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Modeling the solubility and preferential solvation of gallic acid in cosolvent + water mixtures
Modelling the solubility and preferential solvation of gallic acid in cosolvent + water mixtures Abolghasem Jouyban, William E. Acree Jr., Fleming Mart´ınez PII: DOI: Reference:
S0167-7322(16)32567-3 doi:10.1016/j.molliq.2016.10.018 MOLLIQ 6422
To appear in:
Journal of Molecular Liquids
Received date: Revised date: Accepted date:
2 September 2016 28 September 2016 4 October 2016
Please cite this article as: Abolghasem Jouyban, William E. Acree Jr., Fleming Mart´ınez, Modelling the solubility and preferential solvation of gallic acid in cosolvent + water mixtures, Journal of Molecular Liquids (2016), doi:10.1016/j.molliq.2016.10.018
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ACCEPTED MANUSCRIPT Short communication
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Abolghasem Jouyban a,b, William E. Acree Jr.c,,*, Fleming Martínez d
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Modelling the solubility and preferential solvation of gallic acid in cosolvent + water mixtures
a
Pharmaceutical Analysis Research Center and Faculty of Pharmacy, Tabriz University of Medical
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Sciences, Tabriz 51664, Iran b
Kimia Idea Pardaz Azarbayjan (KIPA) Science Based Company, Tabriz University of Medical
Sciences, Tabriz 51664, Iran
Department of Chemistry, University of North Texas, Denton, TX 76203-5070, USA
d
Grupo de Investigaciones Farmacéutico-Fisicoquímicas, Departamento de Farmacia, Facultad de
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c
Ciencias, Universidad Nacional de Colombia –Sede Bogotá, Cra. 30 No. 45-03, Bogotá D.C.,
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Colombia.
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*E-mail address: [email protected]
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ABSTRACT
The aim of this communication was to expand the results of numerical analyses performed by Dali et
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al. on their experimental solubility of gallic acid in aqueous mixtures of acetonitrile, 1-propanol and 2-propanol at different temperatures, in terms of the solubility data modeling according to the Jouyban-Acree model and also the evaluation of the preferential solvation of this compound by
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organic solvents and water in the saturated mixtures based on the inverse Kirkwood-Buff integrals.
Keywords: Gallic acid, Cosolvent + water mixtures, Jouyban-Acree model, Preferential solvation, IKBI.
1. Introduction In a recent paper, Dali et al. [1] reported the experimental solubility of gallic acid in aqueous mixtures of acetonitrile, 1-propanol and 2-propanol at different temperatures along with some numerical analyses. Despite of a number of mistypes in the reported solubility data in Table 2 of the original paper [1] and a number of outlier data points, the generated solubility data extends the available
solubility
database
of
pharmaceuticals
[2]
and
could
be
used
in
the
pharmaceutical/chemical industry. The aim of this communication is merely to expand the results of numerical analyses in terms of the solubility data modeling according to a combined version of the 1
ACCEPTED MANUSCRIPT Jouyban-Acree model [3] + the van’t Hoff model and also the evaluation of the preferential solvation of gallic acid by both cosolvents and water in the saturated mixtures based on the inverse Kirkwood-Buff integrals [4]. These complementary analyses provide trained versions of the cosolvency models for accurate prediction of gallic acid solubility in the investigated solvent
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mixtures at different temperatures and more information on the dissolution process of gallic acid in
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the investigated solutions.
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2. Results and Discussion
The solubility of gallic acid at various temperatures was mathematically represented by
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Apelblat equation in the original article [1]. These equations are represented as:
B C ln T T
(1)
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ln x A
where x is the mole fraction solubility, T is the absolute temperature of the solution, A, B and C are
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deviation (RAD) calculated by:
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the model constants. The accuracy of the computations was evaluated using the relative mean
(2)
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x cal x 100 RAD x N
where N is the number of experimental data points and x cal is the correlated solubility. Dali et al.
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presented the solubility data using the models correlating the solubility data in a given solvent at various temperatures. There are a number of data points producing the percentage errors of >10 in Dali et al. computations using Apleblat equation which could be considered as outliers and need to be re-determined prior to further numerical analyses. For binary solvent mixtures, the Apelblat model should be trained for each solvent composition and there is no possibility to interpolate the solubility data at any composition and temperature of interest. To represent both effects of temperature and solvent composition on the solubility of gallic acid, one may employ a combination of van’t Hoff and Jouyban-Acree models [5,6] as: n J b b i ln xm,T m1 a1 1 m2 a2 2 m1m2 i m1 m2 T T i 0 T
(3).
2
ACCEPTED MANUSCRIPT where x m ,T is the solubility in the mixed solvent at temperature T. The two a terms (i.e. a1 and a2), and two b terms (i.e. b1 and b2) are the constants of the van’t Hoff equation which can be calculated by regressing the experimental solubility data in the mono-solvents against 1/T. The J i terms which
b1 b m2 a 2 2 T T
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intercept least square analysis of ln x m,T m1 a1
T
are the model constants of the Jouyban-Acree model could be computed for n = 2 using a no
m1 m2 , against T
m m m m2 m1 m2 m1 m2 and 1 2 1 . The J terms for representing solubility data of drugs in T T
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2
cosolvent + water mixtures were computed using the experimental solubility data of gallic acid at
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various temperatures and the constants were used to back-calculate the solubility data. The constants and the MPD values are listed in Table 1. It should be noted that we excluded the
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outliers in our computations.
