http://dx.doi.org/10.15446/rcciquifa.v45n2.59941

Solution thermodynamics and preferential solvation of 3-chloro-N-phenyl-phthalimide in acetone + methanol mixtures

Termodinámica de soluciones y solvatación preferencial de 3-cloro-N-fenil-ftalimida en mezclas acetona + metanol

Grecia Angeline del Mar Areiza Aldana¹, Aleida Cuellar Lozano¹, Nasly Alexandra Peña Carmona¹, Diego Iván Caviedes Rubio¹, Abbas Mehrdad², Amir Hossein Miri², Gerson Andrés Rodríguez Rodríguez³, Daniel Ricardo Delgado^1*

¹ Programa de Ingeniería Industrial, Universidad Cooperativa de Colombia, Neiva, Colombia.
² Department of Physical Chemistry, Faculty of Chemistry, University of Tabriz, Tabriz, Iran.
³ Grupo de Investigaciones Farmacéutico-fisicoquímicas, Departamento de Farmacia, Facultad de Ciencias, Universidad Nacional de Colombia, Sede Bogotá, Cra 30 N. ° 45-03, Bogotá D.C., Colombia.
^* E-mail: danielr.delgado@campusucc.edu.co

Received: June 8, 2016 Accepted: June 23, 2016

Summary

The thermodynamic properties of the 3-chloro-N-phenyl-phthalimide in acetone + methanol cosolvent mixtures were obtained from solubility data report in literature. The solubility was higher in near acetone and lower in pure methanol at all temperatures studied. A non-linear plot of ∆_solnH° vs. ∆_solnG° shows a negative slope from pure acetone up to x₁ = 0.691. Beyond this composition, a variable positive slope is obtained with the exception of mixtures with x₁ = 0.121, x₁ = 0.272 and x₁ = 0.356 which is a not common trend in these systems. The preferential solvation of 3-chloro-N-phenyl-phthalimide by the components of the solvents was estimated by means of the inverse Kirkwood–Buff integral method, showing the 3-chloro-Nphenyl-phthalimide is preferential solvated by methanol in more polar mixtures and by acetone in less polar ones.

Keywords: 3-Chloro-N-phenylphthalimide, solubility, solution thermodynamics, activity coefficients, preferential solvation.

Resumen

Las propiedades termodinámicas de 3-cloro-N-fenil-ftalimida en mezclas cosolventes acetona + metanol fueron obtenidas a partir de los datos de solubilidad reportados en la literatura. La mayor solubilidad se presentó en acetona y la menor en metanol puro en todas las temperaturas estudiadas. La grafica Δ_solnH° vs. Δ_solnG° presenta una tendencia no lineal, con una pendiente negativa desde la acetona pura hasta x₁ = 0,691 a partir de esta composición hasta el metanol puro se obtiene una pendiente positiva variable con la excepción de las mezclas con x₁ = 0,121, x₁ = 0,272 y x₁ = 0,356, la cual es una tendencia poco común en estos sistemas. La solvatación preferencial de 3-cloro-N-fenil-ftalimida por cada uno de los solventes de la mezcla se estimó por medio del método de las integrales inversas de Kirkwood-Buff mostrando que la 3-cloro-N-fenil-ftalimida se solvata preferencialmente por metanol en las mezclas más polares y por acetona en las menos polares.

Palabras clave: 3-cloro-N-fenil-ftalimida, solubilidad, termodinámica de soluciones, coeficiente de actividad, solvatación preferencial.

Introduction

3-chloro-N-phenyl-phthalimide (Fig. 1) (Synonyms: 4-chloro-2-phenyl-isoindoline1,3-dione; 4-Chloro-2 phenyl-isoindolin-1,3-dion; 3-Chloro-N-phenyl-phthalimid; 4-chloro-2-phenyl-isoindole-1,3-dione; 3-chloro-N-phenyl-phthalimide) is an interesting compound because of its use in the synthesis of 3,3'-bis(N-phenylphthalimide) and 2,2',3,3'-diphenylthioether dianhydride, which are monomers for the preparation of polyimide, and those synthetic routes require a high purity 3-chloro-N-phenylphthalimide [1].

Knowledge of thermodynamic properties and preferential solvation is important in order to optimize synthesis processes like aforementioned [2]. For this reason, the purpose of this study is to evaluate the effect of the co-solvent composition on solubility, solution thermodynamics and preferential solvation of 3-chloro-N-phenyl-phthalimide in binary mixtures of acetone and methanol. The temperature dependence of the solubility allows a thermodynamic analysis that permits insight into the molecular mechanisms involved in the solution processes. The other hand, the estimate of the preferential solvation of the solute by the components of the solvent mixture, it is performed by the application of the inverse Kirkwood-Buff integral (IKBI) method [3-5].

