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Langmuir 2004, 20, 8966-8969
Articles Monitoring the Simultaneous Ostwald Ripening and Solubilization of Emulsions Thi Kieu Nguyen Hoang,† Luc Deriemaeker,† Van Binh La,‡ 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 March 30, 2004. In Final Form: August 2, 2004 The simultaneous Ostwald ripening of an emulsion and the solubilization of its oil droplets by added micellar surfactant solutions are monitored by measurements of time-averaged scattered intensities. A simple computer simulation model for the interpretation of the measurements is presented. Experimental data are analyzed with this model using one single parameter: an effective ratio of oil to surfactant molecules involved in the withdrawal of oil from the Ostwald ripening process by the added micelles. The fitted value of this parameter appears to be more than twice the one that can be predicted from the equilibrium solubilization of oil by the surfactant micelles, indicating that more oil is involved in the nonequilibrium exchange of oil and surfactant between micelles and droplets.
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 as a result of the higher solubility of the smaller particles (Gibbs-Thomson or Kelvin effect) and of 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 and Dm is the dispersed phase molecular diffusion coefficient, C(∞) is the dispersed phase bulk solubility, and R * To whom correspondence should be sent. Telephone: +32 2 629 3485. Fax: +32 2 629 3320. E-mail:
[email protected]. † 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. Electrochemistry 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.
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. Ostwald ripening is often monitored by measurements of the average droplet size with time.6-22 From the experimental measurements of the ripening rate, one of the factors of the right-hand side of eq 1 can be determined. Most emulsions are protected against other aging factors such as coagulation and coalescence by surfactants. If (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) Hoang, T. K. N.; La, V. B.; Deriemaeker, L.; Finsy, R. Langmuir 2003, 19, 6019. (21) De Smet, Y.; Deriemaeker, L.; Parloo, E.; Finsy, R. Langmuir 1999, 15, 2327. (22) De Smet, Y.; Danino, D.; Deriemaeker, L.; Talmon, Y.; Finsy, R. Langmuir 2000, 16, 961.
10.1021/la049184b CCC: $27.50 © 2004 American Chemical Society Published on Web 09/04/2004
Ostwald Ripening and Solubilization of Emulsions
Langmuir, Vol. 20, No. 21, 2004 8967
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. This effect can even be enhanced dramatically by adding micellar surfactant solutions to ripening emulsions. If enough surfactant is added, a competition can occur between droplet size increase by Ostwald ripening on one hand and droplet size decrease by solubilization of the oil in the added micelles on the other hand. In this contribution, the monitoring of this competition by time-averaged light scattering is reported. The experimental results are analyzed with a simple simulation model of Ostwald ripening and solubilization.
lose according to eq 3, the number M is replaced with Mj ) nN,j /PN,j, particle “N” is discarded from the set, and the number particles becomes N - 1. At each step of the simulation the size distribution and the number-average particle radius are computed. Assuming that time is proportional to the number of exchanged molecules, k
tk ∼
3. Simulation of the Coarsening Process 3.1. Simulation Method. In this study, a simple game simulating the coarsening and solubilization of a polydisperse set of N spherical particles on a common personal computer is used.23 The main simulation steps are the following: (1) An initial set of N particles with radii ai (i ) 1, ..., N) is generated according to an a priori model for the particle size distribution (PSD). Each particle “i” is filled up with ni,0 molecules with fixed molecular volume. (2) The exchange of molecules between particles is carried out according to growth rules. In each step “j” of the simulation, the number of molecules ni,j in particle “i” is given by
ni,j ) ni,j-1 + MPi,j-1(ai,j-1)
(3)
In eq 3, M is proportional to the total number of exchanged molecules and Pi,j embodies the growth law. A particle will grow if Pi,j is positive and will shrink if Pi,j is negative. The mass balance requires that at each step
∑i Pi,j ) 0
(4)
(3) The simulation starts with a set of 5000 particles. During the simulation process, when the smallest particle (“i” ) N) contains less molecules than the number it should (23) De Smet, Y.; Deriemaeker, L.; Finsy, R. Langmuir 1997, 13, 6884.
(5)
the dimensionless time can be expressed as k
Tk )
2. Experimental Section Several emulsions of alkanes in water stabilized by the surfactant hexaoxyethylene glycol dodecyl ether (C12E6; Nikkol, purity >98%) were prepared. The alkanes used were decane, undecane, and dodecane (Aldrich, purity 99+%). Decane, undecane, and dodecane emulsions with an oil volume fraction of 0.05 and C12E6 surfactant concentrations of 2.5 × 10-3 M were prepared as follows. 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 during 10 min using an Y-110 microfluidizer. To 2 mL of the emulsions is added an aqueous micellar surfactant solution with a concentration of 5.0 × 10-3 M at different constant rates. The scattered light intensities were recorded. The experimental setup consists of an Ar+ laser (wavelength λ ) 488 nm), a thermostated sample holder allowing the temperature to be controlled within 0.1 °C, and a photomultiplier (EMI 9863A) mounted at a detection angle of 90°. The signal of the photomultiplier was fed to a Brookhaven BI9000 correlator, yielding the time-averaged scattered intensities among other data.
