Langmuir 2008, 24, 7711-7717
7711
Enhancement of Ostwald Ripening by Depletion Flocculation Alex M. Djerdjev and James K. Beattie* School of Chemistry, UniVersity of Sydney, New South Wales 2006, Australia ReceiVed January 15, 2008. ReVised Manuscript ReceiVed April 4, 2008 The time dependence of the dynamic mobility and the ultrasonic attenuation of octane and decane oil-in-water emulsions stabilized by sodium dodecyl sulfate (SDS) was measured. The emulsions grew to larger droplets due to Ostwald ripening. The growth rate measured by attenuation depends on the surfactant concentration and the polydispersity of the emulsion. At surfactant concentrations below the critical micelle concentration (cmc) of SDS, the growth was linear with time and the rate was dependent on the polydispersity of the drops; the rate was several times faster than that predicted on the basis of a diffusion growth mechanism. Above the cmc, however, as the droplets grew in size there was a point at which the rate of growth increased, which corresponds to the droplet size at which depletion forces due to the surfactant micelles become significant. Under these conditions both the electroacoustic dynamic mobility and the acoustic attenuation spectra displayed characteristics of flocs: a large decrease in the phase lag at higher frequencies in the dynamic mobility spectrum and a decrease in the attenuation coefficient at low-megahertz frequencies with an increase at higher frequencies. This depletion flocculation enhancement in ripening rates in the presence of SDS micelles provides another, alternative, and self-consistent mechanism for the effect of surfactant micelles on Ostwald ripening.
Introduction The formation of stable emulsions comprising soluble oils is important in many industrial processes. There are many factors which influence the stability of emulsions: the composition of the dispersed phase, the choice of surfactant, and the control of droplet size. One of the major factors influencing emulsion stability is the solubility of the oil phase in the dispersed medium. In a polydisperse emulsion smaller droplets tend to dissolve and grow into the larger droplets, resulting in an increase in the droplet size with time through a process known as Ostwald ripening. It occurs because the solubility of a droplet increases markedly as its radius, a, becomes smaller, a process described by the Kelvin equation, relating the bulk oil solubility, C∞, its molar volume, Vm, and interfacial tension, γ, as (1),
C(a) ) C ∞e(2γVm ⁄aRT) 2γVm R ≈C ∞ 1 + ) C∞ 1 + aRT a
(
) ( )
(1)
where R ) 2γVm/RT and R and T have their usual meaning. Ostwald ripening is therefore significant in polydisperse emulsions containing oils with significant solubility in the continuous phase. A model of Ostwald ripening was developed independently by Lifshitz and Slyozov and Wagner, and is known as the LSW theory.1 According to this theory, the rate, ω, of ripening is given by
da3n 8DC ∞Vmγ ω) ) dt 9RT
(2)
where an (m) is the number average radius, D (m2 s-1) is the diffusion coefficient of the dissolved dispersed phase, and C∞ is the dimensionless volume fraction solubility. This equation is valid only for dilute systems (much less than ∼1 vol %). For more concentrated systems the ripening rate increases due to droplet interactions.2 The rate of ripening depends on the diffusion * Corresponding author. E-mail:
[email protected]. (1) Taylor, P. AdV. Colloid Interface Sci. 1998, 75, 107. (2) Voorhees, P. W. J. Stat. Phys. 1985, 38, 231.
interactions of particles, and eq 3 is modified by a correction factor ν(φ) that takes into account the dispersed-phase volume fraction to give (3). At 5 vol % ν(φ) ∼ 1.5.3
ω)
da3n 8DC ∞Vmγ ) ν(φ) dt 9RT
(3)
As indicated by eq 2 or 3, the cube of the droplet radius should be a linear function (a3 ) ωt + a03) of time with the slope equal to the rate of ripening. However, the rate of Ostwald ripening of oil-in-water emulsions is sometimes found to be nonlinear.4 Several reasons have been proposed for this nonlinearity. First, the LSW theory only applies to the long-time stationary regime with the limiting LSW distribution which is left-skewed and not to the initial state where the distribution is usually right-skewed. De Smet et al.5 have shown that this transition from right- to left-skewed can result in an initial nonlinear increase in an3 with time, although the nonlinearity is relatively small with an initially log-normal size distribution. The transient regime where the particle size distribution changes from right- to left-skewed was shown by simulation to correspond to an increase in the initial drop size by a factor of at least 4. Second, the LSW theory does not take into account the presence of a surfactant layer of finite thickness which could affect the ripening rate.4 Some researchers have indicated that the presence of a thick interfacial layer can retard Ostwald ripening due to its resistance to deformation.6 However, for most proteinstabilized emulsions the thickness of the interfacial layer is required to be more than half the drop radius.7 A more rigid membrane can be achieved by building up multiple surfactant layers.8 Neither of these effects occurs in the SDS-stabilized droplets used in the present work. (3) Kabalnov, A. S.; Makarov, K. N.; Pertzov, A. V.; Shchukin, E. D. J. Colloid Interface Sci. 1990, 138, 98. (4) De Smet, Y.; Deriemaeker, L.; Parloo, E.; Finsy, R. Langmuir 1999, 15, 2327. (5) De Smet, Y.; Deriemaeker, L.; Finsy, R. Langmuir 1997, 13, 6884. (6) Meinders, M. B. J.; Kloek, W.; van Vleit, T. Langmuir 2001, 17, 3923. (7) Meinders, M. B. J.; van Vleit, T. AdV. Colloid Interface Sci. 2004, 108-9, 119. (8) Mun, S.; McClements, D. J. Langmuir 2006, 22, 1551.
