Thermodynamic study of benzimidazole solubility and preferential solvation in binary alcohol-water systems

2.1. Materials

BZI (BZI, 99.8% cleanliness) was attained from Thermo Fisher Scientific. The study utilized analytical-grade organic solvents (including methanol and ethanol), purchased from Sinopharm Chemical Reagent Co., Ltd, and Sigma-Aldrich. Table 1 presents the detailed information. All chemical reagents were of analytical grade.

2.2. X-ray powder diffraction

X-ray powder diffraction (XRPD) (Bruker D2 PHASER) provides an intuitive means to reveal the structure of materials. In this study, it was used to examine the structural changes in BZI after solid-liquid equilibrium. The instrument employs copper (Cu Kα radiation), with a wavelength of 1.5418 Å as the anode material, operating at 40 kV and 40 mA. Scans were conducted in 2θ steps of 0.1 degrees and a pressure of 101.2 kPa. The instrumental uncertainty in the 2θ position was estimated to be ±0.02°, which is constant for all recorded peaks. Therefore, individual error bars are not shown in the diffraction patterns.

2.3. Solubility measurement

The solubility of BZI in MeOH (1) + water (2), and EtOH (1) + water (2), was ascertained utilizing a gravimetric technique validated in our previous studies [18-22]. Detailed experimental procedures for solubility measurement, along with comprehensive information on the apparatus, are provided in the Supporting Information file. Each data point was measured in triplicate to minimize experimental error, and the final solubility values were calculated from these replicates. The experimental solubility of BZI, expressed as the mole fraction ($x_{\text{exp}tl}$) in the aqueous-alcohol binary mixture, is defined by the following equation (1):

In this context, $m_{\text{BZI}}$​, $m_W$ and $m_{R-OH}$​ denote the masses of BZI, water, and alcohol (MeOH or EtOH), respectively. The molar masses of these components are represented by $M_{\text{BZI}}$​, $M_W$, and $M_{R-OH}$​.

3.1. Powder X-ray diffraction (PXRD) analysis

The PXRD characterization of the BZI raw material and equilibrium solid phase prepared with solvents (water, MeOH, and EtOH) and aqueous binary solvents (MeOH + water and EtOH + water) revealed that all the characteristic peaks were in the same position (Figure 2). The differing intensities of the peaks at the same position are primarily attributable to the varying degrees of crystallinity, grain size, and preferential growth orientation of the samples in different solvent systems. These findings indicate that no polycrystalline transformation occurred during the dissolution process.

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Figure 2.

Powder X-ray diffraction patterns of BZI in equilibration with different solvent systems at 323.15 K.

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3.2. Solubility data

This study ascertained the mole percentage of BZI’s solubility in water, MeOH, EtOH, MeOH (1) + water (2), and EtOH (1) + water (2) at 288.15 to 323.15 K temperature. All the experimental data have been summarized in Tables 2 and 3. As depicted in Figure 3, the solubility of BZI in water, MeOH, and EtOH assessed in our experiments was evaluated against published data [17] to assess the accuracy of our methodology. A relative standard uncertainty of less than 2% was observed between our results and the literature values, demonstrating strong agreement. The consistency of our findings with prior studies confirms the reliability and practical applicability of the experimental system employed in this work.

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Figure 3.

(a) Comparison of experimental and published solubility data for BZI in MeOH, EtOH, and (b) water at various temperatures.

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From Figure 4, it is readily apparent that the solubility of BZI in all the investigated dual mixed solvents presents a positive correlation with the absolute temperature. Generally, adding alcohol improves BZI solubility. In both MeOH (1) + water (2) and EtOH (1) + water (2) combinations, higher alcohol concentrations lead to greater BZI solubility, as illustrated in Tables 2 and 3 and Figure 4. The influence of temperature on BZI solubility is more pronounced in MeOH + water and EtOH + water combinations. The solubility of BZI increases with temperature because the dissolution process is endothermic, where elevated thermal energy disrupts solute-solute hydrogen bonds and enhances solute-solvent interactions, particularly with alcohol molecules that form stabilizing hydrogen bonds around the solute. Moreover, at identical compositions, BZI is more soluble in MeOH + water than in EtOH + water.

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Figure 4.

BZI solubility (x_BZI) in mole fraction dissolved in alcohol (x) + water (1 −x); mixtures with various mole fractions at different temperatures: l, x = 0.0; $▲$, x = 0.2; u, x = 0.4; ¡, x = 0.6; ∆, x = 0.8; ¯, x =1.00; solid line, calculated with (a) van’t Hoff−Acree model and (b) Jouyban Acree.

