Equilibrium Solubility of Triclocarban in (Cyclohexane + 1,4-Dioxane) Mixtures: Determination, Correlation, Thermodynamics and Preferential Solvation

Equilibrium solubility of triclocarban (TCC) expressed in mole fraction in 1,4-dioxane and cyclohexane, as well, as in 19 {cyclohexane (1) + 1,4-dioxane (2)} mixtures, was determined at seven temperatures from T = (288.15 to 318.15) K. Logarithmic TCC solubility in these cosolvent mixtures was adequately correlated with a lineal bivariate equation as function of both the mixtures composition and temperature. Apparent thermodynamic quantities for the dissolution and mixing processes were computed by means of the van’t Hoff and Gibbs equations observing endothermal and entropy-driven dissolution processes in all cases. The enthalpy–entropy compensation plot of apparent enthalpy vs. apparent Gibbs energy was linear exhibiting positive slope implying enthalpy-driving for TCC transfer from cyclohexane to 1,4-dioxane. Ultimately, by using the inverse Kirkwood–Buff integrals it is observed that TCC is preferentially solvated by cyclohexane molecules in 1,4-dioxane-rich mixtures but preferentially solvated by 1,4-dioxane molecules in cyclohexane-rich mixtures.

However, the increasing use of pharmaceutical and cosmetic products containing TCC [4] has been associated with environmental problems from the excessive dumping of these products into wastewater, which increases the presence of this drug in natural systems in such a way that organizations like the NORMAN Network have classified TCC as a "highly toxic emerging pollutant" [5][6][7][8]. In this way, the environmental problem generated by the presence of TCC in aquatic, benthic, sludge, sediment and biota environments has been recorded by many researchers [9][10][11][12].
In this regard, from an industrial viewpoint, one of the best strategies for reducing the volume of TCC dumping is the optimization of production processes and/or the design of clean methodologies for development of pharmaceutical or cosmetic products containing TCC [13,14]. These interesting alternatives could be viable as long as every day there are more data about physicochemical properties involved directly with the development of pharmaceutical products, such as solubility in different media, product stability and partition coefficients, among others, which will allow design of rather than proposing production strategies with low environmental impact [15,16]. Therefore, the availability of important data like TCC solubility in different neat solvents and cosolvent mixtures, could allow the development of more efficient processes, in terms of crystallization, purification, analysis and quality control, which are typical processes in the pharmaceutical industry that involve a significant amount of technical resources [17].
On the other hand, despite some reported studies intended for development of environment-friendly TCC-based products [18], the study of its dissolution physicochemical properties in neat or solvent mixtures is limited. Therefore, the main objective of this research work is to present the solubility and dissolution thermodynamics of TCC in some solvent mixtures, exhibiting mainly Lewis base behavior, involving cyclohexane and 1,4-dioxane owing the physicochemical importance of this cosolvent system [19]. Thus, it expands the available literature solubility data regarding solubility and dissolution thermodynamics of this controversial compound [20][21][22][23][24][25].

Solubility Determinations
TCC solubility was determined using the shake-bottle method [26,27], quantifying the dissolved drug by UV/Vis spectrophotometry. For these purposes, in 30 cm 3 amber bottles, TCC was added to 20 g of solvent mixture until excess of TCC does not dissolve, forming a solid phase at the bottom of the bottle. Subsequently, the flasks were transferred to refrigeration thermostats (Medingen K-22/T100, Germany), initially at 318.15 K for 48 h, with periodic shaking. Once equilibrium is attained (i.e., the composition of the solution remained constant) a liquid sample was taken from each flask and filtered under isothermal conditions through a 0.45 μm membrane (Millipore Corp. Swinnex®-13, USA). Then, each was diluted with absolute ethanol (to avoid TCC precipitation) and the absorbance of the sample was measured at 265 nm (UV/Vis EMC-11-UV spectrophotometer, Germany). Subsequently, the thermostat′s temperature was decreased to 313.15 K allowing the reaching of the new equilibrium for two days and performing the respective analysis procedures. This was repeated at 5-degree intervals (to complete 7 different temperatures) until reaching the lowest temperature, 288.15 K, All experiments were performed three times.

Calorimetric Study
To identify the nature of the TCC solid phases in equilibrium with the saturated solutions in both neat 1,4-dioxane and cyclohexane solvents and the mixture w 1 = 0.50, DSC analyses were performed (DSC 204 F1 Phoenix, Germany). Nearly 5.0 mg of TCC samples were analyzed. The equipment was calibrated using Indium as standard. The sample and reference pans were heated to preserve the programmed temperature at a precise heating rate of 10 K·min -1 in a dynamic nitrogen atmosphere (10 cm 3 ·min -1 ) at constant pressure.