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***Table 1***
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The inverse Kirkwood-Buff integral equations are given by the following general expression:
rcor
Gi ,3 ( g i ,3 1)4r 2 dr 0
(4)
Here gi,3 is the pair correlation function for the molecules of the solvent i in the cosolvent (1) + water
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(2) mixtures around the solute gallic acid (3), r is the distance between the centers of the molecules of gallic acid (3) and those of cosolvent (1) or water (2), and rcor is a correlation distance for which gi,3 (r > rcor) ≈ 1. Thus, for all distances from r > rcor up to infinite, the value of the integral is essentially zero. Thus, the numerical results are expressed in terms of the preferential solvation parameters δxi,3 for gallic acid in solution by each solvent component in the binary solvent mixtures [4, 7]. The preferential solvation parameter of gallic acid (compound 3) by the cosolvent (compound 1) in cosolvent (1) + water (2) mixtures is defined as [4, 7]: L x1,3 x1,3 x1 x2,3
(5)
L where x1,3 is the local mole fraction of cosolvent (1) in the environment near to gallic acid (3) and x1
is the bulk mole fraction composition of cosolvent (1) in the initial binary solvent. If x1,3 > 0 then 3
ACCEPTED MANUSCRIPT the solute is preferentially solvated by cosolvent (1); on the contrary, if this parameter is < 0 the solute is preferentially solvated by water (2). Values of x1,3 are obtainable from the inverse Kirkwood-Buff integrals for the individual solvent components analyzed in terms of some
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x1 x2 G1,3 G2,3 x1G1,3 x2G2,3 Vcor
(6)
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x1,3
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thermodynamic quantities as shown in the following equations [4, 7, 8]:
With,
(7)
G2,3 RT T V3 x1V1 D / Q
(8)
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G1,3 RT T V3 x2V2 D / Q
1/ 3
0.085
3
(9)
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L L Vcor 2522.5 r3 0.1363 x1,3 V1 x2,3 V2
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As has been previously described [7, 8], in these equations κT is the isothermal compressibility of the cosolvent (1) + water (2) solvent mixtures (which is calculated as an additive property by using the
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mixtures compositions and the reported values for neat solvents), V1 and V2 are the partial molar volumes of the solvents in the mixtures, similarly, V3 is the partial molar volume of gallic acid in these mixtures. The function D (Eqn. (10)) is the derivative of the standard molar Gibbs energies of
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transfer of gallic acid from neat water (2) to cosolvent (1) + water (2) mixtures with respect to the solvent composition. The function Q (Eqn. (11)) involves the second derivative of the excess molar Gibbs energy of mixing of the two solvents ( G1Exc2 ) with respect to the water proportion in the mixtures [7, 8]. Vcor is the correlation volume and r3 is the molecular radius of gallic acid calculated by means of Eqn. (12) with NAv as the Avogadro’s number. o tr G3,2 1 2 D x 1 T , p
2 G1Exc 2 Q RT x1 x2 2 x 2
(10)
T , p
(11)
4
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3 10 21V3 r3 4 N Av
(12)
Definitive correlation volume requires iteration because it depends on the local mole fractions
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L recalculate x1,3 until a non-variant value of Vcor is obtained.
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around the solute. This iteration is done by replacing x1,3 and Vcor in the Eqns. (5), (6) and (9) to
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Figure 1 shows the Gibbs energy of transfer behavior of gallic acid (3) from neat water (2) to all cosolvent (1) + water (2) mixtures at 298.15 K. These values were calculated from the mole
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fraction drug solubility data reported by Dali et al. [1], by using the following expression:
x3,2 o tr G3,2 1 2 RT ln x 3,1 2
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(13)
o tr G3,2 1 2 values were correlated according to polynomial presented as Eqn. (14). The obtained
D
coefficients are presented in Table 2.
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o 2 3 tr G3,2 1 2 a bx1 cx1 dx1
(14)
*** Fig. 1 and Table 2***
Thus, D values reported in Tables 3 to 5 were calculated from the first derivative of the
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respective polynomial models as: D b 2cx1 3dx12 , with the constants reported in table 2, and solved according to the cosolvent mixtures composition. For 1-propanol (1) + water (2) mixtures the Q, RTT, V1 and V2 values were taken from the literature [9]. On the other hand, for acetonitrile (1) + water (2) and 2-propanol (1) + water (2) mixtures, the values of Q were calculated from excess Gibbs energies (expressed in J mol–1), which were in turn, calculated at 298.15 K respectively from Eqns. (15) and (16), as described by Marcus [4]:
2 G1Exc 2 x1 (1 x1 ) 5253 639(1 2 x1 ) 1316(1 2 x1 )
2 G1Exc 2 x1 (1 x1 ) 3843 984(1 2 x1 ) 98(1 2 x1 )
(15)
(16)
5
ACCEPTED MANUSCRIPT For these two binary systems, the RTT values were calculated by assuming additive mixing with the reported T values for acetonitrile (1.070 GPa–1), 2-propanol (1.332 GPa–1) and water (0.457 GPa–1) at 298.15 K [10]. In similar way, the partial molar volumes of both solvents in the mixtures were calculated
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from the reported density values of the cosolvent (1) + water (2) mixtures at 298.15 K [11, 12], by
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using Eqns. (17) and (18). In these equations V is the molar volume of the mixtures calculated as V = is 18.02 g mol–1 for water [13].
dV dx1
(17)
dV dx1
(18)
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V 1 V x2
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(x1·M1 + x2·M2)/. Here, M1 is 41.05 g mol–1 for acetonitrile and 60.10 g mol–1 for 2-propanol and M2
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V 2 V x1
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The Q, RTT, V1 and V2 values for acetonitrile (1) + water (2) and 2-propanol (1) + water (2)
***Tables 3 to 5***
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mixtures are shown in Tables 3 and 5.
Because no partial molar volumes of gallic acid (3) in these mixtures are reported in the literature, in this research this property is considered as similar to that for the pure compound as a good approximation, in this way, the molar volume of gallic acid (3) was calculated from the molar
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mass (170.12 g mol–1) and density (1.694 g cm–3) as 100.4 cm3 mol–1 [13, 14]. G1,3 and G2,3 values shown in Tables 3 to 5 are negative in all cases indicating that gallic acid exhibits affinity for both solvents in all the mixtures. Solute radius value (r3) was calculated as 0.341 nm. The correlation volume was iterated three times by using Eqns. (5), (6) and (9) to obtain the values reported in Table 3 to 5. These tables also show the preferential solvation parameters of gallic acid (3) by all the cosolvents (1), x1,3. Figure 2 shows that the values of δx1,3 vary non-linearly with the cosolvent (1) proportion in all the aqueous mixtures. Addition of cosolvent (1) makes negative the δx1,3 values of gallic acid (3) from the pure water to the mixture x1 = 0.26 for acetonitrile (1) + water (2) and x1 = 0.19 for 1propanol (or 2-propanol) (1) + water (2) systems. Maximum negative values are obtained in the mixture x1 = 0.15 (with δx1,3 = –5.53 x 10–2) for acetonitrile (1) + water (2) and x1 = 0.10 (with δx1,3 = –1.15 x 10–2 and –1.38 x 10–2) for 1-propanol (1) + water (2) and 2-propanol (1) + water (2) mixtures, respectively. 6
ACCEPTED MANUSCRIPT *** Fig. 2***
In the 1-propanol (or 2-propanol) (1) + water (2) mixtures with composition 0.19 < x1 <
T
1.00, the δx1,3 values are positive indicating preferential solvation of gallic acid by these alcohols.
