Equilibrium constant, mixed micelle

Medium-chain alcohols such as 2-butoxyethanol (BE) exist as microaggregates in water which in many respects resemble micellar systems. Mixed micelles can be formed between such alcohols and surfactants. The thermodynamics of the system BE-sodlum decanoate (Na-Dec)-water was studied through direct measurements of volumes (flow denslmetry), enthalpies and heat capacities (flow microcalorimetry). Data are reported as transfer functions. The observed trends are analyzed with a recently published chemical equilibrium model (J. Solution Chem. 13,1,1984). By adjusting the distribution constant and the thermodynamic property of the solute In the mixed micelle. It Is possible to fit nearly quantitatively the transfer of BE from water to aqueous NaDec. The model Is not as successful for the transfert of NaDec from water to aqueous BE at low BE concentrations Indicating self-association of NaDec Induced by BE. The model can be used to evaluate the thermodynamic properties of both components of the mixed micelle. 

The chemical equilibrium model of Roux et al (6) is a powerful tool for the study of the thermodynamics of mixed micellar solutions. It can estimate the distribution constant of the surfactant 3 between water and micelles of the surfactant 2 and the thermodynamic properties of the surfactant 3 in the mixed micelles. For this it is necessary to obtain reliable data over a large concentration range of solute 2. 

It is also reasonable to admit that the size of the mixed micelle could be the same in all systems situated along line OW since in all these cases the mixed micelles would always be in equilibrium with a micellar solution of pure Na cholate. Indeed, the chemical potential of the Na cholate in solution remains practically constant whatever the concentration, as long as micelles are present. Consequently, the chemical potential of the Na cholate attached to lecithin on the mixed micelles must also be constant since there is equilibrium. 

The theory of step-wise micelle association and disinter-gration has heen extended to mixed micelles. The relaxation process will again split into a fast and a slow one. During the first one internal (pseudo-)equilibrium is established in the micellar and monomer regions at a constant total number of micelles and characterized by a number of relaxation times equal to the number of components in the micelles. The slow process will be characterized by a single relaxation time the value of which is mainly determined by the properties at a saddle-shaped narrow passage between the micellar and monomer regions. Closed expressions for the relaxation times are deduced and their concentration dependence discussed. 

Monoglycerides and mono-diglycerides have low HLB values and cannot form micelles. They build up a multi-layer at the surface, resulting in a constantly decreasing surface tension as their concentration increases. However, in systems with proteins such as fat-free ice cream mixes, these emulsifiers behave as if they have a CMC. A possible explanation for this observation is that the unbound emulsifier in the fat-free mix is in equilibrium with the protein-bound emulsifier. Above a certain concentration of emulsifier in the mix, any surplus of emulsifier will adhere to the protein in the water phase after the surface has been saturated. The unadsorbed emulsifier is seen as very small crystals less than 200 nm by electron microscopy analysis4. ... 

It should also be considered that the formation of the complex between activator and lipid is an equilibrium reaction with a finite dissociation constant. Under the conditions used for the quantification of activators— that is, with pure glycolipid substrates at concentrations well above the Kq of the respective activator-lipid complex—the activator can be assumed to be saturated with the lipid, so that the activator concentration practically equals the concentration of the substrate of the reaction (the activator-lipid complex). However, the presence of other lipids such as phospholipids in the assay mixture may increase the experimental Kd by orders of magnitude since the mixed aggregates formed may be much more stable than the pure glycolipid micelles. (At a large excess of phospholipids as in the case of liposome-bound substrate, the may depend linearly on the phospholipid concentration.) As a consequence the concentration of the activator-lipid complex may be far below the total activator concentration, and the enzymic reaction will accordingly be much slower than with pure glycolipid substrates. 

This brings us to the structure of the micelle in the strongly charged limit. As usual, the micellar structure in equilibrium reflects the interplay of and corona- In thc present case, with R/b Na and h /Na 1, the elastic term in corona IS a constant while the electrostatic term is negligible. The dominant contribution is due to the mixing entropy of the condensed counterions Fcorona/ kT kTNA In pNa and thus... 

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