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Solution thermodynamics of indomethacin in ethanol + propylene glycol mixtures
Journal of Molecular Liquids 181 (2013) 62–67
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Solution thermodynamics of indomethacin in ethanol + propylene glycol mixtures Eliecer A. Cantillo, Daniel R. Delgado, Fleming Martinez ⁎ Grupo de Investigaciones Farmacéutico-Fisicoquímicas, Departamento de Farmacia, Facultad de Ciencias, Universidad Nacional de Colombia, A.A. 14490, Bogotá, D.C., Colombia
a r t i c l e
i n f o
Article history: Received 8 December 2012 Received in revised form 11 February 2013 Accepted 15 February 2013 Available online 5 March 2013 Keywords: Indomethacin Ethanol Propylene glycol Solubility Cosolvency Thermodynamics
a b s t r a c t Drug solubility is a key parameter during the processes associated to design and development of new liquid pharmaceutical dosage forms. Cosolvency is a commonly used technique to increase the drug solubility in several orders of magnitude and it is relatively simple. Nevertheless the solubility in mixed solvents is scarce for several drugs. For this reason, in this work the solubility of indomethacin was determined by using the stirred flask method as a function of temperature and cosolvent composition in some ethanol + propylene glycol mixtures. From solubility data the solution thermodynamic quantities, Gibbs energy, enthalpy and entropy, were calculated. In similar way, from these new values and information about drug melting properties, the thermodynamic quantities of hypothetical liquids mixing were also calculated. A non-linear ΔsolnH° vs. ΔsolnG° compensation plot was obtained which could indicate that the dissolution mechanism is dependent on the cosolvent mixture composition. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Indomethacin (IMC, 357.79 g mol−1, Fig. 1) is a non-steroidal anti-inflammatory drug, which is sometimes used as analgesic, among other indications [1]. Although IMC is widely used in therapeutics the physicochemical information about its solubility in aqueous and non-aqueous media is not abundant [2]. As has been already described, the solubility behavior of drugs in cosolvent mixtures is very important because cosolvent blends are frequently used in purification methods, preformulation studies, and pharmaceutical dosage form design, among other applications [3]. For these reasons, it is important to determine systematically the solubility of pharmaceutical compounds. Besides, as was already said temperaturesolubility dependence allows us to carry out the respective thermodynamic analysis, which, on the other hand, also permits insight on the molecular mechanisms, involved toward the dissolution processes [3]. As a basic stage toward a deeper understanding of the molecular forces involved in dissolution processes, the present work studied the solution thermodynamics of IMC in several solvent mixtures of ethanol and propylene glycol as has been made with other analgesic drugs such as acetaminophen [4], ibuprofen, naproxen [5], and with the antimicrobial drug triclocarban [6]. It is important to note that ethanol + propylene glycol mixtures exhibit non-ideal behavior on mixing as has been observed by studying excess molar volumes [7]. The equilibrium solubility was determined at several temperatures in the binary mixtures and the respective dissolution thermodynamic analysis was made by using the van't Hoff and Gibbs equations. Otherwise, ⁎ Corresponding author. Tel.: +571 3165000x14608; fax: +571 3165060. E-mail address: [email protected] (F. Martinez). 0167-7322/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molliq.2013.02.008
by using the values reported for IMC ideal solubility the contribution due to the hypothetical liquid mixing-process toward the overall dissolution was also analyzed [8]. In this way, this work is a continuation of those developed with the same drug in ethanol + water and propylene glycol + water cosolvent mixtures [9,10]. It is well known that ethanol and propylene glycol are the cosolvents most widely used in drug formulation design, especially those intended for per oral and parenteral administration and several examples of pharmaceutical formulations using these cosolvents have been presented by Rubino [11]. It is remarkable that both cosolvents have antimicrobial properties [12]. 2. Experimental 2.1. Materials Indomethacin (1-(4-chlorobenzoyl)-5-methoxy-2-methyl-1H-indole3-acetic acid, CAS: 53-86-1, from Sigma Chemical Co.) used conformed to the quality requirements of the British Pharmacopoeia, BP [13]; absolute ethanol A.R. (from Merck) and propylene glycol (from Dow Chemical Co.) conformed to the quality requirements of the American Pharmacopeia, USP [14]; molecular sieve (Merck, numbers 3 and 4); Millipore Corp. Swinnex®-13 filter units. 2.2. Solvent mixtures preparation Both solvents were treated with molecular sieve to remove the small water quantities. All ethanol + propylene glycol solvent mixtures were prepared by mass, using an Ohaus Pioneer TM PA214 analytical balance with sensitivity ± 0.1 mg, in quantities of 50 g. The mass fractions of
E.A. Cantillo et al. / Journal of Molecular Liquids 181 (2013) 62–67
63
groups in the solvents (oxygen atoms in \OH and \O\ groups), although it can also act as a proton-acceptor compound by means of its carbonyl, methoxyl, and hydroxyl moieties (Fig. 1) [8–10].
O Cl N
3.1. Ideal and experimental solubility of IMC
CH3 H3C-O COOH Fig. 1. Molecular structure of indomethacin.
ethanol of the nine binary mixtures prepared varied by 0.10 from 0.10 to 0.90. 2.3. Solubility determinations An excess of IMC was added to approximately 10 g of each solvent mixture or neat solvent, in stoppered dark glass flasks. Solid–liquid mixtures were placed with stirring in a thermostatic mechanical shaker (Julabo SW23) kept at 303.15, 308.15, or 313.15 (±0.05) K or placed in re-circulating thermostatic baths (Neslab RTE 10 Digital One Thermo Electron Company) kept at 293.15 or 298.15 (±0.05) K with sporadic manual stirring at least for 7 days to reach the saturation equilibrium. After this time the supernatant solutions were filtered (at isothermal conditions) to ensure that they were free of particulate matter before sampling. IMC concentrations were determined, after appropriate aqueous dilution with NaOH 0.10 N, by measuring the light absorbance and interpolation from a previously constructed UV spectrophotometry calibration curve at λmax 281 nm (UV/VIS BioMate 3 Thermo Electron Company spectrophotometer). Equilibrium time was established by measuring the IMC concentrations till they became constant. All the solubility experiments were run in triplicate at least. In order to make the equivalence between molarity and mole fraction concentration scales, the density of the saturated solutions was determined with a digital density meter (DMA 45 Anton Paar) connected to the same recirculating thermostatic baths, according to procedures described previously [15]. 3. Results and discussion In order to propose the possible intermolecular interactions present in the saturated solutions of IMC, it is important to remark that this drug acts in solution mainly as a Lewis acid (due to its \OH group) in order to establish hydrogen bonds with proton-acceptor functional
Table 1 shows the experimental solubilities of IMC expressed in mole fractions, x2, as well as the ideal solubilities already reported [8]. It is important to keep in mind that drug ideal solubility is just dependent on solid-solute properties without considering the solvent properties. Thus, ideal solubility depends both on temperature and enthalpy of fusion [16]. In almost all cases the uncertainties in solubility were smaller than 1.0%. Significant figures were defined by using the criterion 3–30 [17]. On similar way, Fig. 2 shows IMC solubility expressed in molarity at all temperatures studied. The molar solubility trends are described by normal polynomials in order 3. It may be observed that the lowest and highest drug solubility values at all temperatures are obtained in neat propylene glycol and ethanol, respectively. Solubility values in neat solvents are similar to those reported previously [9,10]. On the other hand, in the literature, there is no reported solubility values for this drug in these solvents mixed, and therefore, no direct comparison is possible. It is important to keep in mind that both solvents studied are considered as semipolar but being propylene glycol more polar than ethanol, i.e. dielectric constants at 298.15 K are 30.2 and 24.3, respectively [18,19]; whereas Hildebrand solubility parameters are 30.3 and 26.6 MPa 1/2 at the same temperature, respectively [16]. The solubility of IMC was higher in neat ethanol because its reported Hildebrand solubility parameter is 20.9 MPa 1/2; and therefore, its maximum solubility is found in solvent mixtures with lower polarity than the one of neat ethanol, as was reported in mixtures ethyl acetate + ethanol [20]. On the other hand, it is interesting to make a comparison of the IMC solubility with respect to the behavior exhibited by other drugs in the same solvent mixtures. In this way, Table 2 shows the molecular structures, Hildebrand solubility parameters, and the cosolvent composition of the mixtures where the maximum solubilities were found, for acetaminophen, triclocarban, naproxen, indomethacin, and ibuprofen. Hildebrand solubility parameters have been used widely as a key parameter to describe the polarity of solvents and solutes in studies about solubility of drugs [16]. The reported values are demonstrating that the maximum drug solubility, despite the functional groups, is found in solvents where the polarity between solutes and solvents is the same or at least similar as described by solubility parameters. This result is in agreement with the fact described in the literature about the smaller the difference of the solubility parameters between solute and solvent, the higher the solubility of the
Table 1 Experimental and ideal solubility of indomethacin in ethanol + propylene glycol mixtures expressed as 1000 × mole fraction at several temperatures.a wEtOHb
δ1/MPa1/2c
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Ideald
30.30 29.83 29.38 28.97 28.57 28.20 27.84 27.51 27.19 26.89 26.60
a b c d
T/K 293.15
298.15
303.15
308.15
313.15
1.186 1.201 1.246 1.291 1.430 1.509 1.696 1.854 2.109 2.303 2.530 13.99
1.588 1.626 1.696 1.820 1.988 2.181 2.403 2.542 2.824 3.258 3.423 16.84
2.204 2.250 2.284 2.442 2.675 2.960 3.310 3.569 3.861 4.369 4.528 20.22
3.082 3.107 3.148 3.258 3.657 3.980 4.528 4.902 5.406 5.807 5.877 24.19
3.719 3.807 4.031 4.309 4.809 5.289 6.103 6.701 7.509 7.650 7.711 28.86
(0.005) (0.004) (0.003) (0.004) (0.005) (0.006) (0.003) (0.008) (0.020) (0.007) (0.009) (0.07)
Values in parentheses are standard deviations. wEtOH is the mass fraction of ethanol in the cosolvent mixtures free of drug. δ1 is the solubility parameter of cosolvent mixtures free of drug at 298.15 K. From Ruidiaz et al. [8].
