Correlation of surface tension of mixed solvents with solvent composition

Transcription

1 School of harmacy and Drug Applied Research Center ; Kimia Research Institute 2, Tabriz, Iran, and Department of Chemistry 3, University of North Texas, Denton, USA Correlation of surface tension of mixed solvents with solvent composition A. Jouyban, A. Fathi Azarbayjani 2, M. Barzegar-Jalali, W. E. Acree Jr. 3 Dedicated to the memory of rofessor DJ. Farid, who passed away on the 23 rd of November 2003 Received September 25, 2003 accepted March 3, 2004 Dr. A. Jouyban, School of harmacy, Tabriz University of Medical Sciences, Tabriz 5664, Iran ajouyban@hotmail.com harmazie 59: (2004) A simple computational method for calculating surface tension of solvent mixtures based on the Redlich-Kister extension was proposed. The model was applied to the experimental surface tension of binary solvent mixtures and showed accurate results. Overall average percentage deviation (AD) between calculated and experimental surface tensions was calculated as an accuracy criterion. The overall AD for correlating surface tensions in binary solvents was 4.30%. The accuracy of the proposed model has also been compared with those of previously published models and the results showed that the proposed model was superior and capable of providing more accurate results. An extension of the model was also proposed to correlate surface tension of ternary solvents and the overall AD for ternary solvent data was 2.06%.. Introduction In the simplest applications of the surface tension in the pharmaceutical area, it could be considered as the most important parameter for counting the number of drops per ml from aqueous/mixed solvent based ear/eye/oral drop formulations. Surface tension determines the degree of dispersion and the dynamics of motion of liquids in nanopores. It has also been employed in the theoretical description of retention in high performance liquid chromatography (Cheong and Carr 987). Ab initio prediction of the surface tension of solvent systems is not possible at the present time, however, it is possible to calculate surface tension after collecting a number of experimental data and then prediction of surface tension using interpolation techniques. The aim of this work was to provide an accurate model to correlate surface tension of mixed solvents and test its applicability on real experimental data collected from the literature. 2. Investigations, results and discussion 2.. Computational methods A solution model (i.e. the combined nearly ideal binary solvent/redlich-kister equation, CNIBS/R-K) presented by Acree (992) was used to correlate different physicochemical properties in mixed solvent systems; including the solubility of polycyclic aromatic hydrocarbons in nonaqueous binary solvent mixtures (Acree 995), solubility of drugs in water-cosolvent mixtures (Jouyban-Gh. et al. 999), electrophoretic mobility of analytes in mixed solvent electrolyte systems (Jouyban-Gh. et al. 2000a; 2003a; 2003b), the instability rate constants in binary solvent systems (Jouyban et al. 2002a), the acid dissociation constants in water-organic solvent mixtures (Jouyban et al. 2002b) and the dielectric constants of solvent mixtures (Jouyban et al. 2004). Theoretical basis of the CNIBS/R-K equation for describing the chemical potential of solutes dissolved in mixed solvents (Acree 992) and acid dissociation constants in aqueous-organic mixtures (Jouyban et al. 2002b) has been provided in earlier papers. As noted above, Jouyban et al. extended the applications of the basic solution model; therefore, it could be called the Jouyban-Acree model (JAM). The model constants of the JAM represent differences in the various solute-solvent and solvent-solvent interactions in the mixture (Acree 992). Therefore, it should be possible to calculate any other physico-chemical property in mixed solvents, which is a function of solute-solvent and/or solvent-solvent interactions. Based on this assumption, an adopted form of the equation representing the surface tension of a binary solvent mixture is proposed as: lng m ¼ f ln g þ f 2 ln g 2 þ f f 2 2 K i ðf f 2 Þ i ðþ i ¼ 0 Where g m, g and g 2 are the surface tensions of the mixture and solvents and 2, respectively, f and f 2 are the volume (weight or mole) fractions of solvents and 2 in the mixture and K i represent the model constants calculated using a no intercept least square method (Jouyban- Gh and Hanaee 997). Extension of the model to surface tensions of binary mixtures departs from previous applications, which were limited for the most part to partial molar quantities. Surface tension of binary mixtures is more of an integral extrathermodynamic property (Acree and Bertrand 983). The theoretical basis of extra-thermodynamic properties is not as rigorous as that of true thermodynamic properties. Consequently, it might be best to view eq. () more as a math- harmazie 59 (2004) 2 937

