Langmuir 2005, 21, 12047-12052
12047
Steric Repulsion between Internal Aqueous Droplets and the External Aqueous Phase in Double Emulsions Jing Cheng,† Shiai Xu,‡ Lixiong Wen,*,† and Jianfeng Chen*,† Key Lab for Nanomaterials, Ministry of Education, Research Center of the Ministry of Education for High Gravity Engineering & Technology, Beijing University of Chemical Technology, Beijing 100029, China, and Chemical Engineering Department, Yantai University, Yantai 264005, China Received July 13, 2005. In Final Form: October 5, 2005 A theoretical model for analyzing the steric repulsion energy between internal aqueous droplets and the external aqueous phase in double emulsions, which results from the steric interaction between the surfactant molecules adsorbed at the two interfaces, has been established. The steric interaction is dependent on the separation distance between the internal aqueous droplets and the external aqueous phase, the thicknesses of the two adsorbed surfactant layers, and the size of the internal aqueous droplets and the oil globules, all of which determine the extent of the compression of the adsorbed surfactant molecules. The thickness of each of the two surfactant layers have the same effect on the steric repulsion, and stronger steric interaction can be achieved with thicker adsorbed layers, which can effectively prevent coalescence between the internal aqueous droplets and the external aqueous phase. Increasing the internal aqueous droplet size can produce stronger steric repulsion; however, larger oil globules will weaken the steric repulsion, indicating that a more stable double-emulsion system can be achieved by preparing the system with smaller oil globules and larger internal aqueous droplets.
1. Introduction 1
Since first described by Seifriz in 1925, double emulsions have attracted a lot of research interest because of their broad applications in various fields including agriculture, cosmetics, the food industry, removal of toxic materials in wastewater, drug delivery vehicles, and so on.2-7 For their successful utilization, double emulsions have to achieve a desirable stability, which is still not well understood and hard to maintain. With regard to the instability of water-in-oil-in-water (W1/O/W2) or oil-inwater-in-oil (O1/W/O2) double emulsions, Florence has proposed four major forms, among which the coalescence between the internal aqueous phase and the external aqueous phase is the most important8,9 and has spurred both experimental and theoretical research work. Kita et al. applied a viscometric method to estimate the stability of the W1/O/W2-type double emulsions and showed that it was possible to estimate the stability by measuring the viscosity change.10 Other researchers have demonstrated that oil-soluble surfactants have the most significant * Corresponding authors. E-mail:
[email protected]. E-mail:
[email protected]. Tel: +86-10-64429059. Fax: +86-10-64434784. † Beijing University of Chemical Technology. ‡ Yantai University. (1) Seifriz, W. J. Phys. Chem. 1925, 29, 738. (2) Matsumoto, S.; Kita, Y.; Yonesawa, D. J. Colloid Interface Sci. 1976, 57, 353. (3) Tadros, T. F. Int. J. Cosmet. Sci. 1992, 14, 93. (4) Raghuraman, B.; Tirmizl, N.; Wiencek, J. Environ. Sci. Technol. 1994, 28, 1090. (5) Silva, C. A.; Crossiord, J. L.; Puisieux, F.; Seiller, M. J. Nature 1968, 219, 856. (6) Hirai, T.; Haraguchi, S.; Komosowa, I. Langmuir 1997, 13, 6650. (7) Larson, K.; Raghuraman, B.; Wiencek, J. Ind. Eng. Chem. Res. 1994, 33, 1612. (8) Florence, A. T.; Whitehill, D. J. Colloid Interface Sci. 1981, 79, 213. (9) Villa, C. H.; Lawson, L. B.; Li, Y.; Papadopoulos, K. D. Langmuir 2003, 19, 244. (10) Kita, Y.; Matsumoto, S.; Yonezawa, D. J. Colloid Interface Sci. 1977, 62, 87.
