- Email: [email protected]
Comments concerning “Study of solute–solvent and solvent–solvent interactions in pure and mixed binary solvents”
Journal of Molecular Liquids 142 (2008) 158–160
Contents lists available at ScienceDirect
Journal of Molecular Liquids j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / m o l l i q
Comments concerning “Study of solute–solvent and solvent–solvent interactions in pure and mixed binary solvents” Abolghasem Jouyban a,⁎, William E. Acree Jr. a b
b
Faculty of Pharmacy and Drug Applied Research Center, Tabriz University (Medical Sciences), Tabriz 51664, Iran Department of Chemistry, University of North Texas, Denton, TX 76203-5070, USA
A R T I C L E
I N F O
Article history: Received 2 February 2008 Received in revised form 1 May 2008 Accepted 12 June 2008 Available online 18 June 2008
A B S T R A C T A number of mathematical equations representing the solute solubility in monosolvent and binary solvent mixtures are discussed. This work is a commentary to the article of Maitra and Baghchi that appeared in this journal. Published by Elsevier B.V.
Keywords: Solubility Modeling Binary solvents
In a recent publication by Maitra and Baghchi that appeared in this journal [1], the solubility of a dye was determined in a couple of pure solvents and also some water–cosolvent mixtures and the observed solubilities described in terms of the mathematical equations. The authors used LSER equations (Eqs. (1) and (2)) for representing the solubility data in pure solvents and classified the solubility profiles in binary solvent mixtures into two groups; i.e. the solubility profiles without any maximum in the logarithm of solubility plot against solvent composition and those with a maximum. The authors represented the solubility behaviour of the first group with Eq. (3) and the second group using Eq. (4). The equations are: log s ¼ −2:72 þ 2:17α−0:99β þ 3:91π⁎−3:98 δ2H =1000 ð1Þ ð2Þ log s ¼ −3:05 þ 1:20α−3:54 δ2H =1000 log s12 ¼ xL1 log s1 þ xL2 log s2
ð3Þ
log s ¼ A þ Bxw þ Cx2w þ Dx3w
ð4Þ
where s is the molar solubility of the solute in the monosolvents, α is hydrogen-bond donation, β is hydrogen-bond acceptance, π⁎ is dipolarity–polarizability descriptor, δ2H is the Hildebrand solubility parameter of the solvents, s12 is the molar solubility in the binary solvent, s1 and s2 are the solubilities in neat solvents 1 and 2, xw is the mole fraction of the water in binary mixtures and A, B, C and D are the model constants [1]. The aim of this communication is not to criticise the
⁎ Corresponding author. E-mail addresses: [email protected] (A. Jouyban), [email protected] (W.E. Acree). 0167-7322/$ – see front matter. Published by Elsevier B.V. doi:10.1016/j.molliq.2008.06.009
work of Maitra and Baghchi, but rather to suggest alternative forms of the mathematical representations, prediction methods and also recall some old references dealing with the equations. Alternative LSER equations for representing the solute solubility data in monosolvents are the Abraham models which provided more accurate calculations. The Abraham model for processes within condensed phases is: log
CS CW
¼cþeEþsSþaAþbBþvV
ð5Þ
and for processes involving gas-to-condensed phase transfer is: log
CS CG
¼cþeEþsSþaAþbBþlL
ð6Þ
where CS and CW are the solute solubility in the organic solvent and water (in mole per liter), respectively, CG is the gas phase concentration of the solute, E is the excess molar refraction, S is dipolarity–polarizability of solute, A denotes the solute's hydrogen-bond acidity, B stands for the solute's hydrogen-bond basicity, V is the McGowan volume of the solute, and L is the logarithm of the solute gas-hexadecane partition coefficient at 298.15 K. In Eqs. (5) and (6)) the coefficients c, e, s, a, b, v and l are the model constants (i.e. solvent's coefficients), which depend upon the solvent system under consideration. Numerical values of the model constants of Eqs. (5) and (6) have been reported in the literature [2] for several water-to-organic solvent and gas-to-organic solvent systems. The main advantage of Eqs. (5) and (6) over Eqs. (1) and (2) is that there is no curve-fitting parameter and the solvent coefficients were reported earlier [2]. The only required parameters for Eqs. (5) and (6) are the solute's Abraham parameters which could be easily computed using the PharmaAlgorithm software [3].
