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Langmuir 1997, 13, 7008-7011
Water-in-Oil Emulsions: Role of the Solvent Molecular Size on Droplet Interactions F. Leal-Calderon,* O. Mondain-Monval, K. Pays, N. Royer, and J. Bibette Centre de recherche Paul Pascal, CNRS, Av. A. Schweitzer, 33600 PESSAC, France Received July 15, 1997. In Final Form: October 16, 1997X We prepare monodisperse inverted (water-in-oil) emulsion droplets and observe their phase behavior in various types of nonaqueous continuous phases. By using linear polydimethylsiloxanes or linear alkanes of length n (monomer units), mixed at volume fraction φ with dodecane, we determine the boundary within the φ/n plane which describes the colloidal aggregation. In the limit of large n, the boundary is well predicted by a hard core depletion model of polymer chains. Deviations to this prediction become increasingly pronounced as n is reduced.
Introduction Emulsions are colloidal systems made of liquid droplets dispersed in another liquid phase. They are produced by shearing the two immiscible liquids, which provides the necessary energy to reach a metastable state through fragmentation of one phase into the other. The persistence of such dispersions is generally ensured by the presence of surface active species (surfactant or polymer molecules) which are known to cover the interfaces and are responsible for delaying significantly the recombination (coalescence) of the droplets. This long term stability can be exploited to produce systems of practical or industrial interest such as medicines, cosmetic products, paints, pesticides, etc. From their preparation to their destruction, emulsions reveal numerous kinds of both reversible and irreversible transitions. Irreversible phenomena lead to coarsening, which may originate from either coalescence or Ostwald ripening. Reversible transitions may arise from the presence of attractive droplet interactions and generally lead to the formation of various structures: flocs coexisting with dilute droplets or gels which consist of a network of connected droplets. As an example, two droplets and more generally two colloidal particles may attract each other when surrounded by smaller ones. This attraction is purely entropic in origin: when the two large particles approach, the small ones may be expelled, leading to an uncompensated pressure within the depleted region. Therefore, the so-called depletion interaction scales with the osmotic pressure of the small particles and also with the size of the depleted volume in between the two large interacting particles.1 Many experimental facts suggest the validity of such a mechanism. As an example, various mixtures of colloidal particles may phase separate owing to the presence of attractive depletion forces: colloidal particles mixed with polymer coils2-7 or surfactant aggregates,8-10 or simply binary colloidal mixtures composed of particles of two sizes.11,12 X Abstract published in Advance ACS Abstracts, December 1, 1997.
(1) Asakura, S.; Oosawa, J. J. Polym. Sci. 1958, 32, 183. (2) de Hek, H.; Vrij, A. J. Colloid Interface Sci. 1981, 84, 409. (3) Sperry, P. R. J. Colloid Interface Sci. 1984, 99, 97. (4) Vincent, B. Colloids Surf. 1987, 24, 269. (5) Leal-Calderon, F.; Bibette, J.; Biais, J. Europhys. Lett. 1993, 23, 653. (6) Illet, S. M.; Orrock, A.; Poon, W. C. K.; Pusey, P. N. Phys. Rev. E 1995, 51, 1344. (7) Meller, A.; Stavans, J. Langmuir 1996, 12, 301. (8) Aronson, M. P. Langmuir 1989, 5, 494. (9) Bibette, J.; Roux, D.; Nallet, F. Phys. Rev. Lett. 1990, 65, 2470. (10) Binks, B. P.; Fletcher, P. D. I.; Horsup, D. I. Colloids Surf. 1991, 61, 291. Leal-Calderon, F.; Gerhardi, B.; Espert, A.; Brossard, F.; Alard, V.; Tranchant, J. F.; Stora, T.; Bibette, J. Langmuir 1996, 12, 872.
