum of the form factor is in the vicinity of the suspected second peak. For further discussion see text.
particle size and thus that the value of the surface charge of the particles (Table 1) is inconsequential to the formation of the crystals, although electrostatic forces keep the particles apart. The center-to-center distance varies from 4 to 2.5 times the particle radius (see Table 2), so the colloidal crystallites are relatively loose and fluid. Similar results have been found by Gurfein et al.3 These experiments show clearly the formation of particle-rich and particle-lean phases near the critical point of surfactant-water mixtures. This observation is also consistent with the behavior of particles in simple near-critical binary liquids. As an example, silica in 2,6lutidine-water mixtures aggregates in clusters whose mass grows in proportion to the cube of the radius and with time to the 1/3 power. These are the signatures of growth of a dense aggregate with fluid bonds.6,29 The observed growth law is consistent with phase separation following nucleation and growth.30,31 The compactness and nonfractal nature of the aggregate are also in accord with the process of phase separation and are not consistent with the result of a flocculation process. In spite of the wide size disparity between the particles and the other components of the mixture, an important insight is that particles dispersed in a binary fluid mixture (29) Broide, M. L.; Beysens, D. In Materials Research Society Symposium; Materials Research Society: Boston, 1993; p 75. (30) Lifshitz, I. M.; Slyozov, V. V. J. Phys. Chem. Solids 1961, 19, 35. (31) Schmelzer, J.; Ulbricht, H. J. Colloid Interface Sci. 1987, 117, 325.
represent a true third component in the three-component mixture.32 These experiments suggest there is a contribution to the free energy of the particle that depends on whether water or surfactant is present at its surface. This contribution leads to instability and phase separation. Such a contribution could also lead to the asymmetry observed in the behavior of these solutions.32 What follows is a reexamination of the experimental results in light of this phase separation hypothesis. Returning to solutions with C12E5, recall Figure 8 shows that the peak position moves to lower scattering vector with decreasing surfactant concentration, so the particles are farther apart in samples with compositions deeper in the colored region. This suggests that the volume of the minority (crystalline) phase increases with successively deeper quenches into the ordered region, even though the total particle concentration remains constant. This is what would be expected for a true phase separation. Thus, in this interpretation, the boundary of the colored region represents the true two-phase boundary for the threecomponent system. Figure 11 is the appropriate phase prism representation of the ternary phase behavior with temperature for surfactant-water-particle solutions. The general shape of the tie lines in the phase diagram of Figure 11 is expected for reasons of thermodynamic consistency and is supported by both these experimental results and those with silica (Ludox)-C4E1-water solutions.19,20 The phase behavior of the ternary system is a consequence of the interplay of the phase behavior of the constituent binary pairs. On the water-surfactant binary side is the familiar upper miscibility gap (shown by line X, see below) characterized by the critical concentration and temperature. The phase maps of Figure 1 are projections onto this side of the phase prism and show the phase behavior of the ternary solution along a line of constant particle concentration. Line Y in Figure 11 is the boundary of the colored region projected onto the surfactant-water face of the prism, as in Figure 1. (32) Sluckin, T. J. Phys. Rev. A 1990, 41, 960.
Aqueous Nonionic Surfactant Solutions
Figure 12. Schematic ternary phase diagram for the surfactant-water-particle solution at a temperature above the critical point of the surfactant-water solution. The miscibility gap on the surfactant-water side of the phase diagram connects to the postulated miscibility gap on the surfactant-particle side. Along the water-particle axis there is a transition from a liquid-like particle phase to a crystal particle phase with increasing particle concentration (point X). Movement along a line of constant particle concentration near the surfactantwater side of the ternary diagram shows two-phase samples (points c and b) whose minority particle-rich phase is a colloidal crystal, as a consequence of the end of the tie line lying above the dotted line (point X). The minority particle-rich phase becomes a colloidal liquid with deeper quenches (part a). For further discussion see text.
