Mixtures interfacial free energy

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],... 

This mean-field theory to calculate the interfacial profile and interfacial free energy can be extended to compute also for a critical droplet the order parameter profile (for a binary mixture near the critical point,... 

When analyzing melting temperature-composition relations according to Eq. (3.13) the implicit assumption is made that the crystallite structure and size do not vary over the composition range studied. It is also assumed that the interfacial free energy associated with the crystallites remains constant. Since the crystallization of the polymer was conducted from the mixture, there could be concern that these factors vary with composition. However, there are no problems when... 

Mixtures of aqueous electrolytes, hydrocarbons, and amphiphilic compounds have been the subjects of extensive research, especially those systems forming amorphous isotropic solutions, called microemulsions. Several books and papers have treated this subject [1-5]. The term microemulsion was first introduced by Hoar and Schulman [5]. Microemulsions are thermodynamically stable, isotropic, transparent colloidal solutions of low viscosity, consisting of three components a surfactant (amphiphile), a polar solvent (usually water), and a nonpolar solvent (oil) [1-7]. The surfactant monomers in these fluids reside at oil water interface and effectively lower the interfacial-free energy, resulting in the formation of optically clear, thermodynamically stable formulations. The innate formation of colloidal particles is typically up to nanometer scale globular droplets each... 

Here is the interfacial free energy characteristic of the lateral surface of the nucleus and <7e is the interfacial free energy for the nucleus. We must carefully distinguish between and the other interfacial free energies that have been introduced earlier. When the complete free energy function is treated the development that follows can also include heterogeneous polymers, polymer-diluent mixtures and copolymers. We restrict consideration here to homogeneous pure systems. 

The Yg for living cells obtained with a dilution series of PEG/DEX biphasic mixtures is clearly only a partial solution to the problem of obtaining measurements of cell surface energy. The difficulty is that Yg refers only to the particular PEG/DEX mixture having a liquid-liquid interfacial tension equal to the interfacial free energy at the surface of cells exposed to the less-dense (bulk) phase of the mixture. This leaves two major problems unsolved ... 

Table III. Cell-Medium Interfacial Free Energies Estimated from Contact Angles in PEG-DEX Biphasic Mixtures.

Figure 2. The relation between the critical interfacial tension for spreading, determined with PEG (6000)/DEX(500,000) biphasic mixtures (vertical axis), and the interfacial free energy at the cell surface determined as described in the text (horizontal...

There are thus two specific places where the dilution directly influences AG (v2) the In V2 term and AG (V2). The latter can be approximated by AG = AH iTm — r)/ Tn,. Tm is now the equilibrium melting temperature of the crystallizing polymer in the mixture. There is also the distinct possibility, which cannot be ruled out, that either, or both, of the interfacial free energies, cTen mid cTun, depend on composition. 

Most characteristics of amphiphilic systems are associated with the alteration of the interfacial stnicture by the amphiphile. Addition of amphiphiles might reduce the free-energy costs by a dramatic factor (up to 10 dyn cm in the oil/water/amphiphile mixture). Adding amphiphiles to a solution or a mixture often leads to the fomiation of a microenuilsion or spatially ordered phases. In many aspects these systems can be conceived as an assembly of internal interfaces. The interfaces might separate oil and water in a ternary mixture or they might be amphiphilic bilayers in... 

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. 

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