effects on stability, whereas other factors including pH value, salinity, and so on play much less important roles.8-11 To study the stability of double emulsions theoretically, the total interaction between the internal droplets and the external aqueous phase is employed to determine the stability, and it needs a repulsive total interaction to keep the system stable. Florence and Whitehill proposed a model for the Hamaker interaction energy between the internal droplets and the external aqueous phase.8 Matsumoto employed the total interaction energy between the two aqueous phases, including the attractive Hamaker interaction and the repulsive electrical double-layer forces, to measure the stability.12 SenGupta and Papadopoulos modeled the van der Waals interaction between a colloid and the wall of its host spherical cavity in the case when there is only an adsorbed surfactant layer on the cavity wall.13 In our previous study, a mathematical model was established to analyze the van der Waals interaction between the internal aqueous droplets and the external aqueous phase of double emulsions when there were two different adsorbed surfactant layers with uniform density.14 However, besides the van der Waals interaction and electrostatic interaction, a repulsive steric interaction between the internal aqueous droplets and the external aqueous phase of double emulsions may also be introduced when there is an adsorbed surfactant layer at each of the two W/O interfaces. When the two interfaces are close enough to induce overlap between the two adsorbed layers, this steric interaction becomes significant and makes a great contribution to the total interaction and in some cases may even dominate it. Such steric interaction between the internal aqueous droplets and the external (11) Hou, W.; Papadopoulos, K. D. Chem. Eng. Sci. 1996, 51, 5043. (12) Matsumoto, S. In Nonionic Surfactants; Schick, M. J., Ed.; Marcel Dekker: New York, 1987; p 549. (13) SenGupta, A. K.; Papadopoulos, K. D. J. Colloid Interface Sci. 1992, 152, 534. (14) Wen, L.; Cheng, J.; Zou, H.; Zhang, L.; Chen, J.; Papadopoulos, K. D. Langmuir 2004, 20, 8391.
10.1021/la051906r CCC: $30.25 © 2005 American Chemical Society Published on Web 11/05/2005
12048
Langmuir, Vol. 21, No. 25, 2005
aqueous phase of double emulsions has not yet been modeled. Many researchers have modeled the steric interaction between other different interfaces. For instance, by applying a statistical mechanism, Mackor proposed a simple model for calculating the steric interaction energy between two parallel flat interfaces. This model treats the adsorbed hydrocarbon chains as rigid rods attached to the interface at fixed points but free to rotate.15 On the basis of Mackor’s model, a mathematical model for calculating the steric repulsion energy between a neighboring pair of spheres was obtained by Rosensweig et al.16 Clayfield and Lumb used a Monte Carlo method to estimate the steric interaction between a plane and sphere and between two spheres.17 By dividing into two parts the free energy of interaction for polymer chains adsorbed onto one plane as a function of the distance from a second plane, Meier gave an expression for the freeenergy change due to the reduction in the number of available configurations of a random flight chain.18 Dolan and Edwards divided the chain into several segments and proposed a model in an exponential form,19 and Huh used it to calculate the steric interaction energy between parallel plane surfaces.20 Taking into account a possible surfactant lateral migration mechanism, Lazaridis et al. reported a steric stabilization model for describing particle stabilization in emulsion polymerization systems in the presence of nonionic oligomeric surfactants.21 In this study, a simple mathematical model for analyzing the steric interaction energy between the internal aqueous droplets and the external aqueous phase in double emulsions was established on the basis of Mackor’s model. Using the deduced model, the effects of the adsorbed surfactant layer thickness, the size of the internal aqueous droplets, and the oil globule on the steric repulsion energy were analyzed. Combining it with the previously established model for calculating the van der Waals interaction and electrostatic interaction, the total interaction between the internal droplets and the external aqueous phase of double emulsions can be investigated more comprehensively. 