(0.005) (0.005) (0.006) (0.005) (0.007) (0.007) (0.004) (0.008) (0.007) (0.010) (0.013) (0.08)
(0.008) (0.003) (0.005) (0.004) (0.010) (0.010) (0.005) (0.010) (0.010) (0.013) (0.017) (0.10)
(0.011) (0.007) (0.010) (0.011) (0.012) (0.015) (0.009) (0.015) (0.020) (0.021) (0.018) (0.12)
(0.012) (0.008) (0.006) (0.014) (0.010) (0.008) (0.016) (0.021) (0.024) (0.026) (0.009) (0.14)
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E.A. Cantillo et al. / Journal of Molecular Liquids 181 (2013) 62–67 Table 3 Activity coefficients of indomethacin in ethanol + propylene glycol mixtures at several temperatures.a wEtOHb T/K 293.15
Fig. 2. Experimental solubility of indomethacin in ethanol + propylene glycol mixtures expressed in molarity at several temperatures. ●: 293.15 K; ■: 298.15 K; ▲: 303.15 K; ○: 308.15 K; □: 313.15 K.
solute in the solvent is [16]. Nevertheless, in the case of ibuprofen some solubility values in mixtures ethyl acetate + ethanol are required to evaluate the composition of maximum drug solubility in order to estimate its solubility parameter because the reported value was calculated by groups' contribution methods [22]. 3.2. IMC activity coefficients The solute activity coefficient in the solution (γ2) is calculated as x2id/x2 and it is an indication of the deviation presented by IMC from its ideal behavior [8–10]. Table 3 shows IMC activity coefficients as a function of composition and temperature. Accordingly, γ2 values Table 2 Physicochemical aspects of indomethacin and other drugs studied in ethanol + propylene glycol mixtures. Drug
Molecular structure
Acetaminophen
NH-CO-CH 3
δ/MPa1/2a
wEtOH max. solub. b
28.2c
0.50c
27.8d
0.60d
20.9e
1.00f
20.9g
1.00h
19.4i
1.00f
OH
Triclocarban
Cl
Cl
O
Cl
N
N
H
H
Naproxen
CH3 COOH H3C O
Indomethacin
O Cl N CH3 H3C-O
Ibuprofen
COOH CH3
CH3
COOH
H3C
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 a b
11.80 11.64 11.22 10.84 9.79 9.27 8.25 7.55 6.63 6.08 5.53
298.15
303.15
308.15
(0.07) 10.60 (0.06) 9.18 (0.06) 7.85 (0.07) 10.36 (0.06) 8.99 (0.05) 7.78 (0.06) 9.93 (0.06) 8.85 (0.05) 7.68 (0.07) 9.25 (0.05) 8.28 (0.04) 7.42 (0.06) 8.47 (0.05) 7.56 (0.05) 6.61 (0.06) 7.72 (0.05) 6.83 (0.04) 6.08 (0.04) 7.01 (0.04) 6.11 (0.03) 5.342 (0.05) 6.62 (0.04) 5.66 (0.03) 4.935 (0.07) 5.96 (0.03) 5.237 (0.029) 4.475 (0.04) 5.17 (0.03) 4.628 (0.027) 4.165 (0.03) 4.92 (0.03) 4.465 (0.028) 4.116
(0.05) (0.04) (0.05) (0.05) (0.04) (0.04) (0.029) (0.029) (0.028) (0.026) (0.024)
313.15 7.76 7.58 7.16 6.70 6.00 5.457 4.729 4.307 3.843 3.773 3.742
(0.05) (0.04) (0.04) (0.04) (0.03) (0.029) (0.027) (0.025) (0.023) (0.023) (0.019)
Values in parentheses are standard deviations. wEtOH is the mass fraction of ethanol in the cosolvent mixtures free of drug.
are varying from 5 to 10, in ethanol and propylene glycol respectively, and they diminish as temperature increases indicating more ideal behavior at high temperatures. These values are lower compared to the ones obtained in neat water, which were near to 18,000 [10]. From the different magnitudes obtained for the γ2 values presented in Table 3 an approximate estimation of solute–solvent intermolecular interactions can be made by considering the following expression:
ln γ 2 ¼ ðe11 þ e22 −2e12 Þ
V 2 ϕ21 RT
ð1Þ
where e11, e22 and e12 represent the solvent–solvent, solute–solute and solvent–solute interaction energies, respectively; V2 is the molar volume of the supercooled liquid solute, and finally, ϕ1 is the volume fraction of the solvent. In a first approach the term (V2ϕ12/RT)T,P may be considered approximately constant at the same temperature, and then γ2 depends almost exclusively on e11, e22 and e12 [23]. While the e12 term favors the solution process, both e11 and e22 terms are unfavorable for solubility. This happens because energy must be supplied first, against the cohesive forces of the solute in solid state to separate them, and second, against the cohesive forces of the solvent to create the respective cavity (for solute accommodation). These processes decrease drug solubility. On the other hand, solute–solvent interaction is exothermic and results mainly from van der Waals and Lewis acid–base interactions, which increases the drug solubility. The contribution of e22 is proportional to the work necessary to transfer drug molecules from the solid to the vapor state and, therefore, it could be considered as constant in all mixtures and pure solvents. The γ2 values vary from 4.92 to 10.60 at 298.15 K indicating almost quasi-ideal solubility behavior of this drug in this binary solvent system. It is important to note that IMC has high temperature and enthalpy of fusion and therefore the term e22 would be great [8]. On similar way, ethanol and propylene glycol are hydrogen-bonded solvents implying the e11 term is relatively great in all mixtures [16,24]. Therefore, the term e12 would be significant to obtain the low γ2 values presented in Table 3. That is, the solute–solvent interactions are very important for dissolution of this drug in these solvent mixtures. 3.3. Apparent thermodynamic functions of solution
a
δ is the Hildebrand solubility parameter. b wEtOH max. solub. is the cosolvent composition where the maximum drug solubility was reported. c From Jiménez and Martínez [4]. d From Holguín et al. [6]. e From Rodríguez et al. [21]. f From Pachecho et al. [5]. g From Ruidiaz and Martínez [20]. h From Table 1 in this work i From Aragón et al. [22].
According to van't Hoff analysis, the apparent standard enthalpy change of solution (ΔsolnH°) for non-electrolyte drugs is obtained by using the mean harmonic temperature (Thm is 303.0 K in the present case) according to Eq. (2) [8,10].
