Other Chromatographic Methods

Capillary electrophoresis (CE) (see Section 3.5) has been used to determine partition coefficients [320-322]. Lipid vesicles or micelles are added to the buffer whose pH is adjusted to different values. Since drug molecules partition to a different extent as a function of pH, the analysis of mobility vs pH data yields log P values.

Centrifugal partition chromatography (CPC) has been used to characterize the partitioning behavior of hydrophilic molecules, where log D values as low as —3 can be obtained [371,377-379]. It is not as popular a method as it used to be, apparently due to instrumental challenges. Cyclic voltammetry (CV) has become the new method used to get access to very low log D values, with partition coefficients reported as low as —9.8 [261,269,362].


In 1952, Dyrssen (using a radiometer titrator) performed the first dual-phase titrations to determine oil-water partition coefficients [324]. In a series of papers on solvent extraction of metal complexes, he and co-workers [324-331] measured neutral and ion pair log P of compounds, studied dimerization reactions of dialkylphos-phates in aqueous as well as chloroform solutions, used log D/pH plots, and derived a method for deducing the pKa of water-insoluble molecules from knowledge of their logP, later called the PDP method [112]. In 1963, Brandstrom [332], using a pH-stat titrator, applied the log P methods to pharmaceutical problems. In the mid-1970s, the technique was "reborn." Seiler described a method where the pKa and log P were determined simultaneously from a single titration [250]. At about the same time, working independently, Koreman and Gur'ev [333], Kaufman et al. [334], and Johansson and Gustavii [335,336] published in this area. Gur'ev and co-workers continued to apply the method, but their work was not well known outside of Russian literature [337-343]. Clarke and others [344,345,350,351] presented a comprehensive treatment of the technique, and applied it to mono-, di- and triprotic substances. Numerical differentiation and matrix algebra were used to solve a number of simultaneous equations. Both graphical and refinement procedures for dealing with ion pair formation were devised. A dual-phase microtitration system has been described [361]. The rigorous development of the pH-metric method continued in a commercial setting by Avdeef and colleagues [25,112,149-151,153,161,162,224,225,275,346-349,352,357,362].

The pH-metric technique consists of two linked titrations. Typically, a pre-acidified 100-500 p.M solution of a weak acid is titrated with standardized 0.5 M KOH to some appropriately high pH; octanol (or any other useful organic partition solvent that is immiscible with water) is then added (in low relative amounts for lipophilic molecules and high amounts for hydrophilic molecules), and the dualsolvent mixture is titrated with standardized 0.5 M HCl back to the starting pH. After each titrant addition, pH is measured. If the weak acid partitions into the octanol phase, the two assays show nonoverlapping titration curves. The greatest divergence between the two curves occurs in the buffer region. Since the pKa is approximately equal to the pH at the midbuffer inflection point, the two-part assay yields two constants: pKa and poKa, where poKa is the apparent constant derived from the octanol-containing segment of data. A large difference between pKa and poKa indicates a large value of log P.

Bjerrum analysis (Section 3.3.1) is used for initial processing of the titration data. Figure 4.7a shows the Bjerrum plots of the two segments of the titration of a weak acid, phenobarbital [150]. The solid curve corresponds to the octanol-free segment, and the dotted curve corresponds to the curve obtained from the octanol-containing data, where r, the octanol-water volume ratio, is 1 in the example. As said before (Sec. 3.3.1), the pKa and poKa may be read off the curve at half-integral values of nH. From the difference between pKa and poKa, one obtains [347]

Figure 4.7b shows an example of a weak base, diacetylmorphine (heroin) [151]. The partition coefficient for the weak base is derived from

If the two phases are equal in volume (1 : 1) and the substance is lipophilic, a very simple relationship can be applied to determine log P;

log Pha « (poKa:1 — pKa) (log Pb « — (oK* — pKa)) (4-14)

Note that for a weak acid, the octanol causes the Bjerrum curve to shift in the direction of higher pH, whereas for a weak base, octanol causes the shift to lower values of pH. Equation (4.14) may be applied to the molecules in Fig. 4.7, and log P deduced from the shifts in the curves.

For diprotic molecules, 12 different characteristic shift patterns have been identified for cases where two species may partition simultaneously into the lipid phase [347]. Three of these cases are shown in Fig. 4.8, picking familiar drug substances as examples. Once the approximate constants are obtained from Bjerrum analysis,

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