5324
Langmuir 1998, 14, 5324-5326
Microemulsions Stabilized by Ionic/Nonionic Surfactant Mixtures. Effect of Partitioning of the Nonionic Surfactant into the Oil Bernard P. Binks, Paul D. I. Fletcher,* and Diana J. F. Taylor Surfactant Science Group, Department of Chemistry, University of Hull, Hull, HU6 7RX, U.K. Received May 5, 1998. In Final Form: June 25, 1998
In a recent publication1 we described a model for the composition and temperature dependence of phase inversion temperature (PIT), maximum solubilization, and oilwater tension for microemulsion phases stabilized by mixtures of ionic and nonionic surfactants. The properties of microemulsions stabilized by mixtures of the ionic surfactant sodium bis(2-ethylhexyl) sulfosuccinate (AOT) and the nonionic surfactant pentaethylene glycol n-dodecyl ether (C12E5) were successfully modeled and allowed independent optimization of both the temperature sensitivity and extent of solubilization for temperature insensitive systems. The model was formulated in terms of the surfactant composition of the monolayers stabilizing the microemulsion aggregates and neglected the partitioning of surfactant species from the aggregate interfaces to the water and oil solvent domains. For many common ionic and nonionic surfactants, the surfactant concentrations in the water domains are negligibly low. However, the concentration of nonionic surfactants such as C12E5 in the oil regions may be significant, particularly if the concentration of aggregated surfactant is low and the oil concentration is high. Thus, the model described in ref 1 where the monolayer composition was equated with the overall composition is valid only for high surfactant concentration and low oil contents. In this note, the model is extended to include the effect of partitioning of the nonionic surfactant from the mixed surfactant monolayers of the aggregates to the oil. The validity of the extended model is tested by comparison with experimental phase inversion temperature (PIT) measurements for AOT/C12E5 microemulsions under conditions where significant partitioning of the C12E5 to the oil occurs. We first briefly review the main relevant features of the model. The radius of a microemulsion droplet is proportional to the extent of solubilization. At the solubilization phase boundary where an excess phase of the dispersed component separates, the solubilization and the droplet radius are maximum. At this boundary, the droplet radius is the “natural” or preferred radius (rnat) since the droplets are free to swell or shrink by solubilization of more or less of the coexisting bulk phase of oil or water. The preferred monolayer curvature is given by 1/rnat. For many pure surfactant systems, the preferred monolayer curvature 1/rnat scales linearly with temperature in the region around the PIT when the curvature 1/rnat changes from positive (oil-in-water drops) to negative (water-in-oil drops).1,2 For either a pure ionic surfactant (subscript I) or a pure nonionic surfactant (subscript N), * Proofs and Correspondence to: Prof. Paul Fletcher, Department of Chemistry, University of Hull, Hull, HU6 7RX, U.K. E-mail:
[email protected]. (1) Binks, B. P.; Fletcher, P. D. I.; Taylor, D. J. F. Langmuir 1997, 13, 7030. (2) Strey, R. Colloid Polym. Sci. 1994, 272, 1005.
the temperature dependence of the preferred monolayer curvature is assumed to be linear as follows.