S0743-7463(97)00792-0 CCC: $14.00
The simplest description of this force consists in ascribing a characteristic separation d* at which the small particles are excluded. Therefore the pressure goes abruptly to zero within the depleted region when the large droplet surface separation becomes less than d*. This simple model is in agreement with direct force measurements performed with the surface force apparatus (SFA), when depletion interactions are induced by charged surfactant micelles.13,14 Indeed, small surfactant micelles are good candidates to test this simple limit: they may be considered as nondeformable objects, and the repulsion which eventually arises from their charge may be simply accounted for by considering an effective exclusion diameter.13 By contrast, direct measurements of polymerinducing depletion forces are so far inaccessible in both the diluted and concentrated regimes using the SFA. However, the depletion interaction between a sphere and a plane in the presence of nonadsorbing polymers has been measured using the atomic force microscope (AFM).15 Adhesive energy measurements between lipid bilayer membranes induced by concentrated solutions of nonadsorbing polymer are also reported and show good agreement with mean field theory.16 Moreover, depletion forces are frequently revealed by the equilibrium structure factor between colloids near the phase separation.17,18 In this letter, we observe the aggregation threshold of inverted emulsion droplets (water-in-oil) stabilized by surfactant molecules in the presence of linear flexible chains of various masses. We show that the attraction which is responsible for the transition may be magnified in two different ways. A classical one consists in increasing the refractive index mismatch between the dispersed and continuous phases, therefore increasing the Van der Waals interaction. Another way consists in increasing the size of the molecules that compose the continuous phase. By using linear polydimethylsiloxanes made of n units, mixed at volume fraction φ with dodecane, we determine the boundary φ* within the φ/n plane which describes the colloidal precipitation, from n ) 1 to n ) 3400. φ*(n) is continuously decreasing as n increases. Assuming that the φ*(n) boundary corresponds to a constant contact pair (11) Sanyal, S.; Easwear, N.; Ramaswamy, S.; Sood, A. K. Europhys. Lett. 1993, 18, 107. (12) Steiner, U.; Meller, A.; Stavans, J. Phys. Rev. Lett. 1995, 74, 4750. (13) Richetti, P.; Kekicheff, P. Phys. Rev. Lett. 1992, 68, 1951. (14) Mondain-Monval, O.; Philip, J.; Leal-Calderon, F.; Bibette, J. Phys. Rev. Lett. 1995, 75, 3364. (15) Milling, A.; Biggs, S. J. Colloid Interface Sci. 1995, 170, 604. (16) Evans, E.; Needham, D. Macromolecules 1988, 21, 1822. (17) de Hek, H.; Vrij, A. J. Colloid Interface Sci. 1982, 88, 258. (18) Ye, X.; Narayanan, T.; Tong, P.; Huang, J. S. Phys. Rev. Lett. 1996, 76, 4640.
© 1997 American Chemical Society
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Figure 1. State of aggregation of water and glycerol droplets in different oils (CnH2n+2) as a function of n and of the refractive index mismatch ∆nr between the dispersed and the continuous phases. The surfactant concentration is equal to 1% in mass. The droplet volume fraction is set at 5%. Water droplets have a diameter of 0.41 µm, and glycerol droplets have a diameter of 0.38 µm: black symbols, aggregated droplets; empty symbols, dispersed droplets.
interaction between droplets within the aggregates, our data in the limit of large n agree with a simple hard core depletion model. We believe that the deviations that occur at small n values are due to the possible mixing between chains and the surfactant tails stabilizing the droplet surface, which precludes the simple depletion mechanism from being the unique origin of the colloidal interaction.
Figure 2. Microscopic image of a totally flocculated emulsion (water droplets of 0.41 µm in C26H54, T ) 65 °C).
