Entropy of dispersion

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. 

On the basis of a lattice model, upper and lower bounds have been established for the entropy of dispersion of spherical globules of radius r and volume fraction in the continuous phase (ref. 20). Here r and are the "actual" radius of the globules (including the adsorbed layer of surfactants) and the corresponding... 

Let us consider that the microemulsion contains spherical globules of uniform size. Their dispersion in the continuous medium is accompanied by an increase in the entropy of the system. As noted in Sec. I, the Helmholtz free energyfper unit volume of microemulsion (j=F/V, where V is the volume of the microemulsion) will be written as the sum between a frozen noninteracting free energy fa and a free energy A f due to the entropy of dispersion of the globules in the continuous phase and to their interactions ... 

In addition to the first two terms on the right-hand side, which are present in the case of a single droplet in a continuum, Eq. (11) contains terms that are due to the entropy of dispersion of the globules in the continuous medium and to the energy of interactions among globules. 

A/ is calculated in what follows by neglecting the interactions among globules. Expressions for the entropy of dispersion of the globules in the continuous phase were derived by Ruckenstein and Chi [12] on the basis of a lattice model, assuming (as is usually done in this kind of model) that the volume of a site is equal to the volume of a molecule... 

The change in free energy in going from state I to state II is made from two contributions (i) a surface energy term (that is positive) that is equal to AA Yn (where AA = A2 — Aj) and (ii) an entropy of dispersions term which is also positive (since the production of a large number of droplets is accompanied by an increase... 

As mentioned in Chapter 10, the preparation of an emulsion requires oil, water, a surfactant, and energy. This can be considered on the basis of the energy required to expand the interface, AAy (where AA is the increase in interfacial area when the bulk oil with area Aj produces a large number of droplets with area Aj Aj Aj, where y is the interfacial tension). Since y is positive, the energy to expand the interface is large and positive. This energy term cannot be compensated by the small entropy of dispersion TAS (which is also positive), and the total free energy of formation of an emulsion, AG is positive. 

The driving force for microemulsion formation is the low interfacial energy which is overcompensated by the negative entropy of dispersion term. The low (ultralow) interfacial tension is produced in most cases by the combination of two molecules, referred to as the surfactant and the cosurfactant (e.g., a medium-chain alcohol). 

Ruckenstein and Chi presented a thermodynamic treatment of a microemulsion consisting of fixed amounts of oil, water, and surfactant. The analysis yielded an optimum droplet diameter, demonstrated that the entropy of dispersion made an important contribution to microemulsion free energy, and confirmed that a very low interfacial tension of the droplets was required for thermodynamic stability. Indeed, to a first approximation, we can often estimate droplet size by taking the area per surfactant molecule as that for which interfacial tension would be zero. 

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