Solubility and Thermodynamic Properties of Febuxostat in Various (PEG 400 + Water) Mixtures

The solubility of the poorly soluble medicine febuxostat (FXT) (3) in various {polyethylene glycol 400 (PEG 400) (1) + water (H2O) (2)} mixtures has been examined at 298.2–318.2 K and 101.1 kPa. FXT solubility was measured using an isothermal method and correlated with “van’t Hoff, Apelblat, Buchowski–Ksiazczak λh, Yalkowsky–Roseman, Jouyban–Acree, and Jouyban–Acree-van’t Hoff models”. FXT mole fraction solubility was enhanced via an increase in temperature and PEG 400 mass fraction in {(PEG 400 (1) + H2O (2)} mixtures. Neat PEG 400 showed the highest mole fraction solubility of FXT (3.11 × 10–2 at 318.2 K), while neat H2O had the lowest (1.91 × 10–7 at 298.2 K). The overall error value was less than 6.0% for each computational model, indicating good correlations. Based on the positive values of apparent standard enthalpies (46.72–70.30 kJ mol−1) and apparent standard entropies (106.4–118.5 J mol−1 K−1), the dissolution of FXT was “endothermic and entropy-driven” in all {PEG 400 (1) + H2O (2)} mixtures examined. The main mechanism for FXT solvation in {PEG 400 (1) + H2O (2)} mixtures was discovered to be an enthalpy-driven process. In comparison to FXT-H2O, FXT-PEG 400 showed the strongest molecular interactions. In conclusion, these results suggested that PEG 400 has considerable potential for solubilizing a poorly soluble FXT in H2O.


Introduction
Febuxostat (FXT) ( Figure 1) is a selective nonpurine inhibitor of xanthine oxidoreductase [1][2][3]. It is advised for the management of hyperuricemia in gouty individuals [3,4]. One of FXT's properties is polymorphism [5]. The three polymorphs (forms A, B, and C) and two solvates (BH and D) make up the five distinct forms of FXT [6][7][8]. The preferred form of FXT is Form A, and managing its crystallization process is difficult [7]. Form H, a unique crystalline form of FXT that has been shown to be stable under a number of conditions, is the best form to use for designing dosage forms [1]. FXT is a biopharmaceutical classification system (BCS) class II medicine, which means it shows high permeability and poor aqueous solubility [2]. BCS class II drugs, such as FXT are difficult to formulate due to their extremely poor water (H 2 O) solubility [9]. Different formulation strategies, including the use of microsponges [10], nanosponges [11], polymeric nanoparticles [12], ternary solid dispersion [13], nanoemulsion [14], self-nanoemulsifying formulations [15,16], selfmicroemulsifying formulation [17], ethosomes [18], and nanostructure lipid carriers [19] have been used to enhance the fundamental and physicochemical characteristics of FXT.
The pharmaceutical industry has acknowledged the importance of solubility expertise over many years [20,21]. The solubility profile of pharmaceuticals, in particular in the field of drug research and development, offers valuable information for enhancing the quality of drug candidates and raises the success rate in a clinic by assisting pharmacists in making knowledgeable judgments [22]. Furthermore, solubility data is useful for estimating in vivo pharmacokinetics, which improves dose prediction [23]. A cosolvency PEG 400 has been examined as a potential solubilizer/cosolvent for the solubilization of several weakly soluble pharmacological molecules, such as lornoxicam, tenoxicam, dihydropyrimidine derivative, ferulic acid, pterostilbene, amlodipine besylate, and mesalazine [34][35][36][37][38][39][40]. The solubility data and thermodynamic parameters of FXT (3) in binary {PEG 400 (1) + H2O (2)} mixtures at various temperatures (298.2-318.2 K) and fixed atmospheric pressure (101.1 kPa) are not reported in the literature. Therefore, in order to ascertain the solubility data and thermodynamic parameters of FXT (3) in various {PEG 400 (1) + H2O (2)} combinations, including neat PEG 400 and H2O, at 298.2-318.2 K and 101.1 kPa, this investigation was carried out. The development of the study drug's dosage forms, preformulation testing, and purification could all benefit from the data collected during the data gathering phase of this study.