Water (or glycerol)-in-oil emulsions are prepared by shearing one phase into the other in the presence of an oil soluble surfactant. The initial emulsion is typically composed of 80% (volume) dispersed phase, 10% dodecane, and 10% surfactant.19,20 The surfactant used in this study is Span 80 (Sorbitan Monooleate, which possesses an average C18 unsaturated hydrophobic tail; this surfactant is perfectly liquid at room temperature and does not exhibit any crystallyiation; Sigma). The dispersed phase contains 2% in mass of magnesium sulfate (MgSO4). The presence of salt prevents the emulsion from any irreversible coarsening within the time scale of our experiments.19 Monodisperse emulsions are obtained either by direct emulsification20 or by applying a fractionated crystallization method to a crude polydisperse emulsion.21 After the emulsification and fractionation processes, the emulsions are centrifuged and their initial continuous phase is replaced by different oils. In this study, all the emulsions are diluted to a droplet volume fraction from 1 to 5% and the surfactant concentration within the continuous phase is always set to 1% in mass. From surface tension measurements at the water-dodecane interface, we obtain an apparent surfactant chain density of about 50-60 Å2 per chain (at room temperature). This value corresponds to a density which is lower than the closest packing for aliphatic chains (20-30 Å2 per chain). In Figure 1, we show the phase behavior of both water and glycerol droplets when dispersed in a linear aliphatic solvent of formula CnH2n+2 , from n ) 5 to n ) 30. The diameters deduced from dynamic light scattering are 0.41 µm for water droplets and 0.38 µm for glycerol droplets. Since, for n larger than 16, solvent crystallization takes place above 20 °C, we have performed a second series of experiments at 65 °C. The absolute value of the refractive index mismatch ∆nr between oil and water or glycerol is plotted as a function of n. The state of aggregation,
deduced from direct microscopic observations and sedimentation of macroscopic samples, is reported for each sample (black symbols, aggregated; empty symbols, dispersed). For water droplets, as seen in figure 1, increasing n leads to an increase in |∆nr| and an aggregation threshold appears at large n. Below this threshold, occurring at n ) 24, we observe perfectly Brownian droplets while, above the threshold, the emulsions turn into a completely aggregated system, as shown in Figure 2, where the droplet volume fraction φd is 5%. All the particles are entrapped within large ramified clusters; at the macroscopic scale, we observe a rapid sedimentation and formation of a clear supernatant. By contrast, for glycerol droplets, increasing n reduces |∆nr| and, instead, we observe two distinct thresholds at n ) 7 and n ) 26. Indeed, the droplets are first aggregated (|∆nr| large), become dispersed as |∆nr| is reduced, and finally are aggregated again as |∆nr| is further reduced. Note that this second aggregation threshold occurs in the limit of large n. From these results, we conclude that two distinct and independent mechanisms affect the colloidal aggregation and therefore the contact pair interaction. One is controlled by the refractive index mismatch, which reflects the magnitude of the Van der Waals forces. A rough approximation of the Van der Waals potential between spherical particles is given by uVdW22 ) Aa/24δ, where A is the Hamaker constant, a is the droplet radius, and δ is the thickness of the surfactant-stabilizing layer. Since our droplets (with radius around 0.2 µm) possess high capillary pressure (around 0.3 atm), we neglect the influence of droplet deformation.23 This is supported by microscopic observations performed with very large water and glycerol droplets (around 10 µm in diameter) in the same solvents which do not reveal any deformation or appreciable contact angle between the aggregated droplets. The hydrocarbon-water Hamaker constant lies in the range (3-7) × 10-21 J22 when n varies from 5 to 30. If we assume a layer thickness δ of about 2 nm, the above relation gives a potential energy between 2 and 6kT (kT being the thermal energy), a range in which phase separation is expected to occur, as found experimentally for water droplets (Figure 1). However, for glycerol
(19) Aronson, M. P.; Petko, M. F. J. Colloid Interface Sci. 1993, 159, 134. (20) Mason, T. G.; Bibette, J. Phys. Rev. Lett. 1996, 77, 3481. (21) Bibette, J. J. Colloid Interface. Sci. 1991, 147, 474.
(22) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: London, 1992. (23) Danov, K. D.; Petsev, D. N.; Denkov, N. D. J. Chem. Phys. 1993, 99, 7179.
Experimental Results
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Figure 4. Volume fraction of n-alkane at the onset of flocculation as a function of n-alkane chain length (CnH2n+2). The continuous phase is made of a mixture of n-alkane, dodecane, and Span 80 (1 mass %). Glycerol droplets (5 vol %) have a diameter of 0.38 µm. T ) 65 °C. Figure 3. Microscopic image of a coexisting state made of aggregates in equilibrium with single Brownian droplets (glycerol droplets of 0.38 µm in a dodecane/C26H54 mixture; φ ) 0.9; T ) 65 °C). Due to their very small size, single droplets are not visible in this photograph. However, their motion is perfectly visible under a microscope.