A. Jouyban, W.E. Acree Jr. / Journal of Molecular Liquids 142 (2008) 158–160
It is well known that a solution obeying Raoult's law is known as an ideal solution and its solubility could be calculated from the heat of fusion of the solute (ΔHfm) and the difference in the heat capacities of the solid and its supercooled liquid (ΔCp) using Hildebrand and Scott equation expressed by: log X ¼ −
f ΔHm Tm −T ΔCp Tm −T ΔCp Tm − log þ T 4:575 T Tm 4:575 1:987 T
ð7Þ
where X is the mole fraction solubility at temperature T, Tm is the melting point of the solute, ΔCp = Cpl − Cps where Cpl and Cps are the molal heat capacities of the liquid and solid forms, respectively. For regular solutions, Eq. (7) was modified as: f ΔCp Tm −T ΔCp ΔHm Tm −T Tm − log þ T 4:575 T Tm 4:575 1:987 T Vs ϕm 2 − ðδm −δs Þ 4:575T
logX ¼ −
in which Vs is the molar volume of the solute, ϕm is the volume fraction of the solvent, δm and δs are the solubility parameters of the solvent and solute, respectively. Although Hildebrand restricts the application of the model to non-polar solvents, Chertkoff and Martin [4] used the model for calculating the solubility of benzoic acid in binary mixtures of hexane, ethyl acetate, ethanol and water. The numerical values of δm of binary solvents were calculated using δm =f1δ1 +f2δ2 in which f1 and f2 are the fractions of solvents 1 and 2, δ1 and δ2 are the solubility parameters of solvents 1 and 2. A simple linear relationship of logX =Intercept + slope f1 was used by Yalkowsky et al. [5] to represent the drug solubilities in water–cosolvent mixtures. The model was called the log-linear and expressed as Eq. (9): log Xm ¼ f1 log X1 þ f2 log X2
ð9Þ
where Xm is the mole fraction solubility of the solute, X1 and X2 denote the mole fraction solubility in neat cosolvent and water, respectively [5]. The model could be rearranged as: X1 log Xm ¼ log X2 þ log f1 ¼ Intercept þ Slope f1 : X2
ð10Þ
Eq. (10) is a correlative model, however, it has been demonstrated that a log-linear relationship between the solubility of a non-polar solute and the fraction of the cosolvent exists as [6]: log Xm ¼ log X2 þ σ f1
ð11Þ
where σ is the power of the cosolvent and theoretically solubilization is equal to log XX12 . Valvani et al. [7] reported a linear relationship between σ and logarithm of drug's partition coefficient (logKow). The relationship was expressed as: σ ¼ M log Kow þ N
avoiding Hildebrand's geometric assumption for the interaction term. In the original Hildebrand equation the solute–solvent interaction term is assumed equal to (δm × δs) in which δm and δs are the solubility parameters of mixed solvent and solute, respectively, and the model can describe the regular behaviour of the solution. Instead Martin's group used an empirical solute–solvent interaction parameter (WW). This modification widened the applications of the model to semi-polar crystalline drugs in irregular solutions involving self-association and hydrogen bonding, such as occurs in polar binary mixtures. Using the empirical EHS model, the co-logarithm of the mole fraction solubility (−logXm) can be expressed as: − log Xm ¼
ð8Þ
ð12Þ
where M and N are the cosolvent constants and are not dependent on the solute's nature. The numerical values of M and N were reported for most of the common cosolvents earlier [8]. The main assumptions on which the log-linear model is based are as follows: a) the free energy of transferring a solute to an ideal solvent mixture is the sum of the corresponding energies in pure solvents, b) the solvent molecules behave in a mixture the same way as they do in neat solvents, c) the ratio of the solvent and cosolvent surrounding a solute molecule is the same as volume fraction of the solvents in the mixture, d) the molar volume of solute in the solution is not so different from the molar volumes of the solvent and cosolvent, e) no degradation, solvation or solvent mediated polymorphic transitions of the solute occur [9]. By the extended Hildebrand solubility approach (EHS), Martin and coworkers [10] extended the applicability of the regular solution theory to the solubility of drugs in water–cosolvent mixtures by
