2494
Langmuir 1997, 13, 2494-2497
Phase Inversion Temperatures of Macro- and Microemulsions Eli Ruckenstein Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, New York 14260 Received November 22, 1996. In Final Form: February 20, 1997X There exists a parallelism between emulsions and the corresponding microemulsions. In this framework and on the basis of the Gibbs adsorption equation, an explanation is provided for the experimental observation that the phase inversion temperature of a macroemulsion almost coincides with the phase inversion temperature of the corresponding middle phase microemulsion in equilibrium with the two excess phases.
Introduction There are major differences between macro- and microemulsions, which arise because the stability of the former has a kinetic origin, while the latter are thermodynamically stable. Nevertheless, there are also similarities. For instance, both obey in most cases the Bancroft rule,1 i.e., the phase in which the dispersant is most soluble becomes the continuous phase. It is important to emphasize that the Bancroft rule is valid for macroemulsions and microemulsions for different reasons. Kinetics is responsible for it in the former case and thermodynamics in the latter. More importantly, there is a parallelism between the two. At low temperatures, the emulsions are of the oil in water (O/W) kind, and at relatively high temperatures, they are of the water in oil (W/O) kind. Similarly, at low temperatures, an O/W microemulsion coexists with excess oil, while at high temperatures a W/O microemulsion coexists with excess water. In an intermediate range of temperatures, a middle phase microemulsion in equilibrium with both excess phases is formed. The transition from an O/W microemulsion to a W/O microemulsion occurs in the latter temperature range. It has been noted by Shinoda and Saito2 that the phase inversion temperature provided by the phase diagram of the water-oil-poly(ethylene oxide) surfactant mixture coincides with the phase inversion temperature of the corresponding emulsion. It will be shown in what follows that the parallelism between macro- and microemulsion and the equality of their phase inversion temperatures are a result of the adsorption of the surfactant on the water-oil interface and of the dependence of the interfacial tension at the water-oil interface on temperature. This adsorption ensures in the case of macroemulsions their kinetic stability and is responsible in the case of microemulsions for their thermodynamic stability. The discussion which follows considers that a nonionic surfactant with a poly(ethylene oxide) head group is the dispersant. The treatment is similar, but not identical, to the one used previously3 to explain the effect of HLB (the hydrophiliclipophilic balance) on the stability of macroemulsions when a series of nonionic surfactants with poly(ethylene oxide) head groups are employed at room temperature. Interfacial Tension at a Planar Surface Let us consider an oil-water planar interface and a surfactant with a poly(ethylene oxide) head group disX
Abstract published in Advance ACS Abstracts, April 1, 1997.
(1) Bancroft, W. D. J. Phys. Chem. 1913, 17, 501; 1915, 19, 275. (2) Shinoda, K.; Saito, H. J. Colloid Interface Sci. 1968, 26, 70; 1969, 30, 258. (3) Ruckenstein, E. Langmuir 1988, 4, 1318.
S0743-7463(96)02036-7 CCC: $14.00
tributed at equilibrium between the two phases. The interfacial free energy γ is related to the chemical potential µ per surfactant molecule and temperature T through the Gibbs adsorption equation
dγ ) -Γ dµ - s dT
(1)
where Γ is the surface excess per unit area and s is the surface excess entropy per unit area. For dilute solutions, the chemical potential µ is given by the expressions
µ ) µW° + kT ln CW ) µO° + kT ln CO
(2)
where C is the concentration of surfactant, the subscripts W and O stand for the water and oil phases, respectively, the superscript ° refers to the standard state at infinite dilution, and k is the Boltzmann constant. The concentration CW represents the surfactant concentration below the critical micelle concentration and of the nonaggregated surfactant above the critical micelle concentration (≈critical micelle concentration). At sufficiently low temperatures, the head group of the surfactant has, because of hydrogen bonding, strong interactions with the water molecules; as a result, in most cases, the surfactant is present mainly in the water phase. (There are cases in which, while the interactions between the head group and water are stronger than those between the hydrocarbon chain of the surfactant and the oil phase, those between the entire surfactant molecule and oil are stronger than those between the entire surfactant molecule and water. As a result, the surfactant molecules are distributed mainly in the oil phase but the microemulsion is of the O/W type.4 The mixture 0.01 M aqueous NaCl solution/heptane/poly(oxyethylene) glycol ether (namely C12E5)5 constitutes such a case.) The increase in temperature weakens the hydrogen bonding and hence the interactions between the head group and water. In other words, the hydrophobicity of the surfactant molecules increases with temperature and its concentration decreases in the water phase but increases in the oil phase. On this basis, the following inequalities can be written
dµW°/dT > 0,
dµO°/dT < 0
(3)
dCW/dT < 0,
dCO/dT > 0
(4)
and
(4) Ruckenstein, E. Langmuir 1996, 12, 6351. (5) Binks, B. P. Langmuir 1993, 9, 25.
