The Importance of Dielectric Constant for Drug Solubility Prediction in Binary Solvent Mixtures: Electrolytes and Zwitterions in Water + Ethanol

Abstract

In drug discovery and formulation, drug solubility in water and organic solvent plays an important role and affects many pharmaceutical processes including design, synthesis, extraction, purification, formulation, absorption, and distribution in body fluids (1). In most cases, aqueous solubility of a chemical compound as a medicine is not enough to be applicable in pharmaceutical formulations and clinical administration. Hence, different kinds of solubilization techniques including cosolvency, complexation, micellization, and salt formation have been applied to increase the solubility (1,2). However, in some cases, it is required to reduce solubility in the medium, for example, in crystallization process (3). These methods not only influence the solubility of a compound, but can also alter its stability in the liquid medium (1). Cosolvency is the most feasible method for this purpose, and the most common pharmaceutical cosolvent is ethanol. Another useful and more employed method is salt formation, and an accountable proportion of the available medicinal compounds is in salt form. For developing liquid formulations of these compounds or crystallization process design, the use of cosolvents might be necessary to influence their solubility/stability. To speed up the development processes in the pharmaceutical industry, calculative models for solubility prediction in mixture of solvents have been proposed in recent decades (1,2). Almost all of the proposed models were designed for solubility correlation/prediction of the non-electrolytes in the solvent mixtures (1,2). The main pattern of solubility behavior in water + ethanol mixture has a maximum of solubility in ethanol-rich area for most of the non-electrolyte solutes (1,2). This pattern is not the same for ionizable compounds in water such as sodium salts of medicines and amino acids where the solubility value in water is more than solubility value in neat ethanol (4). Maybe changes in dielectric constant of the medium have a dominant effect on the solubility of the ionizable solute in which higher dielectric constant can cause more ionization of the solute and results in more solubilization (5). As an example, water (DW,298 = 78.5) has higher dissociation strength on ions in comparison with ethanol (DE,298 = 24.2) which is resulted in more solubilization power of ions in water. Born has proposed a theoretical model for solubility correlation in two different phases as following equation (6): 1 where S1 and S2 are the solubilities of the solute in media 1 and 2; e is the charge of an electron; r is the effective radius of the ion in the medium; k is the Boltzmann constant; T is the absolute temperature; and D1 and D2 are the dielectric constants of the media 1 and 2, respectively. Unfortunately, by using this equation, the predicted solubility values (when r values are known) or predicted r values (when solubility values are known) based on experimental data do not seem to be meaningful (7). However, one can consider the constant value of as AT for a specific solute and obtain: 2 where AT is a slope which can be calculated using two experimental solubility data points (e.g., solubility values in water and ethanol).