10.1021/la800140s CCC: $40.75 2008 American Chemical Society Published on Web 06/21/2008
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Table 1. Properties at 298 K of Octane, Decane, and Water Used for Attenuation Sizinga
d
oil
density, F
specific heat Cp (J kg-1K-1)
sound speed c (m s-1)
thermal conductivity κ (W m-1 K-1)
thermal expansion β (K-1)
intrinsic attenuation R/f2 (Np m-1s2)
octane decane water
0.699 0.730 0.997
2230 b 2182 c 4180 c
1193 b 1235.5 c 1496.7 d
0.12 b 0.14 d 0.609 d
11.4 × 10-4 b 9.85 × 10-4 c 2.57 × 10-4 d
6.1 × 10-14 b 5.7 × 10-14 c 2.1 × 10-14
a F, density; Cp, specific heat; c, speed of sound; κ, thermal conductivity; β, thermal expansion; R/f2, intrinsic attenuation. b Reference 21. c Reference 11. Reference 20.
Third, the conversion of droplet size by intensity to a number average size may require more than a constant conversion factor, and, last, it is assumed that the interfacial tension remains constant during the ripening process.4 There are conflicting results on the effect of surfactant micelles on the ripening rate. Some authors have observed an increase in the rate in the presence of micelles,9–12 while others have reported no effect.13–15 A mechanism for an observed increase has also received much attention. Transport of the oil could be enhanced by micelles because they can solubilize oil molecules from the region surrounding the oil drops and transport them through the aqueous phase.14 The rate of ripening should increase, with respect to the micelle-free state, by a factor which depends on the oil solubility in the micelles and the diffusion coefficient of the micelles. If these are used in place of the molecular solubility of the oil and its diffusion coefficient in the continuous phase, an increase in ripening rate of the order of 200-1000 times is predicted.1 Such increases in the rate are not found for anionic surfactants such as sodium dodecyl sulfate (SDS) or sodium dodecylbenzenesulfonate (SDBS). Alternatively, if one considers that the swollen micelles are like small oil drops of radius am, then the Kelvin equation predicts an enhanced solubility due to the smaller size of the micelles. For undecane C(am)/C∞ ) exp(R/am) (R ) 1.72, am ) 2.5 nm) gives C(am)/ C∞ ) 1.4-2.4.16 Therefore, only a small enhancement of the rate is expected. There does not appear to be any independent experimental test of this prediction of an enhanced oil solubility in the presence of surfactant micelles. For nonionic surfactants the situation can be quite different. Hoang et al.17 have shown that for nonionic surfactants the mechanism of ripening depends on the initial state of the system, with some contribution from micellar transport. It is clear that the process of Ostwald ripening in emulsions is complicated and depends on the type of system studied. In the present work we observe the ripening of octane and decane emulsions stabilized with SDS with the techniques of ultrasonic attenuation and electroacoustics, which enable us to measure the droplet size and size distribution as well as the ζ potential of the emulsion drops without dilution. We compare these results with conventional light scattering measurements and propose an alternative effect of surfactant micelles on the ripening rate.