∂ ln x2 Δ H∘ ¼ − soln R ∂ð1=T−1=T hm Þ P
ð2Þ
E.A. Cantillo et al. / Journal of Molecular Liquids 181 (2013) 62–67
where, R is the universal gas constant (8.314 J mol −1 K −1). As an example, Fig. 3 shows the modified van't Hoff plot for IMC in mixtures containing 0.20, 0.40, 0.60, and 0.80 in mass fraction of ethanol. In all cases linear models were obtained with good determination coefficients (r 2) were obtained. The apparent standard Gibbs energy change for the solution process (ΔsolnG°) of non-electrolyte drugs considering the approach proposed by Krug et al. [25] is calculated at mean harmonic temperature by means of: ∘
Δsoln G ¼ −RT hm intercept
ð3Þ
in which, the intercept used is the one obtained in the analysis by treatment of ln x2 as a function of 1/T − 1/Thm (Fig. 3). This intercept corresponds to the value of ln x2 obtained from the respective regression model at 303.0 K, and thus, Eq. (3) is almost coincident with the classical equation ΔsolnG° = − RT × ln x2 at mean harmonic temperature [6]. Finally, the apparent standard entropic change for solution process (ΔsolnS°) is obtained from the respective ΔsolnH° and ΔsolnG° values by using:
∘
Δsoln S ¼
ðΔsoln H∘ −Δsoln G∘ Þ : T hm
ð4Þ
Table 4 summarizes the apparent standard thermodynamic functions for experimental dissolution process of IMC in all ethanol + propylene glycol solvent mixtures. In order to calculate these thermodynamic quantities some propagation of uncertainties' methods were used [26,27]. In particular, the uncertainty in enthalpy was calculated from the respective uncertainty in the van't Hoff plot slope multiplied by R, the uncertainty in Gibbs energy was calculated as the mean of the variation coefficients obtained in solubility values obtained at all temperatures, and finally, the uncertainty in entropy was obtained as the root square of the sum of squares of uncertainties obtained for enthalpy and Gibbs energy. It is found that the standard Gibbs energy of solution is positive in all cases as expected because the mole fraction is always lower than the unit and thus, its logarithmic term is negative, and therefore, standard Gibbs energy will be a positive quantity. ΔsolnG° values diminish from neat propylene glycol to neat ethanol. The apparent enthalpy and entropy of solution are positive in all cases, therefore the process is always endothermic and driven by entropy. In different way to Gibbs energy of solution, ΔsolnH° and ΔsolnS° values increase from neat propylene glycol to the mixture of 0.70 in mass fraction of ethanol and decrease beyond this mixture composition.
Table 4 Apparent thermodynamic functions relative to solution process of indomethacin in ethanol + propylene glycol mixtures at 303.0 K.a wEtOHb
ΔsolnG°/ kJ mol−1
ΔsolnH°/ kJ mol−1
ΔsolnS°/ J mol−1 K−1
TΔsolnS°/ kJ mol−1
ζH c
ζTSc
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Ideal d
15.46 15.41 15.33 15.19 14.93 14.72 14.42 14.22 13.96 13.73 13.63 9.83
45.1 45.1 45.3 45.7 46.35 47.5 48.77 49.25 48.6 45.5 42.29 27.63
97.7 98.1 98.9 100.8 103.7 108.2 113.4 115.6 114.5 104.9 94.6 58.7
29.6 29.7 29.96 30.53 31.42 32.8 34.36 35.03 34.7 31.78 28.66 17.80
0.604 0.603 0.602 0.600 0.596 0.592 0.587 0.584 0.584 0.589 0.596 0.608
0.396 0.397 0.398 0.400 0.404 0.408 0.413 0.416 0.416 0.411 0.404 0.392
(0.05) (0.04) (0.04) (0.04) (0.05) (0.05) (0.03) (0.05) (0.06) (0.05) (0.04) (0.05)
(0.9) (0.8) (0.4) (0.3) (0.21) (0.4) (0.14) (0.24) (0.6) (0.4) (0.17) (0.16)
(2.1) (1.7) (0.8) (0.7) (0.6) (1.1) (0.4) (0.7) (1.6) (0.9) (0.5) (0.4)
(0.6) (0.5) (0.25) (0.22) (0.17) (0.3) (0.12) (0.21) (0.5) (0.28) (0.15) (0.13)
a
Values in parentheses are standard deviations. wEtOH is the mass fraction of ethanol in the cosolvent mixtures free of drug. c ζH and ζTS are the relative contributions by enthalpy and entropy toward Gibbs energy of solution. These values were calculated by means of Eqs. (5) and (6), respectively. d From Ruidiaz et al. [8]. b
With the aim to compare the relative contributions by enthalpy (ζH) and by entropy (ζTS) toward the solution process, Eqs. (5) and (6) were employed, respectively [28]. ∘
ζH ¼
jΔsoln H j jΔsoln H∘ j þ jTΔsoln S∘ j
ζ TS ¼
jTΔsoln S j jΔsoln H ∘ j þ jTΔsoln S∘ j
ð5Þ
∘
ð6Þ
From Table 4 it follows that enthalpy is the main contributor to standard Gibbs energy of solution process of IMC in all the systems studied and thus the energetic factor predominates. It is interesting to note that both contributions in all experimental solubilities are similar to those obtained in the case of the ideal solubility, in particular in neat propylene glycol. 3.4. Apparent thermodynamic functions of mixing of IMC The solution process may be represented by the following hypothetic stages [29]: SoluteðSolidÞ →SoluteðLiquidÞ at T fus →SoluteðLiquidÞ at T hm →SoluteðSolutionÞ where the solution stages are solute fusion, cooling the liquid solute to the mean harmonic temperature Thm (303.0 K), and subsequent mixing of the hypothetical super-cooled liquid solute with the solvent at this temperature. This allows also the calculation of the partial thermodynamic contributions to the overall solution process by means of Eqs. (7) and (8), respectively.
∘
Δsoln H ¼ Δfus H ∘
Δsoln S ¼ Δfus S
Fig. 3. Modified van't Hoff plot for experimental solubility of indomethacin in ethanol + propylene glycol mixtures expressed in mole fraction. ●: wEtOH = 0.20; ■: wEtOH = 0.40: ▲: wEtOH = 0.60; ○: wEtOH = 0.80.
65
303
303
þ Δmix H ∘
þ Δmix S
∘
ð7Þ ð8Þ
where ΔfusH 303 and ΔfusS 303 represent the thermodynamic functions of fusion of IMC and its cooling to the mean harmonic temperature, 303.0 K. However, the ΔsolnH° id and ΔsolnS° id values for the ideal solution processes were used instead of ΔfusH 303 and ΔfusS 303 for reasons described in the literature [8]. Briefly, ΔfusH 303 is calculated as ΔfusH MP − ΔCp(Tfus − T) by using ΔfusS MP instead of ΔCp obtaining a value of 27.63 kJ mol−1, which is coincident with the enthalpic change for an ideal solution of this drug (Table 4); in contrast, the entropy of
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E.A. Cantillo et al. / Journal of Molecular Liquids 181 (2013) 62–67
fusion at 303.0 K (91.2 J mol−1 K −1) is not coincident with the entropy of ideal solution at this temperature (58.7 J mol−1 K−1) [5]. This replacement was used also with some other drugs studied at similar conditions in this binary solvent system [4–6]. Fig. 4 summarizes the thermodynamic functions of mixing of supercooled liquid IMC with the solvent mixtures. ΔmixG° values are positive indicating apparently nonspontaneity of the liquid mixing process. This result is in agreement with the fact that experimental solubility in all cases was lower than the ideal one. The ideal dissolution contributions (related to solute fusion process) to the enthalpy and entropy of the overall dissolution processes of IMC, ΔsolnH° id and ΔsolnS°id, are positive (Table 4), as both thermodynamic quantities of mixing also are (Fig. 4), indicating entropy-driving in this hypothetical sub-process. 3.5. Apparent thermodynamic functions of transfer of IMC In order to verify the effect of cosolvent composition on the thermodynamic function driving the solution process, Table 5 summarizes the thermodynamic functions of transfer of IMC from the more polar solvents to the less polar ones. These new functions were calculated as the differences between the thermodynamic quantities of solution in the more polar mixtures and the less polar mixtures. If the addition of ethanol to neat propylene glycol is considered (being the solvent mixture less polar as the ethanol proportion increases), as has been done earlier [4–6], it happens through the following: from neat propylene glycol to 0.70 in mass fraction of ethanol (ΔA → BG° b 0, ΔA → BH° > 0, and ΔA → BS° > 0) the dissolution process is driven by the entropy; whereas, from this composition up to neat ethanol (ΔA → BG° b 0, ΔA → BH° b 0, and ΔA → BS° b 0) the dissolution process is enthalpy-driven. Nevertheless, the molecular events involved on drug dissolution processes are unclear because of the lack of information about structural effects in this binary alcoholic system. 3.6. Enthalpy–entropy compensation of solution process of IMC According to the literature, the making of weighted graphs of ΔsolnH° as a function of ΔsolnG° at mean harmonic temperature allows us to observe similar mechanisms for the solution process according to the tendencies obtained [30]. In this context, Fig. 5 shows fully that IMC in the ethanol + propylene glycol solvent system exhibits non-linear ΔsolnH° vs. ΔsolnG° compensation with negative slope if an interval from neat propylene glycol to 0.70 in mass fraction of ethanol is considered (near to 0.80 in mole fraction of ethanol), whereas from this ethanol proportion to neat ethanol, a positive slope is obtained. According to this graph it follows that the driving function for IMC solubility is the entropy in the first case, while in the second case, the driving function is the enthalpy.
