van der Waals Interaction between Internal Aqueous Droplets and the

Steric Repulsion between Internal Aqueous Droplets and the External Aqueous Phase in Double Emulsions. Jing Cheng, Shiai Xu, Lixiong Wen, and Jianfeng...
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Langmuir 2004, 20, 8391-8397

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van der Waals Interaction between Internal Aqueous Droplets and the External Aqueous Phase in Double Emulsions Lixiong Wen,*,† Jing Cheng,† Haikui Zou,† Lei Zhang,† Jianfeng Chen,† and Kyriakos D. Papadopoulos‡ Key Lab of 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 Department of Chemical & Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118 Received March 12, 2004. In Final Form: June 10, 2004 A mathematical model for analyzing the van der Waals interaction between the internal aqueous droplets (W1) and the external aqueous phase (W2) of double emulsions has been established. The effects of Hamaker constants of the materials forming the system, especially those of the two different adsorbed surfactant layers with uniform density (A1 and A2), on the van der Waals interaction were investigated. The overall van der Waals interaction across the oil film is a combined result of four individual parts, that is, W1-W2, A1-A2, W1-A1, and A2-W2 van der Waals interaction, and it may be either attractive or repulsive depending on many factors. It was found that the overall van der Waals interaction is dominated by the W1-W2 interaction at large separation distances between the W1/O and O/W2 interfaces, while it is mostly determined by the A1-A2 interaction when the two interfaces are extremely close. Specifically, in the cases when the value of the Hamaker constant of the oil phase is intermediate between those of W1 and W2 and there is a thick oil film separating the two interfaces, a weak repulsive overall van der Waals interaction will prevail. If the Hamaker constant of the oil phase is intermediate between those of A1 and A2 and the two interfaces are very close, the overall van der Waals interaction will be dominated by the strong repulsive A1-A2 interaction. The repulsive van der Waals interaction at such cases helps stabilize the double emulsions.

1. Introduction W1/O/W2 double emulsions have found potential applications in various fields including pharmaceuticals,1 food industry,2 agricultural formulations,3 cosmetics,4 separation processes, and wastewater treatment in the form of emulsified liquid membranes,5,6 and so forth. Though much progress has been achieved in the preparation and stabilization of double emulsions, their stability still remains a big challenge to both research and industries and, therefore, constitutes one of the primary factors limiting the development of more commercial products of double emulsions. Among the four major forms of instability,7 the coalescence of the internal aqueous droplets into the external aqueous phase is the most important one8,9 and has attracted both experimental and theoretical research work. It was found that oil-soluble surfactants have the most significant effects on stability, while other factors including pH value, ionic strength, * Corresponding author. Tel.: +86-10-64429059. Fax: +86-1064434784. E-mail: [email protected]. † Beijing University of Chemical Technology. ‡ Tulane University. (1) Florence, A. T. Chem. Ind. 1993, 20, 1000-1004. (2) Dickinson, E.; Evison, J.; Owusu, R. K. Food Hydrocolloids 1991, 5 (5), 481-485. (3) Matsumoto, S.; Kita, Y.; Yonesawa, D. J. Colloid Interface Sci. 1976, 57, 353-361. (4) Tadros, T. F. Int. J. Cosmet. Sci. 1992, 14 (3), 93-111. (5) Raghuraman, B.; Tirmizi, N.; Wiencek, J. Environ. Sci. Technol. 1994, 28, 1090-1098. (6) Larson, K.; Raghuraman, B.; Wiencek, J. Ind. Eng. Chem. Res. 1994, 33, 1612-1619. (7) Florence, A. T.; Whitehill, D. J. Colloid Interface Sci. 1981, 79, 243-256. (8) Hou, W.; Papadopoulos, K. D. Chem. Eng. Sci. 1996, 51 (22), 5043-5051. (9) Villa, C. H.; Lawson, L. B.; Li, Y.; Papadopoulos, K. D. Langmuir 2003, 19, 244-249.