Materials and Methods Chemicals. n-Octane and n-decane were from Sigma-Aldrich (>99%). Sodium dodecyl sulfate (Sigma, approximately 99% GC) was used as the emulsifying agent, and AR grade NaCl (Ajax (9) Soma, J.; Papadopoulos, K. D. J. Colloid Interface Sci. 1996, 181, 225. (10) Taylor, P. Colloids Surf., A 1995, 99, 175. (11) Weiss, J.; Herrmann, N.; McClements, D. J. Langmuir 1999, 15, 6652. (12) Binks, B. P.; Clint, J. H.; Fletcher, P. D. I.; Rippon, S.; Lubetkin, S. D.; Mulqueen, P. J. Langmuir 1999, 15, 4495. (13) Kabalnov, A. J. Dispersion Sci.Technol. 2001, 22, 1. (14) Kabalnov, A. S. Langmuir 1994, 10, 680. (15) Hoang, T. K. N.; La, V. B.; Deriemaeker, L.; Finsy, R. Langmuir 2002, 18, 10086. (16) De Smet, Y.; Deriemaeker, L.; Finsy, R. Langmuir 1999, 15, 6745. (17) Hoang, T. K. N.; La, V. B.; Deriemaeker, L.; Finsy, R. Phys. Chem. Chem. Phys. 2004, 6, 1413.
Chemicals, 99%) was used to increase the background electrolyte strength. Ultrapure Milli-Q water (Millipore) was used for all samples and solutions. Emulsion Preparation and Measurement. Emulsions were prepared at a concentration of 5 vol % in aqueous solutions of SDS (3.0-70.0 mM) and NaCl (1.0 mM), except in one case where 0.10 M NaCl was used. The emulsions were formed at 25 °C by passages through a homogenizer (Milko-tester Mark III F3140, A/S N. Foss Electric, Denmark) up to 15 times. The emulsions were circulated slowly through a prototype of the AcoustoSizer II cell (Colloidal Dynamics, Warwick, RI) with a peristaltic pump at a rate of approximately 25 mL min-1. The electroacoustic cell had been calibrated with the standard R-dodecatungstosilicate salt solution and was recalibrated whenever the cell was opened, because the attenuation calibration depends on the cell spacing. Electroacoustic and attenuation measurements were made on the emulsions after homogenization followed by gentle sonication to remove entrapped air bubbles. The dynamic mobility and ultrasonic attenuation of the emulsions were measured at 25 °C over several hours. The samples were then stored at room temperature (22-25 °C) in sealed glass jars with gentle stirring with a magnetic stirrer and the dynamic mobility and attenuation signals were measured again the next day. The electroacoustic signal of emulsions depends significantly on the charge and size of the oil droplets. When the size varies with time, the mobility and acoustic attenuation will change accordingly. The electroacoustics software enables both the size and ζ potential to be determined unambiguously. The electroacoustic signal arises from the sound wave, or electrokinetic sonic amplitude (ESA), generated by charged particles in an applied alternating electric field; this is then related to the dynamic mobility of the droplets. The particle size distribution (as a log-normal distribution) and ζ potential can then be fitted to the theoretical mobility of spherical particles with thin double layers.18 The acoustic attenuation of emulsions was also measured between 1 and 20 MHz with the same apparatus. The measured attenuation is fitted to the ultrasonic scattering theory with the AcoustoSizer software with the known thermal and physical constants of the dispersed and continuous phases as given in Table 1. The sizing of emulsion droplets depends on both thermal conduction and scattering losses.19 Light backscattering (Malvern HPPS) measurements on the undiluted emulsions were also made to follow the growth of the drops with time. The intensity weighted average diameter can be converted to a number average value by dividing by (1.18)3,3 but the rates quoted in this paper are based on the intensity weighted average diameter from light backscattering or the volume weighted average diameter measured by the acoustic methods.
Results The ultrasonic attenuations between 1 and 20 MHz of 5 vol % decane-in-water emulsions prepared either below the critical micelle concentration (cmc) in 5 mM SDS or above the cmc in 30 mM SDS change significantly over several hours (Figures 1 and 2). These data can be analyzed with the known physical properties of the alkane (Table 1) to give the mean droplet size at each measurement time. (18) O’Brien, R. W.; Cannon, D. W.; Rowlands, W. N. J. Colloid Interface Sci. 1995, 173, 406. (19) McClements, D. J. Langmuir 1996, 12, 3454.
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Figure 3. Cube of the droplet radius (a3) versus time over 7 h for 5 vol % decane emulsified in 30 mM SDS: (9) Attenuation, (d50/2)3; (b) HPPS (aI3). Linear fit to attenuation data is shown. Figure 1. Change over 1 day of the ultrasonic attenuation with frequency for a 5 vol % decane emulsion stabilized with 5 mM SDS.