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The cosolvent action to increase the solute solubility could be associated to the breaking of the ordered structure of water around the non-polar moieties of gallic acid which increases the solvation
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of this solute exhibiting maximum values in x1 = 0.45 (δx1,3 = 0.1157) for 1-propanol (1) + water (2) mixtures and x1 = 0.55 (δx1,3 = 0.1043) for 2-propanol (1) + water (2) mixtures. It is conjecturable that in 0.19 < x1 < 1.00 region gallic acid is acting as Lewis acid with both alcohols’ molecules
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because these cosolvent are more basic than water as described by the respective Kamlet-Taft hydrogen bond acceptor parameters, as follows: β = 0.90 for 1-propanol, 0.84 for 2-propanol and 0.47 for water [10, 15]. It is noteworthy that some differences in the magnitudes of preferential
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solvation parameters and the mixtures compositions of δx1,3 maximum positive values were observed, although the differences in the cosolvent polarities are no so high as described by the Hildebrand solubility parameters, i.e. 24.5 MPa1/2 for 1-propanol and 23.5 MPa1/2 for 2-propanol,
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being 1-propanol slightly more polar [16].
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In the case of acetonitrile (1) + water (2) mixtures the exhibited behavior in cosolvent-rich mixtures is erratic because even negative δx1,3 values are observed in the region 0.67 < x1 < 0.83
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which could be due to negative Q values observed in these mixtures as a consequence of the highly positive excess Gibbs energy of mixing (Table 3). Similar behaviors have been reported with other compounds in different aqueous solvent mixtures also exhibiting high positive excess Gibbs energies of mixing [9]. However, as a qualitative result for acetonitrile (1) + water (2) mixtures in the region
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0.26 < x1 < 1.00, the δx1,3 positive values could be attributed to polarization effects because water is more acidic and basic than acetonitrile and thus the preferential solvation of gallic acid by acetonitrile molecules could not be due to specific Lewis-acid base interactions [10]. In conclusion, further numerical analyses for modeling the solubility and preferential solvation of gallic acid (3) in several cosolvent (1) + water (2) mixtures were provided. As it is well known, all these sorts of correlations and predicting models are required in the pharmaceutical and chemical industries to save time and money in the optimization of the solubilization and/or crystallization process designs [17, 18].
References
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I. Dali, A. Aydi, C.C. Alberto, Z.A. Wust, A. Manef, Correlation and semi-empirical modeling of solubility of gallic acid in different pure solvents and in binary solvent mixtures of propan-1-ol + water, propan-2-ol + water and acetonitrile + water from (293.2 to 318.2) K. J. Mol. Liq. 222 (2016) 503-519.
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sulfamethazine in ethanol + water solvent mixtures according to the IKBI method, J. Mol. Liq. 193 (2014) 152-159. [9]
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http://dx.doi.org/10.1080/00319104.2016.1218494. [10]
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N. van Meurs, G. Somsen, Excess and apparent molar volumes of mixtures of water and acetonitrile between 0 and 25°C, J. Solution Chem. 22 (1993) 427-436.
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F-M. Pang, Ch-E. Seng, Tj.-T. Teng, M.H. Ibrahim, Densities and viscosities of aqueous solutions of 1-propanol and 2-propanol at temperatures from 293.15 K to 333.15 K, J. Mol. Liq. 136 (2007) 71-78.
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D.R. Lide (Editor-in-Chief), CRC Handbook of Chemistry and Physics, 84th ed., Boca Raton, FL, 2003, p. 3-548.
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M.J. Kamlet, R.W. Taft, The solvatochromic comparison method. I. The beta-scale of solvent hydrogen-bond acceptor (HBA) basicities, J. Am. Chem. Soc. 98 (1976) 377-383.
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A. Barton, Handbook of Solubility Parameters and Other Cohesion Parameters, 2nd ed., CRC Press, New York, 1991. A. Jouyban, F. Martinez, W.E. Acree Jr., Further calculations on solubility of 3-amino-1-
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adamantanol in ethanol + water binary solvent mixtures at various temperatures, J. Mol. Liq. 219 (2016) 211-215.
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F. Martínez, A. Jouyban, W.E. Acree Jr., Further numerical analysis on the solubility of ibrutinib in ethanol + water mixtures at different temperatures, J. Mol. Liq. 218 (2016) 35-
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38.
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[18]
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ACCEPTED MANUSCRIPT Table 1. The model constants for van’t Hoff and Jouyban-Acree models and RAD values for the back-calculated solubility data of gallic acid in solvent 1 + water mixtures at various temperatures b1 -836.887 -808.362 -803.938
a2 7.877 7.877 7.877
b2 -4272.542 -4272.542 -4272.542
J0 1166.692 1087.465 1157.510
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a1 -0.571 -0.474 -0.659
J1 -856.302 -895.713 -804.700
J2 693.851 724.246 798.406 Overall
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Solvent 1 Acetonitrile 1-Propanol 2-Propanol
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Table 2. Equation (14) parameters of gallic acid (3) in cosolvent (1) + water (2) mixtures at 298.15 K. System a a b c d r2 ACN + W –0.03 –25.02 28.99 –11.80 0.9974 1-PrOH + W –0.04 –25.46 30.01 –12.88 0.9971 2-PrOH + W –0.05 –25.02 28.83 –11.74 0.9966 a ACN is acetonitrile, 1-PrOH is 1-propanol, 2-PrOH is 1-propanol, and W is water.
10
RAD 9.9 9.6 9.3 9.6
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–281.7 –327.7 –377.3 –412.3 –410.7 –370.7 –314.5 –263.1 –224.1 –197.2 –180.4 –172.7 –178.0 –230.3 230.1 –35.5 –23.9 –120.8 –102.3 –99.1 –97.8
–99.3 –132.7 –186.2 –256.9 –324.4 –364.2 –372.7 –363.9 –351.8 –345.2 –350.7 –380.0 –470.5 –865.0 2300.9 489.6 827.2 –499.2 –220.1 –168.5 –149.5
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18.07 17.99 17.94 17.88 17.79 17.69 17.58 17.46 17.35 17.24 17.13 17.04 16.97 16.93 16.91 16.92 16.97 17.06 17.20 17.39 17.63
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49.46 50.01 50.56 51.03 51.44 51.79 52.08 52.32 52.52 52.67 52.78 52.86 52.91 52.94 52.95 52.95 52.93 52.91 52.89 52.88 52.87
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1.133 1.209 1.285 1.361 1.437 1.513 1.589 1.665 1.741 1.817 1.893 1.969 2.045 2.121 2.196 2.272 2.348 2.424 2.500 2.576 2.652
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2.479 1.661 1.137 0.830 0.677 0.622 0.617 0.626 0.621 0.586 0.510 0.396 0.253 0.102 –0.027 –0.097 –0.059 0.146 0.584 1.333 2.479
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–25.02 –22.21 –19.58 –17.12 –14.84 –12.74 –10.81 –9.06 –7.49 –6.09 –4.88 –3.83 –2.97 –2.28 –1.77 –1.44 –1.28 –1.30 –1.50 –1.87 –2.43
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00
584 601 617 639 676 728 775 814 848 879 910 943 985 1075 841 961 973 1093 1097 1119 1143
0.00 –2.02 –4.17 –5.53 –4.13 –0.34 2.91 4.72 5.60 6.10 6.61 7.57 10.18 23.18 –25.70 –9.32 –12.17 5.27 1.08 0.32 0.00
a
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D
x1 is the mole fraction of acetonitrile (1) in the acetonitrile (1) + water (2) mixtures free of gallic acid (3).