159
− log Xsi
þ
Vs ϕ2m δ2m þ δ2s −2WW
ð13Þ
2:303RT
where Xis denotes the ideal mole fraction solubility of the solute, Vs is the molar volume of the solute, ϕm represents the volume fraction of the solvent in solution and because of very low solubility of the solute it can be assumed equal to 1, R is the molar gas constant, T denotes absolute temperature and WW is the interaction term which is calculated by a power series of δm: WW ¼ A0 þ A1 δm þ A2 δ2m þ A3 δ3m þ N þ An δnm
ð14Þ
where A0 − An denote the curve-fit parameter and δm is calculated by using Eq. (15): δm ¼ f1 δ1 þ f2 δ2
ð15Þ
in which δ1 and δ2 are the solubility parameters of pure cosolvent and water, respectively [11]. The model was modified to directly relate the solubility of drugs in mixed solvent to the solubility parameters of the solvent mixtures as: log Xm ¼ C0 þ C1 δm þ C2 δ2m þ C3 δ3m þ N þ Cn δnm
ð16Þ
where C terms are the curve curve-fitting parameters. Using this modified version there is no need for experimental determination of ideal solubility of the solute and other terms required in the EHS [11]. This polynomial, i.e. Eq. (16), was coverted to the general single model (Eq. (4)) using simple algebraic manipulations [12]. The Jouyban–Acree model was derived from a thermodynamic mixing model that includes contributions from both two-body and three-body interactions. The model was presented for solubility calculations in mixed solvents by our group [13,14] and was expressed as: 2
i
log Xm ¼ f1 log X1 þ f2 log X2 þ f1 f2 ∑ Ji ðf1 −f2 Þ
ð17Þ
i¼0
where Ji stands for the model constants. The Jouyban–Acree model is able to adequately represent the spectrum of solution behaviour from ideal to highly non-ideal systems [15–17]. The model contains as many curve-fitting parameters (usually 3) as is necessary to accurately describe the actual measured data. The model was also used to correlate other physico-chemical properties (PCP) in mixed solvent systems [18]. Theoretical basis of the model for describing the chemical potential of solutes dissolved in mixed solvents has been provided in an earlier paper [18]. The constants of the Jouyban–Acree model represent differences in the various solute–solvent and solvent–solvent interactions in the mixture [13]. A generalized version of the Jouyban–Acree model was proposed using its combination with the Abraham parameters where the model constants of the Jouyban–Acree model were correlated with the functions of the Abraham solvent coefficients and the solute parameters as: Ji ¼ A0;i þ A1;i ðc1 −c2 Þ2 þA2;i Eðe1 −e2 Þ2 þA3;i Sðs1 −s2 Þ2 þA4;i Aða1 −a2 Þ2 2
2
þA5;i Bðb1 −b2 Þ þA6;i V ðv1 −v2 Þ
ð18Þ
160
A. Jouyban, W.E. Acree Jr. / Journal of Molecular Liquids 142 (2008) 158–160
where A terms were the model constants [19], subscripts 1 and 2 denote cosolvent and water, respectively. The Ji (i.e., J0, J1 and J2) terms of the studied solubility data sets were regressed against (c1 − c2)2, E2(e1 − e2)2, S(s1 − s2)2, A(a1 − a2)2, B(b1 − b2)2 and V(v1 − v2)2 values to compute Aj,i terms, then the Aj,i terms were replaced in Eq. (17) and the solubility of drugs in binary solvents was predicted employing experimental values of X1 and X2. The applicability of the generalized model was shown in a previous work [19]. Using this version, the only required data is the solubility in neat water and cosolvent systems. Acknowledgment The financial support from the Drug Applied Research Center, Tabriz University (Medical Sciences) under Grant No. 85-64 was gratefully acknowledged. References [1] A. Maitra, S.J. Baghchi, Mol. Liq. 137 (2007) 131. [2] D.M. Stovall, W.E. Acree Jr., M.H. Abraham, Fluid Phase Equilib. 232 (2005) 113. [3] PharmaAlgorithms, ADME Boxes, Version 3.0, PharmaAlgorithms Inc., 591 Indian Road, Toronto, ON M6P 2C4, Canada, 2006. [4] M.J. Chertkoff, A.N.J. Martin, Am. Pharm. Assoc. 49 (1960) 444.
