## Determination of Solute Micelle Association Constants and Distribution Coefficients

From eqn [1] in Table 1 it can be seen that a plot of the term VS/(Ve — VM) versus CM is linear and the term 'v(PMW — 1)' can be obtained from the slope: intercept ratio. According to Berezin's treatment the term 'v(PMW — 1)' is equal to the solute-micelle

Figure 3 Variation of the experimental (- -O- -) and theoretical (-A-) selectivity coefficients (a) as a function of the micellized surfactant concentration for three pairs of solutes: pyrene/acenaphthene (A and D), pyrene/toluene (B and E) and pyrene/benzamide (C and F). Mobile phases: A-C, SDS/5% n-propanol; D-F, CTAB/5% n-butanol. Column: Spherisorb C8 (15 cm x 4.0 mm i.d.). (Reproduced with permission from Garcia MA and Marina ML (1996) Influence of alcohol organic modifiers upon the association constants and retention mechanism for aromatic compounds in micellar liquid chromatography. Journal of Liquid Chromatography and Related Technologies 19: 1757-1776, copyright Marcel Dekker, Inc.)

Figure 3 Variation of the experimental (- -O- -) and theoretical (-A-) selectivity coefficients (a) as a function of the micellized surfactant concentration for three pairs of solutes: pyrene/acenaphthene (A and D), pyrene/toluene (B and E) and pyrene/benzamide (C and F). Mobile phases: A-C, SDS/5% n-propanol; D-F, CTAB/5% n-butanol. Column: Spherisorb C8 (15 cm x 4.0 mm i.d.). (Reproduced with permission from Garcia MA and Marina ML (1996) Influence of alcohol organic modifiers upon the association constants and retention mechanism for aromatic compounds in micellar liquid chromatography. Journal of Liquid Chromatography and Related Technologies 19: 1757-1776, copyright Marcel Dekker, Inc.)

association constant per monomer, K2, which is the parameter most used to evaluate solute-micelle interactions. Also, the partition coefficient of the solute between bulk water and micelle, PMW, can be obtained if the surfactant molar volume, v, is known. The distribution coefficient, PSW, is obtained directly from the intercept and the distribution coefficient PSM can be obtained from the ratio PSW/PMW.

In a similar way, the solute-micelle association constant per monomer, K2, can be obtained directly from eqn [2] in Table 1 as the slope/intercept ratio of a straight line obtained from a plot of 1/k versus Cm.

If the solute-micelle association constant per monomer obtained from eqns [1] or [2] is multiplied by the aggregation number of the micelle, the association constant per micelle is obtained. On the other hand, PMW and K2 values only depend on the solute and the micellar system employed but not on the stationary phase.

Equations [1] and [2] have frequently been employed with the aim of determining solute-micelle association constants in pure and modified micellar media. Furthermore, good agreement has been found between the values of the association constants obtained by MLC and other techniques.

Figure 4 provides an example of the good linearity obtained for the variation of the term VS/(Ve — VM) as a function of CM for a group of 12 polycyclic aromatic hydrocarbons when an SDS micellar mobile phase modified by 5% «-butanol is used.

For highly hydrophobic solutes, the retention of which is described by eqn [3] in Table 1, the variation of 1/k as a function of CM should give a straight

Figure 4 Variation of the term Vs/(Ve— Vm) as a function of CM for a group of 12 polycyclic aromatic hydrocarbons in an SDS micellar system modified by 5% n-butanol. Key: 1, naphthalene; 2, 1-naphthol; 3, 2-naphthol; 4, 1-naphthylamine; 5, pyrene; 6, phenanthrene; 7, 2,3-benzofluorene; 8, fluorene; 9, fluoranthene; 10, acenaphthylene, 11, acenaphthene; and 12, anthracene. Column: Spherisorb C8 (15 cm x 4.0 mm i.d.). (Reproduced with permission from Marina ML and Garcia MA (1997) Journal of Chromatography A 780: 103-116, copyright Elsevier Science Publishers B.V.)

Figure 4 Variation of the term Vs/(Ve— Vm) as a function of CM for a group of 12 polycyclic aromatic hydrocarbons in an SDS micellar system modified by 5% n-butanol. Key: 1, naphthalene; 2, 1-naphthol; 3, 2-naphthol; 4, 1-naphthylamine; 5, pyrene; 6, phenanthrene; 7, 2,3-benzofluorene; 8, fluorene; 9, fluoranthene; 10, acenaphthylene, 11, acenaphthene; and 12, anthracene. Column: Spherisorb C8 (15 cm x 4.0 mm i.d.). (Reproduced with permission from Marina ML and Garcia MA (1997) Journal of Chromatography A 780: 103-116, copyright Elsevier Science Publishers B.V.)

line with an intercept equal to zero; the slope of the line should allow calculation of the distribution coefficient PSM. In these cases, calculation of solute-micelle association constants is not possible and has no chemical meaning.

One of the main drawbacks that this method has is the intrinsic error derived from the determination of a magnitude from a quotient. Error obtained during the determination of K2 increases with solute hydro-phobicity since PSW values for these compounds are elevated (intercept very small, see eqn [1]). With hybrid eluents, the value of PSW decreases and the error in the determination of the solute-micelle association constants for very hydrophobic compounds also decreases (the intercept in eqn [1] increases).

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