Figure 2. Change over 1 day of the ultrasonic attenuation with frequency for a 5 vol % decane emulsion stabilized with 30 mM SDS. Table 2. Average Drop Size and Distribution from Ultrasonic Attenuation for a 5 vol % Decane Emulsion Stabilized with 30 mM SDS time(s) 757 1819 3064 5129 7400 9060 10722 12386 14055 15720 17380 19044 20706 22370 24040 87000
d50 (µm)
d15 (µm)
d85 (µm)
0.207 0.221 0.232 0.249 0.265 0.276 0.286 0.296 0.307 0.317 0.327 0.336 0.346 0.355 0.363 0.644
0.171 0.186 0.199 0.214 0.221 0.226 0.232 0.234 0.238 0.241 0.243 0.245 0.249 0.251 0.253 0.361
0.25 0.261 0.271 0.29 0.319 0.337 0.354 0.375 0.395 0.417 0.441 0.462 0.481 0.501 0.521 1.15
The average size of the droplets behaves as expected, with the droplet volume increasing as a linear function of time due to Ostwald ripening (Table 2 and Figure 3). For the decane emulsion stabilized with 30 mM SDS the average droplet diameter almost doubles from 0.2 to 0.4 µm over 7 h (2.5 × 104 s), at a rate of
Figure 4. Initial Ostwald ripening rates of 5% decane emulsions as a function of free SDS concentration (SDS/1 mM NaCl) calculated as described in Table 4. The line is a guide to the eye.
2.1 × 10-25 m3 s-1 (Figure 3) with good agreement between the droplet sizes measured by acoustic attenuation and light backscattering. This rate, however, is about 5 times faster than that calculated from the LSW theory based on the solubility of decane in water. After 1 day the size has increased to 0.6 µm. Below the cmc the Ostwald ripening rate decreased from 3.3 × 10-25 to 1.11 × 10-25 m3 s-1 as the total SDS concentration was increased from 3.0 to 10 mM (Figure 4). This is expected due to the decrease in the interfacial tension, γ, between the oil and surfactant solution, as predicted by eq 3.11 Above the cmc the Ostwald ripening rate was found to increase, however, despite the interfacial tension remaining constant. There is a suggestion of upward curvature in Figure 3. This effect becomes clearly evident when the emulsion is prepared in 60 mM instead of 30 mM SDS (Figure 5). The rate of growth is initially somewhat faster than in 30 mM SDS, and there is a definite further increase in the rate after the droplets have grown to more than 0.3 µ in diameter. This can be seen more clearly from a log-log plot (Figure 5 inset). This curve is clearly nonlinear, and the rate is seen to increase with time. At even higher SDS concentrations the rate of Ostwald ripening increases further (Figure 4), where the initial rates of ripening are shown. Although this increased rate of droplet growth could be a consequence of enhanced oil solubility due to the micelles, we attribute it to the onset of depletion flocculation of the decane
7714 Langmuir, Vol. 24, No. 15, 2008
Figure 5. Cube of the droplet radius (from attenuation (d50/2)3) versus time over 5 1/2 h (2 × 104 s) for a 5 vol % decane emulsion emulsified in 60 mM SDS. The inset shows the log-log plot for the same system.
droplets by SDS micelles after the droplets have grown to a certain critical size. A depletion force leading to flocculation of larger particles by nonadsorbing smaller ones occurs because the center of mass of the smaller particles is excluded from a zone or shell of volume around the larger particles equal to the radius of the smaller particles. If these depletion zones overlap through flocculation the total volume of the excluded zone decreases and the smaller particles enjoy a larger volume of solvent in the dispersion. The depletion force can be effected by polymers (for a review see Jenkins and Snowden),22 by micelles,23 and even by colloidal particles of different sizes.24,25 Our assertion that depletion flocculation is the cause of the enhanced Ostwald ripening rates is based on the following evidence. The argument (phase lag) of the dynamic mobility of the emulsion after 2 × 104 s (5.5 h) is shown in Figure 6, measured while the emulsion is being slowly pumped through the AcoustoSizer measuring cell, then when the flow is stopped, and again after the flow is resumed. After stopping the flow the spectrum alters to one characteristic of a floc, with a large decrease in phase lag at higher frequencies.25 After pumping vigorously to disrupt the floc (at approximately 200 mL min-1), a measurement with moderate pumping showed that the phase lag is increased again, but not to its original value, indicating that the flocculation is not completely reversible. This interpretation is corroborated by observing the effect of pumping on the ultrasonic attenuation of the day-old emulsion (Figure 7). The quiescent emulsion shows a minimum in the attenuation around 5 MHz, which disappears when the emulsion is pumped vigorously and then remeasured with moderate pumping, but reappears when the floc spontaneously re-forms. McClements et al. have shown that when an emulsion is flocculated, the attenuation coefficient decreases at low-megahertz frequencies due to overlap of the thermal waves generated by the flocs but increases at higher frequencies due to an increase in scattering by the flocs.26–28 Qualitatively this describes the attenuation signal of our flocculated emulsions (Figure 7). (20) Weast, R. C., Ed. Handbook of Chemistry and Physics, 55th ed.;CRC: Cleveland, OH, 1974. (21) Anson, L. W.; Chivers, R. C. Ultrasonics 1990, 28, 16. (22) Jenkins, P.; Snowden, M. J. AdV. Colloid Interface Sci. 1996, 68, 57. (23) Bibette, J.; Roux, D.; Nallet, F. Phys. ReV. Lett. 1990, 65, 2470. (24) Vliegenthart, G. A.; Van Blaaderen, A.; Lekkerkerker, H. N. W. Faraday Discuss. 1999, 112, 172. (25) Djerdjev, A. M.; Hunter, R. J.; Beattie, J. K. Langmuir 2006, 22, 84.
