Non-micellar association

The overall equilibrium constant, / , for the self-association reaction 

Equations 3.55 to 3.57 are not directly applicable to ionic surfactants since no account has been taken of the counterions associated with the micelles or the micellar charge. The equilibrium constant, P , for ionic surfactants will incorporate charge effects and, to simplify the treatment, these are assumed to remain constant with increase in aggregate size. This assumption is most likely to be valid for systems containing added electrolyte [93]. Whereas the magnitude of P gives an indication of the tendency for association, it is the way in which K varies with aggregate size which defines the association pattern. 

Ghosh and Mukerjee [230] have described the self-association of the cationic dye, methylene blue, using a stepwise association model in which all the equilibrium constants are assumed to be of equal value 

A similar scheme has been applied to the association of nucleotides [231] and some narcotic drugs [232]. The association of the narcotic drug, pethidine, has been described in terms of a co-operative association model in which X is related to a generalized equilibrium constant, X, by 

The association of the antihypertensive drug, pavatrine, on the other hand, follows an antico-operative association scheme in the absence of added electrolyte [233] in which association to form aggregates of greater size than the 

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Later studies on other drugs with non-micellar association patterns showed that the apparent c.m.c. detected by surface tension techniques arose because of the very limited change of monomer concentration with total solution concentration at high concentrations. 

Conversion of this flexible hydrophobic moiety into a rigid planar structure can, in some cases, lead to a non-micellar association pattern in which the mean aggregate size increases continuously with increase in concentration. Such systems have no CMC and exhibit a considerable degree of polydispersity in the aggregate size. This topic is dealt with in detail in Chapter 4. 

Some of the structural features of the hydrophobic group which are thought to be responsible for non-micellar association patterns are discussed in Chapter 4 and other examples given. 

The results obtained for pavatrine clearly indicate the influence of the structure of the hydrophobic group on the association pattern, a rigid ring structure promoting non-micellar association. This conclusion is further substantiated by the association behaviour of the two antiacetylcholine drugs, propantheline (II) and methantheline bromide (III) both of which have rigid tricyclic ring systems. 

The light-scattering plots of both of these drugs indicate a non-micellar association pattern. Analysis of the data reveals that the association can best be described by a stepwise association model similar to that of pavatrine in high electrolyte concentration with association constants increasing with aggregation number according to the relationship, K = K n — l)/n,... 

In contrast to aqueous systems, micelle formation in non-polar media is driven by the benefit in energy rather than by an increase in entropy. The replacement of polar group - hydrocarbon interaction (as in the case of dissolution) with the interaction between polar groups upon their association into micellar core is thermodynamically beneficial. The benefit in energy upon association of polar groups is so large, that even at low concentrations true surfactant solutions contain small pre-micellar associates rather than individual surfactant molecules. 

The results of Anderson and Slade [207] suggest that hydrogen-ion concentration has little effect on the amount of benzoic acid solubilized. In spite of the fact that they estimate that only one in every 90 ether oxygens in non-micellar glycols are associated with benzoic acid in solution, the authors conclude that solubilization takes place in the PEG region of the micelles. 

Equations are derived which take into account the formation of cyclodextrin to substrate complexes other than simple one to one host guest associations. An equation is also derived which describes the binding of a mono-protic species in which either its ionized or unionized form could bind to one or two cyclodextrin molecules. Because multiple binding constants are difficult to evaluate graphically, a non-linear least squares computer program is utilized. The approach works equally well for the determination of binding constants in micellar media. 

For low molecular mass amphiphiles, hydrophobic interactions and surface effects determine the critical concentration at which micellar aggregates are favored over the molecularly dispersed amphiphilic solutes. For polysurfactants, however, the amphiphiles are linked together and the dynamic exchange of associated and non-associated amphiphilic monomer units is prevented. Consequently the micelle formation does not only depends on the hydrophilic/ hydrophobic balance of the monomer... 

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