Materials
FXT (form H) was provided by "E-Merck (Darmstadt, Germany)". PEG 400 was procured from "Sigma Aldrich (St. Louis, MO, USA)". The Milli-Q unit was used to obtain purified H2O. Table 1 provides a summary of each material's specifics. PEG 400 has been examined as a potential solubilizer/cosolvent for the solubilization of several weakly soluble pharmacological molecules, such as lornoxicam, tenoxicam, dihydropyrimidine derivative, ferulic acid, pterostilbene, amlodipine besylate, and mesalazine [34][35][36][37][38][39][40]. The solubility data and thermodynamic parameters of FXT (3) in binary {PEG 400 (1) + H 2 O (2)} mixtures at various temperatures (298.2-318.2 K) and fixed atmospheric pressure (101.1 kPa) are not reported in the literature. Therefore, in order to ascertain the solubility data and thermodynamic parameters of FXT (3) in various {PEG 400 (1) + H 2 O (2)} combinations, including neat PEG 400 and H 2 O, at 298.2-318.2 K and 101.1 kPa, this investigation was carried out. The development of the study drug's dosage forms, pre-formulation testing, and purification could all benefit from the data collected during the data gathering phase of this study.

Materials
FXT (form H) was provided by "E-Merck (Darmstadt, Germany)". PEG 400 was procured from "Sigma Aldrich (St. Louis, MO, USA)". The Milli-Q unit was used to obtain purified H 2 O. Table 1 provides a summary of each material's specifics.  [31]. Utilizing an isothermal method [41], the mole fraction solubility of FXT against mass fraction of PEG 400 (m = 0.0 − 1.0; m is the mass fraction of PEG 400 in {PEG 400 (1) [32]. After reaching equilibrium, the saturated samples were removed from the shaker and centrifuged at 5000rpm for 30 min. A previously described HPLC method at 354 nm was used to measure the FXT concentration after the supernatants were extracted and diluted (as necessary) [32]. FXT mole fraction solubilities (x e ) were computed using Equations (1) and (2): A solute's solubility in a plain solvent or a cosolvent-H 2 O mixture directly relates to its HSP. According to reports, a solute will be most soluble in a certain solvent when its HSP is closed with that of the solvent [42]. The HSPs for the tested drug, FXT; neat PEG 400; and neat H 2 O were consequently computed. For FXT, Equation (3) was used to determine total HSP (δ t ) value [43][44][45][46]: where "δ d = dispersion HSP; δ p = polar HSP, and δ h = hydrogen-bonded HSP". These values for TXT were calculated using "HSPiP software (version 4.1.07, Louisville, KY, USA)" [44]. The δ t value for neat H 2 O and neat PEG 400, on the other hand, was derived from the literature [38].

FXT Ideal Solubility and Solute-Solvent Interactions
With the help of Equation (5), an "ideal solubility (x idl )" of FXT at 298.2-318.2 K was calculated [47]: where T = absolute temperature; T fus = FXT fusion temperature; R = universal gas constant; ∆H fus = FXT fusion enthalpy, and ∆C p = difference in the molar heat capacity of FXT solid state with its liquid state [48]. Equation (6) was used to compute the ∆C p for FXT [47,48]: According to Reference [2], the T fus and ∆H fus values for FXT were 486.53 K and 27.58 kJ mol −1 , respectively. The ∆C p for FXT was determined to be 56.68 J mol −1 K −1 using Equation (6). Finally, the x idl values for FXT were calculated using Equation (5). Equation (7) The chemical basis of solute-solvent interactions was explained using FXT γ i data.

Thermodynamic Parameters
At the mean harmonic temperature (T hm ), all apparent thermodynamic parameters for FXT were measured [47]. Using the formula from the literature [47,58], the T hm was determined. T hm for FXT was determined to be 308 K. An apparent thermodynamic analysis was used to calculate a number of apparent thermodynamic parameters. The "van't Hoff and Gibbs equations" were applied for this purpose. Equation (13), applied with T hm = 308 K, was used to calculate the apparent standard enthalpy (∆ sol H 0 ) data for FXT (3) in various {PEG 400 (1) + H 2 O (2)} mixtures [47,59]: The graphed "van't Hoff" curves between the ln x e values of FXT and 1 /T − 1 /T hm were used to calculate the "∆ sol H 0 " for FXT. Figure 2 includes the van't Hoff curves for FXT (3) in binary {PEG 400 (1) + H 2 O (2)} mixtures.