Fig. 4. Apparent thermodynamic quantities of mixing of indomethacin in ethanol + propylene glycol mixtures at 303.0 K. ●: ΔmixG°; ■: ΔmixH°; ▲: TΔmixS°.
Table 5 Apparent thermodynamic functions of transfer of indomethacin from more polar solvents to less polar solvents in ethanol + propylene glycol mixtures at 303.0 K.a wEtOHb A
B
0.00 0.70
0.70 1.00
ΔA → BG°/ kJ mol−1
ΔA → BH°/ kJ mol−1
ΔA → BS°/ J mol−1 K−1
TΔA → BS°/ kJ mol−1
−1.24 (0.07) −0.59 (0.06)
4.2 (1.0) −7.0 (0.3)
17.9 (2.2) −21.0 (0.8)
5.4 (0.7) −6.37 (0.25)
a
Values in parentheses are standard deviations. wEtOH is the mass fraction of ethanol in the cosolvent mixtures free of indomethacin; A and B are the more polar and less polar media, respectively. b
Nevertheless, the molecular events involved in the dissolution of this drug in this binary system are unclear as was already said but it is conjecturable that the enthalpy driving in ethanol-rich mixtures could be due to the energy requirement to separate the molecules of each individual solvent to accommodate the drug molecules. On the other hand, a similar compensation plot has been reported for this drug in ethanol + water mixtures, with a maximum in 0.50 in mass fraction of ethanol. In that case the entropy driving in water-rich mixtures was attributed to hydrophobic hydration of the non-polar moieties of IMC [9]. The compensation behavior obtained for IMC is different than those reported for acetaminophen and triclocarban, which were also non-linear, and is also different than those reported for ibuprofen and naproxen, which were almost linear [4–6]. In this way, the almost linear compensation of ibuprofen solubility in this solvent mixture was explained in terms of the same mechanism for dissolution process independent of the mixture composition because non-structural change is observed in the solvent mixture [31]. Nevertheless, this fact is objectionable in the cases of IMC, acetaminophen and triclocarban. By comparing the IMC behavior with other analgesic drugs it is interesting to note that IMC and naproxen solubility parameters are the same (20.9 MPa1/2) being greater than the one of ibuprofen (19.4 MPa1/2) but IMC exhibit two trends, whereas, naproxen exhibits only one trend with negative slope and ibuprofen also exhibits only one trend but with positive slope [5], although the reasons for this results are not clear. On the other hand, it is also interesting to note that when ΔsolnH° vs. TΔsolnS° coordinates are evaluated (Fig. 6) two linear trends with positive slopes are observed, i.e. for the region 0.00 ≤ wEtOH ≤ 0.70 the equation ΔsolnH° = 0.782 (±0.008) × TΔsolnS° + 21.87 (±0.25), with r2 adjusted: 0.9993 and typical error: 0.0438 was obtained; whereas, for the region 0.70 ≤ wEtOH ≤ 1.00 the equation ΔsolnH° = 1.079 (± 0.028) × TΔsolnS° + 11.3 (± 0.9), with r 2 adjusted: 0.9980 and typical error: 0.1419, was obtained. In similar way to that reported in the literature for other drugs in different aqueous systems [10,32–35], this result also demonstrates that entropy-driving is observed in the propylene glycol-rich mixtures and enthalpy-driving in
Fig. 5. ΔsolnH° vs. ΔsolnG° enthalpy–entropy compensation plot for solubility of indomethacin in ethanol + propylene glycol mixtures at 303.0 K. Points correspond to mass fractions of ethanol in the mixtures.
E.A. Cantillo et al. / Journal of Molecular Liquids 181 (2013) 62–67
Fig. 6. ΔsolnH° vs. TΔsolnS° enthalpy–entropy compensation plot for solubility of indomethacin in ethanol + propylene glycol mixtures at 303.0 K. Points correspond to mass fractions of ethanol in the mixtures.
the ethanol-rich ones. This conclusion is based on the slope values obtained in each case, i.e. lower than 1.00 for entropy-driving and greater than 1.00 for enthalpy-driving. 4. Conclusions From all topics discussed previously it can be concluded that the solution process of IMC in ethanol + propylene glycol mixtures is variable depending on the solvent composition. Non-linear enthalpy– entropy compensation was found for this drug in this binary system. In this context, entropy–driving was found for propylene glycol-rich mixtures (0.00 b wEtOH b 0.70) whereas, for ethanol-rich mixtures (0.70 ≤ wEtOH ≤ 1.00) enthalpy-driving was found; nevertheless, the molecular events involved in the dissolution of this drug in this solvent system are unclear. Ultimately, it can be stated that the data presented in this report expand the physicochemical information about analgesic drugs in alcoholic solutions. Acknowledgments We thank the Department of Pharmacy of the Universidad Nacional de Colombia for facilitating the equipment and laboratories used. References [1] R.B. Raffa, in: A.R. Gennaro (Ed.), 21st ed., Lippincott, Williams & Wilkins, Philadelphia, 2005.
