1 Introduction

Triclocarban (TCC, C13H9Cl3N2O, molecular structure shown in Fig. 1, IUPAC name: 1-(4-chlorophenyl)-3-(3,4-dichlorophenyl)-urea, CAS number: 101-20-2, molar mass: 315.58 g·mol−1) is a powerful antimicrobial agent, which affects fungi and bacteria, by inhibiting the enzymatic activity of enoyl-(acyl-carrier protein) (ACP) reductase [1, 2]. This step is essential for the production of fatty acids that are necessary for the development of cell membranes of these organisms [3].

Fig. 1
figure 1

Molecular structure of triclocarban

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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].

2 Experimental

2.1 Materials

In this physicochemical study, TCC (Sigma-Aldrich, USA; compound 3, purity at least 0.990 in mass fraction), cyclohexane (Merck A.R., Germany; solvent component 1, purity at least 0.997 in mass fraction), 1,4-dioxane (Merck A.R., Germany; solvent component 2, purity at least 0.998 in mass fraction), and ethanol (Merck A.R., Germany; used for dilutions previous to UV analyses, purity at least 0.995 in mass fraction) were used without further purification. Chemical suppliers, purities, and other select properties of the reagents are summarized in Table 1.

Table 1 Source and purities of the compounds used in this research
Full size table

2.2 Preparation of Solvent Mixtures

All {cyclohexane (1) + 1,4-dioxane (2)} solvent mixtures were prepared gravimetrically using an (RADWAG AS 220.R2, Poland) analytical balance with sensitivity ± 0.1 mg, in quantities of 20.00 g. The mass fractions of cyclohexane of the 19 mixtures prepared, varied by 0.05 from w1 = 0.05 to w1 = 0.95.

2.3 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 cm3 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.

2.4 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 w1 = 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 cm3·min–1) at constant pressure.

3 Results and Discussion

3.1 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, 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 from 1.68 × 10–7 in neat cyclohexane at 288.15 K to 1.41 × 10–2 in neat 1,4-dioxane at 318.15 K. If T = 298.15 K is considered, TCC solubility is 5648 times higher in neat 1,4-dioxane than in neat cyclohexane. This is a consequence of the Lewis basic behavior of 1,4-dioxane owing the free electron pairs on its oxygen atoms, whereas, cyclohexane can only interact by weak London dispersion forces.

Table 2 Experimental and ideal mole fraction solubility of triclocarban (x3) in {cyclohexane (1) + 1,4-dioxane (2)} mixtures at several temperatures and p = 96 kPa
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Fig. 2
figure 2

Logarithmic mole fraction solubility of triclocarban (ln x3) as function of the mass fraction of cyclohexane in {cyclohexane (1) + 1,4-dioxane (2)} mixtures at different temperatures. Black symbols, circles: T = 288.15 K; triangles: T = 293.15 K; diamonds: T = 298.15 K; squares: T = 303.15 K; White symbols, circles: T = 308.15 K; triangles: T = 313.15 K; squares: T = 318.15 K

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Fig. 3
figure 3

Logarithmic mole fraction solubility of triclocarban (ln x3) as function of temperature in {cyclohexane (1) + 1,4-dioxane (2)} mixtures for different mixtures compositions. × : w1 = 0.00 (neat 1,4-dioxane); empty symbols, squares: w1 = 0.05, diamonds: w1 = 0.10, triangles: w1 = 0.15, circles: w1 = 0.20; blue symbols, squares: w1 = 0.25, diamonds: w1 = 0.30, triangles: w1 = 0.35, circles: w1 = 0.40; green symbols: squares: w1 = 0.45, diamonds: w1 = 0.50, triangles: w1 = 0.55, circles: w1 = 0.60; red symbols, squares: w1 = 0.65, diamonds: w1 = 0.70, triangles: w1 = 0.75, circles: w1 = 0.80; black symbols, squares: w1 = 0.85, diamonds: w1 = 0.90, triangles: w1 = 0.95, circles: w1 = 1.00 (neat cyclohexane) (Color figure online)