Mole Fraction Solubility of TCC
The mole fraction equilibrium solubilities of TCC in the neat solvents and the binary mixtures at seven temperatures from T = (288.15 to 318.15) K and atmospheric pressure of 96 kPa as functions of the mass fraction of 1,4-dioxane in the solvent mixtures are summarized in Table 2 and shown as logarithmic values in Figs. 2 and 3. Minimum and maximum TCC solubilities are observed in neat cyclohexane and neat 1,4-dioxane,  (3), respectively b Standard uncertainty in p is u(p) = 3.0 kPa. Mean relative uncertainties in w 1 and x 1 were u(w 1 ) = 0.0008 and u(x 1 ) = 0.0008. Standard uncertainty in T is u(T) = 0.10 K. Average relative uncertainty in x 3 , u r (x 3 ) = 0.017 respectively, at all temperatures studied. In all cases, TCC solubility increases with increasing temperature, which indicates endothermic dissolution processes. It is noteworthy that TCC logarithmic solubility decreases linearly with the cyclohexane proportion in the mixtures but increases linearly with the temperature. TCC solubility varied   Additionally, Fig. 4 shows the TCC logarithmic solubility as function of the Hildebrand solubility parameters of the {cyclohexane (1) + 1,4-dioxane (2)} mixtures (δ 1+2 ). As is well-known, the Hildebrand solubility parameter is a polarity index widely used in pharmaceutical studies regarding cosolvency effects on physical and chemical stabilities of drugs. Mixtures δ 1+2 values were calculated from the corresponding δ values, i.e., δ 1 = 16.8 MPa 1/2 for cyclohexane and δ 2 = 19.7 MPa 1/2 for 1,4-dioxane [28,29] and volumetric solvent proportions as described in Eq. 1. Volume fractions (f i ) were considered assuming additive behavior [30,31]: Accordingly, it is expected that TCC reaches its maximum solubilities in solvent systems with the same or similar Hildebrand solubility parameters [32,33]. By keeping this in mind, the δ 3 value of TCC would be higher than the δ 1 value (i.e., neat 1,4-dioxane δ value, 19.7 MPa 1/2 ) at T = 298.15 K, where the maximum TCC solubilities are observed at all temperatures. Effectively, the calculated Fedors-van Krevelen δ 3 value of TCC is 26.5 MPa 1/2 as reported in the literature [22]. Hence, it would be important to study the TCC solubility in mixed solvent systems exhibiting higher polarities than that of neat 1,4-dioxane, like {1,4-dioxane (1) + propylene glycol (2)} mixtures (obtaining an interval of 19.7 ≤ δ 1+2 /MPa 1/2 ≤ 30.2), where maximum drug solubility peaks could be observed as they were observed in {1,4-dioxane (1) + water (2)} mixtures [23].
Owing to the practical importance of calculating the TCC solubility at different temperatures or {cyclohexane (1) + 1,4-dioxane (2)} mixtures compositions regarding those experimentally determined, the equilibrium solubilities reported in Table 2 were logarithmically correlated as function of both temperature and mixtures composition to obtain the multivariate model shown as Eq.

TCC Solid Phases' DSC Analyses
DSC thermograms of TCC corresponding to original untreated sample and after equilibrating it in neat 1,4-dioxane, in the mixture of w 1 = 0.50, and in neat cyclohexane, are shown in Fig. 5. There are two endothermic peaks corresponding to the melting and thermal degradation of TCC. These peaks are almost coincident with those reported earlier in the literature for TCC in aqueous mixtures of 1,4-dioxane [23]. Thus, based on DSC results it is observable that TCC did not suffer crystal polymorphic transitions or solvate formation after dissolution and saturation in these organic solvent systems. Therefore, for ideal solubility calculations the following reported values were considered: 41.9 kJ·mol -1 for molar enthalpy of melting and 528.2 K for the temperature of melting [18].

