Ostwald Ripening of Alkane in Water Emulsions Stabilized by

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Ostwald Ripening of Alkane in Water Emulsions Stabilized by Hexaethylene Glycol Dodecyl Ether Thi Kieu Nguyen Hoang,† Van Binh La,‡ Luc Deriemaeker,† and Robert Finsy*,† Department of Physical and Colloid Chemistry, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium, and the Faculty of Chemical Technology, Hanoi University of Technology, Hanoi, Vietnam Received February 17, 2003. In Final Form: May 13, 2003 The Ostwald ripening and the solubilization of alkane in water emulsions stabilized by the nonionic surfactant hexaethylene glycol n-dodecyl ether (C12E6) were investigated. For emulsions prepared under high-shear conditions in a microfluidizer, the presence of micelles swollen by alkane hardly affects the ripening rate. For already formed emulsions to which extra surfactant solutions were added, the ripening rates increased slightly with increasing added surfactant concentration. The ratio of the highest to the lowest observed ripening rate is no more than a factor of 3. The main aging mechanism is the transport of alkane by molecular diffusion through the continuous phase. This mechanism is confirmed by the temperature dependence of the ripening rate. The solubilities and the solubilization rates of different alkanes in several surfactants were determined. The solubilization rates of different alkanes are approximately proportional to their solubilities in micellar surfactant solution and are dependent on the ratio of the number of oil molecules to that of surfactant molecules. An inverse relationship between the solubilization rate and the enhancement of the Ostwald ripening rate by the addition of extra surfactant is observed.

1. Introduction The physical degradation of emulsions is due to the spontaneous trend toward a minimal interfacial area between the dispersed phase and the dispersion medium. Minimizing the interfacial area is mainly achieved by two mechanisms: first, coagulation possibly followed by coalescence, and second, Ostwald ripening. The former is the most studied (see e.g. ref 1). However, if properly stabilized against the coagulation/coalescence process, the latter can cause a substantial breakdown of the emulsion. Ostwald ripening is the process by which larger particles (or, for emulsions, droplets) grow at the expense of smaller ones due to the higher solubility of the smaller particles (Gibbs-Thomson or Kelvin effect) and to molecular diffusion through the continuous phase. A theoretical description of Ostwald ripening in twophase systems has been developed independently by Lifshitz and Slyozov, and Wagner (LSW theory).2-5 One of their major results is that in the long time limit a stationary regime is reached for which the ripening rate v is given by

v)

daN3 4 ) RDmC(∞) dt 9

(1)

In eq 1, aN denotes the number-average particle radius, Dm is the dispersed phase molecular diffusion coefficient, and C(∞) is the bulk solubility of the dispersed phase in * To whom correspondence should be addressed. Telephone: +32 2 629 3485. Fax: +32 2 629 3320. E-mail: Robert.Finsy@ vub.ac.be. † Vrije Universiteit Brussel. ‡ Hanoi University of Technology. (1) Tadros, T.; Vincent, B. In Encyclopedia of emulsion technology; Becher P., Ed.; Marcel Dekker: New York, 1983; p 131. (2) Lifshitz, I. M.; Slyozov, V. V. J. Phys. Chem. Solids 1961, 19, 35. (3) Wagner, C. Z. Electrochem. 1961, 65, 581. (4) Kabalnov, A. S.; Shchukin, E. D. Adv. Colloid Interface Sci. 1992, 38, 69. (5) Taylor, P. Adv. Colloid Interface Sci. 1998, 75, 107.

the continuous one; R is a material-dependent constant called the capillary length, defined by

R)

2γVm RT

(2)

