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Homogeneous Nucleation in a Monodisperse Oil-in-Water Emulsion Jane Morris,* Ulf Olsson, and Håkan Wennerstro¨m Department of Physical Chemistry 1, Centre for Chemistry and Chemical Engineering, Lund University, P. O. Box 124, S-221 00 Lund, Sweden Received September 10, 1996. In Final Form: November 29, 1996X A monodisperse emulsion of oil droplets in water (hydrocarbon radius approximately 8 nm) stabilized by the nonionic surfactant pentaoxyethylene glycol dodecyl ether (C12E5) is prepared from a stable microemulsion containing the oil droplets by lowering the temperature across a phase boundary. At equilibrium a droplet emulsion phase exists in conjunction with excess oil. The first stage in the equilibration process is followed by measuring the turbidity. It is observed that for small temperature quenches the system is metastable, showing no measurable changes over at least 1 h. There is a sharp boundary between metastable and unstable regions, and this, like the phase boundary, is virtually independent of droplet concentration in the range 5-20%. The observation is interpreted qualitatively as an Ostwald ripening-like process, where a few oil droplets grow, allowing the majority to shrink in size. The presence of a nucleation threshold can be understood in terms of the curvature free energy of the surfactant film.
Introduction A wealth of studies have been undertaken on the equilibrium properties of ternary oil-water-surfactant systems (recent review1 ). The focus of the interest has been aggregate structures and phase behavior. There is an intricate interplay between these two kinds of properties, resulting in a very rich physicochemical behavior. With nonionic surfactants of the alkyl polyoxyethylene type, changes in phase structure are conveniently induced by a variation in temperature.2 Here, the variation with temperature can be ascribed to a temperature dependence of the spontaneous curvature, H0, of the surfactant film.1,3-5 For higher temperatures water is a less good solvent for the ethylene oxide head groups, resulting in a surfactant film that preferentially curves toward water while at lower temperatures the preference is the opposite. We can write
H0(T) ) c(T0 - T) (1) where To is called the balance temperature where the film prefers zero mean curvature. The coefficient c depends slightly on the nature of the surfactant, and for C12E5, c approximately equals 10-3 (K nm)-1.4,5 On the basis of the notion of a temperature dependent spontaneous curvature, it is possible to describe changes in the equilibrium phase behavior in great detail. Much less effort has gone to the observation of the kinetics of the various transitions. We and others have made qualitative observations on the ease of attaining equilibrium,6-8 but in this letter we report the first quantitative study of phase change dynamics for a ternary decanewater-nonionic surfactant system. The System Decane-Water-C12E5 A prerequisite for an interpretation of the nonequilibrium dynamic behavior is a proper description and X Abstract published in Advance ACS Abstracts, January 15, 1997.
(1) Olsson, U.; Wennerstro¨m, H. Adv. Colloid Interface Sci. 1994, 49, 113-146. (2) Kunieda, H.; Shinoda, K. J. Dispersion Sci. Technol. 1982, 3, 233-244. (3) Anderson, D.; Wennerstro¨m, H.; Olsson, U. J. Phys. Chem. 1989, 93, 4243-4253. (4) Strey, R. Colloid Polym. Sci. 1994, 272, 1005-1019. (5) Rajagopolan, V.; Bagger-Jo¨rgensen, H.; Fukuda, K.; Olsson, U.; Jo¨nsson, B. Langmuir 1996, 12, 2939-2946. (6) Olsson, U.; Schurtenberger, P. Langmuir 1993, 9, 3389-3394. (7) Clark, S.; Fletcher, P. D. I.; Ye, X. Langmuir 1990, 6, 1301-1309. (8) Strey, R. Personal communication.