DjerdjeV and Beattie
Figure 6. Argument versus frequency for the 5 vol % decane emulsion in SDS (60 mM) after 5 1/2 h (2 × 104 s): (9) pumped; (b, 2, 1) stopped; ([) pumped again.
Figure 7. Attenuation coefficient versus frequency for a flocculated 5 vol % decane emulsion in 60 mM SDS after 1 day.
Figure 8. Droplet size distributions obtained by light scattering of a 5 vol % decane emulsion in 60 mM SDS after 51/2 h and then highly diluted in water.
The evidence for flocculation is also consistent with light scattering observations (Figure 8). Initial measurements indicate a monomodal distribution, but after 51/2 h the 5 vol % emulsion in 60 mM SDS shows a bimodal distribution of droplet sizes, with some large sizes of 3-5 µm indicative of flocs. When this emulsion is highly diluted in water, these large particles disappear,
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Table 3. Drop Size and Distribution at the Onset of Flocculation for Different SDS Micelle Volume Fractions, Om [SDS]tot. (M)
[NaCl] (M)
φm
exp-floc d15-d50-d85 (nm)
0.03 0.05 0.06 0.07 0.07
0.001 0.001 0.001 0.001 0.10
0.0050 0.013 0.015 0.018 0.018
361-644-1149 260-420-710 223-339-514 182-281-435 >700 nm
and the distribution narrows, consistent with the view that the flocs are the result of depletion forces that no longer exist in the diluted emulsion. To test further the existence of depletion flocculation in the decane emulsion system, the effect of the SDS micelle concentration on the onset of observable flocculation was examined. The onset of flocculation was estimated from the change in the slope of the ripening rates versus time from the ultrasonic attenuation as well as from the swing in the arguments to more positive values from the dynamic mobility. As the micelle concentration increases above the cmc, the depletion force acts on smaller and smaller drops. Figure 9 and Table 3 show that the size of the drops undergoing flocculation clearly decreases with increasing micelle concentration. Another feature of depletion flocculation in ionic systems is that as the electrolyte concentration increases, the excluded volume around charged drops decreases due to compression of the double layer. This reduces the overall depletion force for the same micelle concentration. This effect was observed in the 70 mM SDS system, which does not undergo depletion flocculation in the presence of 0.1 M NaCl over the same time period when flocculation occurs in 1 mM NaCl (Table 3). The behavior of octane emulsions is more complex. The rates of Ostwald ripening are greater than those of the decane emulsions, due to the greater solubility of octane in water (Figure 10). As with the decane emulsions, below the cmc an increase in SDS concentration leads to a decrease in the ripening rate, and above the cmc the rate of ripening is again significantly increased by the presence of SDS micelles. The low-frequency attenuation data, however, are not well-described by a single particle size distribution but are better fit with a bimodal size distribution, illustrated in Figure 11a (top),b (bottom) for the emulsion prepared with 5 mM SDS, i.e., in the absence of micelles. There is a small population (∼15%) of droplets of less than 200 nm diameter, which slowly grows in average diameter and decreases in weight fraction, W1, while the major component of larger droplets grows in diameter from ∼0.5 to 0.7 µm. The volume of the growth of the larger droplets is too great to be fed solely by the smaller ones but must be mainly at the expense of the smaller among the larger population. In Table 4 the experimental Ostwald ripening rates for the octane and decane emulsions studied are compared with those calculated from the concentration-modified LSW theory, eq 3. The experimental Ostwald ripening rates below the cmc are only up to 2 times faster for both oils but above the cmc up to 22 times faster, which we ascribe to depletion forces. The initial ripening rates are 8 times faster in the presence of 0.1 M salt, where depletion forces would be much smaller. (26) Chanamai, R.; Herrmann, N.; McClements, D. J. J. Colloid Interface Sci. 1998, 204, 268. (27) McClements, D. J.; Herrmann, N.; Hemar, Y. J. Phys. D: Appl. Phys. 1998, 31, 2950. (28) Chanamai, R.; Herrmann, N.; McClements, D. J. J. Phys. D: Appl. Phys. 1998, 31, 2956. (29) Rehfeld, S. J. J. Phys. Chem. 1967, 71, 738. (30) Staples, E.; Penfold, J.; Tucker, I. J. Phys. Chem. B 2000, 104, 606. (31) Hayduk, W.; Laudie, H. AIChE J. 1974, 20, 611.