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Additionally, Fig. 4 shows the TCC logarithmic solubility as function of the Hildebrand solubility parameters of the {cyclohexane (1) + 1,4-dioxane (2)} mixtures (δ1+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 δ1+2 values were calculated from the corresponding δ values, i.e., δ1 = 16.8 MPa1/2 for cyclohexane and δ2 = 19.7 MPa1/2 for 1,4-dioxane [28, 29] and volumetric solvent proportions as described in Eq. 1. Volume fractions (fi) were considered assuming additive behavior [30, 31]:

$$\delta_{{{1} + {2}}} = \sum\limits_{i = 1}^{2} {f_{i} \delta_{i} }$$
(1)
Fig. 4
figure 4

Logarithmic mole fraction solubility of triclocarban (ln x3) as function of the Hildebrand solubility parameter in {cyclohexane (1) + 1,4-dioxane (2)} mixtures at different temperatures. Black symbols, circles: T = 288.15 K; triangles: T = 293.15 K; diamonds: T = 298.15 K; squares: T = 303.15 K; White symbols, circles: T = 308.15 K; triangles: T = 313.15 K; squares: T = 318.15 K

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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 δ3 value of TCC would be higher than the δ1 value (i.e., neat 1,4-dioxane δ value, 19.7 MPa1/2) at T = 298.15 K, where the maximum TCC solubilities are observed at all temperatures. Effectively, the calculated Fedors–van Krevelen δ3 value of TCC is 26.5 MPa1/2 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 ≤ δ1+2/MPa1/2 ≤ 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. 2:

$$\ln x_{3,1 + 2} = - 32.95 - 8.654w_{1} + 9.044 \cdot 10^{ - 2} T$$
(2)

With adj. r2 = 0.9998, typical error = 0.0345, and F = 475,593. Mean percentage deviations (MPD) obtained with Eq. 2 were calculated by means of Eq. 3, where \(x_{{3,1 + 2}}^{{{\text{exptl}}}}\) and \(x_{{3,1 + 2}}^{{{\text{calcd}}}}\)are experimental and calculated solubilities, respectively. The following results were obtained: for logarithmic solubility, MPD = 0.31% (minimum PD = 0.006% in w1 = 0.55 at T = 293.15 K, maximum PD = 1.98% in neat 1,4-dioxane at T = 318.15 K), for linear solubility, MPD = 2.72% (minimum PD = 0.068% in w1 = 0.55 at T = 293.15 K, maximum PD = 10.32% in w1 = 0.90 at T = 288.15 K) [34,35,36].

$${\text{MPD}} = \frac{100}{N}\sum \frac{{\left| {x_{3,1 + 2}^{{{\text{exptl}}}} - x_{3,1 + 2}^{{{\text{calcd}}}} } \right|}}{{x_{3,1 + 2}^{{{\text{exptl}}}} }}$$
(3)

3.2 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 w1 = 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].

Fig. 5
figure 5

DSC thermograms of the triclocarban solid phases in equilibrium with the saturated solutions. From top to bottom: neat 1,4-dioxane, mixture w1 = 0.50, neat cyclohexane, and original untreated sample

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3.3 Ideal Solubility and Activity Coefficients of TCC in Neat and Mixed Solvents

Ideal solubilities of TCC (\(x_{3}^{{{\text{id}}}}\)) at the temperatures of interest from 288.15 to 318.15 K were calculated by means of the well-known equation:

$$\ln x_{3}^{{{\text{id}}}} = - \frac{{\Delta_{{{\text{fus}}}} H(T_{{{\text{fus}}}} - T)}}{{RT_{{{\text{fus}}}} T}} + \left( {\frac{{\Delta C_{p} }}{R}} \right)\left[ {\frac{{(T_{{{\text{fus}}}} - T)}}{T} + \ln \left( {\frac{T}{{T_{{{\text{fus}}}} }}} \right)} \right]$$
(4)

Here, ΔfusH is the molar enthalpy of melting of the pure TCC (obtained at the melting point, i.e., 41.9 kJ·mol–1 [18]), Tfus 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 ΔCp 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 ΔCp determination, this value has been considered in this research as the same as the one of the entropy of fusion (ΔfusS = ΔfusH/Tfus, 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 (γ3) in neat solvents and in {cyclohexane (1) + 1,4-dioxane (2)} mixtures at all temperatures. These γ3 values were calculated as the quotient: \({{x_{3}^{{{\text{id}}}} } \mathord{\left/ {\vphantom {{x_{3}^{{{\text{id}}}} } {x_{3}^{{}} }}} \right. \kern-\nulldelimiterspace} {x_{3}^{{}} }}\) from the experimental and ideal solubilities summarized in Table 2. As observed, at T = 298.15 K γ3 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, γ3 values decrease with the temperature arising. All obtained γ3 values are higher than the unity because the experimental solubilities in all the solvent systems are lower than \(x_{3}^{{{\text{id}}}}\) 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 γ3 values, based on Eq. 5 [38]:

$$\ln \gamma_{3} = (e_{ss} + e_{33} - 2e_{s3} )\frac{{V_{3} \varphi_{s}^{2} }}{RT}$$
(5)
Table 3 Activity coefficients of triclocarban (γ3) in {cyclohexane (1) + 1,4-dioxane (2)} mixtures at several temperatures and p = 96 kPa
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Here subscript s stands for the solvent system (which corresponds to neat solvents or cyclohexane-1,4-dioxane binary mixtures), ess, e33 and es3 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. V3 is the molar volume of the super-cooled liquid TCC and φs is the volume fraction of the solvent system in every saturated solution. It is noteworthy that when low x3 values are obtained, the term (V3φs2/RT) can be considered as constant regardless the solvent system because φs is almost 1.0. Thus, the γ3 values would depend mainly on the terms ess, e33 and es3 [38]. As well-known, ess and e33 are not favorable for drug dissolution processes and equilibrium solubilities but es3 favors the respective drug dissolution processes and solubilities. Moreover, the contribution of e33 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 ess, e33 and es3 energetic terms of Eq. 5. Hence, based on polarities it follows that ess is highest in neat 1,4-dioxane (δ = 19.7 MPa1/2) and lowest in neat cyclohexane (δ = 16.8 MPa1/2) [28, 29]. Neat cyclohexane and cyclohexane-rich mixtures, exhibiting γ3 values higher than 1600 at T = 298.15 K, would imply high e33 and low es3 values. Otherwise, in 1,4-dioxane-rich mixtures, exhibiting γ3 values lower than 10, the ess values are also relatively low but the es3 values would be comparatively higher regarding cyclohexane-rich mixtures.

3.4 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 (Thm), which in turn was calculated by using Eq. 6 [39, 40]:

$$T_{{{\text{hm}}}} = {n \mathord{\left/ {\vphantom {n {\sum\limits_{i = 1}^{n} {\left( {1/T} \right)} }}} \right. \kern-\nulldelimiterspace} {\sum\limits_{i = 1}^{n} {\left( {1/T} \right)} }}$$
(6)

where n = 7 is the number of temperatures studied. Thus, from T = (218.15 to 318.15) K, the obtained Thm value is 302.8 K. In this way, the apparent standard enthalpic changes for TCC dissolution processes (∆solnH°) were obtained by means of the modified van’t Hoff equation, as [40, 41]:

$$\left( {\frac{{\partial \ln x_{3} }}{{\partial \left( {1/T - 1/T_{{{\text{hm}}}} } \right)}}} \right)_{P} = - \frac{{\Delta_{{{\text{soln}}}} H^\circ }}{R}$$
(7)

The apparent standard Gibbs energy changes for the TCC dissolution processes (∆solnG°) were calculated by means of:

$$\Delta_{{{\text{soln}}}} G^\circ = - R \cdot T_{{{\text{hm}}}} \cdot {\text{intercept}}$$
(8)

Here, the intercepts used are those obtained in the respective linear regressions of ln x3 vs. (1/T − 1/Thm). As visual help, Fig. 6 shows the solubility van’t Hoff plots obtained in the neat solvents and in the 19 {cyclohexane (1) + 1,4-dioxane (2)} mixtures. Linear regressions with determination coefficients higher than 0.997 were obtained in all cases [34,35,36]. Standard apparent entropic changes for TCC dissolution processes (∆solnS°) were obtained from the respective ∆solnH° and ∆solnG° values by using Eq. 9 [41]:

$$\Delta_{{{\text{soln}}}} S_{{}}^{{\text{o}}} = \frac{{\left( {\Delta_{{{\text{soln}}}} H^\circ - \Delta_{{{\text{soln}}}} G^\circ } \right)}}{{T_{{{\text{hm}}}} }}$$
(9)
Fig. 6
figure 6