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The influence of solute-solvent intermolecular interactions on dissolution behavior at 298.15 K was investigated using the KAT-LSER model, as demonstrated in (Eq. 2) [23]. A number of solvent properties are considered in this model, such as the acidity of hydrogen bonds (α), the dipolarity/polarizability (π*), hydrogen bond basicity (β), and Hildebrand solubility variable (δ_H).

Here, $V_s$ is the molar capacity of the solute particle, while c₀, c₁, c₂, c₃, and c₄ are the model’s regression parameters.

Table S1 in the Supporting Information [24-26] presents literature values for α , β , and π* for different blends, including MeOH + water, EtOH + water, 1-PrOH + water, and 2-PrOH + water. Subsequently, we calculate the δ _H of the dual combinations by substituting ϕ₁δ_H1+ϕ₂δ_H2 for the volume percentage of solvent i , ϕ _i, in the mixture, as detailed in Table S2 [23]. Additionally, Tables S2-S5 in the supplementary materials display the results of multiple linear regression analyses, including R² values and F-test scores.

${\text{R}}^{\text{2}}=0.\text{99}\text{and}\text{F}=\text{62}.\text{37}$

${\text{R}}^{\text{2}}=0.\text{99}\text{and}\text{F}=\text{1194}.\text{13}$

From many statistical criteria, the KAT-LSER model provided the most accurate representation of the MeOH + water, and EtOH + water mixtures. The statistics in Tables S2 and S3 confirm that this model offers the best fit, featuring the lowest standard deviation, the highest F-value, and an R² value closest to one.

Data from Table S2 and (Eq. 3) show that the KAT-LSER model for BZI solubility in MeOH-water mixtures correlates strongly with hydrogen bond basicity (β ) and the cavity concept. The regression coefficients, c₂ and c₄, reveal that β is responsible for 71.44% of the solubility difference, while the cavity term contributes 28.56%. In ethanol-water mixtures, Table S3 and (Eq. 4) demonstrate significant relationships between BZI solubility and the parameters β , π* , and the cavity concept, with the model completely explaining the solubility variation; here, hydrogen bond basicity, dipolarity/polarizability, and the cavity concept contribute 46.28%, 7.47%, and 46.25%, respectively.

3.3. Correlation of solubility data

Experimental solubility data for BZI in both pure and combined solvents were analyzed using the Jouyban-Acree-van’t Hoff, Jouyban-Acree, and Apelblat-Jouyban-Acree models. These models integrate multiple thermodynamic parameters to predict solubility trends, providing insights into the dissolution behavior of drugs. To assess the accuracy of these correlations, we calculated and compared the relative average deviation (RAD) and root mean square deviation (RMSD). Lower RAD and RMSD values indicate a closer match between the model predictions and the experimental data, thereby confirming the effectiveness of these models in capturing complex solvation phenomena. Definitions for RAD and RMSD have been provided in (Eqs. 5, 6), respectively.

where, n signifies the total value of the experimental data points and $x_{calcd}$ and $x_{\text{exp}tl}$ correspondingly refer to the experimental mole percentage solubilities.

3.4. Preferential salvation evaluation

Preferential solvation occurs when a solute connects more to one solvent over another, offering advantages in controlling solubility and reaction environments. The expression quantifies the difference in interaction energies between solute-solvent pairs, providing insight into mixture behavior and guiding the design of more efficient formulations and separation processes.

The IKBI equations are typically formulated through the following equation [33]:

In (Eq. 12), ​ g_i,BZI, denotes the pair correlation function for solvent iii molecules in cosolvent–water mixes surrounding the BZI solute. Here, r represents the distance between the centers of the BZI molecule and either the cosolvent (1) or water (2), and r_cor​ is the cutoff distance beyond which g_i,BZI ​(r > r_cor​) ≈ 1. Thus, the integral is effectively zero for r > r_cor ​. The preferred solvation parameters $\delta x_{1,BZI}$​ for BZI in binary solvent mixtures are used to present the numerical results [ 27, 28, 33- 37]. One definition of the favored solvation parameter for the organic cosolvent (1) is:

In (Eq. 13), x ₁​ represents both the local mole percentage of solvent (1) close to BZI and its bulk mole percentage in the binary mixture (excluding solute contributions). Preferential dissolution of BZI in solvent (2) occurs when $\delta x_{1,BZI}$ < 0, while $\delta x_{1,BZI}$ < 0 indicates affinity for solvent (1). The parameter $\delta x_{1,BZI}$​ is calculated using the following expressions Eq (14-17) [ 33, 38]:

with,

The isothermal compressibility of solutions at a specific temperature is represented by the symbol $k_T$. When considering coupled solvents, determining the exact value of $k_T$ is not feasible due to the nature of the environment. However, this factor has a negligible effect on $G_{i,BZI}$, which is described by (Eq. 18), where $k_{T,i}^o$ is the isothermal compressibility of the pure element i , as outlined in studies such as [ 38, 39].