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x1 a
Table 3. Some properties associated to preferential solvation of gallic acid (3) in acetonitrile (1) + water (2) mixtures at 298.15 K. 100 D/ Q/ V1 / V2 / G1,3 / G2,3 / Vcor / RT T / kJ mol–1 kJ mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 x1,3
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ACCEPTED MANUSCRIPT Table 4. Some properties associated to preferential solvation of gallic acid (3) in 1-propanol (1) + water (2) mixtures at 298.15 K.
T
Vcor / cm3 mol–1 584 622 670 721 776 836 903 976 1046 1094 1123 1147 1176 1210 1249 1295 1346 1381 1392 1416 1450
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G2,3 / cm3 mol–1 –99.3 –127.8 –152.3 –181.2 –220.3 –276.2 –355.0 –452.7 –534.6 –548.6 –495.6 –426.4 –375.3 –353.3 –368.9 –444.2 –608.9 –694.5 –481.7 –305.4 –221.4
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G1,3 / cm3 mol–1 –284.9 –234.9 –217.5 –213.1 –216.7 –226.6 –241.0 –253.5 –251.1 –225.6 –189.5 –159.4 –140.1 –129.1 –124.2 –123.9 –126.5 –121.4 –107.5 –100.4 –97.9
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0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00
D/ kJ mol–1 –25.46 –22.56 –19.84 –17.33 –15.00 –12.87 –10.93 –9.19 –7.64 –6.28 –5.11 –4.14 –3.36 –2.77 –2.38 –2.18 –2.17 –2.36 –2.74 –3.31 –4.08
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x1 a
100 x1,3 0.00 –1.04 –1.15 –0.76 0.10 1.62 4.12 7.64 10.89 11.57 9.80 7.61 5.99 5.09 4.89 5.51 6.87 6.23 2.70 0.75 0.00
a
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D
x1 is the mole fraction of 1-propanol (1) in the 1-propanol (1) + water (2) mixtures free of gallic acid (3).
12
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–281.0 –257.2 –238.8 –224.2 –212.6 –203.3 –196.0 –190.3 –186.0 –182.8 –179.7 –174.1 –162.0 –142.4 –122.8 –110.3 –103.9 –100.9 –99.2 –98.1 –97.1
–99.3 –132.5 –162.3 –190.4 –218.3 –247.5 –279.6 –316.3 –360.0 –412.7 –473.8 –531.7 –551.4 –492.0 –378.6 –279.9 –220.4 –190.9 –178.6 –175.5 –177.3
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18.01 17.98 17.92 17.82 17.68 17.53 17.35 17.16 16.97 16.78 16.59 16.41 16.25 16.12 16.02 15.95 15.92 15.94 16.02 16.15 16.36
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71.21 72.12 72.94 73.65 74.28 74.82 75.28 75.67 76.00 76.26 76.47 76.63 76.75 76.83 76.88 76.90 76.91 76.91 76.90 76.89 76.88
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1.13 1.24 1.35 1.46 1.57 1.68 1.78 1.89 2.00 2.11 2.22 2.33 2.43 2.54 2.65 2.76 2.87 2.98 3.09 3.19 3.30
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2.479 2.402 2.262 2.074 1.852 1.610 1.359 1.113 0.882 0.677 0.508 0.385 0.315 0.307 0.367 0.503 0.719 1.021 1.412 1.897 2.479
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–25.02 –22.22 –19.60 –17.16 –14.89 –12.80 –10.89 –9.15 –7.59 –6.20 –4.99 –3.96 –3.10 –2.42 –1.92 –1.59 –1.44 –1.46 –1.66 –2.03 –2.59
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00
583 621 668 721 778 836 895 953 1012 1071 1129 1184 1226 1250 1267 1291 1322 1359 1397 1436 1474
0.00 –1.23 –1.38 –0.82 0.16 1.38 2.74 4.21 5.79 7.47 9.16 10.43 10.29 8.07 5.03 2.79 1.56 0.92 0.55 0.28 0.00
a
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D
x1 is the mole fraction of 2-propanol (1) in the 2-propanol (1) + water (2) mixtures free of gallic acid (3).
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x1 a
Table 5. Some properties associated to preferential solvation of gallic acid (3) in 2-propanol (1) + water (2) mixtures at 298.15 K. 100 D/ Q/ V1 / V2 / G1,3 / G2,3 / Vcor / RT T / kJ mol–1 kJ mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 x1,3
13
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D
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Figure 1. Gibbs energy of transfer of gallic acid (3) from neat water (2) to cosolvent (1) + water (2) mixtures at 298.15 K. ○: acetonitrile (1) + water; □: 1-propanol (1) + water (2); : 2-propanol (1) + water (2). Lines correspond to the best regular polynomials correlating the data.
Figure 2. δx1,3 values of gallic acid (3) in cosolvent (1) + water (2) mixtures at 298.15 K. ○: acetonitrile (1) + water; □: 1-propanol (1) + water (2); : 2-propanol (1) + water (2). Lines correspond to IKBI results according to Eq. (6).
14
ACCEPTED MANUSCRIPT HIGHLIGHTS
Modelling the solubility and preferential solvation of gallic acid in cosolvent + water
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mixtures
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Abolghasem Jouyban a,b, William E. Acree Jr.c,,*, Fleming Martínez d
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D
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Jouyban-Acree-van’t Hoff equations given for estimating gallic acid in aqueousacetonitrile mixtures Jouyban-Acree-van’t Hoff equations given for estimating gallic acid in aqueouspropanol mixtures Preferential solvation of gallic acid in aqueous-organic mixtures based on inverse Kirkwood-Buff integrals
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S0167-7322(16)32567-3 doi:10.1016/j.molliq.2016.10.018 MOLLIQ 6422
To appear in:
Journal of Molecular Liquids
Received date: Revised date: Accepted date:
2 September 2016 28 September 2016 4 October 2016
Please cite this article as: Abolghasem Jouyban, William E. Acree Jr., Fleming Mart´ınez, Modelling the solubility and preferential solvation of gallic acid in cosolvent + water mixtures, Journal of Molecular Liquids (2016), doi:10.1016/j.molliq.2016.10.018
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ACCEPTED MANUSCRIPT Short communication
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Abolghasem Jouyban a,b, William E. Acree Jr.c,,*, Fleming Martínez d
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Modelling the solubility and preferential solvation of gallic acid in cosolvent + water mixtures
a
Pharmaceutical Analysis Research Center and Faculty of Pharmacy, Tabriz University of Medical
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Sciences, Tabriz 51664, Iran b
Kimia Idea Pardaz Azarbayjan (KIPA) Science Based Company, Tabriz University of Medical
Sciences, Tabriz 51664, Iran
Department of Chemistry, University of North Texas, Denton, TX 76203-5070, USA
d
Grupo de Investigaciones Farmacéutico-Fisicoquímicas, Departamento de Farmacia, Facultad de
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c
Ciencias, Universidad Nacional de Colombia –Sede Bogotá, Cra. 30 No. 45-03, Bogotá D.C.,
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Colombia.