and so on play much less important roles.8,10-13 On the theoretical side, this stability is decided by the total interaction between the internal droplets and the external aqueous phase, 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.7 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.11 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.14 When there are two adsorbed layers of the same surfactant and same thickness at both of W1/O and O/W2 interfaces, the van der Waals interaction energy between the internal water droplets and the external aqueous phase was simulated in a further work by Hou and Papadopoulos,8 which helped explain those authors’ experimental results. However, there may be different surfactants adsorbed at the W1/O and O/W2 interfaces with different layer thicknesses in a double emulsion system, as a result of different water-soluble surfactants presented in the W1 and W2 phases separately. These different adsorbed (10) Kita, Y.; Matsumoto, S.; Yonezawa, D. J. Colloid Interface Sci. 1977, 62, 87-94. (11) Matsumoto, S. In Nonionic Surfactants; Schick, M. J., Ed.; Marcel Dekker: New York, 1987; pp 549-600. (12) Ficheux, M. F.; Bonakdar, L.; Leal-Calderon, F.; Bibette, J. Langmuir 1998, 14, 2702-2706. (13) Wen, L.; Papadopoulos, K. D. Langmuir 2000, 16 (20), 76127617. (14) SenGupta, A. K.; Papadopoulos, K. D. J. Colloid Interface Sci. 1992, 152 (2), 534-542.

10.1021/la049353s CCC: $27.50 © 2004 American Chemical Society Published on Web 07/31/2004

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interfaces and the two aqueous phases are separated by a vacuum instead of an oil film, the van der Waals interaction energy Evdw in eq 1 is as simple as14

EP-C ) AP-CH(RC, RP)

Figure 1. Scheme of a W1/O/W2 globule with two different adsorbed surfactant layers.

surfactant layers contribute significantly to the van der Waals interaction between the two aqueous phases, but their effects are not yet computable with the currently available theoretical models. It is, therefore, necessary to develop a general mathematical model to calculate the van der Waals interaction energy between the two aqueous phases under various conditions, including the case when the two interfaces have different adsorbed surfactant layers of different thicknesses. By employing two adsorbed layer thickness parameters, which represent the different amount of surfactants adsorbed at the W1/O and O/W2 interfaces, respectively, with varying Hamaker constants for different surfactants, such a model has been derived in this study. Using this model, the effects of the internal droplets, the intervening oil globule, the external aqueous phase, and the adsorbed surfactant layers on the van der Waals interaction energy were investigated by changing their Hamaker constants and their corresponding dimensional parameters. 2. Theoretical Model for van der Waals Interaction Energy The coalescence between the internal aqueous droplet and the external aqueous phase is primarily due to the lack of repulsion between the W1/O and O/W2 interfaces, which causes the rupture of the intervening oil film. The total interaction energy determines whether the interaction between the two phases is attractive or repulsive; therefore, the effects of each factor on the total interaction energy reflect their influences on the system stability. 2.1. Total Interaction Energy. As shown in Figure 1, a single oil drop (consisting of M) with radius of RC is suspended in a continuous aqueous phase W2 (consisting of C), and an aqueous droplet W1 (consisting of P) with radius of RP is entrapped in the oil globule. Two different surfactants (A1 and A2) are adsorbed at the O/W2 and W1/O interfaces with layer thickness of δA1 and δA2, respectively, and the density of each of them is assumed to be uniform. S represents the separation distance between the centers of the two spheres. If there are only van der Waals interaction and electrical double-layer forces between the two aqueous phases, the total interaction energy will be8

Etotal ) Evdw + Eel

(1)

The electrostatic interaction Eel can be approximated by applying Coulomb’s law as described by Hou and Papadopoulos,8 and, therefore, is not described in detail here. The focus of this study is to model the van der Waals interaction Evdw for various cases as follows. 2.2. van der Waals Interaction Energy. 2.2.1. van der Waals Interaction Energy without the Adsorbed Layer. If there is no surfactant layer at the