van’t Hoff plot of the solubility of triclocarban (3) in some {cyclohexane (1) + 1,4-dioxane (2)} solvent systems. × : w1 = 0.00 (neat 1,4-dioxane); empty symbols, squares: w1 = 0.05, diamonds: w1 = 0.10, triangles: w1 = 0.15, circles: w1 = 0.20; blue symbols, squares: w1 = 0.25, diamonds: w1 = 0.30, triangles: w1 = 0.35, circles: w1 = 0.40; green symbols: squares: w1 = 0.45, diamonds: w1 = 0.50, triangles: w1 = 0.55, circles: w1 = 0.60; red symbols, squares: w1 = 0.65, diamonds: w1 = 0.70, triangles: w1 = 0.75, circles: w1 = 0.80; black symbols, squares: w1 = 0.85, diamonds: w1 = 0.90, triangles: w1 = 0.95, circles: w1 = 1.00 (neat cyclohexane) (Color figure online)

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Table 4 summarizes the standard apparent molar thermodynamic functions of the dissolution processes of TCC (3) in neat solvents and in all the {cyclohexane (1) + 1,4-dioxane (2)} mixtures at Thm = 302.8 K.

Table 4 Apparent thermodynamic functions relative to dissolution processes of triclocarban (3) in {cyclohexane (1) + 1,4-dioxane (2)} mixtures at Thm = 302.8 K and p = 96 kPa
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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 endothermic and entropy-driven dissolution processes in all cases. Moreover, ΔsolnG° values increase continuously from neat 1,4-dioxane (13.93 kJ·mol–1) to neat cyclohexane (35.69 kJ·mol–1) indicating more affinity of TCC by 1,4-dioxane-rich media. As observed, ΔsolnH° values increase continuously from neat 1,4-dioxane (66.37 kJ·mol–1) to reach the maximum value in neat cyclohexane (71.67 kJ·mol–1) but on the contrary, ΔsolnS° values decrease from neat 1,4-dioxane (173.2 J·mol–1·K–1) to reach the minimum value in neat cyclohexane (118.8 J·mol–1·K–1). Additionally, the relative contributions by enthalpy (ζH) and entropy (ζTS) toward the TCC dissolution processes were calculated by means of the following equations [42]:

$$\zeta_{H} = \frac{{\left| {\Delta_{{{\text{soln}}}} H^\circ } \right|}}{{\left| {\Delta_{{{\text{soln}}}} H^\circ } \right| + \left| {T\Delta_{{{\text{soln}}}} S^\circ } \right|}}$$
(10)
$$\zeta_{TS} = \frac{{\left| {T\Delta_{{{\text{soln}}}} S^\circ } \right|}}{{\left| {\Delta_{{{\text{soln}}}} H^\circ } \right| + \left| {T\Delta_{{{\text{soln}}}} S^\circ } \right|}}$$
(11)

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.

3.5 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:

Solute(Solid) at T → Solute(Solid) at Tfus → Solute(Liquid) at Tfus → Solute(Liquid) at T → Solute(Solution) at T.

Here the hypothetical stages are as follows: (i) the heating and melting of TCC at Tfus = 528.2 K, (ii) the cooling of the liquid TCC to the considered temperature (Thm = 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 Thm = 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:

$$\Delta_{{{\text{soln}}}} H^\circ = \Delta_{{{\text{fus}}}} H^{{T_{{{\text{hm}}}} }} + \Delta_{{{\text{mix}}}} H^\circ$$
(12)
$$\Delta_{{{\text{soln}}}} S^\circ = \Delta_{{{\text{fus}}}} S^{{T_{{{\text{hm}}}} }} + \Delta_{{{\text{mix}}}} S^\circ$$
(13)

where \(\Delta_{{{\text{fus}}}} H^{{T_{{{\text{hm}}}} }}\) and \(\Delta_{{{\text{fus}}}} S^{{T_{{{\text{hm}}}} }}\) indicate the thermodynamic quantities of TCC fusion and its cooling at Thm = 302.8 K. In turn, these two functions were calculated by means of Eqs. 14 and 15, respectively [44]:

$$\Delta_{{{\text{fus}}}} H^{{T_{{{\text{hm}}}} }} = \Delta_{{{\text{fus}}}} H^{{T_{{{\text{fus}}}} }} - \Delta C_{p} \left( {T_{{{\text{fus}}}} - T_{{{\text{hm}}}} } \right)$$
(14)
$$\Delta_{{{\text{fus}}}} S^{{T_{{{\text{hm}}}} }} = \Delta_{{{\text{fus}}}} S^{{T_{{{\text{fus}}}} }} - \Delta C_{p} \ln \left( {\frac{{T_{{{\text{fus}}}} }}{{T_{{{\text{hm}}}} }}} \right)$$
(15)

