Free energy surfactants transferred from

As expected from the relation of HLD with the free energy of transfer from oil to water, the removal of one carbon atom to the alkyl tail of the surfactant would make it easier for the surfactant to be transferred, and would hence tend to reduce the value of HLD, through a reduction of the characteristic parameter a or a. The experience shows in effect that [23] ... 

The early proposal by Davies (40) to use the partition coeffici ii of the surfactant between the oil and water phase as a formulation parameter was retaken by Marquee and eollaboraiors (98) a.s a way of measuring the free energy of transfer from water to oil. a. successful technique to deal with complex fractionating surfactant mi.stures (99j. Ilie free energy of transfer of a molecule of surfactant from water to oil is ... 

Kronberg et al. have examined the thermodynamics of surfactant micellization and adsorption onto hydrophobic surfaces [47]. They considered two main contributions for the Gibbs free energy of transfer from the aqueous solution to the micelle or the surface ... 

The value of a corresponds to a decrease of the cmc value by factors 2 and 3 per additional methylene group in the alkyl chain for ionic and nonionic surfactants, respectively. In both instances, this corresponds to a free energy of transfer from the micelles to the aqueous phase of l.l T per methylene... 

Use the cmc values of a homologous series of single-chained sodium sulphate surfactants, given below, to estimate the standard free energy of transfer of a methylene (-CH2-) group from an aqueous to a hydrocarbon environment. 

Micelles are dynamic structures where a frequent exchange of monomers between micelles and the bulk solution occurs. Thermodynamics of the self-assembly of surfactants or aggregates is determined by the free energy of transfer of a surfactant monomer from water to the micelle. 

The equations developed in previous sections can be used to calculate the structural features of microemulsions, provided explicit expressions for the standard free energies of transfer of surfactant and alcohol molecules from their infinitely dilute states in water and of oil molecules from the pure oil phase to the interfacial layer of the microemulsion droplets are available. Such expressions are given below for spherical layers of O/W droplets and W/O droplets and also for flat layers. The difference in the standard state free energy consists of a number of contributions ... 

The effect of the additive on the CMC is given as the ratio of the CMC in the presence of the additive to that in its absence, CMCaICMCh. AGt is the standard free energy of transfer of the surfactant from water to an aqueous solution containing the given concentration of the additive. 

For surfactants, the hydrophobic free energy of transfer of the lipophilic hydrocarbon tail from water to oil provides the driving force for aggregation. But the hydrophilic head-groups prefer an aqueous environment and an interface between the polar region and the lipophilic domains results. With hydrocarbon tails, like alkanes, there are a large number of accessible tail conformations, so that the hydrophobic region is usually fluid-like aroimd room temperature. The interface can be a dynamic one of a well-defined... 

The lateral energy in the adsorbed layer calculated from Eq.(5) experimentally varies from 1.36+0.03 kT to 1.93+0.1 kT. It corresponds to an adsorbed layer in which the aliphatic chains are parallel and stretched towards the solvent. The free energy on transfer between CH2 is not constant. It is not the case for smooth or plane surface. In the present case the adsorbed phase is in a very condensed state. In this case the molecular area of the surfactants in the adsorbed layer is minimal 20.8[14]. Therefore the specific surface area of each solid precipitated at pH 6.5 and 7.5 may be calculated. At the monolayer the adsorbed amount Qq is ... 

In nonionic surfactants generally, the efficiency of adsorption is much greater than in ionic surfactants with the same number of carbon atoms in the hydrophobic group. This is because in the adsorption of ionic surfactants, electrical repulsion between the ionic heads of surfactant ions already at the interface and the similarly charged oncoming surfactant ions increases the positive free energy of transfer of the hydrophilic head from the interior of the bulk phase to the interface. 

The surfactant affinity difference (SAD) is used to model emulsion phase behaviour based on the chemical potentials of surfactant in aqueous and oil phases. SAD is the negative of the free energy of transfer of a surfactant molecule from an oil to a water phase (see the papers by Salager et al. [132, 142, 143]). 

It is worth noting that the tie-line slope in the polyphasic region clearly indicates the amphiphile partitioning, which is related to physicochemical formulation, for instance through the free energy of transfer of an amphiphile molecule from water to oil in a low surfactant concentration system, i.e., below the cmc [23]. 

This kind of correlation was first attained from empirical experimentation, and a few years later it was recognized to be an expression of the surfactant affinity difference SAD (affinity is the negative of the chemical potential), i.e., the free energy of transfer of a surfactant molecule from the excess water to the excess oil in a three-phase system, which is related to the partitioning coefficient [32-34]. 

Comparing this expression with Eq. (10), which determines the difference between the standard chemical potentials of surfactants in the aqueous and oil phases (i.e., by the definition of the free energy of the surfactant transfer from the oil phase into the aqueous phase) ... 

According to various experimental information the hydrocarbon core of the "aqueous micelle has a liquid-like structure (3,4). This has been confirmed, in particular, by spectroscopic probing techniques (5,6). Hence the micelle in aqueous surfactant solutions presents itself to the surfactant monomer as an equivalent with respect to the (macroscopical) oil/water interface. It might be not unreasonable, therefore, to consider this type of micelle formation an "auto-solubilization" to stress the close resemblance between adsorption and homoassociation processes. The hydrocarbon core of a micelle in aqueous surfactant solutions is characterized by its excellent solvent power for crystalline non-polar compounds (7). This latter feature appears remarkable and could serve as a more fundamental distinction between "normal" and inverted micelles than the generally cited apparently more obvious differences. The free energy of micellization is customarily (8) referred to the standard free energy of a monomer in a micelle, i.e. AG° represents the free energy of transfer of a monomer from the aqueous solution to a micelle of size n. 

This is clearly independent of the nature of the head group of the surfactant, which is the reason why such slopes are similar for many different single-chained conventional surfactants. The first conclusion here is that [C C PyrrJBr surfactants act exactly like the corresponding conventional single-chained surfactants, represented by C TAB. Moreover, not only the two plots show a similar slope, but they lie almost superimposed to each other, indicating that the structural similarity of the two head groups leads to similar free energies of transfer of one surfactant molecule from the aqueous to the micellar environment. 

AG° is the activation energy for the transfer of a surfactant from the micellar to the free state. AG° is close to AGji, free energy of transfer of a surfactant from a micelle proper to the aqueous phase. AG°tr varies linearly with the alkyl chain carbon number m and can be expressed as... 

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