Three-phase equilibrium, surfactant

Therefore, the physical meaning of the solubility curve of a surfactant is different from that of ordinary substances. Above the critical micelle concentration the thermodynamic functions, for example, the partial molar free energy, the activity, the enthalpy, remain more or less constant. For that reason, micelle formation can be considered as the formation of a new phase. Therefore, the Krafft Point depends on a complicated three phase equilibrium. 

With nonionic surfactants of the PEO [poly(ethylene oxide)] type, the temperature is an important variable. They are water-soluble at lower temperatures and oil-soluble at high temperatures. In the narrow temperature range where the solubility changes, called PIT (phase inversion temperature [6]), the interfacial tension becomes extremely low, as sketched in Fig. 2. Below the PIT an O/W (oil-in-water) microemulsion is formed, above it a W/O (water-in-oil) microemulsion, with a continuous transition between them, possibly a bicontinuous mixture of oil and water, which at low surfactant concentrations may show a three-phase equilibrium with excess oil and water. Such equilibria are designated Winsor I (O/W-fO), Winsor II (W/O-bW), and Winsor III [(bicontinuous 0-fW)-fO-f W] after P. A. Winsor [7-9], who studied phase equilibria in (mostly ionic) microemulsion systems extensively and at an early date. 

If more and more surfactant is added to a Winsor III system, the surfactant-rich phase swells at the expense of the excess oil and water phases. From a certain point, a single surfactant-rich phase is found. Upon increasing the amount of surfactant even further, a first-order transition to a lamellar phase may be observed. In a special case, it has been shown that the coexistence region between the (bicontinuous) microemulsion phase and a lamellar phase was extended into the region where the surfactant-rich phase coexists with excess oil and water, leading to a four-phase equilibrium water-lamellar phase-microemulsion phase-oil [58]. In Ref. 46, even a three-phase equilibrium, water-lamellar phase-oil, was observed, the bicontinuous microemulsion phase apparently being absent. 

In order to illustrate the phase behaviour of microemulsions, it is most convenient to consider the systems with nonionic surfactants of the ethylene oxide type. These have been studied extensively by Shinoda and Kunieda and co-workers and by Kahlweit and Strey and co-workers (for more recent reviews, see, e.g. refs (9) and (10)). At low surfactant concentrations, there is a general sequence of phase equilibria, often referred to as Winsor equilibria (11). The equilibrium conditions for the microemulsion phase, L, changes from equilibrium with excess oil (Winsor I) to equilibrium with excess water (Winsor II), via a three-phase equilibrium with excess water and oil (Winsor III). For nonionics, this sequence occurs when increasing the temperature, while for quaternary or ternary systems, it can be observed with increasing salinity or cosurfactant-to-surfactant ratio. 

Figure 17.3. (a) Illustration of the section through the phase prism at equal volumes of water and oil. (b) A schematic phase diagram plotted as temperature versus the surfactant concentration 0s 7i and Tj, are the lower and upper temperatures, respectively, of the three-phase equilibrium W + L -)- O, while Tq is the temperature at which the three-phase triangle is isosceles, i.e. when the middle-phase microemulsion contains equal amounts of water and oil. The latter condition is also termed as balanced . The parameter 0 is the surfactant concentration in the middle-phase microemulsion at balanced conditions... 

In the early 1940s, Schulman and co-workers discovered that using two surfactants of an opposite packing type i.e. a mixture of oil-soluble and water-soluble surfactants) could drastically improve emulsion stability. The authors attributed it to the formation of molecular complexes between the surfactants at the oil-water interface. It was discovered that two surfactants together reduced the interfacial tension to very low values ( 0.1 mNm" ), much lower than each of them separately. Many years later the studies of the phase behavior of similar systems revealed that the idea of molecular complexes was incorrect. The surfactants do not form a stoichiometric complex, but associate into a mixed bilayer and form a lamellar phase, which co-exists with oil and water in a three-phase equilibrium. 

For the solid-liquid system changes of the state of interface on formation of surfactant adsorption layers are of special importance with respect to application aspects. When a liquid is in contact with a solid and surfactant is added, the solid-liquid interface tension will be reduced by the formation of a new solid-liquid interface created by adsorption of surfactant. This influences the wetting as demonstrated by the change of the contact angle between the liquid and the solid surface. The equilibrium at the three-phase contact solid-liquid-air or oil is described by the Young equation ... 

An example for a partially known ternary phase diagram is the sodium octane 1 -sulfonate/ 1-decanol/water system [61]. Figure 34 shows the isotropic areas L, and L2 for the water-rich surfactant phase with solubilized alcohol and for the solvent-rich surfactant phase with solubilized water, respectively. Furthermore, the lamellar neat phase D and the anisotropic hexagonal middle phase E are indicated (for systematics, cf. Ref. 62). For the quaternary sodium octane 1-sulfonate (A)/l-butanol (B)/n-tetradecane (0)/water (W) system, the tricritical point which characterizes the transition of three coexisting phases into one liquid phase is at 40.1°C A, 0.042 (mass parts) B, 0.958 (A + B = 56 wt %) O, 0.54 W, 0.46 [63]. For both the binary phase equilibrium dodecane... 

If we assume that the data of Figs. 22 and 23 can be treated by equilibrium thermodynamics, the discontinuities in the ESP versus temperature phase diagram should indicate the presence of a three-way equilibrium between bulk surfactant and two different film types in both homo- and hetero-chiral systems. The surface heats of transition (U) between the two film types in either system may be obtained by relation (15), where IT is the equilibrium... 