droplets the Hamaker constant is continuously decreasing as n increases and the flocculation observed for n > 26 gives fairly good certitude that the attraction in the presence of long alkanes is not produced only by Van der Waals forces. Another interaction may arise from the overlapping of the surfactant chains covering the droplets, resulting from a complex interplay between enthalpic and entropic effects. This interaction is controlled by the chain length of the solvent, which certainly suggests an entropically driven mechanism. Indeed, enthalpic contributions to the non-Van der Waals forces should be weakly changing by varying n because the chemical nature of the solvent remains the same (alkanes) and the surfactant chain is also kept the same. To test this idea, we explore the coupling between the length parameter n and the volume fraction φ of flexible chains when mixed with dodecane. Because the variable φ allows us to continuously vary the magnitude of the attraction, we are able to induce the transition from the dispersed state to the totally aggregated state (as in Figure 2) with a coexisting state in between. In the coexisting region, we observe compact clusters in equilibrium with single Brownian droplets (fluid-solid equilibrium; see Figure 3); after a few hours of settling, a milky supernatant coexists with a dense sediment. In Figure 4, we show the aggregation threshold φ* of glycerol droplets (0.38 µm in diameter, φd ) 5%) within the φ/n plane from n ) 25 to n ) 40. φ* is defined as the volume fraction of linear alkane CnH2n+2 required to reach the coexisting state. Observations are performed at 65 °C. We checked that, up to the concentration treshold and a few percent above it, the dodecane/CnH2n+2 mixture is liquid and does not exhibit any crystallization. As expected, there is a strong coupling between φ and n: the longer the chain is, the less is required for reaching the coexisting state. Note that φ*(n) dramatically decreases when n becomes significantly larger than the number of unit segments that compose the adsorbed surfactant tail (n ≈ 18); this is in good agreement with exclusion effects, as already predicted.24 It is also worth noting that the flocculation is reversible: dilution of a flocculated emulsion with pure dodecane allows us to totally redisperse the droplets. (24) Leemakers, F. A. M.; Sdranis, Y. S.; Lyklema, J.; Groot, R. D. Colloids Surf. 1994, 85, 135.
Figure 5. PDMS volume fraction versus average number of unit segments at the onset of flocculation. The dashed line corresponds to the scaling n-0.1. (T ) 20 °C; water droplet diameter ) 0.28 µm; φd ) 1%; 1% in mass of Span 80). Inset: same plot in a log-log scale.
In order to explore the form of the function φ*(n) on a larger scale, we study the behavior of water droplets (0.28 µm in diameter) dispersed in a mixture of polydimethylsiloxane (PDMS) chains and dodecane (with 1 mass % Span 80). PDMS chains conform to the general formula (CH3)3Si[OSi(CH3)2]nCH3. Hexamethyldisiloxane (n ) 1) was analytical grade (Fluka) while the other PDMS chains were commercial products (Rhoˆne Poulenc, Rhodorsil). Their average molecular weights were measured by GPC. We determine the proportion φ* of PDMS oil in dodecane necessary to reach the coexisting state at 20 °C. In Figure 5, we plot the concentration threshold at fixed water volume fraction (φd ) 1%) as a function of the logarithm of the average number n of monomers per chain. The boundary is clearly governed by two distinct regimes: a sharp drop that occurs for low n as for alkanes (see Figure 4) and a smoother decrease at large n. As for normal alkanes (Figure 4), the aggregation is totally reversible, since it disappears by simple dilution with pure dodecane. Discussion We now discuss the microscopic origin of the attraction originated by the presence of long molecules in the continuous phase. The colloidal aggregation at low droplet volume fraction can be considered as a gas-solid phase transition and may be simply described by equating both the chemical potentials and pressures of an ideal gas and a purely incompressible dense phase involving only nearest neighbors:9 ln φd ) (z/2kT)(u + ∆µ°), where z is the coordination number of a droplet within the dense phase, u is the total contact pair potential energy, and ∆µ° is the
Water-in-Oil Emulsions