(2)

where A is the nonretarded Hamaker constant, with the two subscripts reflecting interaction between those two materials with the vacuum separating them. AP-C can be approximated as (AP-PAC-C)1/2, and the same is for the subsequent other Hamaker constants. H is a dimensionless interaction energy defined by SenGupta and Papadopoulos:14

{[

]

(RC - RP)2 - S2 1 + H(RC, RP) ) - ln 6 (RC + RP)2 - S2 2

2

4RCRP(RC + RP - S2)

((RC + RP)2 - S2)((RC - RP)2 - S2)

}

(3)

If the intervening phase changes from a vacuum to an oil globule, the van der Waals interaction energy becomes: 14

EP-M-C ) EP-C + EM-M - EP-M - EM-C ) (AP-C + AM-M - AP-M - AM-C)H(RC, RP) (4) 2.2.2. van der Waals Interaction Energy with Only One Adsorbed Layer at the O/W2 Interface. If there is only one water-soluble surfactant (A1) that is present in the W2 phase, the system will have a single adsorbed layer at the O/W2 interface. In this case, the effects of the adsorbed layer on the van der Waals interaction must be considered. The bulk of the surfactant layer can be regarded as being located at the oil side of the interface because the length of the hydrophobic tail is much greater than the dimension of the hydrophilic head of the surfactant molecules. The van der Waals interaction energy in this case can be approximated by that between a colloid and the coated wall of its host spherical cavity as reported by SenGupta and Papadopoulos:14

EP-M-A1C ) EP-A1C + EM-M - EP-M - EM-A1C ) AP-A1H(RC - δA1,RP) AP-A1H(RC, RP) + AP-CH(RC, Rp) + AM-MH(RC - δA1, RP) AP-MH(RC - δA1, RP) AM-A1H(RC - δA1, RP) + AM-A1H(RC, RP) - AM-CH(RC, Rp) ) (AP-C - AP-A1 + AM-A1 - AM-C) × H(RC, RP) + (AP-A1 + AM-M AP-M - AM-A1)H(RC - δA1, RP) (5) 2.2.3. van der Waals Interaction Energy with Two Different Adsorbed Layers. When there is only one oilsoluble surfactant in the double emulsion system, a surfactant layer will be adsorbed at both W1/O and O/W2 interfaces. If two different water-soluble surfactants are present in the W1 and W2 phases separately, the adsorbed surfactant layers at the W1/O and O/W2 interfaces will be

Interaction between W1 and W2 in Double Emulsions

different, and so will their thicknesses, as shown in Figure 1. In both cases, the van der Waals interaction energy between the internal droplets and the external aqueous phase can be written as

EPA2-M-A1C ) EA2-M-A1C - E′A2-M-A1C + EP-M-A1C (6) where EP-M-A1C is the same as in section 2.2.2, E′A2-M-A1C is identical to EP-M-A1C with the only difference being that the internal droplet consists of surfactant A2 instead of P, and EA2-M-A1C is the same as E′A2-M-A1C but the radius of the internal particle is RP + δA2. With similar derivation of EP-M-A1C, EA2-M-A1C and E′A2-M-A1C can be obtained separately as

EA2-M-A1C ) EΑ2-Α1C + EΜ-Μ - EΑ2-Μ - EΜ-Α1C ) AA2-A1H(RC - δA1, RP + δA2) AA2-A1H(RC, RP + δA2) + AA2-CH(RC, RP + δA2) + AM-MH(RC - δA1, RP + δA2) AA2-MH(RC - δA1, RP + δA2) AM-A1H(RC - δA1, RP + δA2) + AM-A1H(RC, RP + δA2) AM-CH(RC, RP + δA2) ) (AA2-A1 + AM-M - AM-A1 - AA2-M) × H(RC - δA1, RP + δA2) + (-AA2-A1 + AA2-C + AM-A1 - AM-C) × H(RC, RP + δA2) (7) E′A2-M-A1C ) E′A2-A1C + E′M-M - E′A2-M - E′M-A1C ) AA2-A1H(RC - δA1, RP) AA2-A1H(RC, RP) + AA2-CH(RC, RP) + AM-MH(RC - δA1, RP) AA2-MH (RC - δA1, RP) AM-A1H(RC - δA1, RP) + AM-A1H(RC, RP) - AM-CH(RC, RP) ) (AA2-A1 + AM-M - AA2-M - AM-A1) × H(RC - δA1, RP) + (AA2-C - AA2-A1 + AM-A1 - AM-C)H(RC, RP) (8) After substitution of the corresponding terms in eq 6 with eqs 5, 7, and 8, the general model for the van der Waals interaction energy between the internal droplets and the external aqueous phase is obtained:

EPA2-M-A1C ) (AA2-A1 - AM-A1 + AM-M - AA2-M) × H(RC - δA1, RP + δA2) + (-AA2-A1 + AA2-C + AM-A1 AM-C)H(RC, RP + δA2) + (-AA2-A1 + AA2-M + AP-A1 AP-M)H(RC - δA1, RP) + (-AA2-C + AA2-A1 + AP-C AP-A1)H(RC, RP) (9)

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3. Effects of Hamaker Constants on van der Waals Interaction Energy With the general theoretical model established above, the effects of different materials, different sizes of the oil globules and the internal aqueous droplets, and different adsorbed surfactant layer thicknesses on the van der Waals interaction energy for the W1/O/W2 emulsion systems can be calculated for the cases when there is no adsorbed layer, only one adsorbed layer, or two adsorbed layers. Only the effects of Hamaker constants, which represent different materials forming the double emulsion systems, on the van der Waals interaction energy were examined in this study by using various Hamaker constant combinations for the computation. For the purpose of simplification, RC and RP were set as

RC ) 5000 × 10-10 m, RP ) 4000 × 10-10 m for most of the calculations. As will be shown later, the choice of these values does not affect the results and conclusions presented in this paper, because computations with a range of Rc and Rp showed the same trends. Other parameters including the adsorbed layer thickness, Hamaker constants, and S were set to some random values as needed to form certain parameter combinations to explore their effects on the van der Waals interaction. 3.1. van der Waals Interaction Energy without or with Only One Adsorbed Layer. Using the same parameter values, the computed van der Waals interaction energy for these two cases is exactly the same as that obtained in the previous work by SenGupta and Papadopoulos.14 This result showed the validity of this general theoretical model, and it is also in agreement with the following theories on van der Waals interaction:15 (1) the van der Waals interaction between any two different objects across a vacuum is attractive; (2) the van der Waals interaction between any two identical objects across any other medium is attractive; and (3) the van der Waals interaction between any two dissimilar objects across another medium may be either attractive or repulsive. When the Hamaker constant of the medium is between the Hamaker constants of the two objects, the interaction is repulsive. Otherwise, it is attractive. It also suggested that the van der Waals interaction between W1 and W2 of a W1/O/W2 emulsion system is always attractive when W1 and W2 consist of the same material and there is no adsorbed surfactant layer, indicating the inherent instability of double emulsions. However, if the oil Hamaker constant has a value intermediate between those of the Hamaker constants of the two dissimilar W1 and W2 phases, the van der Waals interaction will become repulsive. When there is one adsorbed layer, the van der Waals interaction will be either attractive or repulsive, depending on the Hamaker constants and adsorbed layer thickness combination. In the case when the adsorbate (A1) is at the O/W2 interface, the van der Waals interaction across the oil film is contributed by two parts, that is, the W2-W1 interaction and A1-W1 interaction. If the two interactions are the same type (repulsive or attractive), the A1-W1 interaction enhances the W2-W1 interaction. If the two interactions assume the opposite type (one is repulsive and another is attractive), the nature of the overall van der Waals interaction will be decided by the one with a greater absolute value. (15) Israelachvili, J. N. Intermolecular and Surface Forces with Applications to Colloidal and Biological Systems; Academic Press: Orlando, 1985.