At constant temperature, the shift in the two-phase boundary on the ternary diagrams with added particles is due to unfavorable interactions between the particles and the surfactant. Although the particles have an adsorbed layer of surfactant, this dressed particle is very hydrophilic and prefers not to be in contact with high concentrations of surfactant. Thus there is a miscibility gap on the particle-surfactant binary side of the phase prism. In experimental systems with hydrophobic particles (fused quartz or weakly charged polystyrene in lutidine-water mixtures3,9) the phase separation occurs on the water-rich side of the liquid binary critical point. In such a case, the particles are hydrophobic, so the appropriate miscibility gap is on the water-particle side of the phase prism. With the hydrophilic dressed particles of interest here there is no miscibility gap on the waterparticle side of the phase prism. However, increasing particle concentration in the water-particle mixture produces a transition from a liquid-like colloidal particle phase to a solid-like or crystalline colloidal phase.33-35 Figure 12 shows a schematic ternary phase diagram at a temperature above the critical temperature. Note how the miscibility gap on the surfactant-water side connects to the miscibility gap on the surfactant-particle side, with a corresponding change in the angle of the tie lines. The experiments reported here have been performed along a line of constant particle concentration. At point c the sample is in the two-phase region and thus separates into a small particle-rich phase and a large surfactant-rich phase as a consequence of the location of point c and the slope of the tie lines. For a sample at point c, the particle concentration in the particle-rich phase is high enough that the phase is crystalline. Thus the sample will be colored, as is observed experimentally. Decreasing the surfactant concentration leads to point b, which is on a different tie line than point c. Still, the particle-rich phase is concentrated enough to form a colloidal crystal, and the sample is colored. Further dilution with water leads to point a, where the particle(33) Monovoukas, Y.; Gast, A. P. J. Colloid Interface Sci. 1989, 128, 533. (34) Wood, W. W.; Jacobson, J. D. J. Chem. Phys. 1957, 27, 1207. (35) Alder, B. J.; Wainwright, T. E. J. Chem. Phys. 1957, 27, 1208.
Langmuir, Vol. 13, No. 9, 1997 2469
rich phase is not concentrated enough to form a colloidal crystal, so the sample phase separates without the appearance of colors. The particles remain almost exclusively in the water-rich phase, of course, but now are too dilute to crystallize. A boundary between samples which separate with the appearance of colors (points c and b) and those which separate without the appearance of colors (point a) is clearly delineated (line X in Figure 11). The projection of this boundary onto the surfactantwater side of the phase prism falls onto the particle-free surfactant-water miscibility gap. This is because, at this temperature and surfactant concentration, the solution will phase separate even in the absence of particles. Thus in this case sufficient minority phase forms that the particles do not crystallize. Point X in Figure 12 indicates schematically the crystallization concentration of particles alone in water. Hard colloidal spheres solidify at a volume fraction of 0.55,34,35 and highly charged spheres at low ionic strength form colloidal crystals at volume fractions as low as φ ) 0.005.33 The data of Figure 7 and Table 2 show that the crystals here have particle volume fractions from 0.06 to 0.23, assuming a simple cubic structure. This range of volume fraction is consistent with the behavior of charged spheres in a mixed solvent (CiEj and water), but lack of knowledge of the properties of the solvent and the Debye length prevents more detailed analysis of this point. This mechanism of phase separation is consistent with all of the experimental facts. In contrast to this approach, previous hypotheses for the cause of aggregation of particles in critical binary fluid mixtures have focused on contributions to the attractive interactions between particles but fail to explain the universal behavior observed. The results expected from each of these hypotheses of depletion flocculation, capillary condensation, wetting, and critical fluctuations can now be compared with this experimental data as follows. Depletion flocculation results in increased attraction between particles in the presence of surfactant micelles.11,12 However, while aggregates are certainly present in aqueous solutions of C12E5, only tenuous short-lived micelles are present in C4E1-water solutions.25 The aggregation behavior observed is qualitatively similar in both of these systems and does not scale with micelle size. Moreover, microstructures do not form in lutidine-water solutions, yet particles dispersed in these solutions aggregate in very similar ways.1-9 Thus depletion flocculation is not governing this separation. The distance between the particles, as measured in these experiments, clearly precludes the possibility of capillary condensation as a mechanism for particle aggregation.36 The particle surfaces are on the order of a particle radius apart (see Table 2), so formation of a three-dimensional liquid network stabilizing the colloidal crystal is unlikely. The proximity of the aggregation behavior to the critical point of the binary mixture suggests critical fluctuations may play a role, and the increase in correlation length near a critical point can lead to an attractive force between two flat surfaces.37 Long range Casimir forces are predicted to exist between particles in a near critical fluid when the correlation length for fluctuations is larger than the distance between particles.38 Nonetheless, the lack of symmetry about the critical point of the aggregation behavior in other systems, and the asymmetric colored region in these experiments, contradicts an important role (36) Israelachvilli, J. Intermolecular and Surface Forces; 2nd ed.; Academic Press: London, 1992. (37) Fisher, M. E.; Gennes, P.-G. d. C. R. Acad. Sci. 1978, 287, 207. (38) Burkhardt, T. W.; Eisenriegler, E. Phys. Rev. Lett. 1995, 74, 3189.