Ideal Solubility and Activity Coefficients of TCC in Neat and Mixed Solvents
Ideal solubilities of TCC ( x id 3 ) at the temperatures of interest from 288.15 to 318.15 K were calculated by means of the well-known equation: Here, Δ fus H is the molar enthalpy of melting of the pure TCC (obtained at the melting point, i.e., 41.9 kJ·mol -1 [18]), T fus is the absolute melting point (i.e., 528.2 K), T is the absolute dissolution temperature, R is the universal gas constant (8.3145 J·mol -1 ·K -1 ), and ΔC p is the difference between the molar heat capacities of TCC in its crystalline form and its hypothetical super-cooled liquid form at every dissolution temperature [37]. However, owing the experimental difficulty in ΔC p determination, this value has been considered in this research as the same as the one of the entropy of fusion (Δ fus S = Δ fus H/T fus , i.e., 79.4 J·mol -1 ·K -1 ). Table 2 shows that the ideal solubilities of TCC are higher than the experimental solubilities at almost all the temperatures studied, except in the case of neat 1,4-dioxane at temperatures of (308.15, 313.15 and 318.15) K.
On the other hand, Table 3 summarizes the asymmetrical activity coefficients of TCC (γ 3 ) in neat solvents and in {cyclohexane (1) + 1,4-dioxane (2)} mixtures at all temperatures. These γ 3 values were calculated as the quotient: x id 3 x 3 from the experimental and ideal solubilities summarized in Table 2. As observed, at T = 298.15 K γ 3 values vary from 1.777 in neat 1,4-dioxane (where the maximum TCC solubility is obtained) to 10,039 in neat cyclohexane (where the minimum TCC solubility is achieved). In all solvent systems, γ 3 values decrease with the temperature arising. All obtained γ 3 values are higher than the unity because the experimental solubilities in all the solvent systems are lower than x id 3 at all temperatures tested, except in neat 1,4-dioxane at temperatures of (308.15, 313.15 and 318.15) K. Furthermore, a rough estimate of the respective solute-solvent intermolecular interactions present in the solutions was performed from the γ 3 values, based on Eq. 5 [38]: Here subscript s stands for the solvent system (which corresponds to neat solvents or cyclohexane-1,4-dioxane binary mixtures), e ss, e 33 and e s3 represent the solvent-solvent, solute-solute and solvent-solute interaction energies, respectively. However, it is important to keep in mind that in multicomponent systems like cyclohexane-1,4-dioxane-TCC, some cosolvent-cosolvent interactions would be present, which could also play an important role in the magnitudes of dissolution and equilibrium solubility of this antibacterial agent. V 3 is the molar volume of the super-cooled liquid TCC and φ s is the volume fraction of the solvent system in every saturated solution. It is noteworthy that when low x 3 values are obtained, the term (V 3 φ s 2 /RT) can be considered as constant regardless the solvent system because φ s is almost 1.0. Thus, the γ 3 values would depend mainly on the terms e ss , e 33 and e s3 [38]. As well-known, e ss and e 33 are not favorable for drug dissolution processes and equilibrium solubilities but e s3 favors the respective drug dissolution processes and  solubilities. Moreover, the contribution of e 33 toward the dissolution rate and equilibrium solubility of TCC was considered as constant regardless the solvent system studied.
As indicated above, a qualitative approach to intermolecular interactions was made based on the e ss, e 33 and e s3 energetic terms of Eq. 5. Hence, based on polarities it follows that e ss is highest in neat 1,4-dioxane (δ = 19.7 MPa 1/2 ) and lowest in neat cyclohexane (δ = 16.8 MPa 1/2 ) [28,29]. Neat cyclohexane and cyclohexane-rich mixtures, exhibiting γ 3 values higher than 1600 at T = 298.15 K, would imply high e 33 and low e s3 values. Otherwise, in 1,4-dioxane-rich mixtures, exhibiting γ 3 values lower than 10, the e ss values are also relatively low but the e s3 values would be comparatively higher regarding cyclohexane-rich mixtures.

Apparent Thermodynamic Functions of TCC Dissolution
All the apparent thermodynamic quantities of dissolution of TCC in neat solvents and in {cyclohexane (1) + 1,4-dioxane (2)} mixtures were estimated at the harmonic mean temperature (T hm ), which in turn was calculated by using Eq. 6 [39,40]: where n = 7 is the number of temperatures studied. Thus, from T = (218.15 to 318.15) K, the obtained T hm value is 302.8 K. In this way, the apparent standard enthalpic changes for TCC dissolution processes (∆ soln H°) were obtained by means of the modified van't Hoff equation, as [40,41]: The apparent standard Gibbs energy changes for the TCC dissolution processes (∆ soln G°) were calculated by means of: Here, the intercepts used are those obtained in the respective linear regressions of ln x 3 vs.
Apparent standard Gibbs energies, enthalpies and entropies relative to the TCC dissolution processes are positive in all cases as shown in Table 4. This implies  value in neat cyclohexane (118.8 J·mol -1 ·K -1 ). Additionally, the relative contributions by enthalpy (ζ H ) and entropy (ζ TS ) toward the TCC dissolution processes were calculated by means of the following equations [42]:   As shown in Table 4, the main contributor to the positive standard apparent molar Gibbs energies of dissolution of TCC was the positive enthalpy, which demonstrates the energetic predominance in all these TCC dissolution processes.