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Table 1. Effects of Different Hamaker Constants on van der Waals Interaction between the W1/O and O/W2 Interfaces

no.

AP-P (× 10-20 J)

AA2-A2 (× 10-20 J)

AM-M (× 10-20 J)

AA1-A1 (× 10-20 J)

AC-C (× 10-20 J)

Hamaker constant relationship

vdW interaction at big Da

1-1 1-2 1-3 1-4 1-5 2-1 2-2 2-3 2-4 2-5 3-1 3-2 3-3 3-4 3-5

4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 3.0 3.0 3.0 3.0 3.0 2.0 2.0

b 0.5 4.5 0.5 1.5 b 2.5 3.5 0.5 4.5 b 3.5 4.5 0.5 5.5

2.0 2.0 2.0 1.0 1.0 3.0 3.0 3.0 2.0 2.0 4.0 4.0 4.0 3.0 3.0

b 1.0 1.0 3.0 3.0 b 2.0 2.0 4.0 4.0 b 2.0 2.0 4.0 4.0

3.0 3.0 3.0 2.0 2.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

AM-M < AC-C < AP-P AA2-A2 < AA1-A1 < AM-M < AC-C < AP-P AA1-A1 < AM-M < AC-C < AP-P < AA2-A2 AA2-A2 < AM-M < AC-C < AA1-A1 < AP-P AM-M < AA2-A2 < AC-C < AA1-A1 < AP-P AC-C < AM-M < AP-P AC-C < AA1-A1 < AA2-A2 < AM-M < AP-P AC-C < AA1-A1 < AM-M < AA2-A2 < AP-P AA2-A2 < AC-C < AM-M < AP-P < AA1-A1 AC-C < AM-M < AP-P < AA1-A1 < AA2-A2 AC-C < AP-P < AM-M AC-C < AA1-A1 < AP-P < AA2-A2 < AM-M AC-C < AA1-A1 < AP-P < AM-M < AA2-A2 AA2-A2 < AC-C < AP-P < AM-M < AA1-A1 AC-C < AP-P < AM-M < AA1-A1 < AA2-A2

A A A A A R R R R R A A A A A

vdW interaction at very small Da A A R R A R A R R A A A R R A

a D, separation distance between W /O and O/W interfaces; A, attractive; R, repulsive. b The corresponding adsorbed layer was not 1 2 present.

Figure 2. Effects of adsorbed layers on van der Waals interaction energy when AM-M < AC-C < AP-P.

3.2. van der Waals Interaction Energy with Two Different Adsorbed Layers. Besides the fixed RC and RP as declared above, other adjustable parameters of this model include the Hamaker constants of the internal droplets, the external aqueous phase, the intervening oil and the two adsorbed surfactants A1 and A2, the thickness of the two adsorbed layers, and S. The effects of adsorbed layer thickness on the van der Waals interaction energy were not covered in this paper and, therefore, δA1 and δA2 were both set to 20 × 10-10 m in the subsequent computations. By changing the Hamaker constants, a part of the calculated results are listed in Table 1, and the effects of different materials on the van der Waals interaction energy are discussed as follows. 3.2.1. When the Oil Hamaker Constant Is Less than Those of the Two Aqueous Phases. When AM-M < AC-C < AP-P, the van der Waals interaction between the internal droplets W1 and the external aqueous phase W2 is inherently attractive if there is no surfactant presented, as shown by the decreasing van der Waals interaction energy in Figure 2. With a surfactant layer A1 adsorbed at the O/W2 interface and A2 at the W1/O interface, three more van der Waals interactions are introduced across the oil film. Besides the W1-W2 interaction, the nature (repulsive or attractive) of the overall van der Waals interaction between the internal droplets and the external aqueous phase will also depend on the A1-A2, W1-A1, and A2-W2 interactions.