2. Model Establishment for the Steric Repulsion Energy between the Two Adsorbed Surfactant Layers The steric repulsive interaction and electrostatic interaction between the internal aqueous droplets and the external aqueous phase are always repulsive, but the van der Waals interaction can be either attractive or repulsive.15 The nature of the combined total interaction determines whether the coalescence between the two aqueous phases will happen; that is, a repulsive total interaction is required for the two aqueous phases to remain stable. A general model for the van der Waals interaction energy between the internal aqueous droplets and the external aqueous phase was obtained previously, and it can be applied in cases when there is no adsorbed layer but only a single adsorbed layer, the same two adsorbed layers, or two different adsorbed layers at the W1/O and O/W2 (15) Mackor, E. L. J. Colloid Sci. 1951, 6, 492. (16) Rosensweig, R. E.; Nestor, J. W.; Timmins, R. S. AIChE-I. Chem. E. Symp. Ser. n5 1965, 5, 104. (17) Clayfield, E. J.; Lumb, E. C. J. Colloid Interface Sci. 1966, 22, 285. (18) Meier, D. J. J. Chem. Phys. 1967, 71, 1861. (19) Dolan, A. K.; Edwards S. F. Proc. R. Soc. London 1974, A377, 509. (20) Huh, C. J. Colloid Interface Sci. 1979, 71, 408. (21) Lazaridis, N.; Aplexopoulos, A. H.; Chatzi, E. G.; Kiparissides, K. Chem. Eng. Sci. 1999, 54, 3251.
Cheng et al.
interfaces.14 Applying Coulomb’s law, the electrostatic interaction (Eel) between the two interfaces has been described by Hou and Papadopoulos,11 which arises from the interaction of the electrical double layers. In double emulsions, when the internal aqueous droplets and the external aqueous phase are very close, the steric repulsive interaction between the long hydrocarbon chains of the adsorbed surfactant molecules plays an important role in helping stabilize the whole emulsion system. At a short distance, this repulsion energy may overcome the attraction potentials in many cases. When the two interfaces approach each other closely, they tend to compress the tails of the surfactant molecules adsorbed at each interface; therefore, these molecules can act as bumpers to prevent the coalescence between the internal aqueous phase and the external aqueous phase. By applying the statistical mechanism, Mackor obtained the expression for the steric repulsion between two parallel flat surfaces in which the adsorbed surfactant molecules were treated as rigid rods, each with a ball-joint attachment to the flat surface,15
{
S S e1 1- , Ef 2δ 2δ ) S NkT >1 0, 2δ
}
where Ef is the steric repulsion energy per unit area of the flat surface, δ is the length of the adsorbed surfactant molecules, N is the number of adsorbed surfactant molecules per unit surface area (also known as the surface concentration), T is the temperature, k is the Bolzmann constant, and S is the surface-to-surface separation distance. Therefore, Ef is determined by the compressed length fraction and the surface concentration of the adsorbed surfactant molecules. If the two adsorbed surfactant layers have different molecular lengths δ1 and δ2, then
[
Ef ) NkT 1 -
]
D δ1 + δ2, there will be no compressed molecules of the adsorbed surfactant layers; therefore, the steric repulsion energy is
For any given θ in the compressed zone, the total area of the two interfaces within the spherical cap of θ is
Esr ) 0
A ) 2πR12(1 - cos φ) + 2πR22(1 - cos θ)
From eq 12, when the internal W1/O interface contacts the external O/W2 interface (D ) 0, S ) R1 - R2), the
(7)
(13)
12050
Langmuir, Vol. 21, No. 25, 2005
Cheng et al.