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 Thm = 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 w1 = 0.05 at 318.15 K, as indicated above. As observed, the contributions by the mixing thermodynamic quantities, ΔmixH° and ΔmixS°, 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 (ζH) and entropy (ζTS) 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.

Table 5 Apparent thermodynamic functions relative to mixing processes of triclocarban (3) in {cyclohexane (1) + 1,4-dioxane (2)} mixtures at Thm = 302.8 K and p = 96 kPa
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3.6 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 increase or decrease the drugs solubility depending on the solvent mixtures compositions. Normally, weighted plots of ΔsolnH° vs. ΔsolnG° and/or ΔmixH° vs. ΔmixG° have been used for performing these analyses [47,48,49]. In particular, Fig. 7 clearly shows that TCC exhibits a linear ΔsolnH° vs. ΔsolnG° trend in the studied organic mixtures, adjusted to ΔsolnH°/kJ·mol–1 = 0.250·ΔsolnG°/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.

Fig. 7
figure 7

∆solnH° vs. ∆solnG° enthalpy–entropy compensation plot for the dissolution processes of triclocarban (3) in {cyclohexane (1) + 1,4-dioxane (2)} mixtures at Thm = 302.8 K

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3.7 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 (δx1,3) are defined as [50,51,52]:

$$\delta x_{{1,3}} = x_{{1,3}}^{L} - x_{{1}} = - \delta x_{{2,3}}$$
(16)

where \(x_{{1,3}}^{L}\) is the local mole fraction of cyclohexane in the molecular environment of TCC and x1 is the bulk mole fraction of cyclohexane in the initial {cyclohexane (1) + 1,4-dioxane (2)} binary solvent mixture free of TCC. Thus, if δx1,3 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 δx1,3 parameter is negative. The values of δx1,3 were obtained from the inverse Kirkwood–Buff integrals (IKBI) as described earlier [50,51,52], based on the following expressions:

$$\delta x_{{1,3}} = \frac{{x_{{1}} x_{{2}} \left( {G_{{1,3}} - G_{{2,3}} } \right)}}{{x_{{1}} G_{{1,3}} + x_{{2}} G_{{2,3}} + V_{{{\text{cor}}}} }}$$
(17)

with

$$G_{{1,3}} = RT\kappa_{T} - \overline{V}_{{3}} + x_{{2}} \overline{V}_{{2}} D/Q$$
(18)
$$G_{{2,3}} = RT\kappa_{T} - \overline{V}_{{3}} + x_{{1}} \overline{V}_{{1}} D/Q$$
(19)
$$V_{{{\text{cor}}}} = 2522.5\left( {r_{{3}} + 0.1363\left( {x_{{1,3}}^{L} \overline{V}_{{1}} + x_{{2,3}}^{L} \overline{V}_{{2}} } \right)^{1/3} - 0.085} \right)^{3}$$
(20)

Here, κT denotes the isothermal compressibility of the aqueous-ethanol mixtures. \(\overline{V}_{1}\), \(\overline{V}_{2}\) and \(\overline{V}_{3}\) are, respectively, the partial molar volumes of cyclohexane, 1,4-dioxane, and TCC in the dissolutions. The function D, defined in Eq. 21, corresponds to the first derivative of the standard molar Gibbs energies of transfer of TCC from neat 1,4-dioxane to every {cyclohexane (1) + 1,4-dioxane (2)} mixture regarding the mole fraction of cyclohexane. The function Q, defined in Eq. 22, involves the second derivative of the excess molar Gibbs energy of mixing of cyclohexane and 1,4-dioxane (\(G_{{{1} + 2}}^{\text{Exc}}\)) regarding the mole fraction of 1,4-dioxane. Vcor and r3 are, respectively, the correlation volume and the molecular radius of TCC. Here, r3 was roughly calculated by means of Eq. 23, where NAv is the number of Avogadro.