∑i Mj ∑i Mj
(6)
3.2. Applications to Ostwald Ripening and Solubilization. 3.2.1. Ostwald Ripening. Ostwald ripening is the coarsening process whereby the particle sizes mainly change by solubilization and condensation of molecules. This process is driven by Kelvin’s equation:
C(a) ) C(∞) exp(R/a)
(7)
where C(a) is the solubility of a particle with radius a and C(∞) is the bulk solubility; the capillary length R is a material-dependent parameter. According to this equation, the large particles (or, for emulsions, droplets) will grow by condensation of material diffusing on the molecular level through the continuous phase, coming from smaller particles, which solubilize more than the larger ones. A theoretical description of Ostwald ripening in two-phase systems was given by Lifshitz and Slyozov and by Wagner.2-5 The main results are as follows: (1) There exists a critical radius ac. Droplets with a larger radius grow; smaller droplets shrink. If the radius equal ac, the size of the droplet does not change. (2) In the long time limit a stationary regime is reached for which the Ostwald ripening rate v given by eq 1 is constant and the PSD (LSW-PSD) given by
81eµ2 exp[1/(2µ/3 - 1)]
W(a/ac) ) W(µ) )
3
ac3x32(µ + 3)7/3(1.5 - µ)11/3 (0 e µ e 1.5) (8) W(µ) ) 0 (µ > 1.5)
is self-similar when scaled to the critical radius. To apply the simulation game to Ostwald ripening of emulsions, the main simulation steps are carried out as follows. (1) An initial set of droplets with radius ai (i ) 1, ..., N) is defined by an initially log-normal distribution
W(a) )
1
x2πσ
[
exp -
]
[ln(a) - 〈ln(a)〉]2 2σ2
(9)
In eq 9, σ is a parameter related to the broadness of the PSD. An initially log-normal distribution is used instead of LSW-PSD because a log-normal PSD is more realistic for the size distribution of freshly prepared emulsions.22 (2) The growth law corresponding to Ostwald ripening is derived with the aid of Fick’s first law and Kelvin’s
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Hoang et al.
equation (assuming R , a) yielding
(
dn a ) 4πDmC(∞)R -1 dt ac
)
(10)
In eq 10, ac is the critical radius of a particle. Our simulations are carried out with the following growth law
Pi,j )
ai,j -1 ac,j
(11)
(3) From the mass transfer balance of the dispersed phase, the critical radius ac,j can be calculated yielding24
Figure 1. Comparison of the evolution of intensity between simulations (lines) and experiments (dots) at different addition rates: 0.5, 1, and 2 mL/h (top to bottom). Decane emulsions.
N
ac,j )
ai,j /N ≡ aN ∑ i)1
(12)
3.2.2. Ostwald Ripening of Already Formed Emulsions to which an Aqueous Surfactant Solution Is Added Continuously. The effect of the addition of micellar surfactant solution is that micelles can solubilize oil and, hence, withdraw oil from the Ostwald ripening process. When adding a surfactant solution with molar concentration C at an addition rate r (added volume per unit time), the number of oil molecules Ns withdrawn per unit time from the Ostwald ripening process is given by
Ns ) NA(No/Nm)rC
(13)
Figure 2. Comparison of the evolution of intensity between simulations (lines) and experiments (dots) at different addition rates: 0.25, 0.5, 1, 2, and 3 mL/h (top to bottom). Undecane emulsions. For clarity the different series have been translated along the ordinate by 40 kcounts s-1.
where No is the effective number of oil molecules withdrawn by a micelle with Nm surfactant molecules; NA is Avogadro’s number. Because oil is removed, the mass balance requires now that at each time step j
dni,j
∑i dt
) -Ns
(14)
where dni,j /dt is the change in the number of oil molecules in drop i at time step j. Inserting eq 10 in eq 14 yields the following solution for the critical radius at time tj N
ai,j ∑ i)1
K ac,j )
KN - Ns
(15)
where K ) 4πDmRC(∞). The simulation is run with the growth law defined by eq 11. 3.3. Computation of the Scattered Intensities. Each PSD generated by the previous method is discretized as a set of N particles with different radii (ai; i ) 1, ..., N). For a droplet with given radius ai, the scattering power Si (ai, m, λ, θ) is calculated with the aid of the Mie scattering coefficients for homogeneous spheres,25 using the actual values of the relative refractive index m (respectively 1.0609, 1.0647, and 1.0684 for decane, undecane, and dodecane in water), the wavelength λ0 ) 488 nm of the light, and the scattering angle θ ) 90°. The scattered intensity Ij corresponding to the distribution at time (24) Finsy, R. Langmuir 2004, 20, 2975. (25) Bohren, C. F.; Huffman, D. R. Adsorption and Scattering of Light by Small Particles; John Wiley and Sons: New York, 1983; p 89.