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[2] A. Jouyban, Handbook of Solubility Data for Pharmaceuticals, CRC Press, Boca Raton, FL, 2010. [3] D.P. Pacheco, F. Martínez, Physics and Chemistry of Liquids 45 (2007) 581–595. [4] J.A. Jiménez, F. Martínez, Journal of Solution Chemistry 35 (2006) 335–352. [5] D.P. Pacheco, Y.J. Manrique, F. Martínez, Fluid Phase Equilibria 262 (2007) 23–31. [6] A.R. Holguín, D.R. Delgado, F. Martínez, Química Nova 35 (2012) 280–285. [7] J. Jiménez, F. Martínez, Physics and Chemistry of Liquids 44 (2006) 521–530. [8] M.A. Ruidiaz, D.R. Delgado, F. Martínez, Y. Marcus, Fluid Phase Equilibria 299 (2010) 259–265. [9] F. Martínez, M.Á. Peña, P. Bustamante, Fluid Phase Equilibria 308 (2011) 98–106. [10] A.R. Holguín, G.A. Rodríguez, D.M. Cristancho, D.R. Delgado, F. Martínez, Fluid Phase Equilibria 314 (2012) 134–139. [11] J.T. Rubino, in: J. Swarbrick, J.C. Boylan (Eds.), Encyclopedia of Pharmaceutical Technology, vol 3, Marcel Dekker, Inc., New York, 1988. [12] M.E. Aulton, Pharmaceutics: The Science of Dosage Form Design, 2nd ed. Churchill Livingstone, London, 2002. [13] BP, The British Pharmacopoeia, vol I, Her Majesty's Stationery Office, London, 1988. [14] US Pharmacopeia, The United States Pharmacopeial Convention, Rockville, MD, 23rd ed., 1994. [15] G.A. Rodríguez, D.R. Delgado, F. Martínez, M.A.A. Fakhree, A. Jouyban, Journal of Solution Chemistry 41 (2012) 1477–1494. [16] A. Martin, P. Bustamante, A.H.C. Chun, Physical Pharmacy: Physical Chemical Principles in the Pharmaceutical Sciences, 4th ed. Lea & Febiger, Philadelphia, 1993. [17] D.P. Shoemaker, G.W. Garland, Experimentos de Fisicoquímica, Unión Tipográfica Editorial Hispano Americana, México D.F., 1968. [18] Y. Marcus, S. Glikberg, Pure and Applied Chemistry 57 (1985) 855–864. [19] R.J. Sengwa, R. Chaudhary, S.C. Mehrotra, Polymer 43 (2002) 1467–1471. [20] M.A. Ruidiaz, F. Martínez, Revista Colombiana de Química 38 (2009) 235–247. [21] G.A. Rodríguez, D.R. Delgado, F. Martínez, A. Jouyban, W.E. Acree Jr., Fluid Phase Equilibria 320 (2012) 49–55. [22] D.M. Aragón, J.E. Rosas, F. Martínez, Brazilian Journal of Pharmaceutical Sciences 46 (2010) 227–235. [23] A. Kristl, G. Vesnaver, Faraday Transactions 91 (1995) 995–998. [24] A.T. Florence, D. Atwood, Physicochemical Principles of Pharmacy, 3rd ed. MacMillan Press Ltd., London, 1998. [25] R.R. Krug, W.G. Hunter, R.A. Grieger, Journal of Physical Chemistry 80 (1976) 2341–2351. [26] P.R. Bevington, Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill Book Co., New York, 1969. [27] J.R. Barrante, Applied Mathematics for Physical Chemistry, 2nd ed. Prentice Hall, Inc., Upper Saddle River, N.J., 1998. [28] G.L. Perlovich, S.V. Kurkov, A.N. Kinchin, A. Bauer-Brandl, European Journal of Pharmaceutics and Biopharmaceutics 57 (2004) 411–420. [29] D.R. Delgado, A.R. Holguín, O.A. Almanza, F. Martínez, Y. Marcus, Fluid Phase Equilibria 305 (2011) 88–95. [30] P. Bustamante, S. Romero, A. Reillo, Pharmacy and Pharmacology Communications 1 (1995) 505–507. [31] I. Khalifeh, Ph.D. thesis, Purdue University, Ann Arbor MI, 2000. [32] M. Gantiva, A. Yurquina, F. Martínez, Journal of Chemical & Engineering Data 55 (2010) 113–118. [33] M. Gantiva, F. Martínez, Fluid Phase Equilibria 293 (2010) 242–250. [34] D.R. Delgado, A. Romdhani, F. Martínez, Latin American Journal of Pharmacy 30 (2011) 2024–2030. [35] E.A. Ahumada, D.R. Delgado, F. Martinez, Fluid Phase Equilibria 332 (2012) 120–127.
Contents lists available at SciVerse ScienceDirect
Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Solution thermodynamics of indomethacin in ethanol + propylene glycol mixtures Eliecer A. Cantillo, Daniel R. Delgado, Fleming Martinez ⁎ Grupo de Investigaciones Farmacéutico-Fisicoquímicas, Departamento de Farmacia, Facultad de Ciencias, Universidad Nacional de Colombia, A.A. 14490, Bogotá, D.C., Colombia
a r t i c l e
i n f o
Article history: Received 8 December 2012 Received in revised form 11 February 2013 Accepted 15 February 2013 Available online 5 March 2013 Keywords: Indomethacin Ethanol Propylene glycol Solubility Cosolvency Thermodynamics
a b s t r a c t Drug solubility is a key parameter during the processes associated to design and development of new liquid pharmaceutical dosage forms. Cosolvency is a commonly used technique to increase the drug solubility in several orders of magnitude and it is relatively simple. Nevertheless the solubility in mixed solvents is scarce for several drugs. For this reason, in this work the solubility of indomethacin was determined by using the stirred flask method as a function of temperature and cosolvent composition in some ethanol + propylene glycol mixtures. From solubility data the solution thermodynamic quantities, Gibbs energy, enthalpy and entropy, were calculated. In similar way, from these new values and information about drug melting properties, the thermodynamic quantities of hypothetical liquids mixing were also calculated. A non-linear ΔsolnH° vs. ΔsolnG° compensation plot was obtained which could indicate that the dissolution mechanism is dependent on the cosolvent mixture composition. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Indomethacin (IMC, 357.79 g mol−1, Fig. 1) is a non-steroidal anti-inflammatory drug, which is sometimes used as analgesic, among other indications [1]. Although IMC is widely used in therapeutics the physicochemical information about its solubility in aqueous and non-aqueous media is not abundant [2]. As has been already described, the solubility behavior of drugs in cosolvent mixtures is very important because cosolvent blends are frequently used in purification methods, preformulation studies, and pharmaceutical dosage form design, among other applications [3]. For these reasons, it is important to determine systematically the solubility of pharmaceutical compounds. Besides, as was already said temperaturesolubility dependence allows us to carry out the respective thermodynamic analysis, which, on the other hand, also permits insight on the molecular mechanisms, involved toward the dissolution processes [3]. As a basic stage toward a deeper understanding of the molecular forces involved in dissolution processes, the present work studied the solution thermodynamics of IMC in several solvent mixtures of ethanol and propylene glycol as has been made with other analgesic drugs such as acetaminophen [4], ibuprofen, naproxen [5], and with the antimicrobial drug triclocarban [6]. It is important to note that ethanol + propylene glycol mixtures exhibit non-ideal behavior on mixing as has been observed by studying excess molar volumes [7]. The equilibrium solubility was determined at several temperatures in the binary mixtures and the respective dissolution thermodynamic analysis was made by using the van't Hoff and Gibbs equations. Otherwise, ⁎ Corresponding author. Tel.: +571 3165000x14608; fax: +571 3165060. E-mail address: [email protected] (F. Martinez). 0167-7322/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molliq.2013.02.008
by using the values reported for IMC ideal solubility the contribution due to the hypothetical liquid mixing-process toward the overall dissolution was also analyzed [8]. In this way, this work is a continuation of those developed with the same drug in ethanol + water and propylene glycol + water cosolvent mixtures [9,10]. It is well known that ethanol and propylene glycol are the cosolvents most widely used in drug formulation design, especially those intended for per oral and parenteral administration and several examples of pharmaceutical formulations using these cosolvents have been presented by Rubino [11]. It is remarkable that both cosolvents have antimicrobial properties [12]. 2. Experimental 2.1. Materials Indomethacin (1-(4-chlorobenzoyl)-5-methoxy-2-methyl-1H-indole3-acetic acid, CAS: 53-86-1, from Sigma Chemical Co.) used conformed to the quality requirements of the British Pharmacopoeia, BP [13]; absolute ethanol A.R. (from Merck) and propylene glycol (from Dow Chemical Co.) conformed to the quality requirements of the American Pharmacopeia, USP [14]; molecular sieve (Merck, numbers 3 and 4); Millipore Corp. Swinnex®-13 filter units. 2.2. Solvent mixtures preparation Both solvents were treated with molecular sieve to remove the small water quantities. All ethanol + propylene glycol solvent mixtures were prepared by mass, using an Ohaus Pioneer TM PA214 analytical balance with sensitivity ± 0.1 mg, in quantities of 50 g. The mass fractions of
E.A. Cantillo et al. / Journal of Molecular Liquids 181 (2013) 62–67
63
groups in the solvents (oxygen atoms in \OH and \O\ groups), although it can also act as a proton-acceptor compound by means of its carbonyl, methoxyl, and hydroxyl moieties (Fig. 1) [8–10].