In eq 2, Vm stands for the molar volume of the dispersed phase, γ is the interfacial tension, and R and T have their usual meanings of gas constant and absolute temperature. This result predicts that the aging or average droplet size increase in time is mainly determined by the bulk solubility of the dispersed phase. This feature of Ostwald ripening has been verified in several experimental studies6-21 of alkane in water emulsions stabilized against coagulation by surfactants. (6) Kabalnov, A. S.; Markarov, K. N.; Pertzov, A. V.; Shchukin, E. D. J. Colloid Interface Sci. 1990, 138, 98. (7) Kabalnov, A. S. Langmuir 1994, 10, 680. (8) Taylor, P. Colloids Surf., A 1995, 99, 175. (9) Soma, J.; Papadopoulos, K. D. J. Colloid Interface Sci. 1996, 181, 225. (10) Bremer, L.; De Nijs, B.; Deriemaeker, L.; Finsy, R.; Gelade´, E.; Joosten, J. Part. Part. Syst. Charact. 1996, 13, 350. (11) De Smet, Y.; Malfait, J.; De Vos, C.; Deriemaeker, L.; Finsy, R. Bull. Soc. Chim. Belg. 1996, 105, 789. (12) De Smet, Y.; Malfait, J.; DeVos, C.; Deriemaeker, L.; Finsy, R. Prog. Colloid Polym. Sci. 1997, 105, 252. (13) De Smet, Y.; Deriemaeker, L.; Finsy, R. Langmuir 1999, 15, 6745. (14) Binks, B. P.; Clint, J. H.; Fletcher, P. D. I.; Rippon, S.; Lubetkin, S. D.; Mulqueen, P. J. Langmuir 1999, 15, 4495. (15) Weiss, J.; Herrmann, N.; McClements, D. J. Langmuir 1999, 15, 6652. (16) Weiss, J.; Cancelier, C.; McClements, D. J. Langmuir 2000, 16, 6833. (17) Hoang, T. K. N.; La, V. B.; Deriemaeker, L.; Finsy, R. Langmuir 2001, 17, 5166. (18) Hoang, T. K. N.; La, V. B.; Deriemaeker, L.; Finsy, R. Langmuir 2002, 18, 1485. (19) Hoang, T. K. N.; La, V. B.; Deriemaeker, L.; Finsy, R. Langmuir 2002, 18, 10086. (20) De Smet, Y.; Deriemaeker, L.; Parloo, E.; Finsy, R. Langmuir 1999, 15, 2327. (21) De Smet, Y.; Danino, D.; Deriemaeker, L.; Talmon, Y.; Finsy, R. Langmuir 2000, 16, 961.

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If added in sufficiently large amounts and after complete coverage of the oil-water interface, surfactants spontaneously form micelles in the continuous aqueous phase. The presence of micelles drastically increases the solubility of the oil. Therefore, an effect of micelles on the Ostwald ripening may be anticipated. It might be simplistically expected that replacing the bulk oil solubility C(∞) in eq 1 by the concentration of oil solubilized by the micelles and using the micellar diffusion coefficient instead of the molecular one would yield the Ostwald ripening rate in the presence of micelles. This approach predicts an increase of the rates by a factor of about 200-1000.5 Experimental works indicate that the rate and the extent of oil solubilization of different surfactant micelles have different, even contrary, effects on Ostwald ripening.7-20 In the studies where anionic surfactants (sodium dodecyl sulfate (SDS) and sodium dodecyl benzene sulfonate (SDBS)) were used,7-13,19 the Ostwald ripening kinetics is not affected considerably by the micellar solubilization of alkane. The ripening rates are enhanced by a factor of 2-38,9 and do not change significantly7,10,19 or decrease slightly13 with increasing surfactant (micellar) concentration above the critical micellar concentration (cmc). With emulsions stabilized by nonionic surfactants, the effects of micelles on Ostwald ripening are more complicated. Some authors14-16 reported that in the presence of nonionic surfactant micelles the ripening rates are 2-4 orders of magnitude larger than those predicted by eq 1, that is, those corresponding to molecular transport of oil molecules through the continuous aqueous phase. For emulsions stabilized by surfactants of the dodecyl noxyethylene glycol ether series (C12En), Binks et al.14 found that the compositional ripening rates correlate with the solubility of the transferring oil species in the micellar solution present in the continuous phase. On the other hand, Weiss et al.16 found no clear correlation between the Ostwald ripening rate and the solubilization capacity and the solubilization kinetics of the micelles for emulsions stabilized by Tween surfactants. In a previous study18 on alkane in water emulsions stabilized by the same surfactant (Tween20) as used in the work of Weiss et al.,16 we observed that the Ostwald ripening rate enhancements with surfactant concentration are less than a factor of 3. In another previous study,17 the measured ripening rates were surprisingly significantly below the rate that can be predicted by LSW theory and decreased in the presence of surfactant micelles although the solubilization capacity of the surfactant used in this study, poly(ethylene glycol) monolaurate (PEM), is about the same as that of Tween20. This result is attributed to the fact that surfactant micelles withdraw oil from emulsion droplets and the oil in micelles does not contribute to the Ostwald ripening process. It is clear that the contribution of oil molecules solubilized into micelles to the ripening process and the role of micelles in the transport of oil between droplets need further research. In this study, the Ostwald ripening rate as a function of micellar surfactant concentration and the solubilization of alkane in water emulsions are investigated. The emulsions are stabilized by the nonionic surfactant hexaoxyethylene glycol dodecyl ether (C12E6) for which the oil solubilization is much higher compared to the surfactants used in previous studies.17-19 The effect of the addition of micellar surfactant solution to already formed emulsions is also studied. Since the properties of micellar C12E6 solutions vary significantly with temperature, a considerable variation of the ripening rate may be anticipated. Therefore, the temperature dependence of the ripening rate is also investigated.