Figure 3. Comparison of the evolution of intensity between simulations (lines) and experiments (dots) at different addition rates: 0.25, 0.5, 1, and 2 mL/h (top to bottom). Dodecane emulsions.
step j is computed in arbitrary units as N
Ij )
Si (ai,j) ∑ i)1
(16)
Because the scattering power of the much smaller micelles containing the solubilized oil is many orders of magnitude smaller than that of the dispersed oil droplets, the contribution of the micelles to the scattered intensity is neglected. Finally, the effect of dilution by adding the surfactant solution is taken into account. 4. Results and Discussion In Figures 1-3, the experimental measurements of scattered intensities as a function of time I(t) are reported. These results are for decane, undecane, and dodecane emulsions stabilized by C12E6 to which extra surfactant is added continuously at different rates. At low addition
Ostwald Ripening and Solubilization of Emulsions Table 1. Parameter Values Used in the Simulation
decane undecane dodecane
C(∞) (mL/mL) × 10-8
Dm (cm2 s-1) × 10-6
Vm (cm3 mol-1)
7.1 2.0 0.52
4.50 4.31 4.10
194.9 211.2 227.4
rates, the intensity initially increases with time due to the ripening (increase in size) of the oil droplets. At longer times and at all times for the higher addition rates, the intensities decrease due to the solubilization of the oil molecules by the added micelles. Because the scattering power of the micelles (swollen by oil) is several orders of magnitude smaller than that of the dispersed oil droplets, the oil solubilized in the micelles does not contribute significantly to the observed scattered intensity. In all experiments, a total amount of about 0.2-0.3 mL of surfactant solution is added so that the final surfactant concentration (2.7-2.8 × 10-3 M) is only slightly higher than the initial concentration (2.5 × 10-3 M). The difference in behavior between the alkanes is that for the more soluble ones the observed intensities drop down after shorter times. The experimental data were fitted by simulations with eqs 15 and 11 for the critical radius and the growth law. In these simulations, the ratio No/Nm is used as the only fitting parameter. The fixed parameter values used in the simulations are the following: T ) 298 K; γ ) 3.5 mN m-1; and the other fixed parameter values are reported in Table 1. During the addition of extra surfactant, the equilibrium distribution of oil and surfactant is disturbed and during the evolution to a new equilibrium situation oil is “dragged” by surfactant. Obviously the oil molecules are not solubilized on the molecular level in the continuous aqueous phase already saturated by oil. Neither can they be transferred to relatively large structures in which case the decrease in intensity cannot be explained. Hence, oil and added surfactant must be present in some small, comparable to the size of micelles, transient structures consisting of aggregates of oil and surfactant molecules in the ratio No/Nm. The values of this ratio in the
Langmuir, Vol. 20, No. 21, 2004 8969 Table 2. Ratio No/Nm Estimated from Simulations for Emulsions to which Surfactant Solution Is Added Continuously with Different Rates and from the Equilibrium Solubilities decane
undecane
dodecane
0.25 0.50 1.00 2.00 3.00
addition rate (mL/h)
4.2 3.8 4.0
2.9 2.8 2.8 2.8 2.8
1.7 1.7 1.7 1.7
from equilibrium solubility
1.5
1.3
0.7
nonequilibrium situation are obtained by fitting. The values given in Table 2 are, for a given alkane, almost constant at different addition rates. On the other hand, the ratio No/Nm can also be estimated from the equilibrium solubilities of the alkanes in a 2.5 × 10-3 M surfactant solution.20 These values are also reported in Table 2. Clearly the values obtained from the simulations show the same trend as the equilibrium values. However, these ratios are more than twice the values predicted from the equilibrium solubilities. Clearly, in the nonequilibrium exchange of oil and surfactant between micelles and droplets more oil is involved than predicted by the equilibrium solubility of oil in surfactant micelles. 5. Conclusion The simultaneous (Ostwald) ripening and the solubilization of oil droplets can be monitored by measurements of the time-averaged scattering intensities. The interpretation is performed on the hand of a simple simulation model with one single fitting parameter: the effective number of oil molecules dragged by a surfactant molecule. These numbers appear to be more than twice the ones predicted by the equilibrium solubilization of oil in the surfactant micelles, indicating that more oil is involved in the nonequilibrium exchange of oil and surfactant between micelles and droplets. LA049184B