1/rnat ) sIT + iI 1/rnat ) sNT + iN
ionic surfactant nonionic surfactant
(1)
where s and i (with appropriate subscripts) denote the slopes and intercepts of plots of 1/rnat versus temperature for the pure ionic or nonionic surfactant, i.e., s ) d(1/ rnat)/dT and i (for T in °C) is the value of 1/rnat at 0 °C. For mixed surfactant monolayers with mole fraction XIm of ionic surfactant (with respect to the total surfactant present in the monolayers) we assume that s and i for the mixed monolayer vary with XIm according to
s ) sIXIm + sN(1 - XIm) + BsXIm(1 - XIm)
(2)
i ) iIXIm + iN(1 - XIm) + BiXIm(1 - XIm)
(3)
where Bs and Bi are parameters which reflect the extent to which s and i deviate from simple linear dependences on XIm. At phase inversion at a temperature equal to the PIT, the natural curvature 1/rnat ) 0 and hence
PIT ) -i/s
(4)
As described in ref 1, the model is extended to include prediction of the oil-water tension as functions of XIm and temperature. Alternative models for mixed surfactant systems not incorporating the temperature dependence of the monolayer curvature (s) have been described by Kunieda et al.3-7 The theory described in eqs 1 to 4 is formulated in terms of the surfactant composition of the monolayers coating the microemulsion aggregates (XIm). As described in early work on surfactant partitioning in microemulsions,8 mixed monolayers are generally in equilibrium with concentrations of monomeric surfactant present in both the water and oil regions of the microemulsions. Except in the case of short chain length surfactants, the monomeric concentrations of ionic surfactant in the water and oil regions are generally negligibly small and the moles of ionic surfactant in the monolayers are, to a good approximation, equal to the total moles added. For nonionic surfactants such as C12E5 for which the monomers distribute strongly in favor of oil,9,10 the monomeric concentration in water can usually be neglected. The nonionic monomeric concentration in oil cannot be neglected unless the aggregated surfactant concentration is high and/or the oil volume fraction is low (as in the study of ref 1). Partitioning of the monomeric nonionic surfactant to the oil is incorporated into the model as described below. (3) Kunieda, H.; Shinoda, K. J. Colloid Interface Sci. 1985, 107, 107. (4) Kunieda, H.; Ishikawa, N. J. Colloid Interface Sci. 1985, 107, 122. (5) Kunieda, H.; Hanno, K.; Yamaguchi, S.; Shinoda, K. J. Colloid Interface Sci. 1985, 107, 129. (6) Pes, M. A.; Aramaki, K.; Nakamura, N.; Kunieda, H. J. Colloid Interface Sci. 1996, 178, 666. (7) Aramaki, K.; Ozawa, K.; Kunieda, H. J. Colloid Interface Sci. 1997, 196, 74. (8) Graciaa, A.; Lachaise, J.; Sayous, J. G.; Grenier, P.; Yiv, S.; Schechter, R. S.; Wade, W. H. J. Colloid Interface Sci. 1983, 93, 474. (9) Shinoda, K.; Fukuda, M.; Carlsson, A. Langmuir 1990, 6, 334. (10) Aveyard, R.; Binks, B. P.; Clark, S.; Fletcher, P. D. I. J. Chem. Soc., Faraday Trans. 1990, 86, 3111.
S0743-7463(98)00520-4 CCC: $15.00 © 1998 American Chemical Society Published on Web 08/07/1998
Notes
Langmuir, Vol. 14, No. 18, 1998 5325 Table 1. Values of the Parameters Used To Obtain the Calculated Curves Shown in Figure 1a sI/nm-1 °C-1 9.0 ×
10-3
sN/nm-1 °C-1
PITI/°C
-9.5 × 10-3
35
PITN/°C 30
Bs/nm-1 °C-1
Bi/nm-1
∆H°/kJ mol-1
Kp at 27 °C
-6.3 × 10-3
0.82
40
2.6 × 10-3
a The values of i and i are obtained from PIT and PIT using I N I N eq 4. Except for ∆H° and Kp, the values correspond to those quoted in ref 1 modified slightly to take account of the mole fraction concentration scale used here.
Figure 1. Variation of PIT with XIt for noil ) 0.067 mol and nsurf ) 1.5 × 10-3 (open circles), 0.8 × 10-3 (filled circles), and 0.5 × 10-3 moles (triangles). The solid lines are calculated using the parameters in Table 1. The dashed line shows the expected variation in the absence of partitioning.
We thus consider a system comprising water, oil, a nonionic surfactant (N) and an ionic surfactant (I) where the ionic surfactant is taken to be all located in the monolayer region and the nonionic surfactant is distributed between the monolayer regions and the oil. The number of moles of each species in the total system are nwater, noil, nN, and nI for water, oil, and nonionic and ionic surfactants, respectively. nsurf is the total moles of surfactant ()nN + nI). The surfactant composition of the mixed monolayers is defined as XIm equal to nIm/(nNm + nIm), where the subscript m indicates the species is located in the monolayer. The overall ionic surfactant composition in the total system XIt is equal to nI/(nN + nI). We assume that the distribution of the nonionic surfactant between the monolayer region and the oil is governed by a distribution coefficient Kp as follows
Kp ) XNoil/XNm
(5)
where XNoil is the mole fraction of nonionic surfactant in the oil ()nNoil/(nNoil + noil)) and XNm is the mole fraction of nonionic in the monolayer ()nNm/(nIm + nNm) ) 1 XIm). Equation 5 is approximate in that it assumes that nonideality within the mixed monolayer can be neglected. Under conditions such that the total nonionic surfactant content is in excess of that required for aggregate formation the value of nNoil is
nNoil )
noil (Kp(1 - XIm))-1 -1
)
noilKp(1 - XIm) (6) 1 - Kp + KpXIm
XIt can be calculated from a given monolayer composition XIm using
(
XIt ) XIm
)
nsurf - nNoil nsurf
(7)
Alternatively, XIm can be calculated from a given Xt using the quadratic expression
(-Kpnoil - Kpnsurf)XIm2 + (-nsurf + Kpnsurf + KpXItnsurf + Kpnoil)XIm + (XItnsurf - KpXItnsurf) ) 0 (8)
X It
X It Figure 2. Calculated variation of rnat with XIt and temperature in the absence of partitioning (upper plot) and with noil ) 0.067 mol and nsurf ) 0.5 × 10-3 mol (lower plot) where partitioning is significant.