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2. Experimental Section 2.1. Material and Emulsion Preparation. Several emulsions of alkanes in water stabilized by the surfactant hexaoxyethylene glycol dodecyl ether (Nikkol; purity, >98%) were prepared. The alkanes used were dodecane, undecane, and decane (Aldrich; purity, 99+%). The preparation method was the following. The oil component was added to the aqueous surfactant solution. After 10 min of premixing with an Ultra-Turrax T25 with rotor S25-186, the coarse emulsion was further homogenized under high-shear conditions for 10 min using an Y-110 microfluidizer. In a second series of experiments, mother emulsions were prepared according to the previous procedure. These emulsions were monitored until the average radius was about 50 nm. At that moment, surfactant solutions of different concentrations were added. 2.2. Characteristics of the Surfactant C12E6: Critical Micellar Concentration and Specific Surface Area (As). According to the manufacturer, the cmc is 6.8 × 10-5 M. The specific area is 0.69 nm2.22 2.3. Particle Size Measurement. Droplet sizes were determined with dynamic light scattering (DLS). The experimental setup consists of an Ar+ laser (wavelength λ ) 488 nm), a thermostated sample holder allowing control of the temperature, and a photomultiplier (EMI 9863A) mounted at a detection angle of 90°. The signal of the photomultiplier was fed to a Brookhaven BI9000 correlator. Intensity-averaged radii were computed from the intensity autocorrelation data with the cumulants method.23 2.4. Determination of the Ostwald Ripening Rate. From the data of intensity-averaged radii as a function of time, the experimental Ostwald ripening rates are determined following the procedure explained in ref 20. This procedure accounts for the initial nonstationary growth regime.21 Thereby the time evolution of a model of the droplet size distribution is computed during the ripening process.24 At every step of the ripening, the intensity- and number-weighted droplet sizes are computed from the actual size distribution. With such tables of corresponding intensity and number averages, the intensity-weighted average sizes determined experimentally by DLS are converted into number-average sizes. The ratios of the experimental rates to the theoretical rate predicted by eq 1 are reported as rate enhancement factors. The theoretical ripening rates at 25 °C of decane and undecane emulsions are 1.1 and 0.39 nm3/s, respectively. They were calculated with the following values: Dm ) 4.51 × 10-6 cm2/s, Vm ) 192.27 cm3/mol, and C(∞) ) 7.1 × 10-8 mL/mL for decane emulsions and Dm ) 4.31 × 10-6 cm2/s, Vm ) 211.23 cm3/mol, and C(∞) ) 2.0 × 10-8 mL/mL for undecane emulsions. The values of the interfacial tension were obtained by interpolation of the data from ref 25 and are 0.5 and 0.6 mN/m for decane and undecane emulsions, respectively. Note that the oil volume fraction of the studied emulsion (0.01) is small enough to exclude a volume fraction dependent term in eq 1.26 2.5. Determination of the Alkane Solubility in Micellar Surfactant Solutions. The amount of alkane that can be solubilized by micellar surfactant solutions is determined as follows. As long as the alkane is solubilized by the micelles, the particle size that can be determined for such a solution is about the micellar size (typically about 10 nm diameter). When the micelles are saturated by alkane, the remaining alkane is dispersed in the form of larger droplets. Hence, beyond the maximum solubilization an increase of particle size with the amount of added alkane is to be expected. The experimental procedure consists of the addition of several amounts of alkane to typically 250 mL of a 2.5 × 10-3 M surfactant solution. The solutions to which the alkane was added are (22) Sottmann, T.; Strey, R.; Chen, S. H. J. Chem. Phys. 1997, 15, 106. (23) Koppel, D. J. Chem. Phys. 1972, 57, 4814. (24) De Smet, Y.; Deriemaeker, L.; Finsy, R. Langmuir 1997, 13, 6884. (25) Aveyard, R.; Binks, B. P.; Fletcher, P. D. I.; MacNab, J. R. Langmuir 1995, 11, 2515. (26) Voorhees, P. J. Stat. Phys. 1985, 38, 231.

Ostwald Ripening of Alkane in Water Emulsions

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Table 1. Ostwald Ripening Rates as a Function of Surfactant Concentration for Several Undecane Emulsions

emulsion

initial radius a0 (nm)

C12E6 concentration (M)

UA1 UA2 UA3 UA4 UA5 UA6a

79 57 38 21 19 5

1.0 × 10-3 2.0 × 10-3 5.0 × 10-3 1.0 × 10-2 2.0 × 10-2 5.0 × 10-2

a

C12E6 concentration needed to cover the initial oil/water interface (M)

C12E6 concentration in the continuous phase (M)

experimental aging rate (nm3/s)

rate enhancement factor

1.2 × 10-3 1.5 × 10-3 2.3 × 10-3 4.2 × 10-3 4.5 × 10-3

5.0 × 10-4 2.7 × 10-3 5.8 × 10-3 1.5 × 10-2

3.7 3.2 4.2 5.4 4.9

9.5 8.2 11 14 13

For this system, all the oil is solubilized by micelles.