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*E-mail address: [email protected]
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ABSTRACT
The aim of this communication was to expand the results of numerical analyses performed by Dali et
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al. on their experimental solubility of gallic acid in aqueous mixtures of acetonitrile, 1-propanol and 2-propanol at different temperatures, in terms of the solubility data modeling according to the Jouyban-Acree model and also the evaluation of the preferential solvation of this compound by
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organic solvents and water in the saturated mixtures based on the inverse Kirkwood-Buff integrals.
Keywords: Gallic acid, Cosolvent + water mixtures, Jouyban-Acree model, Preferential solvation, IKBI.
1. Introduction In a recent paper, Dali et al. [1] reported the experimental solubility of gallic acid in aqueous mixtures of acetonitrile, 1-propanol and 2-propanol at different temperatures along with some numerical analyses. Despite of a number of mistypes in the reported solubility data in Table 2 of the original paper [1] and a number of outlier data points, the generated solubility data extends the available
solubility
database
of
pharmaceuticals
[2]
and
could
be
used
in
the
pharmaceutical/chemical industry. The aim of this communication is merely to expand the results of numerical analyses in terms of the solubility data modeling according to a combined version of the 1
ACCEPTED MANUSCRIPT Jouyban-Acree model [3] + the van’t Hoff model and also the evaluation of the preferential solvation of gallic acid by both cosolvents and water in the saturated mixtures based on the inverse Kirkwood-Buff integrals [4]. These complementary analyses provide trained versions of the cosolvency models for accurate prediction of gallic acid solubility in the investigated solvent
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mixtures at different temperatures and more information on the dissolution process of gallic acid in
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the investigated solutions.
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2. Results and Discussion
The solubility of gallic acid at various temperatures was mathematically represented by
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Apelblat equation in the original article [1]. These equations are represented as:
B C ln T T
(1)
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ln x A
where x is the mole fraction solubility, T is the absolute temperature of the solution, A, B and C are
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deviation (RAD) calculated by:
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the model constants. The accuracy of the computations was evaluated using the relative mean
(2)
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x cal x 100 RAD x N
where N is the number of experimental data points and x cal is the correlated solubility. Dali et al.
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presented the solubility data using the models correlating the solubility data in a given solvent at various temperatures. There are a number of data points producing the percentage errors of >10 in Dali et al. computations using Apleblat equation which could be considered as outliers and need to be re-determined prior to further numerical analyses. For binary solvent mixtures, the Apelblat model should be trained for each solvent composition and there is no possibility to interpolate the solubility data at any composition and temperature of interest. To represent both effects of temperature and solvent composition on the solubility of gallic acid, one may employ a combination of van’t Hoff and Jouyban-Acree models [5,6] as: n J b b i ln xm,T m1 a1 1 m2 a2 2 m1m2 i m1 m2 T T i 0 T
(3).
2
ACCEPTED MANUSCRIPT where x m ,T is the solubility in the mixed solvent at temperature T. The two a terms (i.e. a1 and a2), and two b terms (i.e. b1 and b2) are the constants of the van’t Hoff equation which can be calculated by regressing the experimental solubility data in the mono-solvents against 1/T. The J i terms which
b1 b m2 a 2 2 T T
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intercept least square analysis of ln x m,T m1 a1
T
are the model constants of the Jouyban-Acree model could be computed for n = 2 using a no
m1 m2 , against T
m m m m2 m1 m2 m1 m2 and 1 2 1 . The J terms for representing solubility data of drugs in T T
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2
cosolvent + water mixtures were computed using the experimental solubility data of gallic acid at
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various temperatures and the constants were used to back-calculate the solubility data. The constants and the MPD values are listed in Table 1. It should be noted that we excluded the
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outliers in our computations.
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***Table 1***
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The inverse Kirkwood-Buff integral equations are given by the following general expression:
rcor
Gi ,3 ( g i ,3 1)4r 2 dr 0
(4)
Here gi,3 is the pair correlation function for the molecules of the solvent i in the cosolvent (1) + water
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(2) mixtures around the solute gallic acid (3), r is the distance between the centers of the molecules of gallic acid (3) and those of cosolvent (1) or water (2), and rcor is a correlation distance for which gi,3 (r > rcor) ≈ 1. Thus, for all distances from r > rcor up to infinite, the value of the integral is essentially zero. Thus, the numerical results are expressed in terms of the preferential solvation parameters δxi,3 for gallic acid in solution by each solvent component in the binary solvent mixtures [4, 7]. The preferential solvation parameter of gallic acid (compound 3) by the cosolvent (compound 1) in cosolvent (1) + water (2) mixtures is defined as [4, 7]: L x1,3 x1,3 x1 x2,3
(5)
L where x1,3 is the local mole fraction of cosolvent (1) in the environment near to gallic acid (3) and x1
is the bulk mole fraction composition of cosolvent (1) in the initial binary solvent. If x1,3 > 0 then 3
ACCEPTED MANUSCRIPT the solute is preferentially solvated by cosolvent (1); on the contrary, if this parameter is < 0 the solute is preferentially solvated by water (2). Values of x1,3 are obtainable from the inverse Kirkwood-Buff integrals for the individual solvent components analyzed in terms of some
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x1 x2 G1,3 G2,3 x1G1,3 x2G2,3 Vcor
(6)
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x1,3
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thermodynamic quantities as shown in the following equations [4, 7, 8]:
With,
(7)
G2,3 RT T V3 x1V1 D / Q
(8)
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G1,3 RT T V3 x2V2 D / Q
1/ 3
0.085
3
(9)
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L L Vcor 2522.5 r3 0.1363 x1,3 V1 x2,3 V2
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As has been previously described [7, 8], in these equations κT is the isothermal compressibility of the cosolvent (1) + water (2) solvent mixtures (which is calculated as an additive property by using the
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mixtures compositions and the reported values for neat solvents), V1 and V2 are the partial molar volumes of the solvents in the mixtures, similarly, V3 is the partial molar volume of gallic acid in these mixtures. The function D (Eqn. (10)) is the derivative of the standard molar Gibbs energies of
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transfer of gallic acid from neat water (2) to cosolvent (1) + water (2) mixtures with respect to the solvent composition. The function Q (Eqn. (11)) involves the second derivative of the excess molar Gibbs energy of mixing of the two solvents ( G1Exc2 ) with respect to the water proportion in the mixtures [7, 8]. Vcor is the correlation volume and r3 is the molecular radius of gallic acid calculated by means of Eqn. (12) with NAv as the Avogadro’s number. o tr G3,2 1 2 D x 1 T , p
2 G1Exc 2 Q RT x1 x2 2 x 2
(10)
T , p
(11)
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3 10 21V3 r3 4 N Av
(12)
Definitive correlation volume requires iteration because it depends on the local mole fractions
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L recalculate x1,3 until a non-variant value of Vcor is obtained.