O Cl N
3.1. Ideal and experimental solubility of IMC
CH3 H3C-O COOH Fig. 1. Molecular structure of indomethacin.
ethanol of the nine binary mixtures prepared varied by 0.10 from 0.10 to 0.90. 2.3. Solubility determinations An excess of IMC was added to approximately 10 g of each solvent mixture or neat solvent, in stoppered dark glass flasks. Solid–liquid mixtures were placed with stirring in a thermostatic mechanical shaker (Julabo SW23) kept at 303.15, 308.15, or 313.15 (±0.05) K or placed in re-circulating thermostatic baths (Neslab RTE 10 Digital One Thermo Electron Company) kept at 293.15 or 298.15 (±0.05) K with sporadic manual stirring at least for 7 days to reach the saturation equilibrium. After this time the supernatant solutions were filtered (at isothermal conditions) to ensure that they were free of particulate matter before sampling. IMC concentrations were determined, after appropriate aqueous dilution with NaOH 0.10 N, by measuring the light absorbance and interpolation from a previously constructed UV spectrophotometry calibration curve at λmax 281 nm (UV/VIS BioMate 3 Thermo Electron Company spectrophotometer). Equilibrium time was established by measuring the IMC concentrations till they became constant. All the solubility experiments were run in triplicate at least. In order to make the equivalence between molarity and mole fraction concentration scales, the density of the saturated solutions was determined with a digital density meter (DMA 45 Anton Paar) connected to the same recirculating thermostatic baths, according to procedures described previously [15]. 3. Results and discussion In order to propose the possible intermolecular interactions present in the saturated solutions of IMC, it is important to remark that this drug acts in solution mainly as a Lewis acid (due to its \OH group) in order to establish hydrogen bonds with proton-acceptor functional
Table 1 shows the experimental solubilities of IMC expressed in mole fractions, x2, as well as the ideal solubilities already reported [8]. It is important to keep in mind that drug ideal solubility is just dependent on solid-solute properties without considering the solvent properties. Thus, ideal solubility depends both on temperature and enthalpy of fusion [16]. In almost all cases the uncertainties in solubility were smaller than 1.0%. Significant figures were defined by using the criterion 3–30 [17]. On similar way, Fig. 2 shows IMC solubility expressed in molarity at all temperatures studied. The molar solubility trends are described by normal polynomials in order 3. It may be observed that the lowest and highest drug solubility values at all temperatures are obtained in neat propylene glycol and ethanol, respectively. Solubility values in neat solvents are similar to those reported previously [9,10]. On the other hand, in the literature, there is no reported solubility values for this drug in these solvents mixed, and therefore, no direct comparison is possible. It is important to keep in mind that both solvents studied are considered as semipolar but being propylene glycol more polar than ethanol, i.e. dielectric constants at 298.15 K are 30.2 and 24.3, respectively [18,19]; whereas Hildebrand solubility parameters are 30.3 and 26.6 MPa 1/2 at the same temperature, respectively [16]. The solubility of IMC was higher in neat ethanol because its reported Hildebrand solubility parameter is 20.9 MPa 1/2; and therefore, its maximum solubility is found in solvent mixtures with lower polarity than the one of neat ethanol, as was reported in mixtures ethyl acetate + ethanol [20]. On the other hand, it is interesting to make a comparison of the IMC solubility with respect to the behavior exhibited by other drugs in the same solvent mixtures. In this way, Table 2 shows the molecular structures, Hildebrand solubility parameters, and the cosolvent composition of the mixtures where the maximum solubilities were found, for acetaminophen, triclocarban, naproxen, indomethacin, and ibuprofen. Hildebrand solubility parameters have been used widely as a key parameter to describe the polarity of solvents and solutes in studies about solubility of drugs [16]. The reported values are demonstrating that the maximum drug solubility, despite the functional groups, is found in solvents where the polarity between solutes and solvents is the same or at least similar as described by solubility parameters. This result is in agreement with the fact described in the literature about the smaller the difference of the solubility parameters between solute and solvent, the higher the solubility of the
Table 1 Experimental and ideal solubility of indomethacin in ethanol + propylene glycol mixtures expressed as 1000 × mole fraction at several temperatures.a wEtOHb
δ1/MPa1/2c
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Ideald
30.30 29.83 29.38 28.97 28.57 28.20 27.84 27.51 27.19 26.89 26.60
a b c d
T/K 293.15
298.15
303.15
308.15
313.15
1.186 1.201 1.246 1.291 1.430 1.509 1.696 1.854 2.109 2.303 2.530 13.99
1.588 1.626 1.696 1.820 1.988 2.181 2.403 2.542 2.824 3.258 3.423 16.84
2.204 2.250 2.284 2.442 2.675 2.960 3.310 3.569 3.861 4.369 4.528 20.22
3.082 3.107 3.148 3.258 3.657 3.980 4.528 4.902 5.406 5.807 5.877 24.19
3.719 3.807 4.031 4.309 4.809 5.289 6.103 6.701 7.509 7.650 7.711 28.86
(0.005) (0.004) (0.003) (0.004) (0.005) (0.006) (0.003) (0.008) (0.020) (0.007) (0.009) (0.07)
Values in parentheses are standard deviations. wEtOH is the mass fraction of ethanol in the cosolvent mixtures free of drug. δ1 is the solubility parameter of cosolvent mixtures free of drug at 298.15 K. From Ruidiaz et al. [8].
(0.005) (0.005) (0.006) (0.005) (0.007) (0.007) (0.004) (0.008) (0.007) (0.010) (0.013) (0.08)
(0.008) (0.003) (0.005) (0.004) (0.010) (0.010) (0.005) (0.010) (0.010) (0.013) (0.017) (0.10)
(0.011) (0.007) (0.010) (0.011) (0.012) (0.015) (0.009) (0.015) (0.020) (0.021) (0.018) (0.12)
(0.012) (0.008) (0.006) (0.014) (0.010) (0.008) (0.016) (0.021) (0.024) (0.026) (0.009) (0.14)
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E.A. Cantillo et al. / Journal of Molecular Liquids 181 (2013) 62–67 Table 3 Activity coefficients of indomethacin in ethanol + propylene glycol mixtures at several temperatures.a wEtOHb T/K 293.15
Fig. 2. Experimental solubility of indomethacin in ethanol + propylene glycol mixtures expressed in molarity at several temperatures. ●: 293.15 K; ■: 298.15 K; ▲: 303.15 K; ○: 308.15 K; □: 313.15 K.
solute in the solvent is [16]. Nevertheless, in the case of ibuprofen some solubility values in mixtures ethyl acetate + ethanol are required to evaluate the composition of maximum drug solubility in order to estimate its solubility parameter because the reported value was calculated by groups' contribution methods [22]. 3.2. IMC activity coefficients The solute activity coefficient in the solution (γ2) is calculated as x2id/x2 and it is an indication of the deviation presented by IMC from its ideal behavior [8–10]. Table 3 shows IMC activity coefficients as a function of composition and temperature. Accordingly, γ2 values Table 2 Physicochemical aspects of indomethacin and other drugs studied in ethanol + propylene glycol mixtures. Drug
Molecular structure
Acetaminophen
NH-CO-CH 3
δ/MPa1/2a
wEtOH max. solub. b
28.2c
0.50c
27.8d
0.60d
20.9e
1.00f
20.9g
1.00h
19.4i
1.00f
OH
Triclocarban
Cl
Cl
O
Cl
N
N
H
H
Naproxen
CH3 COOH H3C O
Indomethacin
O Cl N CH3 H3C-O
Ibuprofen
COOH CH3
CH3
COOH
H3C
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 a b
11.80 11.64 11.22 10.84 9.79 9.27 8.25 7.55 6.63 6.08 5.53
298.15
303.15
308.15
(0.07) 10.60 (0.06) 9.18 (0.06) 7.85 (0.07) 10.36 (0.06) 8.99 (0.05) 7.78 (0.06) 9.93 (0.06) 8.85 (0.05) 7.68 (0.07) 9.25 (0.05) 8.28 (0.04) 7.42 (0.06) 8.47 (0.05) 7.56 (0.05) 6.61 (0.06) 7.72 (0.05) 6.83 (0.04) 6.08 (0.04) 7.01 (0.04) 6.11 (0.03) 5.342 (0.05) 6.62 (0.04) 5.66 (0.03) 4.935 (0.07) 5.96 (0.03) 5.237 (0.029) 4.475 (0.04) 5.17 (0.03) 4.628 (0.027) 4.165 (0.03) 4.92 (0.03) 4.465 (0.028) 4.116
(0.05) (0.04) (0.05) (0.05) (0.04) (0.04) (0.029) (0.029) (0.028) (0.026) (0.024)
313.15 7.76 7.58 7.16 6.70 6.00 5.457 4.729 4.307 3.843 3.773 3.742
(0.05) (0.04) (0.04) (0.04) (0.03) (0.029) (0.027) (0.025) (0.023) (0.023) (0.019)
Values in parentheses are standard deviations. wEtOH is the mass fraction of ethanol in the cosolvent mixtures free of drug.