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understanding of the equilibrium conditions. We have previously made careful studies of the microemulsion phase in the system decane-water-C12E5. Figure 1 shows a partial phase diagram of this system with a fixed C12E5 to decane volume ratio of φs/φo ) 0.815. Between 32 and 25 °C there is an isotopic microemulsion region with the phase boundaries remarkably insensitive to concentration, with 25 °C being the lowest temperature at which all the oil is solubilized, which is termed the solubilization phase boundary (SPB). In the present investigation we focus attention on the region around the SPB which separates the microemulsion from a two-phase area. Rheological9 NMR10 and scattering experiments6,11 unequivocally show that just above the phase boundary spherical oil-in-water microemulsion droplets exist that interact as hard spheres. Below the phase boundary there is a droplet microemulsion, containing smaller droplets, in equilibrium with excess oil. Using the concept of a spontaneous curvature there is a direct interpretation of the observation. On the phase boundary the droplet radius R is12
kBT κj R )1+ + f(φ) (2) R0 2κ κ R0 ) H0-1 is the spontaneous radius, κ and κj are the bending and saddle splay modules, respectively, and the last term [(kBT/κ)f(φ)] is a small contribution from the entropy of mixing the droplets in the medium. The surfactant-to-oil ratio is fixed, and since the area per surfactant molecule, as, in the film is virtually constant, the geometrical constraint of packing a given volume in a given area provides a unique value to the radius of the apolar core Rc: Rc ) 3(φ0/φs + 0.5)vs/as (3) Here vs is the volume of a surfactant molecule and the term 0.5 comes from the observation that approximately half of vs is hydrocarbon volume. At the phase boundary we have the situation that the optimal radius precisely matches the spherical radius determined by the packing constraints. When the temperature is further lowered, R0 decreases, and to optimize the curvature energy, the system responds by expelling oil to give droplets of the (9) Leaver, M. S.; Olsson, U. Langmuir 1994, 10, 3449-3454. (10) Leaver, M. S.; Olsson, U.; Wennerstro¨m, H.; Strey, R. J. Phys. II 1994, 4, 515-531. (11) Fletcher, P. D. I.; Holzwarth, J. F. J. Phys. Chem. 1991, 95, 2550-2555. (12) Safran, S. A. Statistical Thermodynamics of Surfaces, Interfaces, and Membranes; Addison-Wesley: Reading, MA, 1994.
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Figure 2. Variation of turbidity with temperature measured as a function of time for the C12E5/decane system (51.9/48.1 ratio) at 10 wt % droplets showing a stepwise decrease in temperature from 28.2 to 21.9 °C. The arrows indicate the time at which the temperature was decreased to that stated.
Figure 1. Section through the phase diagram determined optically for a fixed surfactant/oil (S/O) % weight ratio of 51.9/ 48.1 at varying weight % of droplets (wt % (S + O)) for the C12E5 with decane system. The labeled phases are oil-in-water microemulsion (L1), oil (O), lamella (LR), a bilayer continuous liquid phase (L3), and water (W).
new optimal radius Rc ) R0 and excess oil. What is the kinetic path to the equilibrium state? Another formulation of the same problem takes the language from emulsion science. Shinoda and Friberg13 have established a method of preparing emulsions using nonionic surfactants without major mechanical agitation. The procedure is to bring the system to a temperature where droplets either form spontaneously or through just a slight shaking and then make a temperature jump (or quench) to reach ‘stable’ emulsion conditions. In our own system, above the phase boundary virtually monodisperse droplets exist, and after a temperature quench the system is an oil-in-water emulsion with monodisperse droplets. The question is then, how stable is the emulsion and what is the destabilization pathway? Results Samples at three concentrations of 5, 10, and 20% (w/ w) of C12E5 and decane at the weight ratio 1.079 in water have been studied. Turbidity was measured at λ ) 406 nm using a Perkin Elmer Lambda 14 UV/visible spectrophotometer, containing a thermostated sample cell holder. The sample was kept in situ in the spectrophotometer, and the turbidity was traced continually with time as the temperature was varied. The temperature was controlled by a Haake circulating water bath which kept the temperature constant to within (0.1 °C. The temperature in the cell was calibrated using a thermocouple. Since we were operating at near room temperature, only a slight temperature gradient was observed within the cell due to the necessary gap in the thermostating block for the measuring window and was found to be better than (0.2 °C. The sample was first equilibrated above the SPB at a temperature of 28.2 ( 0.1 °C. Turbidity was then followed continuously with time as temperature was varied in two different ways. Figure 2 shows, for the 10% sample, turbidity versus time for the case when the temperature was lowered stepwise with 0.5-1.0 °C steps. There are three regions in this figure. Above the SPB of 25.0 °C (TSPB) the single-phase region exists. At each step there is a rapid decrease in turbidity to an equilibrium value. All the structural relaxation times appear to be fast (13) Shinoda, K.; Friberg, S. E. Emulsions and Solubilization; Wiley-Interscience: New York, 1986.
