Free energy surfactant systems

The chemical potential describes the tendency of solute, surfactant, or dye to move from solution to the fiber. It is analogous to a partition coefficient. Gibbs suggested the use of this parameter in place of the free energy for systems where the free energy has the disadvantage of depending on the amount of the system [64],... 

Surfactants Surfactants are amphiphilic compounds with both hydrophilic and hydrophobic moieties. Because of their amphiphilic nature, surfactants accumulate at interfaces and thus minimize system-free energies. Surfactants increase PAH solubility by lowering interfacial tension as well as by accumulating the hydrophobic materials in micelles (the micellar solubilization) (Rosen, 1978 West and Harwell, 1992). 

However, the spreading of a surfactant monolayer from a volatile solvent leaves behind a film that may not be in thermodynamic equilibrium with its bulk crystalline form or the aqueous subphase. It has been proposed that this is a result of the relatively high energy barriers to film collapse or dissolution into the subphase as compared with lowered interfacial free energy when a stable, insoluble surfactant monolayer is formed (Gershfeld, 1976). The rate at which a whole system approaches true equilibrium in such a system is often so slow that the monolayer film can be treated for most purposes as though it were at equilibrium with the subphase. 

Surfactants (a contraction of the term surface-active agent) are substances one of whose properties is that of being adsorbed in surfaces or interfaces of the system and altering the free energy of these surfaces (or interfaces). Here, the term interface refers to the union between two inmiscible phases, while the term surface refers to an interface in which one of the phases is a gas, generally air. 

Most studies of micellar systems have been carried out on synthetic surfactants where the polar or ionic head group may be cationic, e.g. an ammonium or pyridinium ion, anionic, e.g. a carboxylate, sulfate or sulfonate ion, non-ionic, e.g. hydroxy-compound, or zwitterionic, e.g. an amine oxide or a carboxylate or sulfonate betaine. Surfactants are often given trivial or trade names, and abbreviations based on either trivial or systematic names are freely used (Fendler and Fendler, 1975). Many commercial surfactants are mixtures so that purity can be a major problem. In addition, some surfactants, e.g. monoalkyl sulfates, decompose slowly in aqueous solution. Some examples of surfactants are given in Table 1, together with values of the critical micelle concentration, cmc. This is the surfactant concentration at the onset of micellization (Mukerjee and Mysels, 1970) and can therefore be taken to be the maximum concentration of monomeric surfactant in a solution (Menger and Portnoy, 1967). Its value is related to the change of free energy on micellization (Fendler and Fendler, 1975 Lindman and Wennerstrom, 1980). 

The mixed cmc behavior of these (and many other) mixed surfactant systems can be adequately described by a nonideal mixed micelle model based on the psuedo-phase separation approach and a regular solution approximation with a single net interaction parameter B. However, the heats of micellar mixing measured by calorimetry show that the assumptions of the regular solution approximation do not hold for the systems investigated in this paper. This suggests that in these cases the net interaction parameter in the nonideal mixed micelle model should be interpreted as an excess free energy parameter. 

This transition may j-.e. reducing the specific surface energy, f. The reduction of f to sufficiently small values was accounted for by Ruckenstein (15) in terms of the so called dilution effect". Accumulation of surfactant and cosurfactant at the interface not only causes significant reduction in the interfacial tension, but also results in reduction of the chemical potential of surfactant and cosurfactant in bulk solution. The latter reduction may exceed the positive free energy caused by the total interfacial tension and hence the overall Ag of the system may become negative. Further analysis by Ruckenstein and Krishnan (16) have showed that micelle formation encountered with water soluble surfactants reduces the dilution effect as a result of the association of the the surfactants molecules. However, if a cosurfactant is added, it can reduce the interfacial tension by further adsorption and introduces a dilution effect. The treatment of Ruckenstein and Krishnan (16) also highlighted the role of interfacial tension in the formation of microemulsions. When the contribution of surfactant and cosurfactant adsorption is taken into account, the entropy of the drops becomes negligible and the interfacial tension does not need to attain ultralow values before stable microemulsions form. 

The surfactant sodium dodecyl sulphonate (Ci2H2sS03Na) and its sulphate adsorb electrostatically on hematite at low solute concentrations (Han et al., 1973). Hydro-phobic effects operate at high concentrations due to the incompatibility of the hydrocarbon part of the molecule with water. This involves condensation of the alkyl chains at the surface (hemi-micelle interactions), which lowers the free energy of the system and reverses the surface charge. 