© 1997 American Chemical Society
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Langmuir, Vol. 13, No. 9, 1997 2495
In order to gain some insight regarding the variation of γ with temperature, let us consider equal volumes of water and oil phases. It will be also assumed that the concentration in the water phase is lower than the critical micelle concentration. Denoting by C the surfactant concentration per unit volume
CO + CW ) 2C
(5)
Equations 2 and 5 lead to
CW )
2C 1 + e∆µ0/kT
(6a)
CO )
2Ce∆µ0/kT 1 + e∆µ0/kT
(6b)
and
positive
dγ/dT < 0 at relatively low temperatures (11) and
dγ/dT > 0 at relatively large temperatures and γ passes through a minimum (Figure 1). The preceding considerations involve the assumption that the concentration of surfactant in the water phase is below the critical micelle concentration. If it is larger, the calculations become more complex. They can be simplified if one assumes that, above the critical micelle concentration, the concentration of the nonaggregated surfactant remains approximately constant and equal to the critical micelle concentration. With this approximation, one can write that
µ ) µW° + kT ln CW1 ) µO° + kT ln C0
where
where CW1 is the critical micelle concentration (cmc). Consequently
∆µ0 ) µW° - µO° From eq 2, one obtains
kT dCW dµ dµW° ) + k ln CW + dT dT CW dT
(7)
and eq 6a yields
[
]
dCW CW 1 dµW° dµO° ∆µ0 )-∆µ /kT 0 dT kT dT dT T 1+e
(8)
Consequently, combining eqs 1, 7, and 8, one can write
{
dµW° 1 dγ ) -Γ k ln CW + + ∆µ0/kT dT dT 1+e dµO° ∆µ0 1 1 - s (9) + 1 + e-∆µ0/kT dT 1 + e-∆µ0/kT T
}
At low temperatures, µW° is small because of the hydrogen bonding and µO° large; hence ∆µ0 ) µW° - µO° is negative and large, CW ≈ 2C and CO ≈ 0, and eq 9 leads to
(
)
dµW° dγ -s ) -Γ k ln 2C + dT dT
(10a)
At relatively high temperatures µW° is large and µO° small; hence ∆µ0 is positive and large
CW ≈ 0 and CO ≈ 2C and eq 9 leads to
(
)
dµO° dγ -s ) -Γ k ln 2C + dT dT
(10b)
Because the surfactants considered here are very sensitive to temperature, one expects dµW°/dT to be positive and large and dµO°/dT to be negative and large in absolute value. Since the freedom of motion in the bulk is higher than on the interface, the surface entropy excess s is expected to satisfy the inequalities
|
Γ
|
dµW° > |s|, dT
| | Γ
dµO° > |s| dT
If, in addition, C is not too small or too large and Γ is
(
)
dµW° kT dCW1 dγ - s (12) ) -Γ + k ln CW1 + dT dT CW1 dT Since dµW°/dT > 0 and dCW1/dT can be 0 and
T
( ) ∂Γ ∂T
CW
>0
CW
Because, in addition, dCW/dT < 0, Γ has an extremum at a temperature between Tl and T0. The surface excess Γ is small at low temperatures, increases with increasing temperature because of increasing favorable interactions between the surfactant tail and oil, and attains a maximum when its increase with increasing temperature is compensated by its reduction caused by the decrease of CW with increasing temperature. Subsequently, Γ decreases because the change of CW with temperature becomes dominant. Similarly, in the range between the temperatures T0 and Th, it is convenient to write
Γ ) Γ(CO,T) and
( )
∂Γ dΓ ) dT ∂CO
( )
dC0 ∂Γ + ∂T T dT
CO at constant temperature and to decrease, because of decreasing favorable interactions with water, with increasing temperature at constant CO. Consequently,
( ) ∂Γ ∂CO
> 0, T
( ) ∂Γ ∂T
0
At constant temperature, Γ is expected to increase with increasing CW, while at constant concentration, Γ is expected to increase with increasing temperature because of increasingly favorable interactions of the surfactant molecules with oil. Therefore,
( )
Figure 2. Surface excess against temperature for an emulsion.