relative to the time required to equilibrate the temperature in the cuvette. The second region is between 24.3 and 22.4 °C, which is within the two-phase area. After a small initial drop, the turbidity remains constant over at least 20 min. The phase change is slow indeed, and the system appears to be metastable. In the third region, at 21.9 °C the turbidity increases slowly but steadily directly following the temperature drop. The system is no longer metastable. The transition from metastable to an unstable system is illustrated in more detail in Figure 3. In these experiments a direct quench was made from the initial temperature of 28.2 °C to a final temperature below the phase boundary. In Figure 3a this was chosen as 22.4 °C in the metastable region. The graph and inset show that after the initial drop the turbidity stays constant for 20 min and the same turbidity was in fact also observed after 1 h. In Figure 3b the temperature is dropped a further 0.5 °C, and here an increase in turbidity is observed directly after the temperature drop. By quenching deeper into the unstable region (T ) 20.3 °C) the instability is obvious and there is a rapid, nearly linear, change in turbidity. By extrapolating to zero slope of the turbidity versus time curve, we find that the transition from metastability to instability occurs at Tm ) 22.1 ( 0.2 °C. Repeating the experiments for samples at 5% and 20% concentrations yields the same behavior of a metastable and an unstable region. Even the transition temperature Tm is the same within experimental error, showing that this boundary runs parallel to the phase boundary, TSPB. Discussion In a binary system a two-phase area necessarily contains a metastable region close to the phase boundary and an unstable region in the center, where the system changes state through spontaneous concentration fluctuations in a spinodal decomposition. In our three-component system the additional thermodynamic degree of freedom leads to other possibilities. We see no increase in turbidity as the instability is approached, in contrast to the situation for binary systems, where the concentration fluctuations and hence the light scattering increase as the spinodal line is approached. Instead of this continuum approach it is more revealing to adopt a microscopic view and use the knowledge about the aggregate structure. The final equilibrium consists of a phase with smaller droplets and a virtually pure oil phase. The former phase is structurally strongly related to the metastable solution, and the metastability can only be caused by a difficulty of nucleating the oil phase. Nucleation can occur heterogeneously at the liquid-air interface, at the cuvette solid surface, or at some impurity particle, or homogeneously in the bulk solution. We cannot
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Figure 4. Schematic diagram of the structural changes involved on decreasing the temperature (T) below the SPB temperature (TSPB) for an O/W microemulsion. Zone A shows the monodisperse spherical droplets at time t ) 0, whereas zone B, at t ) ∞, shows smaller and more numerous droplets, plus a separated oil film at the top of the sample. Note the decreasing size of the droplets and corresponding increase in the separated oil phase for T , TSPB.
Figure 3. Variation of turbidity with time for a decrease directly to a temperature below the SPB: (a) For a decrease from 28.2 °C directly to 22.4 °C. No increase in turbidity. (b) For a decrease from 28.2 °C directly to 21.9 °C. Increase in turbidity. (c) For a decrease from 28.0 °C (note lower initial temperature for this plot) directly to 20.3 °C. The rate of change of turbidity with time is hugely increased for a temperature only 1.6 °C less than that that for part c above. Slight differences in the initial turbidity are a result of the rapid changes in turbidity at temperatures above the SPB (see text).
definitely exclude some occurrence of heterogeneous nucleation in the experiments, but such processes cannot explain the turbidity measurements which monitor processes in the bulk liquid. In a homogeneous nucleation some of the existing small oil droplets have to grow to macroscopic sizes. However there is a dilemma in that the driving force for the phase change is the preference of the droplets to become smaller to optimize the curvature energy rather than growing in size. From an emulsion perspective the route to a separate oil phase goes via flocculation/coagulation, coalescence, or Ostwald ripening. From studies of the equilibrium system just above the SPB we know that the spherical droplets repel and behave as hard spheres. This would eliminate the coagulation/flocculation pathway. Coales-
cence could still occur as an activated process during droplet collisions. However it is difficult to reconcile this with the observed sharp transition from metastability to instability, with the concentration independence of this transition, and with the fact that the process is more rapid the lower the temperature, implying a negative activation energy. This leaves an Ostwald ripening-like process as the most likely route toward equilibrium. In a conventional Ostwald ripening of an emulsion the total interfacial area and thus the surface free energy decrease as oil molecules diffuse from small droplets to larger ones. In the present case droplets are small and the curvature free energy provides the dominating contribution to the free energy of the surfactant film. In the two-phase area the global maximum of the curvature energy is in the equilibrium state with many small droplets and a macroscopic oil phase. To reach this state, a few droplets need to grow in size to macroscopic dimensions. We now qualitatively interpret the existence of a metastable region in the following way. Just below the SPB the disproportionation of the droplet population to many slightly smaller and a few larger ones is initially uphill in curvature free energy. The uniform droplet size distribution is then locally stable. For deeper quenches to T < Tm there is more curvature free energy to be gained by decreasing the size of the smaller droplets, and this disproportionation of droplet sizes becomes downhill in free energy, allowing for an Ostwald ripening-like process to proceed as illustrated in Figure 4. Conclusions The oil-in-water emulsion prepared by a temperature quench across the SPB is metastable in the temperature range between TSPB and Tm but unstable below Tm. In the unstable region oil droplets are nucleated and they grow in an Ostwald ripening-like process. The existence of a temperature threshold for the Ostwald ripening is ascribed to the role of the curvature energy. In the metastable region the diffusional transport of an oil molecule from one droplet to a slightly larger one leads to an unfavorable increase in curvature energy. For temperatures below Tm this transfer is associated with a favorable monotonic decrease in curvature free energy. LA9608831