As indicated above, miscibiUty gaps are small and intermediate lamellar liquid crystalline phases dissolve rapidly into the aqueous phase if the surfactant or surfactant mixture is rather hydrophihc with a high spontaneous curvature (low (v/la)), for instance at temperatures below Tq for pure nonionic surfactants. In this case dissolution, which converts lamellae of zero curvature to aggregates with significant curvature as surfactant concentration decreases, occurs spontaneously because it reduces system free energy. 

The MAM described here is a generalization of the model previously published (10). Hence, only a summary of the derivation will be given here. Details can be found elsewhere (17). The basic equations are the surfactant and counterion material balances and the minimization of the Gibbs free energy of the system with respect to the micelle concentration c , and mole fraction x (11). Equation 4 from Ref. (11) has been changed to... 

Most of the studies on thermodynamics of mixed micellar systems are based on the variation of the critical micellar concentration (CMC) with the relative concentration of both components of the mixed micelles (1-4). Through this approach It Is possible to obtain the free energies of formation of mixed micelles. However, at best, the sign and magnitude of the enthalpies and entropies can be obtained from the temperature dependences of the CMC. An Investigation of the thermodynamic properties of transfer of one surfactant from water to a solution of another surfactant offers a promising alternative approach ( ), and, recently, mathematical models have been developed to Interpret such properties (6-9). 

Using this approach, a model can be developed by considering the chemical potentials of the individual surfactant components. Here, we consider only the region where the adsorbed monolayer is "saturated" with surfactant (for example, at or above the cmc) and where no "bulk-like" water is present at the interface. Under these conditions the sum of the surface mole fractions of surfactant is assumed to equal unity. This approach diverges from standard treatments of adsorption at interfaces (see ref 28) in that the solvent is not explicitly Included in the treatment. While the "residual" solvent at the interface can clearly effect the surface free energy of the system, we now consider these effects to be accounted for in the standard chemical potentials at the surface and in the nonideal net interaction parameter in the mixed pseudo-phase. 

Free Energy of Adsorption, a) System with only one surfactant. Experimentally, it is found that the adsorption of the single surfactants is well described by an equation of the form... 

Self-organization systems under thermodynamic control (spontaneous processes with a negative free-energy change), such as supramolecular complexes, crystallization, surfactant aggregation, certain nano-structures, protein folding, protein assembly, DNA duplex. 

Where this factor plays a role, the hydrophobic interaction between the hydrocarbon chains of the surfactant and the non-polar parts of protein functional groups are predominant. An example of this effect is the marked endothermic character of the interactions between the anionic CITREM and sodium caseinate at pH = 7.2 (Semenova et al., 2006), and also between sodium dodecyl sulfate (SDS) and soy protein at pH values of 7.0 and 8.2 (Nakai et al., 1980). It is important here to note that, when the character of the protein-surfactant interactions is endothermic (/.< ., involving a positive contribution from the enthalpy to the change in the overall free energy of the system), the main thermodynamic driving force is considered to be an increase in the entropy of the system due to release into bulk solution of a great number of water molecules. This entropy... 

It is apparent that CMC values can be expressed in a variety of different concentration units. The measured value of cCMC and hence of AG c for a particular system depends on the units chosen, so some uniformity must be established. The issue is ultimately a question of defining the standard state to which the superscript on AG C refers. When mole fractions are used for concentrations, AG c directly measures the free energy difference per mole between surfactant molecules in micelles and in water. To see how this comes about, it is instructive to examine Reaction (A) —this focuses attention on the surfactant and ignores bound counterions — from the point of view of a phase equilibrium. The thermodynamic criterion for a phase equilibrium is that the chemical potential of the surfactant (subscript 5) be the same in the micelle (superscript mic) and in water (superscript W) n = n. In general, pt, = + RTIn ah in which... 

Any surfactant adsorption will lower the oil-water interfacial tension, but these calculations show that effective oil recovery depends on virtually eliminating y. That microemulsion formulations are pertinent to this may be seen by reexamining Figure 8.11. Whether we look at microemulsions from the emulsion or the micellar perspective, we conclude that the oil-water interfacial free energy must be very low in these systems. From the emulsion perspective, we are led to this conclusion from the spontaneous formation and stability of microemulsions. From a micellar point of view, a pseudophase is close to an embryo phase and, as such, has no meaningful y value. 

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