[5] S.H. Yalkowsky, G.L. Amidon, G. Zografi, G.L. Flynn, J. Pharm. Sci. 64 (1975) 48. [6] S.H. Yalkowsky, T. Roseman, in: S.H. Yalkowsky (Ed.), Solubilization of Drugs by Cosolvents, Marcel Dekker, New York, 1981, pp. 91–134. [7] S.C. Valvani, S.H. Yalkowsky, T.J. Roseman, J. Pharm. Sci. 70 (1981) 502. [8] A. Li, S.H. Yalkowsky, Ind. Eng. Chem. Res. 37 (1998) 4470. [9] A. Li, S.H. Yalkowsky, J. Pharm. Sci. 83 (1994) 1735. [10] A. Adjei, J. Newburger, A. Martin, J. Pharm. Sci. 69 (1980) 659. [11] P. Bustamante, B. Escalera, A. Martin, E. Selles, J. Pharm. Pharmacol. 45 (1993) 253. [12] M. Barzegar-Jalali, A. Jouyban-Gharamaleki, Int. J. Pharm. 152 (1997) 247. [13] W.E. Acree Jr., Thermochim. Acta 198 (1992) 71. [14] A. Jouyban, H.K. Chan, B.J. Clark, W.E. Acree Jr., Int. J. Pharm. 246 (2002) 135. [15] A.I. Zvaigzne, W.E. Acree Jr., J. Chem. Eng. Data 40 (1995) 917. [16] W.E. Acree Jr., Int. J. Pharm. 127 (1996) 27. [17] A. Jouyban-Gharamaleki, L. Valaee, M. Barzegar-Jalali, B.J. Clark, W.E. Acree Jr., Int. J. Pharm. 177 (1999) 93. [18] A. Jouyban, M. Khoubnasabjafari, W.E. Acree Jr., Pharmazie 60 (2005) 527. [19] A. Jouyban, S.h. Soltanpour, S. Soltani, W.E. Acree Jr., J. Pharm. Pharmaceut. Sci. 10 (2007) 263.
Contents lists available at ScienceDirect
Journal of Molecular Liquids j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / m o l l i q
Comments concerning “Study of solute–solvent and solvent–solvent interactions in pure and mixed binary solvents” Abolghasem Jouyban a,⁎, William E. Acree Jr. a b
b
Faculty of Pharmacy and Drug Applied Research Center, Tabriz University (Medical Sciences), Tabriz 51664, Iran Department of Chemistry, University of North Texas, Denton, TX 76203-5070, USA
A R T I C L E
I N F O
Article history: Received 2 February 2008 Received in revised form 1 May 2008 Accepted 12 June 2008 Available online 18 June 2008
A B S T R A C T A number of mathematical equations representing the solute solubility in monosolvent and binary solvent mixtures are discussed. This work is a commentary to the article of Maitra and Baghchi that appeared in this journal. Published by Elsevier B.V.