Figure 1. The particle radius a as a function of undecane concentration added to a 2.5 × 10-3 M C12E6 solution. homogenized with the Ultra-Turrax and the microfluidizer as explained in section 2.1. As an example, the particle size as a function of the amount of undecane added to a 2.5 × 10-3 M C12E6 solution is shown in Figure 1. Clearly two regimes can be distinguished. In the first, the particle size hardly increases with alkane concentration; in the second, the particle size increases with alkane concentration. The concentration at which linear fits to these two regimes intersect is taken as the concentration of maximum solubilization. In this way, the solubility of undecane in 1.0 × 10-2 M C12E6 and the solubilities of decane and dodecane in 2.5 × 10-3 and 1.0 × 10-2 M C12E6 solutions were determined. The results are reported in Table 5, section 3.2, together with the solubilities in Tween20 and SDBS solutions determined in a previous study.19 2.6. Determination of the Solubilization Rate. The solubilization of the oil of alkane in water emulsions into micellar C12E6 solutions was studied by monitoring the scattered light intensity as a function of time, in parallel with the determination of the average particle size by DLS. The alkane (decane, undecane) in water emulsions were prepared as explained in section 2.1. When the (intensityweighted) average radius reached 50 nm, a surfactant solution was added to a sample of the original emulsions. The scattered light intensity was monitored until it had dropped to the level of a surfactant solution. This decay time of the scattered light intensity was taken as the solubilization time. The solubilization rate (number of oil moles transported per unit time) is then estimated as the number of oil moles present initially, divided by the solubilization time.

3. Results and Discussion 3.1. Ostwald Ripening of Alkane Emulsions Stabilized by the Surfactant C12E6. 3.1.1. Ostwald Ripening or Coalescence? In a first series of experiments, it was investigated whether the increase in particle size could be ascribed to Ostwald ripening or to coalescence. The Ostwald ripening rate is proportional to the solubility of the alkane (the factor C(∞) in eq 1). Since the solubilities of alkanes in water vary significantly with the alkane chain length, a considerable variation of the ripening rate is to be expected on changing the alkane chain length. On the other hand, the coalescence rate depends, for a given system, on the initial particle size and concentration. Hence, changing only the alkane chain length would not alter the coalescence rate.

Figure 2. Evolution of a3 with time for (top to bottom) a decane emulsion, an undecane emulsion, and a dodecane emulsion.

In Figure 2, the cube of the droplet radius a is plotted as a function of time for the decane, undecane, and dodecane mother emulsions. The surfactant (C12E6) concentration was 2.5 × 10-3 M for all emulsions; the alkane volume fraction was 0.005. In all the experiments, no visible traces of creaming or flocculation were observed during the monitoring of the ripening process by DLS. Clearly, replacing decane by undecane or dodecane reduces the ripening rates. Assuming a linear increase of a3 with time, the ripening rates were estimated from the slope of the linear fits. The ratios of 3.2 for ripening rates of decane to undecane emulsion and 3.3 for ripening rates of undecane to dodecane emulsion are in good agreement with the ratios of 3.6 and 3.8 of the bulk solubility (7.1 × 10-8 mL of decane, 2.0 × 10-8 mL of undecane, and 5.2 × 10-9 mL of dodecane in 1 mL of water6). Therefore, the main aging process is Ostwald ripening and not coalescence. This implies that the main aging mechanism results from the transport of the alkane by molecular diffusion through the continuous aqueous phase. This mechanism is further confirmed by, for example, the temperature dependence study of section 3.1.3. 3.1.2. Ostwald Ripening as a Function of Surfactant Concentration. To investigate the effect of an increasing number of surfactant (C12E6) micelles, ripening experiments were carried out as a function of the surfactant concentration. In a first step, six undecane emulsions all with volume fraction 0.01 but with different C12E6 concentrations in the range from 1.0 × 10-3 to 5.0 × 10-2 M were prepared as described in section 2.1. The surfactant concentrations and initial particle sizes are reported in Table 1. The number of moles ns of surfactant needed to cover the initial water/oil interface was estimated by the procedure explained in section 4.2.1 of ref 13. In this procedure, the total interfacial area is estimated from a model (log-normal) droplet size distribution. This leads to surfactant concentrations for complete coverage in the range from 1.2 × 10-3 to 4.5 × 10-3 M (Table 1). Assuming that the first action of the surfactant is to cover the oil-water interface, the initial surfactant concentrations in the continuous phase are for all emulsions, except UA1, above the cmc. The temperature was 25 °C. The

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Figure 3. Evolution of a3 with time for undecane emulsions (UA6, UA1 to UA5, from bottom to top) with increasing surfactant concentration. For clarity, the measurements of UA2 were translated along the ordinate by 6.5 × 105 nm3; the different series (UA3 to UA5) have been translated by 2.5 × 105 nm3.

