Free energy micellar phase

In this study we examined the influence of concentration conditions, acidity of solutions, and electrolytes inclusions on the liophilic properties of the surfactant-rich phases of polyethoxylated alkylphenols OP-7 and OP-10 at the cloud point temperature. The liophilic properties of micellar phases formed under different conditions were determined by the estimation of effective hydration values and solvatation free energy of methylene and carboxyl groups at cloud-point extraction of aliphatic acids. It was demonstrated that micellar phases formed from the low concentrated aqueous solutions of the surfactant have more hydrophobic properties than the phases resulting from highly concentrated solutions. The influence of media acidity on the liophilic properties of the surfactant phases was also exposed. 

On the other hand, micelle formation has sometimes been considered to be a phase separation of the surfactant-rich phase from the dilute aqueous solution of surfactant. The micellar phase and the monomer in solution are regarded to be in phase equilibrium and cmc can be considered to be the solubility of the surfactant. When the activity coefficient of the monomer is assumed to be unity, the free energy of micelle formation, Ag, is calculated by an equation... 

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. 

In this system, in the aqueous phase, the micellar system, NaDDS, on addition of butanol would change in free energy due to mixed micelle formation (i. je. NaDDS+n-Butanol), as we showed in an earlier study (23). The cahnge in free energy is also observed from the fact that both the critical micelle concentration (c.m.c.) and the Krafft point of NaDDS solution change on addition of n-Butanol (23,... 

The partition coefficient relates to the hydrophobic character of a substance. Its logarithm is proportional to the free energy of the transfer of a substance from the aqueous phase to the micellar phase. Correlation of these partition coefficients with the partition coefficients of other systems, such as octanol/water, results in a straight line on a logarithmic scale. Some correlations are given in Chapters 5 and 6. 

Since their effective diffusivities are of the same magnitude as those of micellar solutions, the hquid crystalUne phases, though viscous, do not significantly hinder surfactant dissolution for these rather hydrophihc surfactants. Indeed, a drop of Ci2(EO)6 having Ro = 78 pm dissolved completely in only 16 s at 30 °C. Rapid dissolution is favored because free energy decreases as the surfactant is transferred from the Hquid surfactant phase L2 to liquid crystals) to aqueous micellar solution and the aggregate shape approaches that of a dilute Li phase, where its free energy is minimized at this temperature. 

Rahaman and Hatton [152] developed a thermodynamic model for the prediction of the sizes of the protein filled and unfilled RMs as a function of system parameters such as ionic strength, protein charge, and size, Wq and protein concentration for both phase transfer and injection techniques. The important assumptions considered include (i) reverse micellar population is bidisperse, (ii) charge distribution is uniform, (iii) electrostatic interactions within a micelle and between a protein and micellar interface are represented by nonlinear Poisson-Boltzmann equation, (iv) the equilibrium micellar radii are assumed to be those that minimize the system free energy, and (v) water transferred between the two phases is too small to change chemical potential. 

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. 

The total free energy of the micellar phase contains contributions from the translational entropy of the micelles, the entropy of mixing of homopolymers and copolymers and their interaction outside the micelles. It can be written as (Leibler et al. 1983)... 

Viscosity and density of the component phases can be measured with confidence by conventional methods, as can the interfacial tension between a pure liquid and a gas. The interfacial tension of a system involving a solution or micellar dispersion becomes less satisfactory, because the interfacial free energy depends on the concentration of solute at the interface. Dynamic methods and even some of the so-called static methods involve the creation of new surfaces. Since the establishment of equilibrium between this surface and the solute in the body of the solution requires a finite amount of time, the value measured will be in error if the measurement is made more rapidly than the solute can diffuse to the fresh surface. Eckenfelder and Barnhart (Am. Inst. Chem. Engrs., 42d national meeting, Repr. 30, Atlanta, 1960) found that measurements of the surface tension of sodium lauryl sulfate solutions by maximum bubble pressure were higher than those by DuNuoy tensiometer by 40 to 90 percent, the larger factor corresponding to a concentration of about 100 ppm, and the smaller to a concentration of 2500 ppm of sulfate. 

Typically, micelles tend to be approximately spherical over a fairly wide range of concentration above the c.m.c., but often there are marked transitions to larger, non-spherical liquid-crystal structures at high concentrations. Systems containing spherical micelles tend to have low viscosities, whereas liquid-crystal phases tend to have high viscosities. The free energies of transition between micellar phases tend to be small and, consequently, the phase diagrams for these systems tend to be quite complicated and sensitive to additives. 

