Rm log

For HPLC,

where tc and to are the retention times of the compound and of a non-retained solute respectively.

A range of stationary phases can be used, depending on the nature of the compounds to be chromatographed, to give an appropriate range of Rm or log k' values. For example, a TLC plate may be impregnated with liquid paraffin, and acetone-water mixtures used as

Table 5.2 Fragmentation constants3.

Fragment_f_Fragment_f_

For hydrocarbon chains, 0.12 (n-1) is subtracted, where n is the number of bonds between carbons and between carbon and hetero atoms excepting hydrogen.

aRekker, R.F. (1977) The Hydrophobic Fragment Constant, pp. 39-106. Amsterdam: Elsevier.

A comprehensive account of fragmental constants can be found in: Hansch, C. and Leo, A. (1979) Substituent Constants for Correlation Analysis in Chemistry and Biology. New York: John Wiley. James, K.C. (1986) Solubility and Related Properties. New York: Marcel Dekker.

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the mobile phase; Rf values can then be extrapolated to zero acetone concentration. HPLC stationary phases can be coated with octanol, or chemically bonded with a range of chemicals.

Chromatographic methods generally do not cover a very wide range of hydrophobicity, but have the advantage that compound purity is not so crucial as it is in direct measurement of partition coefficient.

Generally, as partition coefficient increases, aqueous solubility decreases, although the relationship is not all that simple because of factors such as the entropy of melting, which partly controls solubility. Nonetheless, aqueous solubility can be used as a measure of hydrophobicity (or rather of hydrophilicity). It should also be noted, as mentioned in Section 5.2.1, that the ratio of solubilities in octanol and water gives a close approximation of the partition coefficient; values are not identical because of concentration effects and mutual solubility of the solvents.

The negatively charged site on the analgesic receptor described previously suggests that an electron-deficient group on a potential analgesic molecule, positioned so that it will come into contact with the negative site, will help the molecule bind to the receptor. The electron-deficient centre in methadone is provided by the protonated amine group. If the electron-density on the amine group is decreased, its electrostatic attraction for the receptor will become stronger. This can be achieved by attaching an electron-withdrawing group, such as chlorine ((5.1) X=Cl) to the amine group, while an electron-donating group, such as methoxy ((5.1) X=OCH3) will have the opposite effect. Considerations of this sort approach drug design in only a qualitative manner. It is more effective to quantify these qualities; electronic parameters perform this function by giving a value which is a measure of the degree of electron-donating or electron-withdrawing power. The best known electronic parameter is the Hammett substituent constant.

5.2.4 Aqueous solubility

5.3 ELECTRONIC PARAMETERS

5.3.1 Hammett constants

In 1940, Hammett introduced his substituent constants to predict equilibrium constants and rate constants for chemical reactions. He reasoned that an electron-withdrawing group, attached to the aromatic ring of benzoic acid, would increase the acid strength of the carboxyl group, and the greater the electron-withdrawing power, the greater the increase in strength. He was therefore able to assign substituent constants (c) to groups according to their influence on the acid strength of benzoic acid. Hammett's substituent constant is defined by:

Ko represents the dissociation constant of benzoic acid ((5.2) X=H), and Kx that of benzoic acid substituted by the group X. More conveniently, c can be expressed in terms of Equation [5.7].

Thus, considering benzoic acid which has a pKa value of 4.19, and p-toluic acid ((5.2) X =p-CH3) which has a pKa value of 4.36, the change in acid strength brought about by the methyl group (ci-CH3) is equal to 4.19-4.36=-0.17. A small selection of Hammett substituent constants is given in Table 5.3, from which it can be seen that electron-withdrawing groups have positive values, electron-donating groups have negative values, and hydrogen has a value of zero.

Scrutiny of Table 5.3 now shows that the analgesic activities of methadone analogues should increase in the order X=OCH3<CH3<H<Cl<NO2. Unfortunately the situation is not so simple, because there are other factors which influence analgesic activity, in particular the migration of the drug from the site of administration to the site of action. Also, Hammett substituent constants apply specifically to groups attached to an aromatic system, while the part of the parent compound being modified may be aliphatic, as in the present example. Biological results which fit the concept precisely were generated by Fukata and Metcalf, who measured the toxic concentrations of nuclear substituted phenyldiethyl phosphates (5.3) on houseflies. A plot of their results against c, shown in Figure 5.2, gives a good straight line, indicating that biological activity is dependent mainly on the electron density on the aromatic ring, and provides a means of predicting activities of potential new compounds before time is spent synthesizing them.

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