Thermodynamic theory of microemulsions

According to the thermodynamic theory of microemulsion formation, the total interfacial tension of the mixed film of surfactant and cosurfactant must approach zero. The total interfacial tension is given by the following equation. 

Although the thermodynamic theory of microemulsions still has some way to go to be more or less complete, a number of generalizations can be made regarding ionic surfactant microemulsions ... 

Several theories have been proposed to account for the thermodynamic stability of microemulsions. The most recent theories showed that the driving force for microemulsion formation is the ultralow interfacial tension (in the region of 10 4-10 2 mN m 1). This means that the energy required for formation of the interface (the large number of small droplets) A Ay is compensated by the entropy of dispersion —TAS, which means that the free energy of formation of microemulsions AG is zero or negative. 

Micellar aggregates are considered in chapter 3 and a critical concentration is defined on the basis of a change in the shape of the size distribution of aggregates. This is followed by the examination, via a second order perturbation theory, of the phase behavior of a sterically stabilized non-aqueous colloidal dispersion containing free polymer molecules. This chapter is also concerned with the thermodynamic stability of microemulsions, which is treated via a new thermodynamic formalism. In addition, a molecular thermodynamics approach is suggested, which can predict the structural and compositional characteristics of microemulsions. Thermodynamic approaches similar to that used for microemulsions are applied to the phase transition in monolayers of insoluble surfactants and to lamellar liquid crystals. 

These fascinating bicontinuous or sponge phases have attracted considerable theoretical interest. Percolation theory [112] is an important component of such models as it can be used to describe conductivity and other physical properties of microemulsions. Topological analysis [113] and geometric models [114] are useful, as are thermodynamic analyses [115-118] balancing curvature elasticity and entropy. Similar elastic modulus considerations enter into models of the properties and stability of droplet phases [119-121] and phase behavior of microemulsions in general [97, 122]. 

The influence of surfactant structure on the nature of the microemulsion formed can also be predicted from the thermodynamic theory by Overbeek (17,18). According to this theory, the most stable microemulsion would be that in which the phase with the smaller volume fraction forms the droplets, since the osmotic term increases with increasing i. For w/o microemulsion prepared using an ionic surfactant, the hard sphere volume is only slightly larger than the water volume, since the hydrocarbon tails of the surfactant may interpenetrate to a certain extent, when two droplets come close together. For an oil in water microemulsion, on the other hand, the double layer may extend to a considerable extent, depending on the electrolyte concentration... 

In this paper, a molecular thermodynamic approach is developed to predict the structural and compositional characteristics of microemulsions. The theory can be applied not only to oil-in-water and water-in-cil droplet-type microemulsions but also to bicontinuous microemulsions. This treatment constitutes an extension of our earlier approaches to micelles, mixed micelles, and solubilization but also takes into account the self-association of alcohol in the oil phase and the excluded-volume interactions among the droplets. Illustrative results are presented for an anionic surfactant (SDS) pentanol cyclohexane water NaCl system. Microstructur al features including the droplet radius, the thickness of the surfactant layer at the interface, the number of molecules of various species in a droplet, the size and composition dispersions of the droplets, and the distribution of the surfactant, oil, alcohol, and water molecules in the various microdomains are calculated. Further, the model allows the identification of the transition from a two-phase droplet-type microemulsion system to a three-phase microemulsion system involving a bicontinuous microemulsion. The persistence length of the bicontinuous microemulsion is also predicted by the model. Finally, the model permits the calculation of the interfacial tension between a microemulsion and the coexisting phase. 

In this paper, a predictive molecular thermodynamic approach is developed to calculate the structural and compositional characteristics of microemulsions. The theory applies not only to oil-in-water and water-in-oil droplet-type microemulsions but also to bicontinuous microemulsions. The treatment is an extension of our earlier theories for micelles, mixed micelles, and solubilization but also takes into account the self-association of alcohol in oil and the volume-excluded interactions among... 

The formulation of microemulsions or micellar solutions, like that of conventional macroemulsions, is still an art. In spite of exact theories that have explained the formation of microemulsions and their thermodynamic stabihty, the science of microemulsion formulation has not advanced to a point where an accurate prediction can be made as to what might happen when the various components are mixed. The very much higher ratio of emulsifier to disperse phase which differentiates microemulsions from macroemulsions appears at a first sight that the appHcation of various techniques for formulation to be less critical. However, in the final stages of the formulation it can be realised immediately that the requirements are critical due to the greater number of parameters involved. 

This new theory of the non-equilibrium thermodynamics of multiphase polymer systems offers a better explanation of the conductivity breakthrough in polymer blends than the percolation theory, and the mesoscopic metal concept explains conductivity on the molecular level better than the exciton model based on semiconductors. It can also be used to explain other complex phenomena, such as the improvement in the impact strength of polymers due to dispersion of rubber particles, the increase in the viscosity of filled systems, or the formation of gels in colloids or microemulsions. It is thus possible to draw valuable conclusions and make forecasts for the industrial application of such systems. 

The model based on the lattice fluid SCF theory offers a means to calculate fundamental interfacial properties of microemulsions from pure component properties [25]. Because all of the relevant interfacial thermodynamic properties are calculated explicitly and the surfactant and oil molecular architectures are considered, the model is applicable to a wide range of microemulsion systems. The interfacial tension, bending moment, and interaction strength between the droplets can be calculated in a consistent manner and analyzed in terms of the detailed interfacial composition. The mechanism of the density effect on the natural curvature includes both an enthalpic and an entropic component. As density is decreased, the solvation of the surfactant tails is less favorable enthalpically, and the solvent is expelled from the interfacial region. Entropy also contributes to this oil expulsion due to the density difference between the interfacial region and the bulk. The oil expulsion and increased tail-tail interactions decrease the natural curvature. 