Figure 9. Experimental droplet size and spread of decane emulsions at the onset of flocculation as a function of free SDS concentration, compared to the theoretical drop size.23
Figure 10. Cube of the droplet radius (attenuation) versus time for a 5 vol % octane emulsion stabilized with SDS (9, 5; b, 10; or 2, 30 mM) over the course of 3-4 h, analyzed with a monomodal size distribution.
To explore further these enhancements in the ripening rates, we prepared decane emulsions in 5 and 30 mM SDS of varying polydispersity by altering the number of passes through the homogenizer. Above the cmc emulsion formation is more efficient than below the cmc, so fewer passes were required (Table 5). In Figure 12, the Ostwald ripening rate from ultrasonic attenuation sizing is plotted as a function of the geometric standard deviation, d85/d50, which is a measure of the polydispersity. For highly monodisperse emulsions, this ratio would be 1.0 and ω would approach zero. (Ostwald ripening requires polydispersity.) The results show a clear linear relationship between the ripening rate and the polydispersity which approaches zero as the system becomes more monodisperse. The ripening rate increases with increasing sample polydispersity for samples both below the cmc (5 mM SDS) and above the cmc (30 mM).
Discussion The significant advances made in the present work arose from the observation of the electroacoustic dynamic mobility spectrum of a quiescent emulsion that was characteristic of a floc. While there is at present no theoretical model to enable quantitative analysis of these dynamic mobility spectra, the qualitative features have been observed in several different systems known to
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Table 4. Ostwald Ripening Rates from Ultrasonic Attenuation of 5 vol % Octane and Decane Emulsionsa oil octane decane
[SDS] (M) 0.005 0.010 0.030 0.003 0.005 0.010 0.030 0.050 0.060 0.070 0.070 c
γ (N m-1)
ωtheor (m3 s-1)
ωexptl (m3 s-1)
ωf ) ωexptl/ωtheor
0.0254 0.0141 0.0080 0.0348 0.0286 0.0179 0.0086 0.0086 0.0086 flocb 0.0086 0.0046 d
1.65 × 9.10 × 10-25 5.17 × 10-25 1.72 × 10-25 1.42 × 10-25 8.86 × 10-26 4.26 × 10-26 4.26 × 10-26 4.26 × 10-26 4.26 × 10-26 2.28 × 10-26
2.13 × 1.60 × 10-24 1.14 × 10-23 3.28 × 10-25 1.94 × 10-25 1.11 × 10-25 2.06 × 10-25 2.80 × 10-25 2.92 × 10-25 1.4 × 10-24 4.50 × 10-25 1.79 × 10-25
1.3 1.8 22 1.9 1.4 1.3 4.8 6.6 6.9 33 11 7.9
10-24
10-24
a Interfacial tension, γ, estimated from ref 29: γ (mN m-1) ) z0 + z1 ln(C) + z2(ln(C))2, where C is the molar surfactant concentration based on free SDS, calculated from the surface area of the emulsion and the amount adsorbed.30 For octane z0 ) -114.8, z1 ) -34.1, and z2 ) -1.7, and Vm ) 1.63 × 10-4 m3 mol-1. For decane z0 ) -108.6, z1 ) -32.5, z2 ) -1.65, and Vm ) 1.94 × 10-4 m3 mol-1. Diffusivity, Dm, was calculated from ref:31 Dm (10-5 cm2 s-1) ) 13.26 × 10-5η-1.14Vm-0.589. Here η is the viscosity of the aqueous phase ) 1.1 cP and Vm is in units of cm3 mol-1. For octane Dm ) 7.8 × 10-10 m2 s-1; for decane Dm ) 6.8 × 10-10 m2 s-1. The volume fraction solubility C∞ of octane is 9.45 × 10-7; of decane, 6.98 × 10-8. b Measured after 2 × 104 s. c In 0.1 M NaCl. d From ref 32.