reference chemical potential difference between fluid and dense phases. Therefore, we can reasonably assume that the φ/n boundary at which occurs the colloidal aggregation corresponds to a constant contact energy u between droplets within the dense phase (at a constant φd of 1%). This energy has to be of the order of kT when φd is about 1% to satisfy the previous equation.9 In the limit of large n (n > 500) we suspect that a hard core depletion mechanism may govern the evolution of the φ/n boundary of Figure 5. Indeed, the Van der Waals force should remain constant, owing to the very small amount of polymer (φ* < 1%) at which occurs the aggregation. Therefore, since polymer chains are required to induce colloidal aggregation, Van der Waals interactions are obviously not sufficient. However they certainly do contribute as a constant background. The simplest description of the depletion force consists in assuming that, for a droplet surface separation lower than the radius of gyration Rg, the polymer coils are excluded. Such a mechanism leads to a contact energy ud given by 2πPosmaRg2,1,9 where Posm is the osmotic pressure of the polymer solution (once again neglecting droplet deformation). This relation assumes that a/Rg . 1. Since the PDMS concentration remains very low (below the semidilute critical concentration), we take for Posm the perfect gas approximation. For the larger n value (n ≈ 3400), Posm ≈ 60 Pa at the aggregation threshold. Using viscosimetric measurements, we find an hydrodynamic radius of 147 Å at 20 °C that we assume to be equal to Rg. At such temperature, we find that the solvent behaves roughly as a θ solvent (the hydrodynamic radius is found to scale as nR, where R ) 0.53 ( 0.0525.) Therefore, we obtain ud ≈ 2.7kT, which perfectly agrees with our initial assumption: the hard core depletion mechanism might be responsible for the evolution of the φ/n boundary, at least for such a large value of n. In a θ solvent Rg scales as n0.5 and Posm scales as φ/n; therefore, the aggregation boundary in that limit should become essentially independent of n. In a good solvent where Rg scales as n0.6, therefore φ* scales as n-0.2. So, if the depletion interaction is governing the experimental φ/n dependence, we expect that φ* would exhibit a very weak dependence with n, which is clearly the case in the limit of large n. In the inset of Figure 5, we plot the data in a log-log plot and confirm that the slope is becoming comparable to the
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expected one (between 0 and -0.2; as a guide we draw a line of slope -0.1). These results are also in agreement with some previously reported data.26 In the limit of small n (n < 100), we suspect that a simple depletion mechanism which assumes a total exclusion of polymer chains is unrealistic. Indeed, the polymer is small enough to swell the adsorbed surfactant brush and possibly to be only partially excluded when the two droplets are approaching. As an example, at the precipitation threshold corresponding to n ≈ 40 (φ* ≈ 3%), the ideal gas osmotic pressure is 22 × 103 Pa. We find for this system a radius of gyration of about 15 Å, leading to a depletion contact potential of about 10kT. As seen in Figure 5 (inset) for n ≈ 40 the data do not agree with the previous scaling, and accordingly the deduced contact potential at the threshold is already much larger than kT. This suggests that the hard core depletion mechanism is not realistic anymore. Indeed, such a mechanism overestimates the pair interaction at the precipitation threshold, and this overestimation becomes more dramatic as n decreases. For the same reasons, the slope of φ*(n) for n < 100 is continuously deviating from the prediction based on that mechanism. Obviously, such an explanation becomes more speculative in the limit of very small n values (n < 10), where, due to the large amount of silicone oil at the onset of flocculation, Van der Waals attraction and the effective solvent quality (enthalpic effect) may significantly change. Conclusion Flocculation is induced by the presence of long oil molecules in the continuous phase of inverted emulsions. Our results give some basic ideas that control the colloidal interactions induced by solvent or a mixture of solvent and solute, when varying their length n from a molecular scale to a colloidal scale: at large n, a hard core depletion mechanism is dominant whereas at smaller n such an effect vanishes owing to the possible swelling of the surfactant brush. Acknowledgment. The authors gratefully acknowledge M. Feder from Rhoˆne Poulenc Company for providing the polydimethylsiloxane samples and J. F. Joanny and T. Witten for fruitful discussions. LA970792J
(25) de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: London, 1979.
(26) de Hek, H.; Vrij, A. J. Colloid Interface Sci. 1979, 70, 592.
