Theory Applied to Transitional Inversion

Brooks and Richmond - developed a simple surfactant partitioning model that can be applied to isothermal transitional inversions. The linearity and gradient variation of transitional inversion lines in systems containing distributed nonionic surfactant was also explained. The derived model used mixed surfactant theory to predict the slope of the SAD = 0 line with surfactant concentration, for transitional inversion induced by varying the amount of a homogeneous lipophilic and a homogeneous hydrophilic surfactant in an oil-water system. 

Graciaa et al assumed that microemulsion phases (O, W , surfactant phase microemulsion (M5), type 3 oleic microemulsion (M,), type 3 aqueous microemulsion (M )), despite being single thermodynamic phases, are composed of submi-croscopic regions of oil and water separated by an interfacial layer of surfactant. Consequently, it is possible for each of the different microemulsion phases to be constructed from the three constituents parts described earlier. 

If surfactant concentrations in the water and oil phases are below their respective critical micelle concentration (CMC), the partition coefficient for surfactant monomer i between oil and water can be written as  

For conditions above the CMCs, using an analogy to Raoult s law, it is shown that for an ideal solution  

Graciaa et al. in a series of experiments using the isooctane-OPE system found that, using CMC data, isothermal transitional inversion occurs at a specific value of the HLB of the pseudo surfactant phase. They calculated the HLB of the pseudo siufactant phase from the mole average of each chain length in the phase. Phase separation models are known to require a large amount of CMC data. Brooks and 

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