Winsor [15] classified the phase equilibria of microemulsions into four types, now called Winsor I-IV microemulsions, illustrated in Fig. 15.5. Types I and II are two-phase systems where a surfactant rich phase, the microemulsion, is in equilibrium with an excess organic or aqueous phase, respectively. Type III is a three-phase system in which a W/O or an O/W microemulsion is in equilibrium with an excess of both the aqueous and the organic phase. Finally, type IV is a single isotropic phase. In many cases, the properties of the system components require the presence of a surfactant and a cosurfactant in the organic phase in order to achieve the formation of reverse micelles one example is the mixture of sodium dodecylsulfate and pentanol. 

In the Will case, provided that there is enough surfactant but not too much, e.g., 1 wt. %, the system splits into three phases, i.e., a microemulsion in equilibrium with excess water and excess oil. At a higher surfactant concentration than the top vertex of the 3

single phase microemulsion often called WW behavior is attained. However, this occurrence generally requires a large amount of surfactant, e.g., 20 wt. %, which is in most practical cases too much for cost reasons. At a very low surfactant concentration, around the CMC, only two phases are in equilibrium, and the tension is not necessarily very low. Hence, the convenient surfactant concentration to carry out a phase behavior study is in the range 0.5-3 wt. % for which three-phase behavior and a very low inter facial tension is exhibited in most Will cases. 

Phenomena at Liquid Interfaces. The area of contact between two phases is called the interface three phases can have only a line of contact, and only a point of mutual contact is possible between four or more phases. Combinations of phases encountered in surfactant systems are L—G, L—L—G, L—S—G, L—S—S—G, L—L, L—L—L, L—S—S, L—L—S—S—G, L—S, L—L—S, and L—L—S—G, where G = gas, L = liquid, and S = solid. An example of an L—L—S—G system is an aqueous surfactant solution containing an emulsified oil, suspended solid, and entrained air (see Emulsions Foams). This embodies several conditions common to practical surfactant systems. First, because the surface area of a phase increases as particle size decreases, the emulsion, suspension, and entrained gas each have large areas of contact with the surfactant solution. Next, because interfaces can only exist between two phases, analysis of phenomena in the L—L—S—G system breaks down into a series of analyses, ie, surfactant solution to the emulsion, solid, and gas. It is also apparent that the surfactant must be stabilizing the system by preventing contact between the emulsified oil and dispersed solid. Finally, the dispersed phases are in equilibrium with each other through their common equilibrium with the surfactant solution. 

The type III phase environment may contain a maximum of three phases. When this is the case, the emulsion present corresponds to Winsor type III, in which a microemulsion is in equilibrium with pure oil and pure brine phases. However, type II(-) behavior and type II(+) behavior may also be observed under certain conditions. In practice, type II(-) or II(+) behavior occurs when all of the brine or oil can be incorporated into the microemulsion or when insufficient surfactant is present to produce a measurable microemulsion. 

A decade after the empirical determination of the correlations for three-phase behaviour and the corroboration that the linearity and generality could not be coincidental, a simple interpretation was found through the so-called surfactant affinity difference (SAD) concept discussed next. When a simple ternary surfactant-oil-water system exhibits three-phase behaviour, the chemical potential p. of the surfactant is equal in the three phases (oil, water and microemulsion) at equilibrium referred to by subscripts O, W and M. It holds... 

As was mentioned earlier in this chapter, it is not necessary to transfer every reaction mixture into a thermodynamically stable one-phase system. Often the presence of one organised surfactant phase in equilibrium with one or two excess phases is sufficient to give an appropriate reaction rate. In such two- or three-phase systems the reaction occurs in the surfactants phase while the coexisting phases act as reservoir for the reactants. This approach has been demonstrated for alkylation of phenol [28] and for rhodium catalysed hydroformylation of dodecene [50]. A major practical advantage with the multi-phase systems is that substantially less surfactant is needed. This reduces costs and simplifies the work-up. 

Vapor sorption measurements yield equilibrium composition and fugacity or chemical potential the isopiestic version (19) is used to determine the uptake of a pure vapor by a nonvolatile material. This technique determines equilibrium composition of a phase which cannot be separated quantitatively from the liquid phase in equilibrium with it. In our application, a nonvolatile crystalline surfactant specimen S is equilibrated with vapor of V, which is, in turn, at equilibrium with a system of S and V consisting of two phases, one rich in S, and one rich in V. At equilibrium, the Gibbs-Duhem relation guarantees. that the initial specimen of S takes up enough V from the vapor phase that the chemical potential of S, as well as of V, is the same as in the biphasic system, and so the composition of the phase formed by vapor sorption is the same as that of the S-rich phase. This composition is easily determined by weight measurement. If the temperature were a triple point, i.e. three phases at... 

Analogously, at point C the phase separation into a microemulsion of the composition D and a micellar solution of inverse micelles containing solubilized water takes place. This is a Winsor I (WI) type equlibrium. At the intermediate point E the system consists of a single microemulsion phase (ME). At even lower surfactant concentrations (line c), depending on the water/hydrocarbon ratio, the system will either separate into one of the two-phase systems (Winsor I or Winsor II), or a three-phase system may form at point F. This is a Winsor III (Will) equilibrium with an aqueous phase at the bottom, a microemulsion phase in the middle and a hydrocarbon phase at the top. 

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