Measured Solubility Data of FXT
To look into the potential conversion of FXT into polymorphs or solvates/hydrates, the solid phase characterization of FXT before solubility measurement (pure FXT) and after solubility measurement (equilibrated FXT recovered from H 2 O) was conducted. Our most recent work [32] reports the results of this characterization on pure and equilibrated FXT utilizing Fourier transforms infrared spectroscopy (FTIR) and X-ray diffraction (XRD) analyses. In our most recent publication [32], it was discovered that the FTIR and XRD spectra of pure and equilibrated FXT were identical and shared similar peak characteristics. Additionally, no other FTIR or XRD peaks were seen in the equilibrated FXT sample. These findings showed that FXT did not change into polymorphs or solvates/hydrates. The measured solubility data of FXT (3) [9,32]. In this work, the FXT mole fraction solubility was not directly calculated at 310.2 K. However, the interpolation of the curve drawn between ln x e and 1/T revealed that the FXT mole fraction solubility at 310.2 K was 6.19 × 10 −7 . The recorded value was fairly close to the FXT in H 2 O stated value [9]. FXT mole fraction solubility values in neat PEG 400 and H 2 O at 298.2-318.2 K have also been documented [32]. The measured and reported solubility values of FXT in neat H 2 O and PEG 400 at 298.2-318.2 K are graphically compared in Figure 3. A good correlation was found between the observed solubility values of FXT in neat H 2 O and PEG 400 and those described in the literature, as seen in the results summarized in Figure 3 [32]. These results showed that the measured solubility statistics for FXT were in good agreement with the literature that has been published [9,32]. FXT solubility has also been improved using different techniques, such as solid dispersion, nanomatrix, and nanoemulsion approaches [61][62][63]. The comparative solubility data of FXT in PEG 400 with reported solubility approaches are summarized in Table 3. The equilibrium solubility of FXT using nanomatrix and solid dispersion approaches has been reported as 92.91 and 632.0 µg mL −1 , respectively [61,62]. The equilibrium solubility of FXT in PEG 400 was 7053 µg mL −1 in this work, which was approximately 76-and 11-fold higher than its reported solubility in nanomatrix and solid dispersion, respectively. Reddy and Sundari reported the equilibrium solubility of FXT using solid dispersion and nanoemulsion approaches as 1146 and 655.0 µg mL −1 , respectively [63]. The equilibrium solubility of FXT in PEG 400 was approximately 6 and 11-folds higher than its reported solubility in solid dispersion and nanoemulsion, respectively. These outcomes suggested the potential of cosolvency approach in solubilization of FXT over other reported approached of FXT solubilization.

Measured Solubility Data of FXT
To look into the potential conversion of FXT into polymorphs or solvates/hydrates, the solid phase characterization of FXT before solubility measurement (pure FXT) and after solubility measurement (equilibrated FXT recovered from H2O) was conducted. Our most recent work [32] reports the results of this characterization on pure and equilibrated FXT utilizing Fourier transforms infrared spectroscopy (FTIR) and X-ray diffraction (XRD) analyses. In our most recent publication [32], it was discovered that the FTIR and XRD spectra of pure and equilibrated FXT were identical and shared similar peak characteristics. Additionally, no other FTIR or XRD peaks were seen in the equilibrated FXT sample. These findings showed that FXT did not change into polymorphs or solvates/hydrates. The measured solubility data of FXT (3) in binary {PEG 400 (1) + H2O (2)} mixtures at five different temperatures and fixed pressure are documented in Table 2. FXT solubility (3) in binary {PEG 400 (1) + H2O (2)} mixtures has not been reported. However, the solubility of FXT in neat PEG 400 and H2O has been documented. At 310.2 K, the equilibrium solubility of FXT in H2O has been reported to be 10.8 mg L −1 (equivalent to 6.15 × 10 −7 in mole fraction) [9,32]. In this work, the FXT mole fraction solubility was not directly calculated at 310.2 K. However, the interpolation of the curve drawn between ln xe and 1/T revealed that the FXT mole fraction solubility at 310.2 K was 6.19 × 10 −7 . The recorded value was fairly close to the FXT in H2O stated value [9]. FXT mole fraction solubility values in neat PEG 400 and H2O at 298.2-318.2 K have also been documented [32]. The measured and reported solubility values of FXT in neat H2O and PEG 400 at 298.2-318.2 K are graphically compared in Figure 3. A good correlation was found between the observed solubility values of FXT in neat H2O and PEG 400 and those described in the literature, as seen in the results summarized in Figure 3 [32]. These results showed that the measured solubility statistics for FXT were in good agreement with the literature that has been published [9,32]. FXT solubility has also been improved using different techniques, such as solid dispersion, nanomatrix, and nanoemulsion approaches [61][62][63]. The comparative solubility data of FXT in PEG 400 with reported solubility approaches are summarized in Table 3. The equilibrium solubility of FXT using nanomatrix and solid dispersion approaches has been reported as 92.91 and 632.0 µg mL −1 , respectively [61,62]. The equilibrium solubility of FXT in PEG 400 was 7053 µg mL −1 in this work, which was approximately 76-and 11-fold higher than its reported solubility in nanomatrix and solid dispersion, respectively. Reddy and Sundari reported the equilibrium solubility of FXT using solid dispersion and nanoemulsion approaches as 1146 and 655.0 µg mL −1 , respectively [63]. The equilibrium solubility of FXT in PEG 400 was approximately 6 and 11-folds higher than its reported solubility in solid dispersion and nanoemulsion, respectively. These outcomes suggested the potential of cosolvency approach in solubilization of FXT over other reported approached of FXT solubilization.