Keywords: Solubility Modeling Binary solvents
In a recent publication by Maitra and Baghchi that appeared in this journal [1], the solubility of a dye was determined in a couple of pure solvents and also some water–cosolvent mixtures and the observed solubilities described in terms of the mathematical equations. The authors used LSER equations (Eqs. (1) and (2)) for representing the solubility data in pure solvents and classified the solubility profiles in binary solvent mixtures into two groups; i.e. the solubility profiles without any maximum in the logarithm of solubility plot against solvent composition and those with a maximum. The authors represented the solubility behaviour of the first group with Eq. (3) and the second group using Eq. (4). The equations are: log s ¼ −2:72 þ 2:17α−0:99β þ 3:91π⁎−3:98 δ2H =1000 ð1Þ ð2Þ log s ¼ −3:05 þ 1:20α−3:54 δ2H =1000 log s12 ¼ xL1 log s1 þ xL2 log s2
ð3Þ
log s ¼ A þ Bxw þ Cx2w þ Dx3w
ð4Þ
where s is the molar solubility of the solute in the monosolvents, α is hydrogen-bond donation, β is hydrogen-bond acceptance, π⁎ is dipolarity–polarizability descriptor, δ2H is the Hildebrand solubility parameter of the solvents, s12 is the molar solubility in the binary solvent, s1 and s2 are the solubilities in neat solvents 1 and 2, xw is the mole fraction of the water in binary mixtures and A, B, C and D are the model constants [1]. The aim of this communication is not to criticise the
⁎ Corresponding author. E-mail addresses: [email protected] (A. Jouyban), [email protected] (W.E. Acree). 0167-7322/$ – see front matter. Published by Elsevier B.V. doi:10.1016/j.molliq.2008.06.009
work of Maitra and Baghchi, but rather to suggest alternative forms of the mathematical representations, prediction methods and also recall some old references dealing with the equations. Alternative LSER equations for representing the solute solubility data in monosolvents are the Abraham models which provided more accurate calculations. The Abraham model for processes within condensed phases is: log
CS CW
¼cþeEþsSþaAþbBþvV
ð5Þ
and for processes involving gas-to-condensed phase transfer is: log
CS CG
¼cþeEþsSþaAþbBþlL
ð6Þ
where CS and CW are the solute solubility in the organic solvent and water (in mole per liter), respectively, CG is the gas phase concentration of the solute, E is the excess molar refraction, S is dipolarity–polarizability of solute, A denotes the solute's hydrogen-bond acidity, B stands for the solute's hydrogen-bond basicity, V is the McGowan volume of the solute, and L is the logarithm of the solute gas-hexadecane partition coefficient at 298.15 K. In Eqs. (5) and (6)) the coefficients c, e, s, a, b, v and l are the model constants (i.e. solvent's coefficients), which depend upon the solvent system under consideration. Numerical values of the model constants of Eqs. (5) and (6) have been reported in the literature [2] for several water-to-organic solvent and gas-to-organic solvent systems. The main advantage of Eqs. (5) and (6) over Eqs. (1) and (2) is that there is no curve-fitting parameter and the solvent coefficients were reported earlier [2]. The only required parameters for Eqs. (5) and (6) are the solute's Abraham parameters which could be easily computed using the PharmaAlgorithm software [3].
A. Jouyban, W.E. Acree Jr. / Journal of Molecular Liquids 142 (2008) 158–160
It is well known that a solution obeying Raoult's law is known as an ideal solution and its solubility could be calculated from the heat of fusion of the solute (ΔHfm) and the difference in the heat capacities of the solid and its supercooled liquid (ΔCp) using Hildebrand and Scott equation expressed by: log X ¼ −
f ΔHm Tm −T ΔCp Tm −T ΔCp Tm − log þ T 4:575 T Tm 4:575 1:987 T
ð7Þ
where X is the mole fraction solubility at temperature T, Tm is the melting point of the solute, ΔCp = Cpl − Cps where Cpl and Cps are the molal heat capacities of the liquid and solid forms, respectively. For regular solutions, Eq. (7) was modified as: f ΔCp Tm −T ΔCp ΔHm Tm −T Tm − log þ T 4:575 T Tm 4:575 1:987 T Vs ϕm 2 − ðδm −δs Þ 4:575T
logX ¼ −