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around the solute. This iteration is done by replacing x1,3 and Vcor in the Eqns. (5), (6) and (9) to
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Figure 1 shows the Gibbs energy of transfer behavior of gallic acid (3) from neat water (2) to all cosolvent (1) + water (2) mixtures at 298.15 K. These values were calculated from the mole
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fraction drug solubility data reported by Dali et al. [1], by using the following expression:
x3,2 o tr G3,2 1 2 RT ln x 3,1 2
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(13)
o tr G3,2 1 2 values were correlated according to polynomial presented as Eqn. (14). The obtained
D
coefficients are presented in Table 2.
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o 2 3 tr G3,2 1 2 a bx1 cx1 dx1
(14)
*** Fig. 1 and Table 2***
Thus, D values reported in Tables 3 to 5 were calculated from the first derivative of the
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respective polynomial models as: D b 2cx1 3dx12 , with the constants reported in table 2, and solved according to the cosolvent mixtures composition. For 1-propanol (1) + water (2) mixtures the Q, RTT, V1 and V2 values were taken from the literature [9]. On the other hand, for acetonitrile (1) + water (2) and 2-propanol (1) + water (2) mixtures, the values of Q were calculated from excess Gibbs energies (expressed in J mol–1), which were in turn, calculated at 298.15 K respectively from Eqns. (15) and (16), as described by Marcus [4]:
2 G1Exc 2 x1 (1 x1 ) 5253 639(1 2 x1 ) 1316(1 2 x1 )
2 G1Exc 2 x1 (1 x1 ) 3843 984(1 2 x1 ) 98(1 2 x1 )
(15)
(16)
5
ACCEPTED MANUSCRIPT For these two binary systems, the RTT values were calculated by assuming additive mixing with the reported T values for acetonitrile (1.070 GPa–1), 2-propanol (1.332 GPa–1) and water (0.457 GPa–1) at 298.15 K [10]. In similar way, the partial molar volumes of both solvents in the mixtures were calculated
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from the reported density values of the cosolvent (1) + water (2) mixtures at 298.15 K [11, 12], by
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using Eqns. (17) and (18). In these equations V is the molar volume of the mixtures calculated as V = is 18.02 g mol–1 for water [13].
dV dx1
(17)
dV dx1
(18)
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V 1 V x2
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(x1·M1 + x2·M2)/. Here, M1 is 41.05 g mol–1 for acetonitrile and 60.10 g mol–1 for 2-propanol and M2
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V 2 V x1
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The Q, RTT, V1 and V2 values for acetonitrile (1) + water (2) and 2-propanol (1) + water (2)
***Tables 3 to 5***
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mixtures are shown in Tables 3 and 5.
Because no partial molar volumes of gallic acid (3) in these mixtures are reported in the literature, in this research this property is considered as similar to that for the pure compound as a good approximation, in this way, the molar volume of gallic acid (3) was calculated from the molar
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mass (170.12 g mol–1) and density (1.694 g cm–3) as 100.4 cm3 mol–1 [13, 14]. G1,3 and G2,3 values shown in Tables 3 to 5 are negative in all cases indicating that gallic acid exhibits affinity for both solvents in all the mixtures. Solute radius value (r3) was calculated as 0.341 nm. The correlation volume was iterated three times by using Eqns. (5), (6) and (9) to obtain the values reported in Table 3 to 5. These tables also show the preferential solvation parameters of gallic acid (3) by all the cosolvents (1), x1,3. Figure 2 shows that the values of δx1,3 vary non-linearly with the cosolvent (1) proportion in all the aqueous mixtures. Addition of cosolvent (1) makes negative the δx1,3 values of gallic acid (3) from the pure water to the mixture x1 = 0.26 for acetonitrile (1) + water (2) and x1 = 0.19 for 1propanol (or 2-propanol) (1) + water (2) systems. Maximum negative values are obtained in the mixture x1 = 0.15 (with δx1,3 = –5.53 x 10–2) for acetonitrile (1) + water (2) and x1 = 0.10 (with δx1,3 = –1.15 x 10–2 and –1.38 x 10–2) for 1-propanol (1) + water (2) and 2-propanol (1) + water (2) mixtures, respectively. 6
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In the 1-propanol (or 2-propanol) (1) + water (2) mixtures with composition 0.19 < x1 <
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1.00, the δx1,3 values are positive indicating preferential solvation of gallic acid by these alcohols.
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The cosolvent action to increase the solute solubility could be associated to the breaking of the ordered structure of water around the non-polar moieties of gallic acid which increases the solvation
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of this solute exhibiting maximum values in x1 = 0.45 (δx1,3 = 0.1157) for 1-propanol (1) + water (2) mixtures and x1 = 0.55 (δx1,3 = 0.1043) for 2-propanol (1) + water (2) mixtures. It is conjecturable that in 0.19 < x1 < 1.00 region gallic acid is acting as Lewis acid with both alcohols’ molecules
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because these cosolvent are more basic than water as described by the respective Kamlet-Taft hydrogen bond acceptor parameters, as follows: β = 0.90 for 1-propanol, 0.84 for 2-propanol and 0.47 for water [10, 15]. It is noteworthy that some differences in the magnitudes of preferential
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solvation parameters and the mixtures compositions of δx1,3 maximum positive values were observed, although the differences in the cosolvent polarities are no so high as described by the Hildebrand solubility parameters, i.e. 24.5 MPa1/2 for 1-propanol and 23.5 MPa1/2 for 2-propanol,
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being 1-propanol slightly more polar [16].