Apparent Thermodynamic Quantities of Mixing
Global dissolution processes of TCC in {cyclohexane (1) + 1,4-dioxane (2)} mixtures may also be represented by means of the following hypothetical process: Here the hypothetical stages are as follows: (i) the heating and melting of TCC at T fus = 528.2 K, (ii) the cooling of the liquid TCC to the considered temperature (T hm = 302.8 K), and (iii) the subsequent mixing of both the hypothetical TCC super-cooled liquid and the {cyclohexane (1) + 1,4-dioxane (2)} solvent system under consideration at T hm = 302.8 K [43]. This allowed us the calculation of the individual thermodynamic contributions by fusion and mixing toward the overall TCC dissolution processes, by means of the following equations: where Δ fus H T hm and Δ fus S T hm indicate the thermodynamic quantities of TCC fusion and its cooling at T hm = 302.8 K. In turn, these two functions were calculated by means of Eqs. 14 and 15, respectively [44]: Table 5 summarizes the apparent thermodynamic quantities of mixing of the hypothetical TCC as super-cooled liquid with all the {1,4-dioxane (1) + cyclohexane (2)} mixtures and the neat solvents, at T hm = 302.8 K. Apparent Gibbs energies of mixing are positive because the experimental solubilities of TCC in all these solvent systems are lower than the ideal solubilities at almost all temperatures, except in neat 1,4-dioxane at T ≥ 308.15 K and the mixture of w 1 = 0.05 at 318.15 K, as indicated above. As observed, the contributions by the mixing thermodynamic quantities, Δ mix H° and Δ mix S°, to the overall dissolution processes of TCC in neat solvents and {1,4-dioxane (1) + cyclohexane (2)} mixtures, are positive in all the systems, indicating endothermic and entropy-driven mixing processes. Moreover, to compare the relative contributions by enthalpy (ζ H ) and entropy (ζ TS ) to the mixing processes, two equations analogous to Eqs. 10 and 11 were also employed. As shown in Table 5, the main contributor to the positive standard apparent molar Gibbs energies of mixing of TCC was the positive enthalpy, which demonstrates the energetic predominance in all these TCC mixing processes, although in neat 1,4-dioxane and 1,4-dioxane-rich mixtures the contributions are similar.

Enthalpy-Entropy Compensation Analysis
As well-known, the extra-thermodynamic studies, which includes enthalpy-entropy compensation analysis, provide powerful tools to inquiry into the main molecular mechanisms implicated in a lot of physical and chemical processes involving several organic compounds like a variety of drugs [45,46]. These physicochemical studies have been performed in order to identify the main mechanisms involved in the cosolvent action to Table 5 Apparent thermodynamic functions relative to mixing processes of triclocarban (3) in {cyclohexane (1) + 1,4-dioxane (2)} mixtures at T hm = 302.8 K and p = 96 kPa a p is the atmospheric pressure in Neiva, Huila, Colombia. w 1 and x 1 are the mass and mole fraction of cyclohexane (1) in the {cyclohexane (1) + 1,4-dioxane (2)} mixtures free of triclocarban (3), respectively b Standard uncertainty in T hm is u(T hm ) = 0.13 K. Standard uncertainty in p is u(p) = 3.0 kPa. Mean relative uncertainties in w 1 and x 1 were u(w 1 ) = 0.0008 and u(x 1 ) = 0.0008. Average relative standard uncertainty in apparent thermodynamic quantities of mixing processes are u r (∆ mix G°) = 0.028, u r (∆ mix H°) = 0.033, u r (∆ mix S°) = 0.043, u r (T∆ mix S°) = 0.043 c ζ H and ζ TS are the relative contributions by enthalpy and entropy toward apparent Gibbs energy of mixing  [47][48][49]. In particular, Fig. 7 clearly shows that TCC exhibits a linear Δ soln H° vs. Δ soln G° trend in the studied organic mixtures, adjusted to Δ soln H°/kJ·mol -1 = 0.250·Δ soln G°/kJ·mol -1 + 62.75/kJ·mol -1 [34][35][36]. The positive slope indicates that the transfer processes of TCC from neat cyclohexane to neat 1,4-dioxane is enthalpy-driven, probably owing the better drug solvation by 1,4-dioxane molecules.

