Solid solubility of drugs in polymers

Similar to the miscibility, drug-polymer solid solubility is also a concept derived from aqueous solution theory. But unlike miscibility regarding the mixing of two liquids, solubility is defined as dissolving a solid state material into a solvent until the equilibrium maximum concentration at a certain temperature under a certain pressure. Under a condition of a certain temperature and pressure, a solute can dissolve in a solvate if the amount of the solute is below the solubility in the solvate. After dissolution, no recrystallisation or precipitation of the solute should be observed as the concentration of the solution is below the solubility. Therefore, assuming drug-polymer solid dispersions as liquid solution, if the drug loading in the solid dispersion is below the solid solubility of the drug in the polymer, no phase separation or recrystallization should occur. Based on this hypothesis, a few studies have correlated the physical stability of solid dispersions with solid solubility of drugs in polymers (19, 34, 122, 162).

1.6.5.1 Prediction of solid solubility of drugs in polymers

Several theoretical methods have been reported for the prediction of solid solubility of drugs in polymers (56, 122, 162). Melting point depression combined with Flory-Huggins lattice based theory has been reported to predict solid solubility of felodipine and nifedipine in PVP (122). The interaction parameter χ from Flory-Huggins theory can be calculated using the detected depressed melting points from drug-polymer physical mixtures with different ratios, and by further using the obtained interaction parathion the solid solubility of drugs in polymers can be predicted. This method was applied in this project and details are discussed in Chapter 4 (section 4.3.2.1).

Another model based on the measurement of melting enthalpy of crystalline drugs in physical mixtures with polymers by DSC was recently developed by Qi et al(56). This model was a modification of a previous melting enthalpy based method (163). It assumed the dissolution of drugs in polymers on heating is endothermic and two extremes which involved drugs completely dissolved in polymers and vice versa were included in the model. The expected results did not agree with the model in that article, and it was attributed to the relatively high heating rate in DSC.

This method was also utilised in the project and details of the model will be discussed in Chapter 4 (section 4.3.3.1).

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In addition to the methods mentioned above, a rheology method was reported in articles to determine the solid solubility of drugs in polymers (164). This method involved the preparation of a series of drug-polymer physical mixtures. The viscosity of individual physical mixture was tested at the temperature above the glass transition temperature of the polymer but below the melting point of the drug. If the drug can dissolve in the polymer, the plasticising effect provided by the dissolved drug should decrease the viscosity of the physical mixture. With increasing drug loading, the viscosity should continue decreasing. However, if the drug loading was beyond the solid solubility, the non-dissolved drug as another phase in the physical mixture will increase the viscosity. Therefore, by plotting the viscosity against drug loading (drug-polymer ratios in physical mixtures) a negative slope should be seen until the turning point where the slope started to be positive, and the turning point was suggested as the solid solubility of the drug in the polymer.

Assume the dispersed particles (drugs) are single sized spheres, the reduced viscosity ŋ/ŋ0

decreases with the increased volume fraction X of the drug in the mixtures (164):

ŋ/ŋ0 = 1 + 2.5 X Eq 1.8

where ŋ is the viscosity of the drug–polymer mixture, ŋ0 is the viscosity of the pure molten polymer and X is the volume fraction of the drug in the mixture. Eq 1.8 suggests the viscosity of the mixture will increase when the drug-polymer ratio crosses the solubility of drug in polymer. This method was applied to pacacetamol-polyethylene systems in a study (164). The plot of measured viscosity against drug loading from the study is shown in Figure 1.12 (164). Measured solubility using different shearing rates are listed in the figure. The turning point as described in the method was clearly observed.

Figure 1.12: Measured viscosity of the mixture against drug loading at 120 °C at three different shear rates: 1, 10 and 100 1/s. The critical drug loadings are 37.6%, 32.9% and 32.4% for the shear rates of 1, 10 and 100 1/s, respectively (164).

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However, this method can be limited as polymers still can be very viscous even at the temperature above their Tgs, and thus the method is highly relied on the rheological and thermal properties of drugs and polymers and may not be applied widely.

Recently, a new protocol to determine the solubility of drugs into polymer matrix using co-milling method was reported (162). In the study, super-saturated indomethacin-PVP K12 solid dispersions were prepared by using milling up to 8 hours. The super-saturated systems were heat-treated in DSC at high temperature (120^oC) for 2 hours to ensure the completion of de-mixing of drugs from the amorphous solid dispersions, and by re-scanning the same sample (after treated with heat at 120^oC) from room temperature an increased Tg value was detected in comparison to the Tg value in the fresh untreated sample. Using Gordon-Taylor equation, the drug concentration in the heat-treated sample can be estimated using the Tg value from re-scanning, and this drug concentration was considered as the solubility of indomethacin in PVP K12. Although this method made the contribution to faster drug-polymer solubility prediction, there still could be some potential issues concerning the accuracy and application of the method. Firstly, although milling has the potential to prepare amorphous solid dispersions with formulations containing PVP and drugs, it is not a processing method which can be generally and widely used to transform drug-polymer mixtures into super-saturated amorphous solid dispersions (61). This can restrict the application of this milling method to a broad range of drugs and polymers. Secondly, there was no physical stability study of amorphous solid dispersions to support the estimated solubility as amorphous solid dispersions with the drug loading below the predicted solubility were expected to be physically stable on aging. More importantly, this method did not take into account the effect of processing method on the drug-polymer solubility and it has been reported that apparent drug-polymer solubility may vary depending on preparation methods (73).

In this project, a practical milling method was specifically developed for the apparent solubility of drugs in melt extrudates. Details of this method are discussed in Chapter 5.

1.6.5.2 Limitations on the prediction of drug-polymer solid solubility

Although great efforts have been made to predict or measure the solid solubility of drugs in polymers, there still remain a few challenges. Firstly, solubility is a constant associated with temperature and pressure. Solid solubility predicted by approaches such as melting point depression method or rheology method is the value at the temperature significantly higher than room temperature, and therefore at room temperature where pharmaceutical products are normally stored the solid solubility could be lower as solubility can decrease with decreasing temperature.

Secondly, predicted solid solubility by those approaches did not take into account the effect of preparation processes. For instance, practical solid solubility of drugs in solid dispersions prepared by hot melt extrusion can be higher than the predicted value by theoretical models as extra energy

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in terms of high temperature and pressure during preparation is imposed on the system. It has been reported that the physical stability of solid dispersions with the same composition prepared by different processes varied significantly, which was attributed to the different apparent solid solubility in solid dispersions by different processes(73). Thirdly, those assumptions in the prediction models may underestimate the complication of the real drug-polymer system (such as the existing drug-polymer interactions), which can lead to the less accurate prediction.