Measured Solubility Data of FXT
To look into the potential conversion of FXT into polymorphs or solvates/hydrates, the solid phase characterization of FXT before solubility measurement (pure FXT) and after solubility measurement (equilibrated FXT recovered from H2O) was conducted. Our most recent work [32] reports the results of this characterization on pure and equilibrated FXT utilizing Fourier transforms infrared spectroscopy (FTIR) and X-ray diffraction (XRD) analyses. In our most recent publication [32], it was discovered that the FTIR and XRD spectra of pure and equilibrated FXT were identical and shared similar peak characteristics. Additionally, no other FTIR or XRD peaks were seen in the equilibrated FXT sample. These findings showed that FXT did not change into polymorphs or solvates/hydrates. The measured solubility data of FXT (3) in binary {PEG 400 (1) + H2O (2)} mixtures at five different temperatures and fixed pressure are documented in Table 2. FXT solubility (3) in binary {PEG 400 (1) + H2O (2)} mixtures has not been reported. However, the solubility of FXT in neat PEG 400 and H2O has been documented. At 310.2 K, the equilibrium solubility of FXT in H2O has been reported to be 10.8 mg L −1 (equivalent to 6.15 × 10 −7 in mole fraction) [9,32]. In this work, the FXT mole fraction solubility was not directly calculated at 310.2 K. However, the interpolation of the curve drawn between ln xe and 1/T revealed that the FXT mole fraction solubility at 310.2 K was 6.19 × 10 −7 . The recorded value was fairly close to the FXT in H2O stated value [9]. FXT mole fraction solubility values in neat PEG 400 and H2O at 298.2-318.2 K have also been documented [32]. The measured and reported solubility values of FXT in neat H2O and PEG 400 at 298.2-318.2 K are graphically compared in Figure 3. A good correlation was found between the observed solubility values of FXT in neat H2O and PEG 400 and those described in the literature, as seen in the results summarized in Figure 3 [32]. These results showed that the measured solubility statistics for FXT were in good agreement with the literature that has been published [9,32]. FXT solubility has also been improved using different techniques, such as solid dispersion, nanomatrix, and nanoemulsion approaches [61][62][63]. The comparative solubility data of FXT in PEG 400 with reported solubility approaches are summarized in Table 3. The equilibrium solubility of FXT using nanomatrix and solid dispersion approaches has been reported as 92.91 and 632.0 µg mL −1 , respectively [61,62]. The equilibrium solubility of FXT in PEG 400 was 7053 µg mL −1 in this work, which was approximately 76-and 11-fold higher than its reported solubility in nanomatrix and solid dispersion, respectively. Reddy and Sundari reported the equilibrium solubility of FXT using solid dispersion and nanoemulsion approaches as 1146 and 655.0 µg mL −1 , respectively [63]. The equilibrium solubility of FXT in PEG 400 was approximately 6 and 11-folds higher than its reported solubility in solid dispersion and nanoemulsion, respectively. These outcomes suggested the potential of cosolvency approach in solubilization of FXT over other reported approached of FXT solubilization.   In general, it was found that the mole fraction solubility of FXT was lowest in neat H 2 O and highest in neat PEG 400. The low polarity of PEG 400 in contrast to the high polarity of H 2 O may help to explain the maximal solubility of FXT in neat PEG 400 [36][37][38]. When the temperature and PEG 400 mass fraction were increased, FXT (3)   In general, it was found that the mole fraction solubility of FXT was lowest in nea H2O and highest in neat PEG 400. The low polarity of PEG 400 in contrast to the high polarity of H2O may help to explain the maximal solubility of FXT in neat PEG 400 [36][37][38]. When the temperature and PEG 400 mass fraction were increased, FXT (3)