Emulsions made by agitation of pure immiscible liquids are usually very unstable and break within a short time. Therefore, a surfactant, mostly termed emulsifier, is necessary for stabilisation. Emulsifiers reduce the interfacial tension and, hence, the total free energy of the interface between two immiscible phases. Furthermore, they initiate a steric or an electrostatic repulsion between the droplets and, thus, prevent coalescence. So-called macroemulsions are in general opaque and have a drop size > 400 nm. In specific cases, two immiscible liquids form transparent systems with submicroscopic droplets, and these are termed microemulsions. Generally speaking a microemulsion is formed when a micellar solution is in contact with hydrocarbon or another oil which is spontaneously solubilised. Then the micelles transform into microemulsion droplets which are thermodynamically stable and their typical size lies in the range of 5-50 nm. Furthermore bicontinuous microemulsions are also known and, sometimes, blue-white emulsions with an intermediate drop size are named miniemulsions. In certain cases they can have a quite uniform drop size distribution and only a small content of surfactant. An interesting application of this emulsion type is the encapsulation of active substances after a polymerisation step [25, 26]. 

Le Grand (36) has developed a model to account for domain formation and stability based on the change in free energy which occurs between a random mixture of block copolymer molecules and a micellar domain structure. The model also considers contributions to the free energy of the domain morphology resulting from the interfacial boundary between phases and elastic deformation of the domains. 

The discussion of the relative stability of solutions with inverse micelles and of liquid crystals containing electrolytes may be limited to the enthalpic contributions to the total free energy. The experimentally determined entropy differences between an inverse micellar phase and a lamellar liquid crystalline phase are small (12). The interparticle interaction from the Van der Waals forces is small (5) it is obvious that changes in them owing to added electrolyte may be neglected. The contribution from the compression of the diffuse electric double layer is also small in a nonaqueous medium (II) and their modification owing to added electrolyte may be considered less important. It appears justified to limit the discussion to modifications of the intramicellar forces. 

Knowing these mole fractions, the distribution constant K, for the partitioning of MMA between the micellar and aqueous environments can be determined from the ratio of X to X, assuming that all activity coefficients are unity. Then,mthe standard free energy of transfer of MMA from the aqueous to micellar phase can be calculated from... 

Table I displays the mole fraction of the MMA which is in the aqueous phase for the Lj phase and microemulsion systems studied. These fractions were found to be reproducible to within 0.04. As can be seen, MMA favors the micellar phase by at least a four-to-one ratio. The free energy of transfer, calculated for systems less than 0.53 M in MMA was found to be -14.0 kJ/mole with an uncertainty of 10%.

An additional indication comes from the measured free energy of transfer of MMA from the aqueous to the micellar phase. Wishnia measured the free energy for the transfer of alkanes from aqueous solution to SLS micelles (22). He studied the homologous series, ethane through pentane, at low concentrations. His result for ethane was -14.5 kJ/mole. 

All the theories described above are based on the ideal solution thermodynamics, on the one hand, and on a rather heuristic molecular treatment of micelles as a phase particle, on the other hand. Despite of their obvious successes in predicting micellar solution properties, these theories have some essential drawbacks. The number of adjusting parameters at the evaluation of different contributions to the free energy is too high, as well as the number of oversimplifications, which have been used in order to estimate these parameters. For example, the micellar core is considered as a very small fluid phase droplet surrounded by a second fluid phase and the free energy of micelle surface is estimated as the interfacial tension between these two fluid phases. In order to elucidate this problem Eriksson et al, [24] attempted to... 

Micelles (normal and reverse) are aggregates of surfactants, which are formed spontaneously in a liquid phase when the surfactant concentration is increased than the critical micelle concentration (CMC). Micellar solutions are formed in aqueous continuous systems, whereas, the reverse micelles are formed in oily continuous systems. In micelles (oil-in-water micelle), the polar heads of the surfactant lie outside in the aqueous phase, whereas the lipophilic hydrocarbon chains lie inside (Figure 58.3). When the surfactant concentration is increased, the free energy of the system increases due to the inauspicious interactions between the water molecules and the lipophilic portions of the surfactant. The water molecules around the oil droplets structures themselves, thereby, resulting in the decrease in the entropy. The reverse micelles (water-in-oil micelle) have opposite structure, that is, the polar heads lie at the centre, while the lipophilic tails are present outside in the oil phase (Figure 58.3). The surfactant concentration need not necessarily be higher than the CMC for the formation of reverse micelle. Many scientists reported formation of reverse micelles by lecithin in different oil phases. " ... 

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