Figure 4. Rate enhancement factors as a function of overall surfactant concentration for undecane emulsions prepared under high-shear conditions.

results of the monitoring of the droplet size as a function of time are displayed in Figure 3 and Table 1. Given the initial particle size, the amount of surfactant present in emulsion UA1 is not enough to cover the wateroil interface. Hence, for this emulsion, the interfacial tension is higher than the one for a completely covered interface (about 0.6 mN/m25). Since the Ostwald ripening rates are proportional to the interfacial tension (see eq 1), this may explain the higher ripening rate compared to the one predicted by eq 1. The average rate enhancement factor of emulsions UA2 to UA5 is 11.6 ( 2.6, implying that no significant variation with surfactant concentration is observed (Figure 4). On an absolute scale, the rate enhancement factors are of order 10 and are higher than those reported for many anionic surfactants.7,8,13,19 On the other hand, Binks et al.14 report compositional ripening rates of emulsions stabilized by the same surfactant (C12E6) that are 3-4 orders of magnitude larger than those predicted by eq 1 for Ostwald ripening. These authors conclude that in their study oil transfer occurred by a micellar-mediated transport mechanism. However, in the present investigation the ripening rates are proportional to the oil solubilities (section 3.1.1), they are also 2-3 orders of magnitude lower than those observed by Binks et al.,14 and the enhancement of the ripening rates is hardly dependent on the micellar surfactant concentration. This all indicates that possible contributions of a micellar-mediated transport mechanism are much less probable in our study. A possible explanation of the apparent enhancement by a factor of about 10 is, besides a factor of about 2 which is observed in many studies,7,8,13,19 an underestimation of the interfacial tension factor in eq 1. (Note that the values of the product DC(∞) obtained by the model proposed in ref 14 are not affected significantly by altering the interfacial tension by a factor of 5.) Finally, for emulsion UA6 no ripening rate is

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Figure 5. Evolution of a3 with time for the undecane emulsions (UB1, bottom, to UB5, top) to which extra surfactant was added at different concentrations. For clarity, the measurements of UA2 to UA5 have been translated by 1 × 105 nm3.

Figure 6. Evolution of a3 with time for the decane emulsions (D1, bottom, to D4, top) to which extra surfactant was added at different concentrations.

observed. The droplet sizes correspond to those of oil solubilized by a micellar solution (see section 2.5, Figure 1). The surfactant concentration needed to solubilize completely a volume fraction of 0.01 of undecane is estimated from the solubility of undecane in a 1.0 × 10-2 M C12E6 solution as 3.9 × 10-2 M, which is below the overall surfactant concentration of 5.0 × 10-2 M in UA6. In a second step, the ripening of five new undecane and four decane emulsions was investigated. Two mother emulsions (undecane and decane) with 2.5 × 10-3 M C12E6 were prepared. Samples of 2 mL of these emulsions were monitored until the average radius was about 50 nm. At that moment, 1 mL portions of surfactant solutions of different concentrations were added. The results of the monitoring of the droplet size as a function of time are displayed in Figures 5 and 6 and Table 2. Ripening rates are determined before and after addition of the surfactant solution. The ratios of these rates are reported in Table 2 and Figure 7. The ripening rates increase with increasing added surfactant concentration. Compared to the emulsions prepared in the first series of experiments at the same overall surfactant concentration, the aging rates are a little higher, by a factor of no more than 2. Ripening rates of decane and undecane emulsions are again proportional to the solubility of alkanes. This implies that the aging mechanism observed in the previous section is not changed by the addition of extra surfactant and remains mainly molecular diffusion through the continuous aqueous phase. In similar experiments on emulsions stabilized by Tween20, the enhancement effect of the addition of surfactant is about an order of magnitude larger.18 A qualitative explanation for this effect was the following.18 Before additional surfactant is added, there is in the already formed emulsion a quasi-equilibrium state whereby the already present surfactant and the alkane


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Table 2. Ostwald Ripening Rates as a Function of Added Surfactant for Several Undecane and Decane Emulsions emulsion and alkane

concentration of added C12E6 (M)

overall surfactant concentration after addition (M)

UB1 UB2 UB3 UB4 UB5

5.0 × 10-4 5.0 × 10-3 1.0 × 10-2 2.0 × 10-2 2.5 × 10-2

1.8 × 10-3 3.3 × 10-3 5.0 × 10-3 8.3 × 10-3 1.0 × 10-2

D1 D2 D3 D4

1.0 × 10-3 5.0 × 10-3 1.0 × 10-2 1.3 × 10-2

2.0 × 10-3 3.3 × 10-3 5.0 × 10-3 6.0 × 10-3

ripening rate after addition of surfactant (nm3/s)

rate enhancement factor

ratio of rates after and before addition

8.7 11 10 16 23

1.0 1.2 1.3 2.1 2.8

9.1 12 15 19

1.0 1.4 1.6 2.1

Undecane 3.4 4.2 4.0 6.1 9.1 Decane 10 13 17 21

Figure 7. The ratio of the ripening rate after surfactant addition to that before addition as a function of overall surfactant concentration for decane (crosses) and undecane (circles) emulsions.