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In the case of acetonitrile (1) + water (2) mixtures the exhibited behavior in cosolvent-rich mixtures is erratic because even negative δx1,3 values are observed in the region 0.67 < x1 < 0.83
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which could be due to negative Q values observed in these mixtures as a consequence of the highly positive excess Gibbs energy of mixing (Table 3). Similar behaviors have been reported with other compounds in different aqueous solvent mixtures also exhibiting high positive excess Gibbs energies of mixing [9]. However, as a qualitative result for acetonitrile (1) + water (2) mixtures in the region
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0.26 < x1 < 1.00, the δx1,3 positive values could be attributed to polarization effects because water is more acidic and basic than acetonitrile and thus the preferential solvation of gallic acid by acetonitrile molecules could not be due to specific Lewis-acid base interactions [10]. In conclusion, further numerical analyses for modeling the solubility and preferential solvation of gallic acid (3) in several cosolvent (1) + water (2) mixtures were provided. As it is well known, all these sorts of correlations and predicting models are required in the pharmaceutical and chemical industries to save time and money in the optimization of the solubilization and/or crystallization process designs [17, 18].
References
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I. Dali, A. Aydi, C.C. Alberto, Z.A. Wust, A. Manef, Correlation and semi-empirical modeling of solubility of gallic acid in different pure solvents and in binary solvent mixtures of propan-1-ol + water, propan-2-ol + water and acetonitrile + water from (293.2 to 318.2) K. J. Mol. Liq. 222 (2016) 503-519.
A. Jouyban, Handbook of Solubility Data for Pharmaceuticals, CRC Press, Florida,
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A. Jouyban-Gharamaleki, W.E. Acree Jr., Comparison of models for describing multiple
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Y. Marcus, Solvent Mixtures: Properties and Selective Solvation, Marcel Dekker, Inc., New York, 2002.
A. Jouyban, M.A.A. Fakhree, W.E. Acree Jr, Comment on “Measurement and Correlation of
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Solubilities of (Z)-2-(2-Aminothiazol-4-yl)-2-methoxyiminoacetic Acid in Different Pure
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Solvents and Binary Mixtures of Water + (Ethanol, Methanol, or Glycol)”. J. Chem. Eng.
F. Sardari, A. Jouyban, A. Solubility of nifedipine in ethanol + water and propylene glycol + water mixtures at (293.2 to 313.2) K. Ind. Eng. Chem. Res., 52 (2013) 14353-14358. Y. Marcus, On the preferential solvation of drugs and PAHs in binary solvent mixtures, J.
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sulfamethazine in ethanol + water solvent mixtures according to the IKBI method, J. Mol. Liq. 193 (2014) 152-159. [9]
F. Martínez, A. Jouyban, W.E. Acree Jr., Solubility of phenobarbital in aqueous cosolvent mixtures revisited: IKBI preferential solvation analysis, Phys. Chem. Liq. (2016). DOI:
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http://dx.doi.org/10.1080/00319104.2016.1218494. [10]
Y. Marcus, The Properties of Solvents, John Wiley & Sons, Chichester, 1998.
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N. van Meurs, G. Somsen, Excess and apparent molar volumes of mixtures of water and acetonitrile between 0 and 25°C, J. Solution Chem. 22 (1993) 427-436.
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F-M. Pang, Ch-E. Seng, Tj.-T. Teng, M.H. Ibrahim, Densities and viscosities of aqueous solutions of 1-propanol and 2-propanol at temperatures from 293.15 K to 333.15 K, J. Mol. Liq. 136 (2007) 71-78.
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S. Budavari, M.J. O’Neil, A. Smith, P.E. Heckelman, J.R. Obenchain Jr., J.A.R. Gallipeau, M.A. D’Arecea (Editors), The Merck Index, An Encyclopedia of Chemicals, Drugs, and Biologicals, 13th ed., Merck & Co., Inc., Whitehouse Station, NJ, 2001.
[14]
D.R. Lide (Editor-in-Chief), CRC Handbook of Chemistry and Physics, 84th ed., Boca Raton, FL, 2003, p. 3-548.
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M.J. Kamlet, R.W. Taft, The solvatochromic comparison method. I. The beta-scale of solvent hydrogen-bond acceptor (HBA) basicities, J. Am. Chem. Soc. 98 (1976) 377-383.
[16]
A. Barton, Handbook of Solubility Parameters and Other Cohesion Parameters, 2nd ed., CRC Press, New York, 1991. A. Jouyban, F. Martinez, W.E. Acree Jr., Further calculations on solubility of 3-amino-1-
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[17]
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adamantanol in ethanol + water binary solvent mixtures at various temperatures, J. Mol. Liq. 219 (2016) 211-215.
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F. Martínez, A. Jouyban, W.E. Acree Jr., Further numerical analysis on the solubility of ibrutinib in ethanol + water mixtures at different temperatures, J. Mol. Liq. 218 (2016) 35-
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38.
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[18]
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ACCEPTED MANUSCRIPT Table 1. The model constants for van’t Hoff and Jouyban-Acree models and RAD values for the back-calculated solubility data of gallic acid in solvent 1 + water mixtures at various temperatures b1 -836.887 -808.362 -803.938
a2 7.877 7.877 7.877
b2 -4272.542 -4272.542 -4272.542
J0 1166.692 1087.465 1157.510
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a1 -0.571 -0.474 -0.659
J1 -856.302 -895.713 -804.700
J2 693.851 724.246 798.406 Overall
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Solvent 1 Acetonitrile 1-Propanol 2-Propanol
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Table 2. Equation (14) parameters of gallic acid (3) in cosolvent (1) + water (2) mixtures at 298.15 K. System a a b c d r2 ACN + W –0.03 –25.02 28.99 –11.80 0.9974 1-PrOH + W –0.04 –25.46 30.01 –12.88 0.9971 2-PrOH + W –0.05 –25.02 28.83 –11.74 0.9966 a ACN is acetonitrile, 1-PrOH is 1-propanol, 2-PrOH is 1-propanol, and W is water.
