Generalised formulation as SAD and HLD

A decade after the empirical determination of the correlations for three-phase behaviour and the corroboration that the linearity and generality could not be coincidental, a simple interpretation was found through the so-called surfactant affinity difference (SAD) concept discussed next. When a simple ternary surfactant-oil-water system exhibits three-phase behaviour, the chemical potential p. of the surfactant is equal in the three phases (oil, water and microemulsion) at equilibrium referred to by subscripts O, W and M. It holds 

In ionic surfactant systems, the partition coefficient between excess phases is often found to be unity, hence an optimum formulation is defined by SAD = 0. With polyethoxylated surfactants, the CMC in water is often extremely low, whereas the monomer solubility in many oils is high. Consequently, the assumption of unit activity coefficient is not valid anymore and the partition coefficient between excess phases is not unity. In such cases, the partition coefficient value at optimum formulation is taken as a reference, and the deviation from this reference, the so-called hydrophilic-lipophilic deviation (HLD) is defined by dividing by RT to make the yardstick dimensionless [34]. 

By definition, HLD = 0 at optimum formulation, and away from it, it is the expression of the relative surfactant affinity difference from it. Since the partition coefficient may be measured with a proper analytical technique, its variation with respect to formulation variables such as surfactant EON, oil ACN, water salinity S etc. may be determined. Such studies have been carried extensively with polyethoxylated surfactants and have shown that HLD dependence on the formulation variables has the same expression than the correlation for three-phase behaviour [35, 36]. It holds 

HLD is a generalised formulation yardstick that is some kind of extended HLB, which is function of all formulation variables (surfactant characteristics, co-surfactant type and concentration, temperature, oil nature, salinity. ..) and it may be numerically estimated or measured with a much better accuracy than HLB, roughly equivalent to one-tenth of an HLB unit. From the physical chemistry point of view, it has a strong foundation, since it represents the change in standard chemical potential when a surfactant molecule passes from oil to water in the conditions of experiments. 

The above expression have been extended to different families of surfactants, whose characteristic parameter (as (3/k or a/ k) is expressed in ACN units, has been found to vary linearly with the surfactant alkyl carbon number (SACN), i.e. the number of atoms 

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