Figure 8. Evolution of a3 with time for the undecane emulsion at 8, 22, and 40 °C (bottom to top).

molecules are distributed between micelles and the larger emulsion droplets. The main factor disturbing this quasiequilibrium is the Ostwald ripening process. On average, the alkane is transported slowly from smaller droplets to larger ones by molecular diffusion through the continuous phase. The rate of this process is mainly determined by the alkane solubility in the continuous phase (the factor C(∞) in eq 1). However, this quasi-equilibrium state is a dynamic one whereby micelles and droplets are continuously broken down and rebuilt. Addition of extra surfactant disturbs this dynamic equilibrium: more alkane droplets and micelles are broken down. During the evolution toward a new quasi-equilibrium distribution of alkane and surfactant, there are now on average more alkane molecules present in the continuous phase. Hence the factor C(∞) in eq 1 is increased, resulting in an increase in the Ostwald ripening rate. It is likely that the difference in effect between the addition of Tween20 and of C12E6 is due to the difference in solubility and solubilization rate of the alkanes in the surfactant solutions. Since the solubility of undecane in C12E6 micelles is about 8 times higher than in Tween20 micelles and the solubilization rate of undecane in C12E6 micelles is at least 2 times faster than in Tween20 micelles (see section 3.2, Tables 5 and 7), there will be on average less molecular oil present in the continuous phase with the C12E6 micelles. Or in other words, in the case of the C12E6 micelles the evolution toward a new quasi-equilibrium distribution of alkane and surfactant, after the addition of extra surfactant, is faster and leaves on average less molecular oil in the continuous phase. Consequently, the factor C(∞) in eq 1 and the ripening rate are less enhanced compared to the experiments with Tween20. 3.1.3. Ostwald Ripening as a Function of Temperature. Since the properties of micellar C12E6 solutions vary significantly with temperature in particular at

molecular diffusion theoretical experimental rate temp coefficient Dm aging rate aging rate enhancement (°C) (nm3/s) (nm3/s) factor (cm2/s)

Table 3. Ostwald Ripening Rates as a Function of Temperature for an Undecane Emulsion

8 22 40

2.6 × 10-6 4.0 × 10-6 6.2 × 10-6

0.25 0.36 0.53

2.4 3.4 5.1

9.6 9.4 9.6

temperatures close to the cloud point of 50 °C,27,28 a considerable variation of the ripening rate is possible on changing the temperature. To investigate the effect of the temperature, an undecane emulsion with volume fraction of 0.005 and surfactant concentration of 2.5 × 10-3 M was monitored at different temperatures. The experimental results are reported in Table 3 and Figure 8. It is found that the increase of the ripening rate with increasing temperature is mainly caused by the increase in the molecular diffusion coefficient and that the rate enhancement does not depend on temperature. This result again confirms that the main aging is due to the transport of alkane through the continuous phase by molecular diffusion. The observed results also indicate that the ripening is not affected significantly by the solubilization capacity and the solubilization rate which are strongly temperature dependent in the region of the cloud point.27-29 In a next series of experiments, the effect of addition of surfactant to an already formed emulsion was investigated at different temperatures. A mother undecane emulsion with the same composition as the previous one was prepared. Samples of 2 mL of this emulsion were monitored at different temperatures until the average radius was about 50 nm. At that moment, 1 mL portions of surfactant solutions of different concentrations were added. The details are reported in Table 4 and Figure 9. (27) Miller, C. A.; Raney, K. H. Colloids Surf., A 1993, 169, 74. (28) Balmbra, R. R.; Clunie, J. S.; Corkill, J. M.; Goodman, J. F. Trans. Faraday Soc. 1962, 58, 1661. (29) Carroll, B. J. J. Colloid Interface Sci. 1981, 79, 126.

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Table 4. Ostwald Ripening Rates at Different Temperatures of Undecane Emulsions with Added Micellar Surfactant Solutions added concentration ) 5 × 10-3 M

added concentration ) 2.5 × 10-2 M

temperature (°C)

ripening rate after addition (nm3/s)

rate enhancement factor after addition


ripening rate after addition (nm3/s)

8 22 40

2.9 4.2 12

12 12 23

1.2 1.4 2.7

5.8 9.1 a

a

rate enhancement factor after addition


23 25

2.3 2.8

All the oil is solubilized.