2 ematical representation, rather than an equation derived from a rigorous thermodynamic model. This would be consistent with our application of the JAM to physical properties like dielectric constants. The calculated surface tensions were compared with experimental (observed) values and mean of the absolute percentage deviation (AD) was used as an accuracy criterion. The AD was calculated using: AD ¼ 00 jcalculated Observedj ðn QÞ Observed ð2þ where N is the number of data points in each set and Q is the number of constant terms of the corresponding equation. The previously presented equations for correlating surface tension of mixed solvents from the literature are as follows: Cheong and Carr (987) used the Redlich-Kister extension to correlate the excess surface tension of the mixture (g E ) with the solvent composition. g E is: g E ¼ g m ðf g þ f 2 g 2 Þ ð3þ and the Redlich-Kister extension is: g E ¼ðf ð f ÞÞ ½S 0 þ S ð 2f ÞþS 2 ð 2f Þ 2 Š ð4þ Where S 0 S 2 are the model constants calculated by regressing g E /[f ( f )] versus ( 2f ) and ( 2f ) 2 using a least square analysis (Cheong and Carr 987). Another numerical method has been proposed to compute the model constants of Redlich-Kister (948) extension which regresses g E versus f ( f ), f ( f )( 2f ) and f ( f )( 2f ) 2 using a no intercept least square analysis (Jouyban-Gh and Hanaee 997). Cheong and Carr (987) also reported the surface tension of mixed solvent as a polynomial function of solvent composition as: ln g m ¼ A þ m B i f i ð5þ where A and B i are the model constants. Connors and Wright (989) proposed eq. (6): g m ¼ g þ bf f 2 ðg af g 2 Þ ð6þ where a and b are the model constants. It has been used in many published works (e.g. Alvarez et al. 998; 2003; i¼ Vazquez et al. 996; 997) as eq. (7). g g m ¼ þ bf g g 2 af 2 f 2 ð7þ In addition to the above-mentioned equations, there are a number of complicated equations of state (e.g. see Escobedo and Manssori 998), which require a high degree of knowledge of physico-chemical properties such as critical temperature, critical pressure, acentric factor, and the critical compressibility factor, which are not easily available. In addition the models require complex computational procedures that are not suitable in the pharmaceutical area where the researchers would like to employ an easy to use model. Therefore, we ignored these equations in the comparison of the models in this study. AD JAM eq. (4) orig. eq. (4) modif. eq. (5) eq. (6) Fig. : Mean and standard deviation of average percentage deviation (AD) values for eqs. studied 2.2. Computational results and discussion Details of experimental surface tensions for various aqueous binary solvents were shown in Table. Different equations were fitted to experimental data and the backcalculated surface tensions were used to calculate ADs, which were shown in Table 2. The minimum and maximum ADs for the proposed model were 0.33 (water-acetonitrile, 25 C) and.62% (water-acetone, 38 C), respectively. The overall AD standard deviation was %. The minimum ADs for eqs. (4, original version), (4, modified version), (5) and (6) were.06, 0.58, 0.50 and 0.02%, respectively, and the corresponding maximum values were 99.06, 9.76, 2.72 and 63.87%. As noted in the computational methods, the model constants of eq. (4) could be calculated using a classical least square method (Cheong and Carr 987) and a no intercept least square method (Jouyban-Gh and Hanaee 997). The latter provided more accurate results, therefore, it is suggested to use a no intercept least square method in using Redlich-Kister extension for describing the mixed solvent systems behaviors. The only difference between JAM and eq. (4) is that, in JAM, we have used a logarithmic transformation of the surface tensions. The overall ADs and their standard deviations were shown in Fig.. The proposed equation (JAM) produced the most accurate results, followed by eqs. (5), (4, modified), (6) and (4, original). The mean AD differences between JAM and eqs. (4, original and modified versions) and (6) were statistically significant (paired t-test, p < 0.004). In addition the mean difference between eqs. (4, modified) and (4, original) was statistically significant (paired t-test, p < ). However, there was no significant difference between eq. (5) and JAM (paired t-test, p > 0.). Employing more curve-fitting parameters provides more accurate results for JAM. Fig. 2 shows AD values for JAM and eq. (5) using different numbers of AD eq. (5) JAM Number of constant terms Fig. 2: Mean and standard deviation of average percentage deviation (AD) values for JAM and eq. (5) for various number of constant terms 938 harmazie 59 (2004) 2

