Free-disperse systems interfacial energy

It is worth recalling here that a dispersion medium akin to the particles, as well as surfactant adsorption, can lower both the interfacial energy, o, and the complex Hamaker constant. A by two to three orders of magnitude. In such a lyophilized system, the adhesive energy and force are also lowered by several orders of magnitude. In a concentrated disperse system in which the dispersed particles are mechanically forced to come into contact with each other, the lyophilization manifests itself as a decrease in the resistance to strain t. This means that in concentrated colloidal systems, plasticizing takes place, while in systems with a low concentration of dispersed particles, the lyophilization results in enhanced colloid stability of the free-disperse system (see Chapter 4). 

One of the most obvious properties of a disperse system is the vast interfacial area that exists between the dispersed phase and the dispersion medium [48-50]. When considering the surface and interfacial properties of the dispersed particles, two factors must be taken into account the first relates to an increase in the surface free energy as the particle size is reduced and the specific surface increased the second deals with the presence of an electrical charge on the particle surface. This section covers the basic theoretical concepts related to interfacial phenomena and the characteristics of colloids that are fundamental to an understanding of the behavior of any disperse systems having larger dispersed phases. 

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],... 

Foams, as well as other liophobic disperse systems are thermodynamically unstable due to their high interfacial free energy. This high free energy provokes processes that lead to foam coarsening and eventual destruction, i.e. to separation of the liquid from the gas phase. 

The difference in the composition and structure of phases in contact, as well as the nature of the intermolecular interactions in the bulk of these phases, stipulates the presence of a peculiar unsaturated molecular force field at the interface. As a result, within the interfacial layer the density of such thermodynamic functions as free energy, internal energy and entropy is elevated in comparison with the bulk. The large interface present in disperse systems determines the very important role of the surface (interfacial) phenomena taking place in such systems. 

The enrichment of the interfacial layers is attended by a decrease in free energy which is the greater the larger the area involved. The adsorption, therefore, stabilizes the finely dispersed system of droplets which constitutes an emulsion. 

Dispersed systems are stabilized by a third component known to have amphiphilic properties and surface activity. The amphiphiles migrate to the interface and modify it to reduce the interfacial free energy and to minimize interactions between particles and droplets. 

A certain amount of controversy has been caused by the question as to what specific characteristics of the AF function represent the universal conditions for spontaneous dispersion To address this subject, we will analyze changes in the free energy, AF, associated with the dispersion, as a function of the size and number of particles, their concentration, and the value of the free interfacial energy at the interface between the disperse phase and the dispersion medium. This analysis is performed for three characteristic conditions (1) varying the particle size at a constant volume of the disperse phase, (2) varying the number of particles at a constant particle size, and (3) varying the particle size at a constant number of particles. The analysis will be restricted to systems that are monodisperse at every stage of the dispersion process and consist of spherical particles with radius r. The volume of the dispersion medium is assumed to be constant, for example, V = 1000 cm. At 300 K, the kF value is 4.14 x 10" J. 

Very small dispersed particles are highly energetic. In order to approach a stable state, they tend to regroup themselves in order to reduce the surface free energy of the system. An equilibrium will be reached when AG = 0. This condition may be accomplished either by a reduction of the interfacial tension or by a decrease of the total surface area. 

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. 

Recent studies showed that amphiphilic properties have to be taken into account for most water-soluble monomer units when their behavior in water solutions is considered. The amphiphilic properties of monomer units lead to an anisotropic shape of the polymer structures formed under appropriate conditions, which is confirmed both by computer simulation and experimental investigations. The concept of amphiphilicity applied to the monomer units leads to a new classification based on the interfacial and partitioning properties of the monomers. The classification in question opens a broad prospective for predicting properties of polymer systems with developed interfaces (i.e., micelles, polymer globules, fine dispersions of polymer aggregates). The relation between the standard free energy of adsorption and partition makes it possible to estimate semiquantitatively the distribution between the bulk and the interface of monomers and monomer units in complex polymer systems. 

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