Figure 9. Evolution of a3 with time for the undecane emulsion with a 5 × 10-3 M solution added at 8, 22, and 40 °C (bottom to top).

Figure 10. Evolution of the scattered light intensity with time during the solubilization of decane (crosses) and undecane (dots) emulsion droplets in an aqueous micellar C12E6 solution.

Table 5. Solubility of Alkanes in Micellar Surfactant Solutions (mL Alkane per mL Solution)

Table 6. Solubilization Rate as a Function of the Ratio No/Ns for Decane and Undecane Emulsions solubilization rate (10-7 mol s-1)

solubilization rate (10-7 mol s-1)

surfactant solution

decane

undecane

dodecane

2.5 × 10-3 M 1.0 × 10-2 M

C12E6 7.2 × 10-4 3.0 × 10-3

6.3 × 10-4 2.5 × 10-3

3.9 × 10-4 1.5 × 10-3

sample

1.4 × 10-3

al.30 who explained it by the argument that the greater the length of the hydrocarbon, the more energetically unfavorable solubilization is. Next, to investigate the solubilization kinetics, the solubilization experiments were carried out as a function of the ratio of the number of oil molecules to that of surfactant molecules (No/Ns). A mother decane emulsion with oil volume fraction of 0.01 and surfactant concentration of 1 × 10-2 M was prepared. Samples of 1 mL of this emulsion were monitored until the average radius was about 50 nm. At that moment, a 1 × 10-2 M surfactant solution in different volumes was added. The ratio No/Ns was computed from the total amounts of oil and surfactant. The evolution of the scattered light intensity with time was observed and the solubilization rate was estimated as explained in section 2.6. The experiments were repeated for an undecane emulsion. Figure 10 shows the evolution of the scattered light intensity of a decane and an undecane emulsion under the same conditions. As more and more oil from the emulsion droplets is solubilized by the micelles, both the number and the sizes of oil droplets decrease, which is reflected in a decreasing scattered light intensity. The solubilization rates are calculated as explained in section 2.6 and are reported in Table 6 and Figure 11. The experimental results indicate that the solubilization rate decreases linearly with increasing ratio of oil to surfactant molecules, that is, the number of oil molecules solubilized in micelles per unit time increases with

1.0 × 10-2 M 1.0 × 10-1 M 1.0 × 10-1 M

Tween20

SDBS 2.5 × 10-3

3.3 × 10-4 3.5 × 10-3 1.9 × 10-3

At 8 and 22 °C, that is, well below the cloud point, the rate enhancement does not change with temperature. However, the rates are enhanced by a factor of about 2 at the higher added surfactant concentration. For the temperature nearest to the cloud point, the rate enhancement is about twice that at 8 and 22 °C for the lower added surfactant concentration; the higher added surfactant concentration solubilizes all the oil at this temperature. A possible explanation is that at temperatures close to the cloud point the kinetics of formation and breakdown of micelles is enhanced and disturbed more easily by the addition of extra surfactant. More alkane droplets and micelles are broken down, resulting in a higher effective oil concentration in the continuous phase. Hence the factor C(∞) in eq 1 is increased, leading to an increase in the Ostwald ripening rate. 3.2. Solubility and Solubilization Kinetics of Some Alkanes in Micellar Surfactant Solutions. The maximum solubilization capacity of C12E6 micelles was determined for different oils following the way described in section 2.5. The results, together with those of Tween20 and SDBS determined previously,19 are reported in Table 5. This shows that the solubility of alkanes in micelles is proportional to the surfactant concentration. Hence, the maximum solubilization capacity corresponds to a single value of the ratio No/Ns of oil to surfactant molecules. The solubilization capacity of the micelles decreases as the hydrocarbon chain length of the oil molecule increases. This result is in agreement with the results of Weiss et

1 2 3 4

No/Ns

Decane 1.5 1.3 1.2 0.95

1.1 1.9 2.8 4.3

sample 1 2 3 4

No/Ns

Undecane 1.4 1.2 1.1 0.86

0.53 1.0 1.9 3.2

(30) Weiss, J.; Coupland, J. N.; Brathwaite, D.; McClements, D. J. Colloids Surf., A 1997, 121, 53.