in which Vs is the molar volume of the solute, ϕm is the volume fraction of the solvent, δm and δs are the solubility parameters of the solvent and solute, respectively. Although Hildebrand restricts the application of the model to non-polar solvents, Chertkoff and Martin [4] used the model for calculating the solubility of benzoic acid in binary mixtures of hexane, ethyl acetate, ethanol and water. The numerical values of δm of binary solvents were calculated using δm =f1δ1 +f2δ2 in which f1 and f2 are the fractions of solvents 1 and 2, δ1 and δ2 are the solubility parameters of solvents 1 and 2. A simple linear relationship of logX =Intercept + slope f1 was used by Yalkowsky et al. [5] to represent the drug solubilities in water–cosolvent mixtures. The model was called the log-linear and expressed as Eq. (9): log Xm ¼ f1 log X1 þ f2 log X2
ð9Þ
where Xm is the mole fraction solubility of the solute, X1 and X2 denote the mole fraction solubility in neat cosolvent and water, respectively [5]. The model could be rearranged as: X1 log Xm ¼ log X2 þ log f1 ¼ Intercept þ Slope f1 : X2
ð10Þ
Eq. (10) is a correlative model, however, it has been demonstrated that a log-linear relationship between the solubility of a non-polar solute and the fraction of the cosolvent exists as [6]: log Xm ¼ log X2 þ σ f1
ð11Þ
where σ is the power of the cosolvent and theoretically solubilization is equal to log XX12 . Valvani et al. [7] reported a linear relationship between σ and logarithm of drug's partition coefficient (logKow). The relationship was expressed as: σ ¼ M log Kow þ N
avoiding Hildebrand's geometric assumption for the interaction term. In the original Hildebrand equation the solute–solvent interaction term is assumed equal to (δm × δs) in which δm and δs are the solubility parameters of mixed solvent and solute, respectively, and the model can describe the regular behaviour of the solution. Instead Martin's group used an empirical solute–solvent interaction parameter (WW). This modification widened the applications of the model to semi-polar crystalline drugs in irregular solutions involving self-association and hydrogen bonding, such as occurs in polar binary mixtures. Using the empirical EHS model, the co-logarithm of the mole fraction solubility (−logXm) can be expressed as: − log Xm ¼
ð8Þ
ð12Þ
where M and N are the cosolvent constants and are not dependent on the solute's nature. The numerical values of M and N were reported for most of the common cosolvents earlier [8]. The main assumptions on which the log-linear model is based are as follows: a) the free energy of transferring a solute to an ideal solvent mixture is the sum of the corresponding energies in pure solvents, b) the solvent molecules behave in a mixture the same way as they do in neat solvents, c) the ratio of the solvent and cosolvent surrounding a solute molecule is the same as volume fraction of the solvents in the mixture, d) the molar volume of solute in the solution is not so different from the molar volumes of the solvent and cosolvent, e) no degradation, solvation or solvent mediated polymorphic transitions of the solute occur [9]. By the extended Hildebrand solubility approach (EHS), Martin and coworkers [10] extended the applicability of the regular solution theory to the solubility of drugs in water–cosolvent mixtures by
159
− log Xsi
þ
Vs ϕ2m δ2m þ δ2s −2WW
ð13Þ
2:303RT
where Xis denotes the ideal mole fraction solubility of the solute, Vs is the molar volume of the solute, ϕm represents the volume fraction of the solvent in solution and because of very low solubility of the solute it can be assumed equal to 1, R is the molar gas constant, T denotes absolute temperature and WW is the interaction term which is calculated by a power series of δm: WW ¼ A0 þ A1 δm þ A2 δ2m þ A3 δ3m þ N þ An δnm
ð14Þ
where A0 − An denote the curve-fit parameter and δm is calculated by using Eq. (15): δm ¼ f1 δ1 þ f2 δ2
ð15Þ
in which δ1 and δ2 are the solubility parameters of pure cosolvent and water, respectively [11]. The model was modified to directly relate the solubility of drugs in mixed solvent to the solubility parameters of the solvent mixtures as: log Xm ¼ C0 þ C1 δm þ C2 δ2m þ C3 δ3m þ N þ Cn δnm
ð16Þ