Preferential Solvation of TCC
The preferential solvation parameters of TCC (indicated as compound 3) by cyclohexane (indicated as compound 1) molecules in the different {cyclohexane (1) + 1,4-dioxane (2)} mixtures (δx 1,3 ) are defined as [50][51][52]: where x L 1,3 is the local mole fraction of cyclohexane in the molecular environment of TCC and x 1 is the bulk mole fraction of cyclohexane in the initial {cyclohexane (1) + 1,4-dioxane (2)} binary solvent mixture free of TCC. Thus, if δx 1,3 value is positive TCC molecules are preferentially solvated by cyclohexane molecules in the solutions. In contrast, TCC molecules are preferentially solvated by 1,4-dioxane molecules if this δx 1,3 parameter is negative. The values of δx 1,3 were obtained from the inverse Kirkwood-Buff integrals (IKBI) as described earlier [50][51][52], based on the following expressions: To obtain definitive V cor values, iteration processes are required because they depend on the local mole fractions of cyclohexane and 1,4-dioxane around the TCC molecules in the respective solutions. Thus, these iteration processes were performed by replacing δx 1,3 and The constant D value shown in Table 6 was determined as the slope of Eq. 25. Required Q, V 1 and V 2 values at T = 303.15 K were calculated from some thermodynamic quantities reported by Deshpande and Oswal that include excess Gibbs energies of mixing and excess volumes [53], whereas RTκ T values were calculated from κ T reported by Marcus [29]. All these values are also summarized in Table 6. Moreover, as-before in the analysis of TCC in {1,4-dioxane (1) + water (2)} mixtures, the V 3 value was considered the same as the one calculated by considering molar mass and density (1.53 g·cm -3 [1]), i.e., 206.26 cm 3 ·mol -1 , despite the solvent mixtures composition. Table 6 shows that the G 1,3 and G 2,3 values are positive in almost all the solvent systems, except for G 1,3 in the interval 0.85 ≤ x 1 ≤ 1.00 and for G 2,3 in the interval 0.00 ≤ x 1 ≤ 0.10. TCC r 3 value was calculated as 0.434 nm. It is noteworthy that V cor values shown in Table 6 were obtained after three iterations. V cor values increase with the cyclohexane proportion in the mixtures because V 1 values are higher than V 2 values. Additionally, Table 6 also summarizes the preferential solvation parameters of TCC by cyclohexane molecules (δx 1,3 ) in the mixtures at T = 303.15 K. Figure 9 shows a nonlinear variation δx 1,3 values for TCC regarding the cyclohexane proportion in the mixtures as expressed by their mole fractions before TCC adding. Initially, the addition of cyclohexane to neat 1,4-dioxane makes positive the δx 1,3 values of TCC in the composition interval of 0.00 < x 1 < 0.44. The maximum positive δx 1,3 value is obtained in the mixture of x 1 = 0.25 (i.e., δx 1,3 = 5.92 × 10 -2 ), which is higher than |1.0 × 10 -2 |. Hence, this result is a consequence of real preferential solvation effects of TCC by cyclohexane molecules, rather than a consequence of uncertainties propagation in the IKBI calculations [54,55].
Based on the negative δx 1,3 values observed in the composition interval of 0.44 < x 1 < 1.00, it follows that the local mole fractions of 1,4-dioxane around TCC molecules are higher than those in the bulk mixtures in the absence of TCC. The maximum negative δx 1,3 value is obtained in the mixture of x 1 = 0.70 (i.e., δx 1,3 = -7.63 × 10 -2 ), which is also higher than |1.0 × 10 -2 |. Preferential solvation by cyclohexane in 1,4-dioxane could be a consequence of polarization effects, whereas, preferential solvation by 1,4-dioxane in cyclohexane-rich mixtures could be a consequence of acidic Lewis behavior of hydrogen amide groups interacting with the basic Lewis oxygen atoms of this solvent [29].  Table 6 Some properties associated to preferential solvation of triclocarban (3)

Conclusions
Based on all previously discussed, it is demonstrated that all dissolution physicochemical properties of TCC in the {cyclohexane (1) + 1,4-dioxane (2)} mixtures depend strongly on the mixtures composition. Logarithmic mole fraction solubilities of TCC vary linearly with temperature and cyclohexane proportion. The apparent thermodynamic quantities of dissolution and mixing of TCC in these mixtures were calculated based on van't Hoff and Gibbs equations. Linear enthalpy-entropy compensation was found for TCC indicating the same mechanism for the drug transfer. Moreover, based on IKBI calculations it was stated that TCC is preferentially solvated by cyclohexane molecules in 1,4-dioxane-rich mixtures but preferentially solvated by 1,4-dioxane molecules in cyclohexane-rich mixtures.