The temperature dependence of the distribution coefficient Kp is known to follow the usual van’t Hoff relationship9,10 as given below in integrated form
Kp(T) ) Kp(T1) exp
(
∆H° 1 1 R T1 T
)
(9)
where Kp(T) is the value at a temperature T (to be calculated), Kp(T1) is a known value at a particular temperature T1, ∆H° is the standard molar enthalpy change associated with the partitioning process, and R is the gas constant. Equations 5 to 9 extend the model to allow the calculation of the microemulsion properties as functions of both XIt and temperature for systems in which there is significant partitioning of the nonionic surfactant into the oil. Significant partitioning is expected to occur when nsurf is low, noil is high, and for high temperatures when Kp is high. To test the extended model, we have measured PIT values for AOT/C12E5 systems as functions of XIt for different values of nsurf. PITs were measured for emulsions containing 10 mL of 0.06 M NaCl in water with 10 mL of n-heptane using the conductivity method described in ref
5326 Langmuir, Vol. 14, No. 18, 1998
1 where all details of materials used can also be found. The input parameters sI, sN, Bs, Bi, and the PIT values for systems with either pure AOT or pure C12E5 were taken from ref 1 with slight adjustment for the fact that we use a mole fraction scale here rather than the weight fraction scale used in that work. The standard molar enthalpy change for the partitioning of C12E5 between the aggregate monolayers and the oil was obtained from the slope of the linear van’t Hoff plot of C12E5 monomer concentration in heptane in equilibrium with C12E5 microemulsions versus reciprocal temperature (Figure 5 of ref 10) and is equal to 40 kJ mol-1. For pure C12E5 microemulsions at 27 °C, the equilibrium C12E5 monomer mole fraction present in the heptane is (2.9 ( 0.4) × 10-3 from the data in ref 10. This value is equal to Kp since XNm is 1 in this case. Figure 1 shows a comparison of the measured PITs with those calculated using the parameters listed in Table 1 together with Kp at 27 °C set to 2.6 × 10-3, equal within the error to the value estimated earlier. Although the accuracy of the high-temperature PIT values is relatively poor (probably due to slight oil evaporation during the measurements), the extended model satisfactorily accounts for the results under conditions when a significant fraction of the C12E5 is lost from the mixed monolayers to
Notes
the oil. An interesting feature of the curve for nsurf ) 5 × 10-4 moles is that samples with XIt less than 0.06 show a “double phase inversion”; i.e., increasing temperature gives transitions from o/w to w/o and back to o/w. This is due to the increased loss of C12E5 from the mixed monolayers at high temperatures; e.g., for XIt ≈ 0.05 at 50 °C, the monolayer composition is XIm ≈ 0.3. Using the same model input parameters, the effect of partitioning on rnat as a function of both XIt and temperature is calculated in Figure 2. In the 3D plot, the PIT values correspond to the “cliffs” in the rnat surfaces. As expected, the effect of C12E5 loss to the oil is most evident for low XIt values where the C12E5 content is highest; i.e., the “cliffs” in the low XIt region of the lower plot bend back to the axis with increasing temperature. Acknowledgment. We thank Dr. D. K. Rodham, Dr. P. Taylor, and Mr. P. D. Winn (Zeneca Agrochemicals, Jealott’s Hill Research Station, U.K.) for support and helpful discussions. We are grateful to the University of Hull and to Zeneca Agrochemicals for financial support. LA980520W