Figure 11. Time dependence of the acoustic attenuation for a 5 vol % octane emulsion stabilized with SDS (5 mM). Top panel: fitted with a monomodal distribution. Bottom panel: fitted with a bimodal distribution described in the insert.
megahertz frequencies due to overlap of the thermal waves generated by the flocs but increases at higher frequencies due to an increase in scattering of the flocs. Qualitatively this describes the attenuation signal of our flocculated emulsions. McClements et al. did not observe this in their Ostwald ripening studies because the emulsions in that work were continuously stirred to avoid creaming. The third piece of evidence consistent with this interpretation is our observation by light scattering that a population of larger particles, presumably a floc, disappeared when the emulsion was diluted in water, eliminating the depletion force. Finally, the formation of a floc and the further enhancement of the rate of ripening occurs when the drops have grown to the expected size. It is well-known that SDS micelles can induce depletion flocculation of SDS-stabilized emulsions, which depends on the micelle concentration, φm, and the size of the emulsion droplets (diameter, d). This effect has been used to fractionate emulsions into monodisperse populations.34 Assuming a micelle radius, rm ()dm/2), of 2 nm and an aggregation number of 80, the micelle volume fraction is given by φm ) 0.252(C), where C is the molar concentration of SDS above the cmc value of ∼8.0 mM. From the phase diagram studies by Bibette et al.23,35 the relationship between micelle volume fraction and oil volume fraction, φ, has the form φm ) A(- ln φ + B), where A ) (d/dm) and B are constants. From this relationship it is predicted that for the decane emulsion in 60 mM SDS depletion flocculation will occur when the drops have grown to about 500 nm in diameter. In Figure 9, the drop size is more like 340 nm in diameter when depletion forces enhance the Ostwald ripening rate. This discrepancy can be explained by the fact that the Bibette emulsions are monodisperse (formed by fractionation) and the drop size at which flocculation begins will occur at a fixed surfactant concentration and will act on all drops simultaneously. Our samples, however, have some degree of polydispersity. The attractive depletion interaction induced by free micelles is35
VD )
[
-4π 3r r3 (a + δ)3Pos 1 + 3 4(a + δ) 16(a + δ)3
]
flocculate.25,33 Moreover, the signal is almost reversible with stirring, consistent with a loose aggregate. The occurrence of depletion flocculation was corroborated by measurements of the ultrasonic attenuation of quiescent emulsions. McClements et al. have shown how the ultrasonic attenuation signal of an emulsion changes as it is flocculated by micelles.26,27 The attenuation coefficient decreases at low-
where δ is the exclusion length which can be assumed to be the micelle radius, Pos ()3φmkT/4πrm3) is the micellar osmotic pressure, a is the drop radius, and r is the center-to-center sphere separation. Examination of this equation reveals that the depletion force depends solely on the micelle characteristics such as
(32) Cockbain, E. G. Trans. Faraday Soc. 1974, 50, 874. (33) Beattie, J. K.; Hunter, R. J.; Zhang, H. Colloids Surf., A 2006, 275, 83.
(34) Bibette, J. J. Colloid Interface Sci. 1991, 147, 474. (35) Bibette, J.; Leal-Calderon, F.; Poulin, P. Rep. Prog. Phys. 1999, 62, 969.