This book is divided into five parts as follows Part I Historieal Perspeetive Part II Structural Aspects and Characterization of Microemulsions Part III Reactions in Microemulsions Part IV Applications of Microemulsions and Part V Future Prospects. The book opens with the chapter on the historical development of microemulsion systems by two leading authorities (Lindman and Friberg) who have significantly contributed to the field of microemulsions. In the next two chapters J. Th. G. Overbeek (the doyen of colloid science) and coworkers and E. Ruckenstein advance different approaches to describe the thermodynamics of microemulsion systems. While a full description of microemulsion thermodynamics is far from complete, the droplet type model predicts the experimental observations quite well. A theory that predicts the global phase behavior and the detailed properties of the phases as a function of experimentally adjustable parameters is still under development. 

The status of the systems commonly referred to as microemulsions among surface and colloid chemists is still somewhat uncertain. Various experimental approaches have been used in an attempt to ascertain the details of their structural and thermodynamic characteristics. As a result, new theories of the formation and stability of these interesting but quite complex systems are appearing. Although a great deal has been learned about microemulsions, there is much more to be learned about the requirements for their preparation and the relationships among the chemical structure of the oil phase, the composition of the aqueous phase, and the structures of the surfactant and the cosurfactant, where needed. 

The spontaneous formation of the microemulsion with decreasing free energy can only be expected if the interfadal tension is so low that the remaining free energy of the interface is overcompensated for by the entropy of dispersion of the droplets in the medium [7, 8]. This concept forms the basis of the thermodynamic theory proposed by Ruckenstein and Chi and Overbeek [7, 8]. 

The thermodynamics of microemulsion discussed in the beginning of the chapter has accounted for the basic conditions required for the formation and stability of reverse micellar systems. The energetics of formation in terms of Gibbs free energy, enthalpy, and entropy need to be quantified with reference to the system composition and the droplet structures. For the formation of w/o systan, a simple method called dilution method can exfiact energetic information for many combinations along with the understanding of their structural features. The method has been amply studied and presented in literature [4,27-32]. We, herein, introduce and present the method with basic theory and examples. 

Microemulsions are microheterogeneous, thermodynamically stable, spontaneously formed mixtures of oil and water under certain conditions by means of surfactants, with or without the aid of a cosurfactant. The first paper on microemulsions appeared in 1943 by Hoar et al but it was Schulman and coworkers who first proposed the word microemulsion in 1959. Since then, the term microemulsions has been used to describe multicomponent systems comprising nonpolar, aqueous, surfactant, and cosurfactant components. The application areas of microemulsions have increased dramatically during the past decades. For example, the major industrial areas are fabricating nanoparticles, oil recovery, pollution control, and food and pharmaceutical industries. This book is a comprehensive reference that provides a complete and systematic assessment of all topics affecting microemulsion performance, discussing the fundamental characteristics, theories, and applications of these dispersions that have been developed over the last decade. 

Microemulsions or swollen micellar systems represent an intermediate state between micellar solutions and true emulsions as shown in the hypothetical phase diagram in Fig. 8.31. They are readily distinguished from emulsions by their transparency and more fundamentally by the fact that they represent single thermodynamically stable solution phases. The term microemulsion was introduced to describe systems first identified by Hoar and Schulman [166]. Interest in these fluid translucent isotropic dispersions of oil or water has grown rapidly a book devoted to the theory and practice of microemulsions was published in 1977 [167]. 

Three key theories to explain microemulsion formation of have been proposed the mixed film, solubilization and thermodynamic theories. As described, these theories are not mutually exclusive, as elements from each can contribute to an understanding of microemulsion formation and stability. 

Modem scaling theory is a quite powerful theoretical tool (appHcable to Hquid crystals, magnets, etc) that has been well estabUshed for several decades and has proven to be particularly useful for multiphase microemulsion systems (46). It describes not just iuterfacial tensions, but virtually any thermodynamic or physical property of a microemulsion system that is reasonably close to a critical poiat. For example, the compositions of a microemulsion and its conjugate phase are described by equations of the foUowiug form ... 

Similar attempts were made by Likhtman et al. [13] and Reiss [14]. Reference 13 employed the ideal mixture expression for the entropy and Ref. 14 an expression derived previously by Reiss in his nucleation theory These authors added the interfacial free energy contribution to the entropic contribution. However, the free energy expressions of Refs. 13 and 14 do not provide a radius for which the free energy is minimum. An improved thermodynamic treatment was developed by Ruckenstein [15,16] and Overbeek [17] that included the chemical potentials in the expression of the free energy, since those potentials depend on the distribution of the surfactant and cosurfactant among the continuous, dispersed, and interfacial regions of the microemulsion. Ruckenstein and Krishnan [18] could explain, on the basis of the treatment in Refs. 15 and 16, the phase behavior of a three-component oil-water-nonionic surfactant system reported by Shinoda and Saito [19],... 

Quantitative predictions of surfactant phase behavior can be made by constructing a thermodynamic model. The classical expression for the free energy of a microemulsion is a function of the interfacial tension, bending moment, and micelle-micelle interactions [47]. Two quantitative models have been developed to describe supercritical microemulsions based on this concept. Here, the key challenge is to find accurate expressions for the oil-surfactant tail interactions and the tail-tail interactions. To do this, the first model uses a modified Flory-Krigbaum theory [43,44], and the second a lattice fluid self-consistent field (SCF) theory [25]. 

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