$$D = \left( {\frac{{\partial \Delta_{{{\text{tr}}}} G_{{{3,2} \to 1 + 2}}^{{\text{o}}} }}{{\partial x_{{1}} }}} \right)_{T,p}$$
(21)
$$Q = RT + x_{{1}} x_{{2}} \left( {\frac{{\partial^{2} G_{{{1} + {2}}}^{\text{Exc} }}}{{\partial x_{{2}}^{2} }}} \right)_{T,p}$$
(22)
$$r_{{3}} = \left( {\frac{{3 \cdot 10^{21} V_{{3}} }}{{4\pi N_{{{\text{Av}}}} }}} \right)^{1/3}$$
(23)

To obtain definitive Vcor 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 δx1,3 and Vcor in Eqs. 17, 18 and 20 to recalculate the \(x_{{1,3}}^{L}\) values until obtaining non-variant values of Vcor.

Figure 8 shows the apparent Gibbs energies of transfer of TCC from neat 1,4-dioxane to all {cyclohexane (1) + 1,4-dioxane (2)} mixtures (\(\Delta_{{{\text{tr}}}} G_{{{3,2} \to {1} + 2}}^{{\text{o}}}\)) at T = 303.15 K. These \(\Delta_{{{\text{tr}}}} G_{{{3,2} \to {1} + 2}}^{{\text{o}}}\) values were calculated from the experimental mole fraction solubility values reported in Table 2 by using:

$$\Delta_{{{\text{tr}}}} G_{{{3,2} \to {1} + 2}}^{{\text{o}}} = RT\ln \left( {\frac{{x_{{3,2}} }}{{x_{{{3,1} + {2}}} }}} \right)$$
(24)
Fig. 8
figure 8

Gibbs energy of transfer of triclocarban (3) from neat 1,4-dioxane (2) to {cyclohexane (1) + 1,4-dioxane (2)} mixtures at T = 303.15 K

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Obtained \(\Delta_{{{\text{tr}}}} G_{{{3,2} \to {1} + 2}}^{{\text{o}}}\) values were correlated by means of the lineal function shown as Eq. 25, where the obtained statistical parameters were as follows: adjusted r2 = 0.9998, typical error = 0.0871, and F = 120,539 [34,35,36].

$$\Delta_{{{\text{tr}}}} G_{{{3,2} \to {1} + 2}}^{{\text{o}}} = 21.81( \pm 0.06)x_{1}^{{}} - 0.18( \pm 0.04)$$
(25)

The constant D value shown in Table 6 was determined as the slope of Eq. 25. Required Q, \(\overline{V}_{1}\) and \(\overline{V}_{2}\) 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 RTκT values were calculated from κT 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 \(\overline{V}_{3}\) 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 cm3·mol–1, despite the solvent mixtures composition.

Table 6 Some properties associated to preferential solvation of triclocarban (3) in {cyclohexane (1) + 1,4-dioxane (2)} mixtures at T = 313.15 K
Full size table

Table 6 shows that the G1,3 and G2,3 values are positive in almost all the solvent systems, except for G1,3 in the interval 0.85 ≤ x1 ≤ 1.00 and for G2,3 in the interval 0.00 ≤ x1 ≤ 0.10. TCC r3 value was calculated as 0.434 nm. It is noteworthy that Vcor values shown in Table 6 were obtained after three iterations. Vcor values increase with the cyclohexane proportion in the mixtures because \(\overline{V}_{1}\) values are higher than \(\overline{V}_{2}\) values. Additionally, Table 6 also summarizes the preferential solvation parameters of TCC by cyclohexane molecules (δx1,3) in the mixtures at T = 303.15 K.

Figure 9 shows a nonlinear variation δx1,3 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 δx1,3 values of TCC in the composition interval of 0.00 < x1 < 0.44. The maximum positive δx1,3 value is obtained in the mixture of x1 = 0.25 (i.e., δx1,3 = 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].

Fig. 9
figure 9

Preferential solvation parameters (δx1,3) of triclocarban (3) by cyclohexane (1) in {cyclohexane (1) + 1,4-dioxane (2)} mixtures at T = 303.15 K

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Based on the negative δx1,3 values observed in the composition interval of 0.44 < x1 < 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 δx1,3 value is obtained in the mixture of x1 = 0.70 (i.e., δx1,3 = –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].

4 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.