are varying from 5 to 10, in ethanol and propylene glycol respectively, and they diminish as temperature increases indicating more ideal behavior at high temperatures. These values are lower compared to the ones obtained in neat water, which were near to 18,000 [10]. From the different magnitudes obtained for the γ2 values presented in Table 3 an approximate estimation of solute–solvent intermolecular interactions can be made by considering the following expression:
ln γ 2 ¼ ðe11 þ e22 −2e12 Þ
V 2 ϕ21 RT
ð1Þ
where e11, e22 and e12 represent the solvent–solvent, solute–solute and solvent–solute interaction energies, respectively; V2 is the molar volume of the supercooled liquid solute, and finally, ϕ1 is the volume fraction of the solvent. In a first approach the term (V2ϕ12/RT)T,P may be considered approximately constant at the same temperature, and then γ2 depends almost exclusively on e11, e22 and e12 [23]. While the e12 term favors the solution process, both e11 and e22 terms are unfavorable for solubility. This happens because energy must be supplied first, against the cohesive forces of the solute in solid state to separate them, and second, against the cohesive forces of the solvent to create the respective cavity (for solute accommodation). These processes decrease drug solubility. On the other hand, solute–solvent interaction is exothermic and results mainly from van der Waals and Lewis acid–base interactions, which increases the drug solubility. The contribution of e22 is proportional to the work necessary to transfer drug molecules from the solid to the vapor state and, therefore, it could be considered as constant in all mixtures and pure solvents. The γ2 values vary from 4.92 to 10.60 at 298.15 K indicating almost quasi-ideal solubility behavior of this drug in this binary solvent system. It is important to note that IMC has high temperature and enthalpy of fusion and therefore the term e22 would be great [8]. On similar way, ethanol and propylene glycol are hydrogen-bonded solvents implying the e11 term is relatively great in all mixtures [16,24]. Therefore, the term e12 would be significant to obtain the low γ2 values presented in Table 3. That is, the solute–solvent interactions are very important for dissolution of this drug in these solvent mixtures. 3.3. Apparent thermodynamic functions of solution
a
δ is the Hildebrand solubility parameter. b wEtOH max. solub. is the cosolvent composition where the maximum drug solubility was reported. c From Jiménez and Martínez [4]. d From Holguín et al. [6]. e From Rodríguez et al. [21]. f From Pachecho et al. [5]. g From Ruidiaz and Martínez [20]. h From Table 1 in this work i From Aragón et al. [22].
According to van't Hoff analysis, the apparent standard enthalpy change of solution (ΔsolnH°) for non-electrolyte drugs is obtained by using the mean harmonic temperature (Thm is 303.0 K in the present case) according to Eq. (2) [8,10].
∂ ln x2 Δ H∘ ¼ − soln R ∂ð1=T−1=T hm Þ P
ð2Þ
E.A. Cantillo et al. / Journal of Molecular Liquids 181 (2013) 62–67
where, R is the universal gas constant (8.314 J mol −1 K −1). As an example, Fig. 3 shows the modified van't Hoff plot for IMC in mixtures containing 0.20, 0.40, 0.60, and 0.80 in mass fraction of ethanol. In all cases linear models were obtained with good determination coefficients (r 2) were obtained. The apparent standard Gibbs energy change for the solution process (ΔsolnG°) of non-electrolyte drugs considering the approach proposed by Krug et al. [25] is calculated at mean harmonic temperature by means of: ∘
Δsoln G ¼ −RT hm intercept
ð3Þ
in which, the intercept used is the one obtained in the analysis by treatment of ln x2 as a function of 1/T − 1/Thm (Fig. 3). This intercept corresponds to the value of ln x2 obtained from the respective regression model at 303.0 K, and thus, Eq. (3) is almost coincident with the classical equation ΔsolnG° = − RT × ln x2 at mean harmonic temperature [6]. Finally, the apparent standard entropic change for solution process (ΔsolnS°) is obtained from the respective ΔsolnH° and ΔsolnG° values by using:
∘
Δsoln S ¼
ðΔsoln H∘ −Δsoln G∘ Þ : T hm
ð4Þ
Table 4 summarizes the apparent standard thermodynamic functions for experimental dissolution process of IMC in all ethanol + propylene glycol solvent mixtures. In order to calculate these thermodynamic quantities some propagation of uncertainties' methods were used [26,27]. In particular, the uncertainty in enthalpy was calculated from the respective uncertainty in the van't Hoff plot slope multiplied by R, the uncertainty in Gibbs energy was calculated as the mean of the variation coefficients obtained in solubility values obtained at all temperatures, and finally, the uncertainty in entropy was obtained as the root square of the sum of squares of uncertainties obtained for enthalpy and Gibbs energy. It is found that the standard Gibbs energy of solution is positive in all cases as expected because the mole fraction is always lower than the unit and thus, its logarithmic term is negative, and therefore, standard Gibbs energy will be a positive quantity. ΔsolnG° values diminish from neat propylene glycol to neat ethanol. The apparent enthalpy and entropy of solution are positive in all cases, therefore the process is always endothermic and driven by entropy. In different way to Gibbs energy of solution, ΔsolnH° and ΔsolnS° values increase from neat propylene glycol to the mixture of 0.70 in mass fraction of ethanol and decrease beyond this mixture composition.
Table 4 Apparent thermodynamic functions relative to solution process of indomethacin in ethanol + propylene glycol mixtures at 303.0 K.a wEtOHb
ΔsolnG°/ kJ mol−1
ΔsolnH°/ kJ mol−1
ΔsolnS°/ J mol−1 K−1
TΔsolnS°/ kJ mol−1
ζH c
ζTSc
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Ideal d
15.46 15.41 15.33 15.19 14.93 14.72 14.42 14.22 13.96 13.73 13.63 9.83
45.1 45.1 45.3 45.7 46.35 47.5 48.77 49.25 48.6 45.5 42.29 27.63
97.7 98.1 98.9 100.8 103.7 108.2 113.4 115.6 114.5 104.9 94.6 58.7
29.6 29.7 29.96 30.53 31.42 32.8 34.36 35.03 34.7 31.78 28.66 17.80
0.604 0.603 0.602 0.600 0.596 0.592 0.587 0.584 0.584 0.589 0.596 0.608
0.396 0.397 0.398 0.400 0.404 0.408 0.413 0.416 0.416 0.411 0.404 0.392
(0.05) (0.04) (0.04) (0.04) (0.05) (0.05) (0.03) (0.05) (0.06) (0.05) (0.04) (0.05)
(0.9) (0.8) (0.4) (0.3) (0.21) (0.4) (0.14) (0.24) (0.6) (0.4) (0.17) (0.16)
(2.1) (1.7) (0.8) (0.7) (0.6) (1.1) (0.4) (0.7) (1.6) (0.9) (0.5) (0.4)
(0.6) (0.5) (0.25) (0.22) (0.17) (0.3) (0.12) (0.21) (0.5) (0.28) (0.15) (0.13)
a
Values in parentheses are standard deviations. wEtOH is the mass fraction of ethanol in the cosolvent mixtures free of drug. c ζH and ζTS are the relative contributions by enthalpy and entropy toward Gibbs energy of solution. These values were calculated by means of Eqs. (5) and (6), respectively. d From Ruidiaz et al. [8]. b
With the aim to compare the relative contributions by enthalpy (ζH) and by entropy (ζTS) toward the solution process, Eqs. (5) and (6) were employed, respectively [28]. ∘
ζH ¼
jΔsoln H j jΔsoln H∘ j þ jTΔsoln S∘ j
ζ TS ¼
jTΔsoln S j jΔsoln H ∘ j þ jTΔsoln S∘ j
ð5Þ
∘
ð6Þ
From Table 4 it follows that enthalpy is the main contributor to standard Gibbs energy of solution process of IMC in all the systems studied and thus the energetic factor predominates. It is interesting to note that both contributions in all experimental solubilities are similar to those obtained in the case of the ideal solubility, in particular in neat propylene glycol. 3.4. Apparent thermodynamic functions of mixing of IMC The solution process may be represented by the following hypothetic stages [29]: SoluteðSolidÞ →SoluteðLiquidÞ at T fus →SoluteðLiquidÞ at T hm →SoluteðSolutionÞ where the solution stages are solute fusion, cooling the liquid solute to the mean harmonic temperature Thm (303.0 K), and subsequent mixing of the hypothetical super-cooled liquid solute with the solvent at this temperature. This allows also the calculation of the partial thermodynamic contributions to the overall solution process by means of Eqs. (7) and (8), respectively.
∘
Δsoln H ¼ Δfus H ∘
Δsoln S ¼ Δfus S
Fig. 3. Modified van't Hoff plot for experimental solubility of indomethacin in ethanol + propylene glycol mixtures expressed in mole fraction. ●: wEtOH = 0.20; ■: wEtOH = 0.40: ▲: wEtOH = 0.60; ○: wEtOH = 0.80.