(4)
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Table 5. Experimental and Theoretical Ripening Rates of Decane Emulsions with Different Polydispersity Prepared with 1 mM NaCl oil
[SDS] (M)
decane
0.005
decane
0.03
no. of passes 2 3 5 15 1 2 3 15
d50 (nm) 372 328 297 253 388 299 277 207
d85 (nm) 559 450 393 280 643 435 375 250
concentration and micelle size, and on the drop size, with no dependence on the dispersed phase concentration. The depletion force for flocculation is greater for larger drops. Figure 9 shows good agreement between the calculated onset of depletion and the size of the larger droplets in the polydisperse sample, measured as d85. The choice of d85 is arbitrary but such that there is a sufficiently large number of drops for flocculation to be detected experimentally. The lowering of the overall ripening rate in 70 mM SDS from 4.5 × 10-25 (1 mM NaCl) to 1.79 × 10-25 m3 s-1 in the presence of salt (0.1 M NaCl) is consistent with the lowering of the interfacial tension from 0.0086 to 0.0046 N m-1.32 However, the enhancement of the rate in the presence of 0.1 M NaCl is still ∼8 times faster than the theoretical rate despite there being no significant depletion forces acting for this system. The enhancement in this case is explained by the relatively high polydispersity (d85/d50 ) 1.4) for this sample. Polydispersity is shown to affect the Ostwald ripening rate of all samples regardless of whether they are below or above the cmc. Recognition of a role for depletion flocculation as well as polydispersity in Ostwald ripening provides an explanation for a number of earlier observations and could account for the inconsistencies in the literature about the effect of SDS micelles on Ostwald ripening. Depletion flocculation is very sensitive to the ratio of the size of the emulsion droplet to that of the micelle. de Smet et al. found that the presence of dodecylbenzenesulfonate micelles increased the rate of ripening of 1 vol % undecane emulsion drops only by a factor of 1.5-2.1.16 The absence of a significant effect of micelles in this case is because they worked with very small drops of 70-200 nm diameter, too small for the depletion force to be effective. Similarly, Hoang et al.15 saw no
Figure 12. Ostwald ripening rate of decane emulsions in 5 and 30 mM SDS solutions as a function of d85/d50.
d85/d50 1.50 1.37 1.32 1.11 1.66 1.45 1.35 1.21
ωtheor (m3 s-1) [eq 3] 1.42 ×
10-25
4.26 × 10-26
ωexptl (m3 s-1)
ωf ) ωexptl/ωtheor
7.17 × 4.81 × 10-25 4.04 × 10-25 1.94 × 10-25 7.36 × 10-25 4.85 × 10-25 3.78 × 10-25 2.06 × 10-25
5.0 3.4 2.8 1.4 18 12 9.0 4.9
10-25
effects of micelles on ripening of undecane emulsions with diameters less than 100 nm and Kabalnov14 found only a slight enhancement of ripening of undecane emulsions as they grew from 100 to 200 nm. In contrast, those studies cited in the Introduction that found an effect of SDS micelles on the ripening rate all began with droplet diameters of at least 200 nm. Differences among these reports could arise because different experimentalists would have prepared emulsions with different sizes and size distributions with different techniques and apparatus. In addition, we have also shown recently that even in the absence of micelles a polydisperse emulsion of SDSstabilized droplets can undergo self-depletion flocculation.25 The history of each sample would be important, as to whether and how vigorously it had been stirred while ripening. Finally, we have shown that the Ostwald ripening rate depends critically on the extent of polydispersity, being larger the more polydisperse the sample. This effect occurs both below and above the cmc. Hence comparison among the various reports cannot be expected to present any quantitative consistency as the Ostwald ripening rate is polydispersity-dependent. McClements and co-workers have previously shown that ultrasonic attenuation is a convenient and sensitive method of observing Ostwald ripening of concentrated oil-in-water emulsions.11 Our results are in qualitative agreement with theirs. We made measurements over a shorter period than they and so did not see any emerging difference between the growing size measured by attenuation and that obtained from light scattering, although our light scattering measurements were made on undiluted emulsions by backscattering, whereas theirs were made on diluted samples. If we plot the primary data shown in their Figures 2 and 4 for the ripening of a 5 wt % decane emulsion in 20 mM SDS over ∼730 h, we obtain a rate of (4-5) × 10-25 m3 s-1, in fair agreement with our value of 2.1 × 10-25 m3 s-1 in 30 mM SDS, but not with the rate of 6.1 × 10-24 m3 s-1 reported in their Table 2. In conclusion, the role of depletion flocculation above the cmc of the surfactant during Ostwald ripening is important in emulsions where the drop size increases to a size where depletion forces become important. The Ostwald ripening rate is enhanced above the cmc due to depletion flocculation and increased polydispersity. This provides an alterative explanation for the role of micelles. The micelle mediated mechanism of oil transport should also apply to small droplets but is not observed in those cases. The Ostwald ripening rates below the cmc were in general about 1.3-2 times faster than that calculated from the LSW theory and are presumably enhanced by the polydispersity of the samples. Acknowledgment. We thank Professor Bob Hunter for enlightening discussions and Colloidal Dynamics Inc. for the use of the AcoustoSizer. The work was supported by the Australian Research Council. LA800140S