where C terms are the curve curve-fitting parameters. Using this modified version there is no need for experimental determination of ideal solubility of the solute and other terms required in the EHS [11]. This polynomial, i.e. Eq. (16), was coverted to the general single model (Eq. (4)) using simple algebraic manipulations [12]. The Jouyban–Acree model was derived from a thermodynamic mixing model that includes contributions from both two-body and three-body interactions. The model was presented for solubility calculations in mixed solvents by our group [13,14] and was expressed as: 2
i
log Xm ¼ f1 log X1 þ f2 log X2 þ f1 f2 ∑ Ji ðf1 −f2 Þ
ð17Þ
i¼0
where Ji stands for the model constants. The Jouyban–Acree model is able to adequately represent the spectrum of solution behaviour from ideal to highly non-ideal systems [15–17]. The model contains as many curve-fitting parameters (usually 3) as is necessary to accurately describe the actual measured data. The model was also used to correlate other physico-chemical properties (PCP) in mixed solvent systems [18]. Theoretical basis of the model for describing the chemical potential of solutes dissolved in mixed solvents has been provided in an earlier paper [18]. The constants of the Jouyban–Acree model represent differences in the various solute–solvent and solvent–solvent interactions in the mixture [13]. A generalized version of the Jouyban–Acree model was proposed using its combination with the Abraham parameters where the model constants of the Jouyban–Acree model were correlated with the functions of the Abraham solvent coefficients and the solute parameters as: Ji ¼ A0;i þ A1;i ðc1 −c2 Þ2 þA2;i Eðe1 −e2 Þ2 þA3;i Sðs1 −s2 Þ2 þA4;i Aða1 −a2 Þ2 2
2
þA5;i Bðb1 −b2 Þ þA6;i V ðv1 −v2 Þ
ð18Þ
160
A. Jouyban, W.E. Acree Jr. / Journal of Molecular Liquids 142 (2008) 158–160
where A terms were the model constants [19], subscripts 1 and 2 denote cosolvent and water, respectively. The Ji (i.e., J0, J1 and J2) terms of the studied solubility data sets were regressed against (c1 − c2)2, E2(e1 − e2)2, S(s1 − s2)2, A(a1 − a2)2, B(b1 − b2)2 and V(v1 − v2)2 values to compute Aj,i terms, then the Aj,i terms were replaced in Eq. (17) and the solubility of drugs in binary solvents was predicted employing experimental values of X1 and X2. The applicability of the generalized model was shown in a previous work [19]. Using this version, the only required data is the solubility in neat water and cosolvent systems. Acknowledgment The financial support from the Drug Applied Research Center, Tabriz University (Medical Sciences) under Grant No. 85-64 was gratefully acknowledged. References [1] A. Maitra, S.J. Baghchi, Mol. Liq. 137 (2007) 131. [2] D.M. Stovall, W.E. Acree Jr., M.H. Abraham, Fluid Phase Equilib. 232 (2005) 113. [3] PharmaAlgorithms, ADME Boxes, Version 3.0, PharmaAlgorithms Inc., 591 Indian Road, Toronto, ON M6P 2C4, Canada, 2006. [4] M.J. Chertkoff, A.N.J. Martin, Am. Pharm. Assoc. 49 (1960) 444.
[5] S.H. Yalkowsky, G.L. Amidon, G. Zografi, G.L. Flynn, J. Pharm. Sci. 64 (1975) 48. [6] S.H. Yalkowsky, T. Roseman, in: S.H. Yalkowsky (Ed.), Solubilization of Drugs by Cosolvents, Marcel Dekker, New York, 1981, pp. 91–134. [7] S.C. Valvani, S.H. Yalkowsky, T.J. Roseman, J. Pharm. Sci. 70 (1981) 502. [8] A. Li, S.H. Yalkowsky, Ind. Eng. Chem. Res. 37 (1998) 4470. [9] A. Li, S.H. Yalkowsky, J. Pharm. Sci. 83 (1994) 1735. [10] A. Adjei, J. Newburger, A. Martin, J. Pharm. Sci. 69 (1980) 659. [11] P. Bustamante, B. Escalera, A. Martin, E. Selles, J. Pharm. Pharmacol. 45 (1993) 253. [12] M. Barzegar-Jalali, A. Jouyban-Gharamaleki, Int. J. Pharm. 152 (1997) 247. [13] W.E. Acree Jr., Thermochim. Acta 198 (1992) 71. [14] A. Jouyban, H.K. Chan, B.J. Clark, W.E. Acree Jr., Int. J. Pharm. 246 (2002) 135. [15] A.I. Zvaigzne, W.E. Acree Jr., J. Chem. Eng. Data 40 (1995) 917. [16] W.E. Acree Jr., Int. J. Pharm. 127 (1996) 27. [17] A. Jouyban-Gharamaleki, L. Valaee, M. Barzegar-Jalali, B.J. Clark, W.E. Acree Jr., Int. J. Pharm. 177 (1999) 93. [18] A. Jouyban, M. Khoubnasabjafari, W.E. Acree Jr., Pharmazie 60 (2005) 527. [19] A. Jouyban, S.h. Soltanpour, S. Soltani, W.E. Acree Jr., J. Pharm. Pharmaceut. Sci. 10 (2007) 263.