2470 Langmuir, Vol. 13, No. 9, 1997
for critical phenomena in its explanation. Such critical behavior is expected to depend on the correlation length at a fixed particle radius. However, the correlation length in C4E1 is much smaller than thatin C12E5, yet the same behavior is observed in the ordered regime with 0.264 µm particles. Traditionally, particles in binary liquid solutions are studied to observe wetting transitions on curved surfaces.1,39 At the wetting temperature a transition from a thin adsorbed layer to a thick adsorbed layer occurs. The interfacial area, and hence the interfacial energy, increases as the thickness of the layer increases. Particle aggregation lowers the total surface area or energy of the cluster, and this mechanism could lead to the formation of a condensed phase of spheres.3,23 Experimentally, there is conflicting evidence, depending on the method used, for and against this putative increase in layer thickness.1,3,9,19,22 In summary, the phase separation mechanism provides a useful framework for understanding the behavior of particles in near-critical binary liquid mixtures. However the origin of the miscibility gap between the particles and one of the liquids has not been established. Indeed one or more of the above hypotheses, which focus on particleparticle interactions, may provide an explanation of the unfavorable interactions between particles and surfactant. For instance, excluded volume interactions between micelles and particles, or the exclusion of particles or polymers from microstructured phases, can contribute to demixing between particles and surfactant.10,12,13,19 In addition, surface energy itself depends on microstructure in solution. Wetting of the microstructured phase in threephase microemulsion systems depends on the presence of (39) Upton, P. J.; Indekeu, J. O.; Yeomans, J. M. Phys. Rev. B 1989, 40, 666.
Koehler and Kaler
structure in the microemulsion.40-44 This result implies that the structure in solution determines both the free energy of the solution and its surface energy.42,43 These and other contributions could be important in setting particle-solution interactions. Conclusions The phase transition of particles dispersed in nonionic surfactant solutions has been observed near the binary upper miscibility gap. The colors that accompany this transition indicate the formation of polycrystalline droplets of a particle-rich phase. This transition occurs only on the surfactant-rich side of the critical point and is appropriately thought of as a phase separation rather than simple particle aggregation. Static light scattering shows an interaction peak, whose location depends strongly on the particle diameter. The phase separation of particles dispersed in critical binary liquid mixtures follows a universal pattern. In this view the particles are a true third component added to the binary liquid mixture. The observed behavior can be interpreted in terms of the ternary phase behavior and likely arises from immiscibility between the particles and one of the liquid components. Acknowledgment. The authors are indebted to S. R. Kline for technical assistance and for invaluable discussions. We acknowledge the support of E. I. duPont de Nemours and Co. and are grateful to M. Schick and D. Beysens for useful discussions. LA960552O (40) Schick, M. J. Phys. IV 1993, 3, 47. (41) Schmid, F.; Schick, M. Z. Phys. B 1995, 97, 189. (42) Schmid, F.; Schick, M. Phys. Rev. E 1994, 49, 494. (43) Schmid, F.; Schick, M. Phys. Rev. E 1993, 48, 1882. (44) Gompper, G.; Schick, M. Phys. Rev. Lett. 1990, 65, 1116.