Theoretical

Ideal solubility

The ideal solubility as a function of temperature can be calculated by using the following equation:

here x₃^id is the ideal solubility of the solute as mole fraction, ∆_fusH is the molarenthalpy of fusion of the pure solute (at the melting point), T_fus is the absolute melting point, T is the absolute solution temperature, R is the gas constant (8.314 J mol^–1 K^–1), and ∆C_p is the difference between the molar heat capacity of the crystalline form and the molar heat capacity of the hypothetical super-cooled liquid form, both at the solution temperature [6]. Since ∆C_p cannot be easy experimentally determined it is usual assuming that it may be approximated to the entropy of fusion, ∆_fusS [7].

Activity coefficients

The activity coefficients γ₃, were calculated as x₃^id/x₃ where x₃ is the experimental solubility. From γ₃ values a rough estimate of solute-solvent intermolecular interactions can be made by considering the following expression [8]:

where e₁₁, e₃₃ and e₁₃ represent the solvent-solvent, solute-solute and solvent-solute interaction energies, respectively, the first two terms are unfavorable for solubility and the third term favors the solution process; V₃ is the molar volume of the super-cooled liquid solute and φ₁ is the volume fraction of the solvent. As reported in the literature, for relatively low solubilities x₃, the term V₃φ₁²/RT may be considered constant; thus, γ₃ depends mainly on e₁₁, e₃₃ and e₁₃ [9]. The contribution of the e₃₃ term could be considered as constant in all mixtures [10].

Thermodynamic functions of solution

Apparent standard enthalpy change of solution is obtained from the Eq. (4) by using the mean harmonic temperature (T_hm) [calculated as:T_hm = ], where n is the number of temperatures studied [4].

The apparent standard Gibbs energy change for the solution process (∆_solnG°), considering the approach proposed by Krug et al. [11], is calculated at T_hm by means of:

where the intercept is obtained from the treatment of ln x3 as a function of 1/T – 1/T_hm. Finally, the standard apparent entropy change for solution process (∆_solnS°) is obtained from the respective ∆_solnH° and ∆_solnG° values at T_hm by using:

the relative contributions by enthalpy (_H) and entropy (_TS) toward the solution process are given by equations 7 and 8 [12-13].

Preferential solvation

The KBIs are given by the following expressions:

here g_1,3 is the pair correlation function for molecules of solvent 1 in the 1 + 2 mixtures around the solute 3, r is the distance between the centers of molecules 3 and 1, and r_cor is a correlation distance for which g₁₃(r > r_cor)≈1. Thus, for all distances r > r_cor up to infinite, the value of the integral is essentially zero. So, the results are expressed in terms of the preferential solvation parameter, δx_1,3, for the solute 3 by the component solvents 1 and 2 [5, 14].

Where x₁ is the mole fraction of 1 in the bulk solvent mixture and x^L _1,3 is the difference between the local mole fraction of 1 in the near environment of the solute. If δx_1,3 > 0 then 3 is preferentially solvated by 1, else by 2, within the correlation volume V_cor = (4π/3)r_cor ³, and the bulk mole fraction of 1, x₁. Values of δx_1,3 are obtainable from those of G_1,3, and these, in turn from thermodynamic data for the solvent mixture with the solute in it as shown below [6, 15].

Algebraic manipulation of expressions presented by Newman [16] leads to expressions for the Kirkwood-Buff integrals (in cm³ mol^-1) for the individual solvent components 1 and 2 in terms of thermodynamic quantities [3, 6-7]:

Where K_T is the isothermal compressibility of the solvent mixtures 1+2 (in GPa^-1), V₁ and V₂ are the partial molar solvent volumes in the mixture, and V₃ is the standard partial molar volume of solute in this mixture (in cm³ mol^-1). The function D is the derivative of the standard molar transfer Gibbs energies of 3 with respect to the solvent composition and the function Q involves the second derivative of the excess molar Gibbs energy of mixing of the two solvents, G^E _1,2, with respect to the solvent composition (in kJ mol⁻¹, as is RT)[17]:

Because of the dependence of K_T on composition this term is not known for all the systems investigated. Moreover, due to the small contribution of RT K_T to the IKBI, the dependence of χ_T on composition will be approximated by [18-19]:

where x_i is the volume fraction of component i in solution and K⁰_T,i is the isothermal compressibility of the pure component i.

Ben-Naim [20] showed that the preferential solvation parameter can be calculated from the Kirkwood-Buff integrals as follows:

The correlation volume, V_cor, is obtained by means of the following expression proposed by Marcus [21]:

Where r₃ is the radius of the solute (in nm), calculated as

However, the correlation volume requires iteration, because it depends on the local mole fractions [14].