As shown in Figure 2 and by nos. 1-2 to 1-5 in Table 1, even with two different surfactant layers adsorbed at the W1/O and O/W2 interfaces, the van der Waals interaction energy is negative at most times and decreases with increasing S, which corresponds to a decreasing separation distance between the W1/O and O/W2 interfaces. This attractive van der Waals interaction will destabilize the double emulsion if there is no other repulsive force in the system. However, if the value of the Hamaker constant of the oil phase is between those of the two adsorbed surfactants A1 and A2, the negatively increasing van der Waals interaction energy will reach a minimum value and then turn into positive when the two interfaces get very close. The overall interaction, therefore, changes to repulsive and the van der Waals interaction energy increases sharply with further closing W1/O and O/W2 interfaces, keeping the internal droplets and the external aqueous phase from coalescing. 3.2.2. When the Oil Hamaker Constant Is between Those of the Two Aqueous Phases. It should be noted that it is entirely possible to have a Hamaker constant for the oil phase (e.g., hexadecane) that lies between the Hamaker constants of W1 (hydrogen peroxide) and W2 (water). The van der Waals interaction between the internal droplets and the external aqueous phase of W1/O/W2 emulsions is always repulsive when AC-C < AM-M < AP-P without surfactant, which is demonstrated by the increasing van der Waals interaction energy in Figure 3. With two different adsorbed surfactant layers, the overall van der Waals interaction can be divided into four parts as discussed above and the repulsive W1-W2 van der Waals interaction may either be exacerbated or weakened by the other three. If AA1-A1 < AM-M < AA2-A2, all of the newly added A1-A2, W1-A1, and A2-W2 van der Waals interactions will be repulsive and, thus, enhance the system stability, as shown by the increased van der Waals interaction energy in Figure 3 (AA2-A2 ) 3.5 × 10-20 J). For other cases of the surfactant Hamaker constants, at least one of these three interactions will remain repulsive. If AA2-A2 < AM-M < AA1-A1, the A1-A2 van der Waals interaction will be repulsive while both W1-A1 and A2-W2 interactions will be attractive, and the overall van der Waals interaction exhibits a repulsive nature at all separation distances between the W1/O and O/W2 interfaces (no. 2-4 in Table 1). For the cases when AM-M is greater or less than both AA1-A1 and AA2-A2, the van der Waals interaction shows a

Interaction between W1 and W2 in Double Emulsions

Figure 3. Effects of adsorbed layers on van der Waals interaction energy when AC-C < AM-M < AP-P.

Figure 4. Effects of adsorbed layers on van der Waals interaction energy when AC-C < AP-P < AM-M.

more complicated behavior. At a large separation distance between the W1/O and the O/W2 interfaces, a weak repulsive van der Waals interaction prevails and it gets intensified with a decreasing separation distance between the two interfaces. When the two interfaces get further closer, the van der Waals interaction energy starts to decline and turns into negative eventually, indicating the repulsive overall van der Waals interaction changes to