Langmuir, Vol. 19, No. 15, 2003 6025 Table 7. Solubilization Rates of Undecane in Several Surfactant Solutions

Figure 11. Solubilization rate as a function of the ratio No/Ns of the number of oil molecules to that of surfactant molecules for decane (crosses) and undecane (circles) emulsions.

increasing number of surfactant molecules. The solubilization rates of different alkanes are approximately proportional to their solubility in micellar solutions. It is clear that the solubilization mechanism in which micelles only take oil from the continuous phase through molecular diffusion13 is not appropriate in this study. According to this mechanism, the solubilization rate of different alkanes should be proportional to the molecular oil solubilities in the aqueous phase for which C(∞) is a fair estimate (note that the difference in molecular diffusion coefficients of the investigated alkanes is negligible). However, such a relationship between the solubilization rate and the bulk oil solubility C(∞) is not observed experimentally. The ratio of 3.6 for the bulk solubilities of decane and undecane (section 3.1.1) is higher than the average ratio of 1.7 for the observed solubilization rates of these alkanes. Furthermore, the dependence of the solubilization rate on the number of surfactant molecules is in favor of a mechanism in which there is a direct exchange of oil between emulsion droplets and micelles. A possible solubilization mechanism is that a group of surfactant molecules desorbs from the droplet’s interface, drags a packet of oil molecules with it, and forms a swollen micelle. This micelle diffuses through the water phase and releases its oil molecules, leaving them solubilized in molecular form.29 This process enhances the molecular oil concentration in the bulk phase, which has the effect of increasing the ripening rate. According to the mentioned mechanism, the solubilization rate is29

k)

∆No(C - cmc) 2Nsτ

where ∆ is the diffusion layer thickness, No is the number of oil molecules in a micelle, Ns is the number of surfactant molecules in a micelle, and τ is the relaxation time for micellar dissociation. Inserting typical values (∆ ) 9.2 nm,31 (No/Ns) ) 1.5 for decane (estimated from the solubility of decane in a 1 × 10-2 M solution), τ ) 2 × 10-3 s,31 C ) 1 × 10-2 M, cmc ) 6.8 × 10-5 M) yields a solubilization rate of 3.4 × 10-7 mol/s. This compares with the experimental value, for decane emulsions, of 1.1 × 10-7 mol/s. A similar computation with (No/Ns) ) 1.2 yields for undecane emulsions 2.8 × 10-7 mol/s, compared with the experimental value of 1.0 × 10-7 mol/s. The agreement in order of magnitude between theory and experiment is likely to support this mechanism. Finally, the solubilization rate of undecane in C12E6 solution is compared to that in Tween20 and SDBS solutions. The solubilization rates are measured at a value (31) Anthony, J. I.; Ward; Quigley, K. J. Dispersion Sci. Technol. 1990, 11, 143.

surfactant solution

No/Ns

solubilization rate (10-7 mol s-1)

C12E6 Tween20 SDBS

1.2 0.17 0.09

1.0 0.46 0.39

of the ratio No/Ns corresponding to the equilibrium solubilities of undecane in the different surfactant solutions (Table 7). The results indicate that the solubilization rate increases as the solubility of alkane in surfactant solution increases. 4. Conclusions The rate of Ostwald ripening in alkane emulsions stabilized by the nonionic surfactant C12E6 was determined. For emulsions prepared in one step under highshear conditions in a microfluidizer, the ripening rates are almost independent of the surfactant concentration. For already formed emulsions to which extra surfactant solution is added, the ripening rates increase slightly with increasing added micellar surfactant concentration. The ratio of the highest to the lowest observed ripening rate is no more than a factor of 3. The main aging process is due to the transport of alkane by molecular diffusion through the continuous phase, and there is no significant contribution of a transport mechanism by micelles. The transport by molecular diffusion is confirmed by the temperature dependence of the experimental rates. The measured solubilization rates are dependent on the ratio of the number of oil to surfactant molecules. The solubilization rates of different alkanes are approximately proportional to their solubilities in micelles. The comparison with the results for emulsions stabilized by Tween20 yields an inverse relationship between solubilization rates and enhancement of the Ostwald ripening rates. These results lead to the following conclusions about the effect of the presence of micelles on the ripening rate. This effect is different for micelles swollen by alkane and for surfactant micelles without alkanes. When an emulsion is prepared under high-shear conditions with an excess of surfactant, the alkane and surfactant molecules are distributed in a quasi-equilibrium state between large oil droplets and micelles swollen by oil. The Ostwald ripening process, which is determined by the amount of alkane molecules in the continuous phase, is not or hardly affected by the presence of the swollen micelles. When an already formed emulsion is diluted with a surfactant solution, the quasi-equilibrium distribution of alkanes and surfactant is disturbed. During the evolution toward a new quasiequilibrium distribution, more alkane molecules are present in the continuous phase, enhancing the Ostwald ripening process. Emulsions stabilized by surfactants with higher solubilization rates evolve faster to a new quasiequilibrium state, leaving on average fewer alkane molecules in the continuous phase, and therefore enhance less the Ostwald ripening rate. On the other hand, the study of the rate of solubilization is in favor of a fusion-fission mechanism rather than molecular diffusion. This indicates that the mechanism is different when the systems are close to equilibrium, that is, the case of Ostwald ripening, compared to systems far away from equilibrium, that is, for the solubilization kinetics case and for the compositional ripening study of Binks et al.14 LA034267Y

Ostwald Ripening of Alkane in Water Emulsions Stabilized by

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