Results and discussion

The solubility of 3-chloro-N-phenyl-phthalimide (3) in acetone (1) + methanol (2) mixtures (Fig. 2) was taken from the literature [1].

The solubility increases with temperature in all cases indicating that the dissolution process is endothermic. The highest solubility of 3-chloro-N-phenyl-phthalimide expressed as a mole fraction were obtained in near acetone at T = 323.15 K, whereas the lowest values were found in pure methanol (2) at 288.15 K (Fig. 2).

Table 1 shows the ideal solubilities expressed as a mole fraction of the solutes (x₃ ^id) calculated by using Eq. (1) with the temperature and heat of fusion of 3-chloro-N-phenylphthalimide taken from literature, i.e. T_fus = 466.05 K and ∆_fusH = 29.14 kJ mol^–1 [22].

On the other hand, Fig. 2 shows the solubility profiles as a function of the polarity of the mixtures, expressed by their solubility parameters (δ_mix). For a binary mixture δ_mix is calculated from the solubility parameters of the pure solvents (δ₁ = 19.6 MPa^1/2 and δ₂ = 29.78 MPa^1/2 [23]).

The solubility parameter of solute, estimated according to the groups contribution method proposed by Fedors [24], is δ₃ = 27.08 MPa^1/2 (Table 2), which is higher than the experimental value obtained (δ₃ ≤ 27.08 MPa^1/2). This indicates that the actual polarity of solute is lower than the expected from the additive contribution of its groups, which is lower than the experimental value [25].

The activity coefficients of 3-chloro-N-phenyl-phthalimide expressed as natural logarithms are also shown in Table 1. These values were calculated from experimental solubility was taken from Xie et al. (2016) [1]) and ideal solubility data (table 1). In the vast majority of cases, γ₃ values were lower than unit (negative logarithmic values) due to the experimental solubilities are greater than the ideal ones in those cosolvent systems (acetone-rich mixtures).

As a qualitative approach, the following analysis could be made based on the energetic quantities and magnitudes described in the Eq. (2): The term e₁₁ is highest in neat methanol and methanol-rich mixtures having larger γ₃ values (0.855-1.825) which implies higher e11 and lower e₁₃ values. On the other hand, in intermediate composition mixtures and acetone-rich mixtures (having γ₃ values <1), the e11 values are relatively low but the e₁₃ values could not to be so high. Accordingly, the solvation of 3-chloro-N-phenyl-phthalimide could be just a little higher in acetone-rich mixtures.

Thermodynamic functions of solution

From the solubility data, the thermodynamic functions in solution are calculated (Table 3). Over the range of temperatures studied (288.15 to 323.15 K) the heat capacity change of solution may be assumed to be constant, hence Δ_solnH° should be valid for the mean harmonic temperature, T_hm = 305.27 K.

The standard Gibbs free energy of solution is positive in all cases as is the enthalpy of solution; therefore the process is always endothermic. Figure 3 shows the change of enthalpy versus the mole fraction of acetone. The decreasing enthalpy between pure methanol up to the mixture with x₁ = 0.121 indicates that solubility is favored for enthalpy in these mixtures. Besides, from the mixture with x₁ = 0.121 up to the mixture with x₁ = 0.565 the enthalpy of solution tends to increase and then decrease, for this reason it is not possible to identify the thermodynamics properties driving the solution process. Finally, between the mixture x₁ = 0.691 and the pure acetone, the enthalpy increases.

The main contributor to the (positive) standard molar Gibbs energy of solution of 3-chloro-N-phenyl-phthalimide, in all cases, is the (positive) enthalpy (ζH > 0.754). The experimental data of thermodynamic functions of solution are collected in Fig. 4. The regions where (Δ_trH° > TΔ_trS° > 0) ≡ sector I; corresponds to enthalpy determined processes [4, 26-27], which is proposed by the equations 7 and 8.

Thermodynamic functions of transfer

In order to verify the effect of co-solvent composition on the thermodynamic function driving the solution process, Fig. 5 collects the thermodynamic functions of transfer of 3-chloro-N-phenyl-phthalimide (3) from the more polar solvents to the less polar ones. These new functions were calculated as the differences between the thermodynamic quantities of solution obtained in the less polar mixtures and the more polar ones, by means of:

Where ∆_solnF° represents the thermodynamic functions (∆_solnG°, ∆_solnH° or ∆_solnS°). This procedure is the same followed previously in other studies reported by Holguín et al. and Delgado et al. [28-29].

Theregionswhere(Δ_trH°>TΔ_trS°>0)≡sector I;(Δ_trH°<0;T_trΔS°>0;∣Δ_trH°∣>∣T_trΔS°∣) ≡sector IV and (ΔtrH° < 0; TΔ_trS° < 0; ∣Δ_trH°∣ >∣TΔtrS°∣) ≡ sector V corresponds to enthalpy determined processes. The regions of the diagram where (TΔ_trS° > Δ_trH° > 0)≡ sector II correspond to entropy determined processes [4, 26-27]. A schematic depiction of these relationships is given in figure 5.