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attractive between closer W1/O and O/W2 interfaces, as shown in Figure 3 and by nos. 2-2 and 2-5 in Table 1. 3.2.3. When the Oil Hamaker Constant Is Greater than Those of the Two Aqueous Phases. As similar to the case when AM-M < AC-C < AP-P, the van der Waals interaction energy between the internal droplets and the external aqueous phase is always negative and decreases with increasing S when AM-M > AP-P > AC-C and there is no surfactant, indicating an attractive van der Waals interaction. As shown in Figure 4 and Table 1, this attractive interaction may get enhanced or, on the contrary, turn into repulsive when there are two different surfactant layers adsorbed at the interfaces, in which case the overall van der Waals interaction consists of four parts as declared previously. Specifically, if AM-M is greater than both AA1-A1 and AA2-A2, all of the four individual interactions (W1-W2, A1A2, W1-A1, and A2-W2) will be attractive and lead to a strong attractive overall van der Waals interaction. On the other hand, if AM-M is less than both AA1-A1 and AA2-A2, the W1-W2 and A1-A2 van der Waals interactions are still attractive while W1-A1 and A2-W2 both turn to repulsive. However, the overall van der Waals interaction remains attractive at all separation distances between the W1/O and O/W2 interfaces, as a result of the stronger W1-W2 and A1-A2 attractive interaction combination (no. 3-5 in Table 1). Only when AM-M is intermediate between AA1-A1 and AA2-A2, the decreasing van der Waals interaction energy may turn to increase with further decreasing separation distance between the W1/O and O/W2 interfaces after the energy reaches a minimum value, indicating that the attractive overall van der Waals interaction changes to repulsive when the two interfaces get extremely close (nos. 3-3 and 3-4 in Table 1). 3.3. van der Waals Interaction Energy at Different Internal Aqueous Droplet Sizes. All the above calculations were also conducted with different internal droplet sizes, and similar trends for all cases have been obtained. Figure 5 shows some of the calculations with RC and RP being set to 5000 × 10-10 m and 400 × 10-10 m, respectively. In Figure 5a, the oil Hamaker constant is between those of the two aqueous phases, and the van der Waals interaction energy between W1 and W2 increases slightly with increasing S when the two interfaces are not very close, indicating a weak repulsive van der Waals interaction. When the two interfaces get closer, the van der Waals interaction energy changes with different Hamaker constants of the two adsorbed surfactant layers. If AM-M is intermediate between AA1-A1 and AA2-A2, the van der

Figure 5. van der Waals interaction energy at a smaller W1 droplet size (0.04 µm).

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Waals interaction energy increases sharply as the two interfaces get close, suggesting that the repulsive van der Waals interaction gets intensified by the adsorbed surfactant layers. If both of AA1-A1 and AA2-A2 are either greater or less than AM-M, the repulsive van der Waals interaction turns to attractive when the two interfaces are extremely close, as shown by the decreasing van der Waals interaction energy. Figure 5b shows that the van der Waals interaction is always repulsive at very small separation distances between the two interfaces when AM-M is intermediate between AA1-A1 and AA2-A2, while the interaction is either repulsive or attractive at a larger separation distance, depending on whether AM-M is intermediate between AP-P and AC-C or not. As seen in the previous calculations, when there are two different adsorbed surfactant layers in W1/O/W2 double emulsions with A1 at the O/W2 interface and A2 at the W1/O interface, the overall van der Waals interaction between W1 and W2 is the combined result of four individual parts (W1-W2, A1-A2, W1-A1, and A2-W2). At large separation distances between the W1/O and O/W2 interfaces, the W1-W2 interaction dominates the overall interaction. Figures 2-5 and Table 1 all showed that the overall van der Waals interaction assumes the same nature (attractive or repulsive) as that of W1-W2 interaction at small S, which corresponds to a large separation distance between the W1/O and O/W2 interfaces. However, with increasing S, the overall van der Waals interaction will be gradually determined by the A1-A2 interaction. If the W1-W2 interaction is attractive and A1-A2 is repulsive, the overall van der Waals interaction energy decreases to reach a minimum value and then turns to increase with further increasing S, indicating that the attractive overall van der Waals interaction becomes repulsive, which is the same as the A1-A2 interaction, at very close separation distances between the W1/O and O/W2 interfaces, as shown in Figures 2, 4, and 5. When the W1-W2 interaction is repulsive and A1-A2 is attractive (Figures 3 and 5), the overall van der Waals interaction energy will increase to reach a maximum value and then decrease with further increasing S, suggesting that the repulsive overall van der Waals interaction becomes attractive at a very close separation distance between the W1/O and O/W2 interfaces. If W1-W2 and A1-A2 interactions are the same type, the overall van der Waals interaction will have the same nature and get enhanced dramatically when the two interfaces are very close. All the above results showed that, when a certain amount of surfactants are adsorbed at the two interfaces, the overall van der Waals interaction would be dominated by the A1-A2 interaction when the intervening oil film is very thin. As we know, the van der Waals interaction between two objects is very sensitive to their separation distance and is intensified sharply when the two objects get very close. In the W1/O/W2 emulsion systems with two different adsorbed surfactant layers, the W1-W2 interaction makes the biggest contribution to the overall van der Waals interaction at large separation distances between the W1/O and O/W2 interfaces, as a result of the relatively larger dimensional sizes of W1 and W2. When the W1 and W2 phases get closer, the A1-A2 interaction is enhanced more quickly than the W1-W2 interaction because the separation distance between A1 and A2 is smaller than that between the W1 and the W2 phases, as shown in Figure 1. Therefore, the A1-A2 interaction becomes the major contributor to the overall van der Waals interaction and dominates it when the two interfaces are extremely close.