In the formulation, $x_i$​ is the mole fraction of component i in the mixture, and $k_{T,1}^o$ signifies the isothermal squeezability of the pristine constituent i . The partial molar volumes for solvent (1), solvent (2), and BZI are given by V ₁, V ₂, and V _BZI, respectively, with V _cor​ representing the correlation volume. (Eq. 19) defines function D as the first derivative of G with respect to solvent (1)’s composition, while (Eq. 20) defines function Q as the second derivative of the molar additional Gibbs energy with respect to solvent (2) ($x_2$​). The BZI molecule’s radius, r_BZI​, is calculated using (Eq. 21) along with the Avogadro constant (N _Av ​) [34,39,40].

The magnitude of $V_{cor}$ is related to the local mole fraction, denoted as $x_{1,BZI}^L$​. Consequently, an iterative method simultaneously considering (Eqs. 13, 14, 17) is required to determine its value. For MeOH (1) + water (2) and EtOH (1) + water (2) mixtures, the standard transfer Gibbs energy, ${\Delta }_{tr}{G}_{BZI,2\to 1+2}^o$​, for BZI moving from pure water (2) to the alcohol-water mixture is calculated utilizing the solubility from (Eq. 22) and then correlated via (Eq. 23).

In this equation, a , b , c , d and e signify the variables. Figure S1 illustrates the behavior of ${\Delta }_{tr}{G}_{BZI,2\to 1+2}^o$ at various temperatures, while Table S4 summarizes this behavior across all studied temperatures. The determined coefficients are listed in Table S5.

The D values listed in Table S6 were obtained from the first derivatives of the polynomial equations (Eq. 24), calculated using the composition of the mixtures. The methodology involved systematically adjusting the mole percentage of the organic cosolvent in 0.05 increments.

The compositional dependence of the excess Gibbs energy ($G_{1+2}^{Exc}$) for MeOH (1) + water (2) and EtOH (1) + water (2) systems at 298.15 K is described by (Eqs. 25, 26), respectively. These equations are grounded in the theoretical framework developed by Marcus [33]. To determine $G_{1+2}^{Exc}$ values at varying temperatures, (Eq. 27) is applied, which integrates the extra molar enthalpy ($H_{1+2}^{Exc}$) of the co-solvent blends. Here, T₁ represents the reference temperature of 298.15 K, and T₂ corresponds to the other temperatures under investigation [33]. Following Marcus’s methodology [33], the $H_{1+2}^{Exc}$values for methanol (1) + water (2) and ethanol (1) + water (2) combinations are derived employing (Eqs. 28, 29), respectively.

The Q values for all temperatures are included in Tables S7 and S8 of the Supplementary material. To calculate the $RT{k}_T$ values in these binary systems, additive mixing principles were applied, utilizing the reported temperature-independent $k_T$ values for MeOH (1.248 GPa⁻¹), EtOH (1.153 GPa⁻¹), and water (0.457 GPa⁻¹) at 298.15 K [41]. For determining the fractional molar volume of the co-solvent (1) + water (2) mixes, density data from Mikhail [34] (methanol + water) and Khattab [42] (ethanol + water) were incorporated into (Eqs. 30, 31), respectively. Here, V denotes the molar capacity of the blends, calculated via (Eq. 32). The molar masses (M₁ ) of methanol and ethanol are 32.04 g⋅mol⁻¹ and 46.07 g⋅mol⁻¹, respectively, while water (M₂ ) has a molar mass of 18.02 g⋅mol⁻¹.

Since the exact values are not reported in the literature, this study takes the reasonable assumption that the fractional molar volumes of BZI in different combinations are similar to the pure compound [21,43,44]. By use of its molar mass (118.14 g·mol⁻¹) and density (1.23 g·cm⁻³), the molar volume of BZI is thus calculated to be 96.049 cm³·mol⁻¹. Tables S9 and S10 show, respectively, the values for $V_1$ and $V_2$ for the combinations of MeOH (1) + water (2) and EtOH (1) + water (2).

Except for $G_{1,BZI}$ in the interval 0.00 ≤ x ₁ ≤ 0.20 for MeOH (1) + water (2), the $G_{1,BZI}$ and $G_{2,BZI}$ values found in Tables S11 and S12 of the supplemental material consistently exhibit a negative pattern. Furthermore, using (Eq. 21), one finds the solute radius (r_BZI) to be 0.329 nm based on these volume estimates.

