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In conclusion, the advantages of using HPLC for the estimation of hydrophobicity of compounds are the following: a much smaller amount of compound with less purity requirements is sufficient to carry out the analysis. The HPLC procedure can be completely automatized by using computer-controlled HPLC equipment. The conditions of the measurements (temperature, mobile phase pH, ionic strength) can be controlled and maintained constant for a large number of compounds. There is no need to develop an analytical method for the concentration determination of the compounds in the two phases. In general, it is less time-consuming to measure retention data, than concentration.
III. DETERMINATION OF EQUILIBRIUM CONSTANTS BY HPLC
Chromatography was developed for the separation of compound mixtures. The separation takes place by different migration patterns of the molecules. The different velocity of each type of compound is due to the different strength of the interaction with the mobile phase. The strength of the solute-stationary-phase interaction depends on the equilibrium constant of the distribution of the solute between the mobile and the stationary phase. Although during chromatography the system is never in equilibrium, the velocity of the molecules can be directly related to the equilibrium constant. Therefore, from the retention behavior of com-pounds, the so-called dynamic equilibrium constants can be determined. That was also the basis of the previously discussed hydrophobicity determination. When the solute stationary-phase distribution depends only on hydrophobic forces, the retention will refer only to the hydrophobicity of the molecules. When the solute stationary-phase interaction depends on complex formation, the retention will be proportional to the complex stability constants.
A. Determination of Complex Stability Constants by HPLC
Theoretically, there are two possibilities for the application of HPLC for the determination of complex stability constants. When the complex-forming agent (for example, cyclodextrin) is
chemically bonded to the stationary phase, the solute retention will be proportional to the
complex stability constant K, according to Eq. (24).
log Ê = log
where tR is the retention time of the solute, t0 is the retention time of another solute that has no interaction with the chemically bonded complexing agent. VJVm is the volume of the stationary and the mobile phases. Ê is the stability constant of the complex, which can be expressed by Eq. (25):
Ê - [C1 tX] (25)
K ~ [CX] <25)
where [C] and [X] are the concentration for the complex forming two molecules, [CX] is the concentration of the complex. When the complex-forming agent Ñ is chemically bonded to the stationary phase, the complex molecule cannot move at all. Only the free X molecules can move by the mobile phase, and then the new equilibrium distribution takes place. Through this series of equilibrium distributions the X molecules go through the column. The velocity of the migration will be proportional to the concentration of X molecules in the mobile phase. The higher portion of the molecules are in the mobile phase (i.e., the lower the stability constant is, the lower will be the retention time). This general theory was applied, for example, for the determination of the interaction of ^-cyclodextrin and some drugs by Sebille et al. . The /Ç-cyclodextrin polymer was prepared by reacting mono-6-0-tosyl-/3-cyclodextrin with poly(ethyleneimine). The /Ç-cyclodextrin content of the polymer was 60% w/w. A 5% solution of polymer was stirred with silica gel for 24 h at room temperature. Another stationary phase was similarly prepared that contained the poly(ethyleneimine) polymer, but without the cyclodextrin molecule, to compare the retention of the drug molecules on the two stationary phases. This is necessary because types of interactions other than the inclusion complex formation are also possible. The presence of immobilized j3-cyclodextrin makes the retention of the solute higher as the association constant becomes stronger. The relation between the elution volume of the solute and its affinity for /Ç-cyclodextrin can be described by Eq. (26):
Óê~Ï = (X) nfc (26)
This equation is valid only if the amount of solute A is very small. VA is the elution volume of A molecule; is the elution volume of A on a stationary phase that does not contain the cyclodextrin molecule; Vs is the volume of the stationary phase; X is the molar concentration of immobilized cyclodextrin (considered to be uniformly distributed through the volume accessible to the solute); Ê, is the equilibrium constant; n is the number of the interacting sites. Figure 8 shows the chromatograms obtained for several drug molecules on the stationary phases containing the ^-cyclodextrin in the stationary phase. The same method can also be applied for the determination of other complex stability constants. The only difficulty is in the preparation of the HPLC stationary phases, which needs special skill and technology.