Wen et al.

Both W1-A1 and W2-A2 interactions contribute to the overall van der Waals interaction, but neither of them is a primary factor. 4. Conclusions A theoretical model for analyzing the van der Waals interaction between the internal aqueous droplets (W1) and the external aqueous phase (W2) of double emulsions has been established, which is applicable for computing the van der Waals interaction energy in double emulsion systems with either one or two different adsorbed layers (with uniform density) at the interfaces. Using this model, the effects of Hamaker constants, especially those of the two different adsorbed surfactant layers, on the van der Waals interaction between W1 and W2 were investigated. The van der Waals interaction between W1 and W2 can be either attractive or repulsive depending on many factors. When there is no surfactant, the van der Waals interaction will be repulsive if the oil Hamaker constant (AM-M) is between those of the two aqueous phases (AC-C and AP-P), otherwise it is attractive. When there are two different adsorbed surfactant layers (A1 and A2) at the O/W2 and W1/O interfaces, the nature of the overall van der Waals interaction across the oil film is a combined result of four parts, that is, W1-W2, A1-A2, W1-A1, and A2-W2 van der Waals interaction, and it is summarized as follows: (1) If the oil Hamaker constant is the maximum or minimum one among those of all the materials, the overall van der Waals interaction will be attractive at all separation distances between the W1/O and O/W2 interfaces. (2) In the cases when AC-C and AA1-A1 are both greater than AM-M while both AP-P and AA2-A2 are less than AM-M, or when AC-C and AA1-A1 are both less than AM-M while both AP-P and AA2-A2 are greater than AM-M, the overall van der Waals interaction will always be repulsive. (3) For all other cases, the overall van der Waals interaction may be either attractive or repulsive, depending on the separation distance between the W1/O and O/W2 interfaces. (4) The overall van der Waals interaction is dominated by the W1-W2 interaction at large separation distances between the W1/O and O/W2 interfaces, while it is mostly determined by the A1-A2 interaction when the two interfaces are extremely close. Notation A Eel Etotal Evdw O RC RP S W1 W2 δ

Hamaker constant, J electrostatic interaction energy, J total interaction energy, J van der Waals interaction energy, J intervening oil phase radius of oil drop, m radius of internal aqueous droplet, m center-to-center distance between the aqueous droplet and the oil drop, m internal aqueous droplet external aqueous phase thickness of the adsorbed layer, m

Subscripts A1 A2 C

adsorbed surfactant at the O/W2 interface adsorbed surfactant at the W1/O interface material of the external aqueous phase

Interaction between W1 and W2 in Double Emulsions M P

material of the intervening oil phase material of the internal aqueous droplet

Acknowledgment. The authors gratefully acknowledge the financial support provided by the Talent Training Program of Beijing City (No. H020821270120), National High Tech Program (“863” Plan, No. 2003AA302620), NSF

Langmuir, Vol. 20, No. 19, 2004 8397

of China (No. 20325621), the Research Fund of MultiPhase Reaction Laboratory, Institute of Process Engineering (CAS, No. 2003-1), the New Faculty Research Foundation of BUCT (No. QN0230), and SRF for ROCS, SEM. LA049353S