Determination of HSPs
Using "HSPiP software", the δ t for FXT was calculated to be 21 The highest and lowest δ mix values were consequently measured at m = 0.1 and m = 0.9, respectively. However, it was discovered that a decrease in δ mix values improved the solubility values of FXT. Generally speaking, the HSP for neat PEG 400 (δ 1 = 18.90 MPa 1/2 ) and FXT (δ t = 21.70 MPa 1/2 ) were comparable. FXT solubility in neat PEG 400 was likewise discovered to be the highest during the investigations. As a result, the FXT solubility data obtained from experiments using mixes of {PEG 400 (1) + H 2 O (2)} closely matched these results.

Determination of Ideal Solubility and Solute-Solvent Interactions
The values of FXT's x idl are documented in Table 2. FXT's x idl values were determined to be 3.55 × 10 −2 to 5.52 × 10 −2 between 298.2 and 318.2 K. In neat H 2 O, FXT had much higher x idl values than x e values. FXT's x idl values, however, were nearly identical to its x e values in neat PEG 400 at all study temperatures. It can be used as the optimum cosolvent for FXT solubilization because neat PEG 400 has the highest solubility of FXT.
The γ i values for FXT in various {PEG 400 (1) + H 2 O (2)} mixtures at five different temperatures are documented in Table 4. The γ i value of FXT was greatest in neat H 2 O at all studied temperatures. However, in neat PEG 400, the γ i of FXT was lowest at each temperature examined. The γ i values for FXT were noticeably lower for neat PEG 400 than for neat H 2 O. The largest γ i for FXT in neat H 2 O may be explained by the least solubility of FXT in that solution. These results suggest that when compared to FXT-H 2 O combination, FXT-PEG 400 combination has the greatest number of solute-solvent interactions at the molecular level.
The main drawback of this study is that just one set of {PEG 400 (1) + H2O (2 binations was used to measure the solubility and physicochemical parameters of F pharmaceutical and chemical industries, however, may be able to use the research lished results to aid in the purification, recrystallization, pre-formulation testing, velopment of the study drug's dosage form. In the future, a wide range of H2O-co mixes at different temperatures can be used to conduct FXT solubility experiment

Conclusions
The solubility of FXT in several {PEG 400 (1) + H2O (2)} combinations is no mented in the literature. In this study, FXT (3) solubility in binary {PEG 400 (1) + H combinations and neat PEG 400 and H2O was tested at various temperatures and pheric pressure. With an increase in temperature and PEG 400 mass fraction in a 400 (1) + H2O (2)} combinations, including neat PEG 400 and H2O, FXT (3) mole solubilities rose. The highest and lowest solubilities of FXT were found in neat P and neat H2O, respectively, at each temperature examined. Experimentally record (3) solubility data were strongly correlated using six distinct computational mode {PEG 400 (1) + H2O (2)} combinations including neat PEG 400 and H2O. All the namic quantities, including ΔsolH°, ΔsolG°, and ΔsolS° in different {PEG 400 (1) + H combinations and neat PEG 400 and H2O were found to be positive, demonstrati dothermic and entropy-driven" FXT dissolution. The main mechanism for FXT so was enthalpy-driven in all {PEG 400 (1) + H2O (2)} mixtures and in neat PEG 400 an The obtained data of this study could be useful in the development of the studied dosage forms, pre-formulation testing, and purification. The main drawback of this study is that just one set of {PEG 400 (1) + H 2 O (2)} combinations was used to measure the solubility and physicochemical parameters of FXT. The pharmaceutical and chemical industries, however, may be able to use the research's published results to aid in the purification, recrystallization, pre-formulation testing, and development of the study drug's dosage form. In the future, a wide range of H 2 O-cosolvent mixes at different temperatures can be used to conduct FXT solubility experiments.

Conclusions
The solubility of FXT in several {PEG 400 (1)  Data Availability Statement: This study did not report any data.