Tables 6 and 7 list the $V_{cor}$ and $\delta x_{1,BZI}$​ values for the binary mixed solvents, respectively. Figure 5 graphically depicts the relationship between $\delta x_{1,\text{BZI}}$​ and the solvent mole fraction. All aqueous mixtures show an indirect connection between the fraction of solvent (1) and $\delta x_{1,\text{BZI}}$​. As seen in Figure 5, adding water (1) to MeOH (1) + water (2) and EtOH (1) + water (2) mixes results in a positive shift in the ${\text{δx}}_{1,\text{BZI}}$​ values for BZI.

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Figure 5.

$\delta x_{1,\text{BZI}}$values of BZI from water to (a) MeOH (1) + water (2) and (b) EtOH (1) + water (2) mixtures at several temperatures.

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In the EtOH (1)–water (2) and MeOH (1)–water (2) systems, for mole percentage compositions ranging from 0.00 < x ₁ < 1.00, the local mole fractions of EtOH/or MeOH around BZI are higher compared to those in the bulk solution, indicating a preference for EtOH/or MeOH to solvate BZI. This is evidenced by the positive values of the preferential solvation parameter, $\delta x_{1,\text{BZI}}$. EtOH/or MeOH solvates BZI by dissolving the surrounding water molecules near its nonpolar region. The maximum degree of solvation at studied temperatures is observed at x ₁ = 0.15 and x ₁ = 0.70, where $\delta x_{1,\text{BZI}}$ ranges from (4.03 to 4.33) ×10⁻² for MeOH (1)–water (2). Similarly, EtOH (1)–water (2) system the maximum degree of solvation by alcohol is observed at and x ₁ = 0.15–0.20 and x ₁ = 0.70–0.75 where $\delta x_{1,\text{BZI}}$ ranges from (1.06 to 10.18) ×10⁻². In the intermediate composition range, the experimental temperature has a minimal impact on the dissolution degree of BZI in alcohol aqueous solutions, as shown in Figure 5. Conversely, in the MeOH (1)–water (2) and EtOH (1)–water (2) systems with compositions of 0.40 < x ₁ < 0.45, neither alcohol (MeOH or EtOH) nor water preferentially solvate BZI, as evidenced by all $\delta x_{1,\text{BZI}}$ values being below 1.0×10⁻². This indicates that uncertainty propagation, instead than preferential solvation, accounts for this result [45-47].

The​‍​‌‍​‍‌ molecular structure of BZI can help us understand why alcohol molecules preferentially solvate BZI (Figure S2). BZI has a conjugated π-system and two nitrogen atoms which can both donate and accept hydrogen bonds. In the case of mixed solvents, the alcohol molecules, which are less polar and better hydrogen bond acceptors (β = 0.66 for MeOH, β = 0.75 for EtOH) [41,48], thus, they interact preferentially with the imidazole N–H groups via N–H···O hydrogen bonds and also stabilize the aromatic system by weak π–π and dispersion ​‍​‌‍​‍‌interactions (Figure S2). Water molecules, on the other hand, form a stronger hydrogen-bond network among themselves, which limits their approach to the hydrophobic π-surface of BZI. Consequently, BZI becomes locally enriched in the alcohol-rich domain, as reflected by the positive $\delta x_{1,\text{BZI}}$ values. The stronger π–π and hydrophobic associations with EtOH relative to MeOH explain the slightly higher preferential solvation in the EtOH–water system, whereas MeOH’s higher polarity leads to somewhat stronger H-bond donation but weaker π-stacking interactions.

The preferential solvation behavior of BZI at 313.15 K has been illustrated in Figure 6, which compares two binary solvent systems: MeOH–water and EtOH–water. In both systems, alcohol is identified as the preferred solvent for BZI. Notably, solvation is more pronounced in the EtOH– water system compared to the MeOH–water system. The​‍​‌‍​‍‌ most significant solvation is achieved at certain co-solvent ratios, with the highest solvation for MeOH–water being at a mole fraction of 0.15, resulting in a value of 4.33×10⁻², and for EtOH–water at x ₁= 0.75, with a value of 6.16×10⁻². These preferential solvation results have a great practical implication, as they indicate that the concentration of BZI, which has a stronger affinity for alcohol molecules than for water, could be deliberately used in the designing of pharmaceutical formulations and drug delivery systems where solvent composition tuning may work solubility, stability, and bioavailability of BZI-based ​‍​‌‍​‍‌compounds.

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Figure 6.

$\delta x_{1,\text{BZI}}$ values of BZI in alcohol (1) + water (2) mixtures at 313.15 K.

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