Purely Aqueous Micellar Systems

From equilibria taking place in MLC represented in Figure 1, equations have been developed relating chromatographic retention and concentration of micellized surfactant in solution.

Equation [1] (Table 1) relates the solute elution volume (Ve) in MLC with the micellized surfactant concentration in the mobile phase (CM) (total surfactant concentration in solution minus c.m.c.). VS, VM and v are the stationary phase volume, the void volume of the column and the surfactant molar volume,

Table 1 Retention modelling in MLC

Model

Equations

Physico-chemical

Empirical relationships

VS/V — Vm) = {v(Pmw - 1)/Psw}Cm + 1/Psw 1/k= {K#[Ls]K}Cm + 1/flLJK k=(Vs/VM).(Psw/vq«)

1 + KCM] + (1 + K4[CM])K.m/[«+] 0K,[LS](1 + K4[AMD

1 + (K + K4)[Am] + K>[Cm](1 + K3[Am]) + KsK,[Am]2 ln k= — Sep + ln k0

1/k=An + Bcp + Cup + D 1/k= An + Bp2 + Cp + Dup + E

respectively. If solute retention is expressed as the retention factor (k), a similar equation is obtained (eqn [2]) relating 1/k with CM through the solute-micelle association constant per monomer, K2. Here is the phase ratio (the ratio of the stationary phase volume to the volume of the mobile phase in the column, VS/VM), [LS] is the stationary phase concentration and K1 is the binding constant for the solute between the bulk solvent and the stationary phase.

Equations [1] and [2] show that retention of a solute in MLC decreases when micelle concentration in the mobile phase increases. This is in contrast to reversed-phase ion-interaction (or ion-pairing) chromatography, where the surfactant concentration is below the c.m.c. (that is, no micelles exist), and the addition of an ionic surfactant increases retention for compounds that interact electrostatically with it.

For very hydrophobic compounds, a direct transfer retention mechanism from the micellar mobile phase to the modified stationary phase has been proposed. A limit theory has been developed for those compounds where the amount of the solute in the non-micellar aqueous mobile phase can be considered negligible. In this case, k is related to CM through eqn [3] in Table 1.

For ionized solutes (weak acids, bases and zwit-terionic solutes), some equations have also been developed relating k with CM and pH. As an example, eqn [4] in Table 1 is the derived model for a weak acid. In this equation k0 and k1 are the limiting retention factors for the neutral and dissociated forms, respectively, K4 is the association constant of the ionized form of the solute with the micellar phase, and Kam is the acid dissociation equilibrium constant. The variation of k with pH at a constant micellized surfactant concentration is sigmoidal. Since a shift in the ionization constants can be obtained when the micellized surfactant concentration is modified, optimization of separation conditions must be attained considering both variables simultaneously.

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