65
303
303
þ Δmix H ∘
þ Δmix S
∘
ð7Þ ð8Þ
where ΔfusH 303 and ΔfusS 303 represent the thermodynamic functions of fusion of IMC and its cooling to the mean harmonic temperature, 303.0 K. However, the ΔsolnH° id and ΔsolnS° id values for the ideal solution processes were used instead of ΔfusH 303 and ΔfusS 303 for reasons described in the literature [8]. Briefly, ΔfusH 303 is calculated as ΔfusH MP − ΔCp(Tfus − T) by using ΔfusS MP instead of ΔCp obtaining a value of 27.63 kJ mol−1, which is coincident with the enthalpic change for an ideal solution of this drug (Table 4); in contrast, the entropy of
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E.A. Cantillo et al. / Journal of Molecular Liquids 181 (2013) 62–67
fusion at 303.0 K (91.2 J mol−1 K −1) is not coincident with the entropy of ideal solution at this temperature (58.7 J mol−1 K−1) [5]. This replacement was used also with some other drugs studied at similar conditions in this binary solvent system [4–6]. Fig. 4 summarizes the thermodynamic functions of mixing of supercooled liquid IMC with the solvent mixtures. ΔmixG° values are positive indicating apparently nonspontaneity of the liquid mixing process. This result is in agreement with the fact that experimental solubility in all cases was lower than the ideal one. The ideal dissolution contributions (related to solute fusion process) to the enthalpy and entropy of the overall dissolution processes of IMC, ΔsolnH° id and ΔsolnS°id, are positive (Table 4), as both thermodynamic quantities of mixing also are (Fig. 4), indicating entropy-driving in this hypothetical sub-process. 3.5. Apparent thermodynamic functions of transfer of IMC In order to verify the effect of cosolvent composition on the thermodynamic function driving the solution process, Table 5 summarizes the thermodynamic functions of transfer of IMC from the more polar solvents to the less polar ones. These new functions were calculated as the differences between the thermodynamic quantities of solution in the more polar mixtures and the less polar mixtures. If the addition of ethanol to neat propylene glycol is considered (being the solvent mixture less polar as the ethanol proportion increases), as has been done earlier [4–6], it happens through the following: from neat propylene glycol to 0.70 in mass fraction of ethanol (ΔA → BG° b 0, ΔA → BH° > 0, and ΔA → BS° > 0) the dissolution process is driven by the entropy; whereas, from this composition up to neat ethanol (ΔA → BG° b 0, ΔA → BH° b 0, and ΔA → BS° b 0) the dissolution process is enthalpy-driven. Nevertheless, the molecular events involved on drug dissolution processes are unclear because of the lack of information about structural effects in this binary alcoholic system. 3.6. Enthalpy–entropy compensation of solution process of IMC According to the literature, the making of weighted graphs of ΔsolnH° as a function of ΔsolnG° at mean harmonic temperature allows us to observe similar mechanisms for the solution process according to the tendencies obtained [30]. In this context, Fig. 5 shows fully that IMC in the ethanol + propylene glycol solvent system exhibits non-linear ΔsolnH° vs. ΔsolnG° compensation with negative slope if an interval from neat propylene glycol to 0.70 in mass fraction of ethanol is considered (near to 0.80 in mole fraction of ethanol), whereas from this ethanol proportion to neat ethanol, a positive slope is obtained. According to this graph it follows that the driving function for IMC solubility is the entropy in the first case, while in the second case, the driving function is the enthalpy.
Fig. 4. Apparent thermodynamic quantities of mixing of indomethacin in ethanol + propylene glycol mixtures at 303.0 K. ●: ΔmixG°; ■: ΔmixH°; ▲: TΔmixS°.
Table 5 Apparent thermodynamic functions of transfer of indomethacin from more polar solvents to less polar solvents in ethanol + propylene glycol mixtures at 303.0 K.a wEtOHb A
B
0.00 0.70
0.70 1.00
ΔA → BG°/ kJ mol−1
ΔA → BH°/ kJ mol−1
ΔA → BS°/ J mol−1 K−1
TΔA → BS°/ kJ mol−1
−1.24 (0.07) −0.59 (0.06)
4.2 (1.0) −7.0 (0.3)
17.9 (2.2) −21.0 (0.8)
5.4 (0.7) −6.37 (0.25)
a
Values in parentheses are standard deviations. wEtOH is the mass fraction of ethanol in the cosolvent mixtures free of indomethacin; A and B are the more polar and less polar media, respectively. b
Nevertheless, the molecular events involved in the dissolution of this drug in this binary system are unclear as was already said but it is conjecturable that the enthalpy driving in ethanol-rich mixtures could be due to the energy requirement to separate the molecules of each individual solvent to accommodate the drug molecules. On the other hand, a similar compensation plot has been reported for this drug in ethanol + water mixtures, with a maximum in 0.50 in mass fraction of ethanol. In that case the entropy driving in water-rich mixtures was attributed to hydrophobic hydration of the non-polar moieties of IMC [9]. The compensation behavior obtained for IMC is different than those reported for acetaminophen and triclocarban, which were also non-linear, and is also different than those reported for ibuprofen and naproxen, which were almost linear [4–6]. In this way, the almost linear compensation of ibuprofen solubility in this solvent mixture was explained in terms of the same mechanism for dissolution process independent of the mixture composition because non-structural change is observed in the solvent mixture [31]. Nevertheless, this fact is objectionable in the cases of IMC, acetaminophen and triclocarban. By comparing the IMC behavior with other analgesic drugs it is interesting to note that IMC and naproxen solubility parameters are the same (20.9 MPa1/2) being greater than the one of ibuprofen (19.4 MPa1/2) but IMC exhibit two trends, whereas, naproxen exhibits only one trend with negative slope and ibuprofen also exhibits only one trend but with positive slope [5], although the reasons for this results are not clear. On the other hand, it is also interesting to note that when ΔsolnH° vs. TΔsolnS° coordinates are evaluated (Fig. 6) two linear trends with positive slopes are observed, i.e. for the region 0.00 ≤ wEtOH ≤ 0.70 the equation ΔsolnH° = 0.782 (±0.008) × TΔsolnS° + 21.87 (±0.25), with r2 adjusted: 0.9993 and typical error: 0.0438 was obtained; whereas, for the region 0.70 ≤ wEtOH ≤ 1.00 the equation ΔsolnH° = 1.079 (± 0.028) × TΔsolnS° + 11.3 (± 0.9), with r 2 adjusted: 0.9980 and typical error: 0.1419, was obtained. In similar way to that reported in the literature for other drugs in different aqueous systems [10,32–35], this result also demonstrates that entropy-driving is observed in the propylene glycol-rich mixtures and enthalpy-driving in
Fig. 5. ΔsolnH° vs. ΔsolnG° enthalpy–entropy compensation plot for solubility of indomethacin in ethanol + propylene glycol mixtures at 303.0 K. Points correspond to mass fractions of ethanol in the mixtures.
E.A. Cantillo et al. / Journal of Molecular Liquids 181 (2013) 62–67
Fig. 6. ΔsolnH° vs. TΔsolnS° enthalpy–entropy compensation plot for solubility of indomethacin in ethanol + propylene glycol mixtures at 303.0 K. Points correspond to mass fractions of ethanol in the mixtures.
the ethanol-rich ones. This conclusion is based on the slope values obtained in each case, i.e. lower than 1.00 for entropy-driving and greater than 1.00 for enthalpy-driving. 4. Conclusions From all topics discussed previously it can be concluded that the solution process of IMC in ethanol + propylene glycol mixtures is variable depending on the solvent composition. Non-linear enthalpy– entropy compensation was found for this drug in this binary system. In this context, entropy–driving was found for propylene glycol-rich mixtures (0.00 b wEtOH b 0.70) whereas, for ethanol-rich mixtures (0.70 ≤ wEtOH ≤ 1.00) enthalpy-driving was found; nevertheless, the molecular events involved in the dissolution of this drug in this solvent system are unclear. Ultimately, it can be stated that the data presented in this report expand the physicochemical information about analgesic drugs in alcoholic solutions. Acknowledgments We thank the Department of Pharmacy of the Universidad Nacional de Colombia for facilitating the equipment and laboratories used. References [1] R.B. Raffa, in: A.R. Gennaro (Ed.), 21st ed., Lippincott, Williams & Wilkins, Philadelphia, 2005.
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