So, the process of transfer in acetone-rich mixtures may indicate that the 3-chloro-Nphenyl-phthalimide molecule interacts more strongly with the acetone, however in all cases, the behavior is very random.

Enthalpy-entropy compensation of 3-chloro-N-phenyl-phthalimide

There are several reports in the literature that have demonstrated enthalpy-entropy compensation effects for the solubility of drugs in aqueous co-solvent mixtures. This analysis has been used in order to identify the mechanism of the co-solvent action. Weighted graphs of Δ_solnH° as a function of Δ_solnG° at the mean temperature allow such an analysis [30-31].

Figure 6 shows that 3-chloro-N-phenyl-phthalimide (3) in the acetone (1) + methanol (2) solvent system presents a non-linear behavior of Δ_solnH° vs. Δ_solnG° with a variable negative slope from pure acetone up to x1 = 0.691. Beyond this composition a variable positive slope is obtained with exception of mixtures with x₁ = 0.12, x₁ = 0.272 and x₁ = 0.36, showing a non-common trend in these systems. Accordingly, the driving mechanism for solubility is the entropy in the former case, whereas in the latter case the driving mechanism is the enthalpy, probably due to better solvation of the 3-chloro-Nphenyl-phthalimide by acetone molecules.

Preferential solvation

Standard molar Gibbs energy of transfer of 3-chloro-N-phenyl-phthalimide from neat methanol to acetone + methanol mixtures is calculated and correlated to a third grade polynomial from the drug solubility data by using equation (13). Figure 7 shows the Gibbs energy of transfer behavior at 323.15 K.

Thus, D values are calculated from the first derivative of polynomial models (Eq. 20) solved according to the co-solvent mixtures composition. This procedure was done varying by 0.05 in mole fraction of methanol but in the following tables the respective values are reported varying only by 0.10.

In order to calculate the Q values the excess molar Gibbs energies of mixing G^Exc_1,2 at 323.15 Kwere used as is reported by Marcus [18], the isothermal compressibility (K_T ) is given,asagoodapproximation,bythelinearexpression:x₁ K_T1+x₂ K_T2(K_T1 =1,324GPa^-1; (K_T2 = 1.248 GPa^-1) [21] and the partial molar volumes can be replaced by the molar volumes of the pure substances [32-34].

The application of the IKBI method with the gyration radius r = 0.397 nm leads to the preferential solvation parameter, δx_1,3 for acetone around 3-chloro-N-phenylphthalimide which is shown in Fig. 8 at 323.15 K. The values of δx_1,3 vary non-linearly with the proportion of acetone in the alcoholic mixtures (figure 8). The addition of acetone to methanol causes a negative change in δx_1,3 from pure methanol up to the 0.35 in molar fraction of acetone reaching minimum values near to – 0.018 at 0.15 in molar fraction of acetone at 323.15 K. In this composition, methanol is preferred over acetone around the 3-chloro-N-phenyl-phthalimide.

The local mole fractions of methanol are greater than those of acetone from pure methanol up to 0.35 mole fractions of acetone and minors beyond this up to pure acetone. From the preferential solvation results, it may be conjectured that, in intermediate compositions and in acetone-rich mixtures, 3-chloro-N-phenyl-phthalimide is acting as a Lewis base with acetone molecules because it is more acid than methanol (the Kamlet–Taft hydrogen bond acceptor parameters are β = 0.66 for methanol and 0.507 for acetone [35]).

Conclusions

From this work it can be concluded that the solution process of 3-chloro-N-phenylphthalimide (3) in acetone (1) + methanol (2) mixtures is endothermic. A nonlinear enthalpy–entropy compensation was found for this solute in this solvent system. In this context, entropy-driving was found for the solution process in rich-acetone mixtures, whereas, for mixtures methanol-rich enthalpy-driving was found. On the other hand, 3-chloro-N-phenyl-phthalimide is preferentially solvated for methanol in mixtures more polar and preferentially solvated for acetone in minus polar ones.

Disclosure statement

No potential conflict of interest was reported by the authors.

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How to cite this article

G.A.M. Areiza-Aldana, A. Cuellar-Lozano, N.A. Peña-Carmona, D.I. Caviedes-Rubio, A. Mehrdad, A.H. Miri, G.A. Rodríguez-Rodríguez, D.R. Delgado, Solution thermodynamics and preferential solvation of 3-chloro-N-phenyl-phthalimide in acetone + methanol mixtures, Rev. Colomb. Cienc. Quím. Farm., 45(2), 256-274 (2016).