The phase rule can be used to determine the thermodynamic solubility of a drug substance. The requirements for an analysis are simple, where basically the drug is added in a specific amount of solvent. After equilibrium is achieved, excess drug is removed (usually by filtering) and then the concentration of the dissolved drug is measured using standard analysis techniques such as high-performance liquid chromatography.
A phase-solubility diagram for a pure drug substance is shown in Figure 9-6.21
At concentrations below the saturation concentration there is only one degree of freedom since the studies are performed at constant temperature and pressure. In other words, only the concentration changes. This is represented in Figure 9-6 by the segment A-B of the line. Once the saturation concentration is reached, the addition of more drug to the system does not result in higher solution concentrations (segment B-C). Rather, the drug remains in the solid state and the system becomes a two-phase system. Since the temperature, pressure, and solution concentration are constant at drug concentrations above the saturation concentration, the system has zero degree of freedom (C = Zero)
The situation in Figure 9-6 is valid only for pure drug substances but if the drug substance is not pure, then the situation is described in Figure 9-7.22 If the system has one impurity, the solution becomes saturated with the first component at point B. The situation becomes interesting at this point. In segment B-C of the line, the solution is saturated with component 1 (which is usually the major component such as the drug), so the drug would precipitate out of solution at concentrations greater than this. However, the impurity (the minor component or component 2) does not reach saturation until it reaches point C on the line. The concentrations of the two components are saturated beyond point C (segment C-D) of the line. Once true equilibrium is achieved, one can extrapolate back to the Y axis (solution concentration) to determine the solubility of the two components. Therefore, the thermodynamic solubility of the drug would be equal to the distance A-E and the solubility of the impurity would be equal to the distance represented by E-F. As one can see, this procedure can be used to measure the exact solubility of the pure drug without having a pure form of the drug to start with. The practical aspect of measuring thermodynamic solubility is relatively simple but it can be quite time-consuming. Some methods have been developed in attempt to reduce the time that it takes to get a result. Starting the experiment with a high purity crystalline form of the substance will give the best chance that the solubility measured after a reasonable incubation period will represent the true equilibrium solubility. However, this may still take several hours to several days. Also, there is still a risk that the incubation period will not be sufficient for metastable crystal forms to convert to the most stable form. This means that the measured concentration may represent the apparent solubility of a different crystal form. This risk must be taken into consideration when running a solubility experiment with material that is not known to be the most stable crystalline form.
The amount of compound required to measure a thermodynamic solubility measurement depends on the volume of solvent used to make the saturated solution and the solubility of the compound in that solvent. Recent reports for miniaturized systems list compound requirements ranging from about 100 mg per measurement for poorly soluble compounds to 3 to 10 mg for pharmaceutically relevant compounds
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