10
RAD 9.9 9.6 9.3 9.6
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–281.7 –327.7 –377.3 –412.3 –410.7 –370.7 –314.5 –263.1 –224.1 –197.2 –180.4 –172.7 –178.0 –230.3 230.1 –35.5 –23.9 –120.8 –102.3 –99.1 –97.8
–99.3 –132.7 –186.2 –256.9 –324.4 –364.2 –372.7 –363.9 –351.8 –345.2 –350.7 –380.0 –470.5 –865.0 2300.9 489.6 827.2 –499.2 –220.1 –168.5 –149.5
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18.07 17.99 17.94 17.88 17.79 17.69 17.58 17.46 17.35 17.24 17.13 17.04 16.97 16.93 16.91 16.92 16.97 17.06 17.20 17.39 17.63
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49.46 50.01 50.56 51.03 51.44 51.79 52.08 52.32 52.52 52.67 52.78 52.86 52.91 52.94 52.95 52.95 52.93 52.91 52.89 52.88 52.87
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1.133 1.209 1.285 1.361 1.437 1.513 1.589 1.665 1.741 1.817 1.893 1.969 2.045 2.121 2.196 2.272 2.348 2.424 2.500 2.576 2.652
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2.479 1.661 1.137 0.830 0.677 0.622 0.617 0.626 0.621 0.586 0.510 0.396 0.253 0.102 –0.027 –0.097 –0.059 0.146 0.584 1.333 2.479
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–25.02 –22.21 –19.58 –17.12 –14.84 –12.74 –10.81 –9.06 –7.49 –6.09 –4.88 –3.83 –2.97 –2.28 –1.77 –1.44 –1.28 –1.30 –1.50 –1.87 –2.43
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00
584 601 617 639 676 728 775 814 848 879 910 943 985 1075 841 961 973 1093 1097 1119 1143
0.00 –2.02 –4.17 –5.53 –4.13 –0.34 2.91 4.72 5.60 6.10 6.61 7.57 10.18 23.18 –25.70 –9.32 –12.17 5.27 1.08 0.32 0.00
a
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x1 is the mole fraction of acetonitrile (1) in the acetonitrile (1) + water (2) mixtures free of gallic acid (3).
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x1 a
Table 3. Some properties associated to preferential solvation of gallic acid (3) in acetonitrile (1) + water (2) mixtures at 298.15 K. 100 D/ Q/ V1 / V2 / G1,3 / G2,3 / Vcor / RT T / kJ mol–1 kJ mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 x1,3
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ACCEPTED MANUSCRIPT Table 4. Some properties associated to preferential solvation of gallic acid (3) in 1-propanol (1) + water (2) mixtures at 298.15 K.
T
Vcor / cm3 mol–1 584 622 670 721 776 836 903 976 1046 1094 1123 1147 1176 1210 1249 1295 1346 1381 1392 1416 1450
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G2,3 / cm3 mol–1 –99.3 –127.8 –152.3 –181.2 –220.3 –276.2 –355.0 –452.7 –534.6 –548.6 –495.6 –426.4 –375.3 –353.3 –368.9 –444.2 –608.9 –694.5 –481.7 –305.4 –221.4
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G1,3 / cm3 mol–1 –284.9 –234.9 –217.5 –213.1 –216.7 –226.6 –241.0 –253.5 –251.1 –225.6 –189.5 –159.4 –140.1 –129.1 –124.2 –123.9 –126.5 –121.4 –107.5 –100.4 –97.9
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0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00
D/ kJ mol–1 –25.46 –22.56 –19.84 –17.33 –15.00 –12.87 –10.93 –9.19 –7.64 –6.28 –5.11 –4.14 –3.36 –2.77 –2.38 –2.18 –2.17 –2.36 –2.74 –3.31 –4.08
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x1 a
100 x1,3 0.00 –1.04 –1.15 –0.76 0.10 1.62 4.12 7.64 10.89 11.57 9.80 7.61 5.99 5.09 4.89 5.51 6.87 6.23 2.70 0.75 0.00
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x1 is the mole fraction of 1-propanol (1) in the 1-propanol (1) + water (2) mixtures free of gallic acid (3).
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–281.0 –257.2 –238.8 –224.2 –212.6 –203.3 –196.0 –190.3 –186.0 –182.8 –179.7 –174.1 –162.0 –142.4 –122.8 –110.3 –103.9 –100.9 –99.2 –98.1 –97.1
–99.3 –132.5 –162.3 –190.4 –218.3 –247.5 –279.6 –316.3 –360.0 –412.7 –473.8 –531.7 –551.4 –492.0 –378.6 –279.9 –220.4 –190.9 –178.6 –175.5 –177.3
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18.01 17.98 17.92 17.82 17.68 17.53 17.35 17.16 16.97 16.78 16.59 16.41 16.25 16.12 16.02 15.95 15.92 15.94 16.02 16.15 16.36
IP
71.21 72.12 72.94 73.65 74.28 74.82 75.28 75.67 76.00 76.26 76.47 76.63 76.75 76.83 76.88 76.90 76.91 76.91 76.90 76.89 76.88
SC R
1.13 1.24 1.35 1.46 1.57 1.68 1.78 1.89 2.00 2.11 2.22 2.33 2.43 2.54 2.65 2.76 2.87 2.98 3.09 3.19 3.30
NU
2.479 2.402 2.262 2.074 1.852 1.610 1.359 1.113 0.882 0.677 0.508 0.385 0.315 0.307 0.367 0.503 0.719 1.021 1.412 1.897 2.479
MA
–25.02 –22.22 –19.60 –17.16 –14.89 –12.80 –10.89 –9.15 –7.59 –6.20 –4.99 –3.96 –3.10 –2.42 –1.92 –1.59 –1.44 –1.46 –1.66 –2.03 –2.59
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00
583 621 668 721 778 836 895 953 1012 1071 1129 1184 1226 1250 1267 1291 1322 1359 1397 1436 1474
0.00 –1.23 –1.38 –0.82 0.16 1.38 2.74 4.21 5.79 7.47 9.16 10.43 10.29 8.07 5.03 2.79 1.56 0.92 0.55 0.28 0.00
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x1 is the mole fraction of 2-propanol (1) in the 2-propanol (1) + water (2) mixtures free of gallic acid (3).
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Table 5. Some properties associated to preferential solvation of gallic acid (3) in 2-propanol (1) + water (2) mixtures at 298.15 K. 100 D/ Q/ V1 / V2 / G1,3 / G2,3 / Vcor / RT T / kJ mol–1 kJ mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 cm3 mol–1 x1,3
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Figure 1. Gibbs energy of transfer of gallic acid (3) from neat water (2) to cosolvent (1) + water (2) mixtures at 298.15 K. ○: acetonitrile (1) + water; □: 1-propanol (1) + water (2); : 2-propanol (1) + water (2). Lines correspond to the best regular polynomials correlating the data.
Figure 2. δx1,3 values of gallic acid (3) in cosolvent (1) + water (2) mixtures at 298.15 K. ○: acetonitrile (1) + water; □: 1-propanol (1) + water (2); : 2-propanol (1) + water (2). Lines correspond to IKBI results according to Eq. (6).
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Modelling the solubility and preferential solvation of gallic acid in cosolvent + water
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Abolghasem Jouyban a,b, William E. Acree Jr.c,,*, Fleming Martínez d
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Jouyban-Acree-van’t Hoff equations given for estimating gallic acid in aqueousacetonitrile mixtures Jouyban-Acree-van’t Hoff equations given for estimating gallic acid in aqueouspropanol mixtures Preferential solvation of gallic acid in aqueous-organic mixtures based on inverse Kirkwood-Buff integrals
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