steric repulsion energy has its largest value as
(Esr)max )
[
]
2 2πkT N1R1 (R2 + δ2) + N2R22 × δ1 + δ2 R1 + δ1
{
[ ) ]
(R1 - δ1)2 - (R1 - R2)2 R2 + δ2 + R2 - δ1 2(R1 - R2)
(
}
(δ1 + δ2)2 R2 - δ1 -1 + ln R2 + δ2 4S
(14)
However, when D ) δ1 + δ2, the steric repulsion energy vanishes corresponding to the case in which the two adsorbed layers are just in contact with each other. 3. Analysis of the Steric Repulsion Energy in Different Cases The steric repulsive force is a short-distance interaction; therefore, only when the two adsorbed layers in double emulsions are in contact with each other will the steric repulsion affect the stability of the system. With the aboveestablished model for the steric repulsion energy, the effects of the two different layer thicknesses, the oil globule size, and the size of the internal aqueous droplets on the steric repulsion energy were studied. Bolzmann constant k is 1.3806 × 10 - 23J/K, and T was set at room temperature (298 K) during the computation. The densities of the two adsorbed layers were assumed to be identical and set as
N1 ) N2 ) 1 × 1018/m2 3.1. Effects of the Two Adsorbed Layer Thicknesses on the Steric Repulsion Energy. When the two layer thicknesses are the same (δ1 ) δ2 ) δ), eq 12 becomes
[ {
]
2 πNkT R1 (R2 + δ) + R22 × Esr ) δ R1 + δ 2
[
2
(R1 - δ) - S R2 + δ + 2S R2 - δ + D ln
(
) ]
}
R2 - δ + D (2δ - D)2 -1 + R2 + δ 4S
(15)
To calculate the steric repulsion energy in this case, we set the radius of the oil globule and the internal aqueous droplet, respectively, as
R1 ) 5000 × 10-10 m
R2 ) 4000 × 10-10 m
As seen from Figure 2, the steric repulsive interaction energy rose with the decrease of the separation distance between the two interfaces (D) because of the increased overlap between the two adsorbed surfactant layers. When D remained the same, the magnitude of the steric repulsion energy was dependent on the thickness of the adsorbed surfactant layers: thicker adsorbed surfactant layers produced stronger repulsive interaction, owing to the intensified overlap between the two adsorbed surfactant layers as well. This finding is in good agreement with some experimental observations, which indicated that with increasing surfactant concentration the stability of the double emulsion increased and the system was generally stable within the time of observation when the surfactant concentration was above a certain value.11
Figure 2. Effects of the two adsorbed surfactant layer thicknesses on the steric repulsion energy when δ1 ) δ2 ) δ.
Similarly, when the thicknesses of the two adsorbed surfactant layers were different, the same trend of the steric repulsion energy was obtained, as shown in Figure 3. It was found that, with increasing δ1 or δ2, stronger steric repulsion interaction was produced to prevent the two W/O interfaces from approaching each other, which helps stabilize the emulsion system. To further investigate the difference between the effects of each of the two adsorbed surfactant layers on the steric repulsion energy, the changes in the steric repulsion energy at different D values were calculated and plotted in Figure 4 as δ1 changed from 10 × 10-10 to 40 × 10-10 m while δ2 was kept as 20 × 10-10 m or δ2 changed from 10 × 10-10 to 40 × 10-10 m while δ1 was kept as 20 × 10-10 m. The two curves are nearly completely overlapped with each other, suggesting that the effects of each of the two adsorbed surfactant layers on the steric repulsion energy are almost the same and the change in either of the layer thicknesses can achieve the same desired adjustment of the steric repulsion. 3.2. Steric Repulsion Energy at Different Sizes of Internal Aqueous Droplets and Oil Globules. Besides the adsorbed layer thickness, the sizes of the internal aqueous droplets and the oil globules are also important factors in determining the steric repulsion energy. Figure 5 reveals the effects of the internal aqueous droplet size (R2) on the steric repulsion energy with the two adsorbed layer thicknesses being set to δ1 ) 30 × 10-10 and δ2 ) 20 × 10-10 m, respectively. With the oil globule size (R1) set to 5000 × 10-10 m, a stronger repulsive interaction was obtained at a larger internal aqueous droplet size (R2) and the same separation distance D between the two interfaces, indicating that increasing internal aqueous droplet size can enhance the emulsion stability if all other conditions remain the same. As illustrated in Figure 1, if R2 increases and there is no change in any other parameter, then shadow zone C (i.e., the overlapped portion of the two surfactant layers) will increase, leading to the intensified repulsive interaction. Unlike the internal aqueous droplet, the oil globule size (R1) has an adverse effect on the steric repulsion energy as shown in Figure 6, in which δ2 and δ1 were the same as those in Figure 5 and the internal aqueous droplet size was set to R2 ) 4000 × 10-10 m. At the same separation distance, the steric repulsion energy decreases with increasing R1 because the increase in R1 will reduce the crossed region of the two adsorbed layers and therefore lower the steric repulsion energy. As a result, smaller oil
Droplet/External Aqueous Phase Repulsion
Langmuir, Vol. 21, No. 25, 2005 12051
Figure 3. Effects of the two adsorbed surfactant layer thicknesses on the steric repulsion energy when δ1 * δ2: (a) δ1 is fixed (δ1 ) 20e - 10m); (b) δ2 is fixed (δ2 ) 20e - 10m).