CO
The surface excess Γ is expected to increase with increasing
dΓ/dT becomes zero at a temperature between T0 and Th. In the neighborhood of T0, Γ increases with increasing temperature because CO increases. Γ attains a maximum when the above increase is compensated by its decrease with temperature at constant CO. It is clear that T0 is the phase inversion temperature and that at this temperature Γ passes through a minimum, and the emulsion is very unstable. Figure 2 provides a qualitative picture about the change of Γ with increasing temperature. II. When the minimum of γ against T is negative (Figure 1), then there is a range of temperatures in which the interfacial tension at the planar surface between oil and water becomes negative. The negative interfacial tension makes the interface extremely unstable to thermal and mechanical perturbations, and spontaneous emulsification occurs with the formation of globules of water in oil and oil in water. The large interfacial area generated increases the amount of surfactant adsorbed and decreases its concentrations in the bulk liquids. As a result, the interfacial tension increases. At low temperatures, the globules of water coalesce with the water phase while those of oil survive, after they attain through coalescence and splitting the equilibrium radius; thus an O/W microemulsion in equilibrium with excess oil is formed. Of course, the interfacial tensions at the surface of the globules and at the interface between microemulsion and excess oil are small and positive. At high temperatures, a W/O microemulsion in equilibrium with excess water is formed and at intermediate temperatures a middle phase microemulsion coexists with both excess phases. At low temperatures, the microemulsion is of the O/W type because the interactions between the head groups of the surfactant molecules adsorbed on the surface of the
Phase Inversion Temperatures of Emulsions
Langmuir, Vol. 13, No. 9, 1997 2497
globules and water are stronger than those between the hydrocarbon chains and oil.4 As a result, the interfacial tension is lower for the water-head group interface than for the oil-chain interface. The globules of oil in water will be preferred thermodynamically because their larger external area has the lower interfacial tension and the smaller internal area the higher interfacial tension. At high temperatures, the opposite is true and the microemulsion is of the W/O kind. At intermediate temperatures, a middle phase microemulsion coexists with the two excess phases. The temperature corresponding to the negative minimum of the interfacial tension (Figure 1) represents the phase inversion temperature. Phase Inversion Temperatures The interfacial tension γ at the planar interface between the two phases has a minimum for a temperature near T0. Indeed, at this temperature Γ is small (consequently, s is also small), and in addition, because the concentrations in the two phases are equal, ∆µ0 ) 0. As a result, eq 9 becomes
{
(
)}
1 dµW° dµO° dγ ) -Γ k ln CW + + dT 2 dT dT
-s
(13)
which, if CW is not too small or too large and µW° and µO° have symmetrical dependencies on T, leads to dγ/dT ≈ 0. The temperature corresponding to the minimum can be calculated using the equation
k ln CW +
(
)
1 dµW° dµO° ≈0 + 2 dT dT
(14)
below the critical micelle concentration and equation
dµW° kT dCW1 + k ln CW1 + ≈0 dT CW1 dT
(15)
above the critical micelle concentration. Equation 14 indicates that the temperature of the minimum (which is near the temperature T0) is for not too small or exceedingly large surfactant concentrations almost independent of concentration and dependent only on the natures of the surfactant and oil phase. Similarly, eq 15 indicates that the temperature corresponding to the minimum depends on the nature of surfactant only. This means that the minima of the two curves of Figure 1 are located almost on the same vertical, hence that the phase inversion temperatures of macro- and microemulsions are near to one another. This explains the observation of Shinoda and Saito2 that the phase inversion temperature (PIT) in emulsions coincides with that provided by the ternary phase diagram. In fact, only because this temperature is almost independent on concentration, one can extend results obtained for two liquids separated by a planar interface to emulsions. Conclusion On the basis of the Gibbs adsorption equation one can identify domains of microemulsions and macroemulsions. The curve interfacial tension γ against temperature at the planar surface between oil and water has a minimum. When the minimum is positive, macroemulsions are generated, while when the minimum is negative, microemulsions form. The curve γ against temperature with negative values of γ cuts the curve γ ) 0 in two points. The temperature corresponding to the minimum is in the middle of the middle phase microemulsion, provides the phase inversion temperature for the microemulsion, and almost coincides with the phase inversion temperature of the corresponding emulsion. LA9620364