Figure 4. Changes in the steric repulsion energy resulting from the changes in δ1 and δ2.
globules can help prevent the coalescence between the internal aqueous droplets and the external aqueous phase, hence bringing better stability to double emulsions. It is worth noting that the steric interaction is a shortdistance interaction and can be introduced only when the two adsorbed layers in double emulsions are in contact with each other; that is, the separation distance between the two adsorbed layers is zero. However, all currently available models for the van der Waals interaction for double-emulsion systems are not applicable when the separation distance between the two adsorbed layers is zero. Therefore, to analyze the total interaction, which is the combination of the van der Waals interaction, the electrostatic interaction, and the steric interaction, further modifications to the current models for the van der Waals interaction will be needed in future investigations. 4. Conclusions On the basis of Mackor’s model for the steric interaction energy between two parallel flat surfaces, a theoretical
Figure 5. Effects of internal aqueous droplet size on steric repulsion energy.
model for analyzing the steric repulsion energy between internal aqueous droplets and the external aqueous phase in double emulsions was established. As a short-distance interaction, the steric repulsion is introduced by the overlap of the two adsorbed surfactant layers at the two interfaces, and its amplitude is determined by the extent of the compression between the two adsorbed layers. Applying this new model, the effects of the two adsorbed surfactant layer thicknesses, the internal aqueous droplet size, and the oil globule size on the steric repulsion energy can be investigated. It was found that thicker adsorbed surfactant layers can produce stronger steric repulsive interaction at a constant separation distance between the two interfaces and the effects of each of the two adsorbed surfactant layers on the steric repulsive interaction are almost the same if the two layers are not uniform. The internal aqueous droplet size has a very different effect on the steric repulsive interaction as compared to that of
12052
Langmuir, Vol. 21, No. 25, 2005
Cheng et al.
Acknowledgment. We gratefully acknowledge the financial support provided by the Talent Training Program of Beijing City (no. H020821270120), NSF of China (nos. 20506001, 20325621), the Program for New Century Excellent Talents in University (no. NCET-04-0123), the Beijing Municipal Commission of Education (JD100100403), the National High Tech Program (“863” Plan, no. 2003AA302620), the Research Fund of MultiPhase Reaction Laboratory, the Institute of Process Engineering (CAS, No. 2003-1), and the SRF for ROCS, SEM. Notation
Figure 6. Effects of oil globule size on steric repulsion energy.
the oil globule size. Whereas larger internal aqueous droplets can strengthen the steric repulsive interaction and help stabilize the double-emulsion system, larger oil globules will reduce this steric interaction and hence weaken the stability.
W1 ) internal aqueous droplet W2 ) external aqueous phase O ) intervening oil phase R1 ) radius of oil globule, m R2 ) radius of internal aqueous droplet, m δ1 ) external adsorbed surfactant layer thickness on O/W2 interface, m δ2 ) internal adsorbed surfactant layer thickness on W1/O interface, m S ) center-to-center distance between the aqueous droplet and the oil drop, m D ) separation distance between O/W2 interface and W1/O interface, m Esr ) steric repulsion energy, J LA051906R