3 Table : Details of experimental data sets including the name of cosolvent, references, the number of data points in each set (N), temperature (T) and surface tensions of water (solvent ) and cosolvent (solvent 2) No. Cosolvent (solvent 2) Reference N a T g g 2 Acetone Howard and McAllister Acetone Howard and McAllister Acetone Howard and McAllister Acetone Howard and McAllister Acetonitrile Cheong and Carr Amino-2-propanol Alvarez et al Amino-2-propanol Alvarez et al Amino-2-propanol Alvarez et al Amino-2-propanol Alvarez et al Amino-2-propanol Alvarez et al Amino-2-propanol Alvarez et al Amino-2-methyl--propanol Vazquez et al Amino-2-methyl--propanol Vazquez et al Amino-2-methyl--propanol Vazquez et al Amino-2-methyl--propanol Vazquez et al Amino-2-methyl--propanol Vazquez et al Amino-2-methyl--propanol Vazquez et al Amino--propanol Alvarez et al Amino--propanol Alvarez et al Amino--propanol Alvarez et al Amino--propanol Alvarez et al Amino--propanol Alvarez et al Amino--propanol Alvarez et al tert-butanol Cheong and Carr Diethanolamine Vazquez et al Diethanolamine Vazquez et al Diethanolamine Vazquez et al Diethanolamine Vazquez et al Diethanolamine Vazquez et al Diethanolamine Vazquez et al Dimethyl sulphoxide Cheong and Carr Dioxane Hovorka et al Dioxane Hovorka et al Dioxane Hovorka et al Dioxane Hovorka et al Dioxane Hovorka et al Dioxane Hovorka et al Dioxane Hovorka et al Dioxane Hovorka et al Isopropanol Cheong and Carr Methanol Weast Methanol Weast Methanol Weast Methanol Cheong and Carr N-Methyldiethanolamine Alvarez et al N-Methyldiethanolamine Alvarez et al N-Methyldiethanolamine Alvarez et al N-Methyldiethanolamine Alvarez et al N-Methyldiethanolamine Alvarez et al N-Methyldiethanolamine Alvarez et al Monoethanolamine Vazquez et al Monoethanolamine Vazquez et al Monoethanolamine Vazquez et al Monoethanolamine Vazquez et al Monoethanolamine Vazquez et al Monoethanolamine Vazquez et al Tetrahydrofuran Cheong and Carr Triethanolamine Vazquez et al Triethanolamine Vazquez et al Triethanolamine Vazquez et al Triethanolamine Vazquez et al Triethanolamine Vazquez et al Triethanolamine Vazquez et al a N is the number of data points in each set harmazie 59 (2004) 2 939

4 Table 2: Average percentage deviation (AD) for different equations No. a JAM eq. (4) original eq. (4) modified eq. (5) eq. (6) a Details of the set numbers are the same as in Table constant terms. For JAM, two of the constant terms are g and g 2, and as shown in the figure for JAM, the more curve-fitting parameters the more accurate the results. This is because of an appropriate independent variable arrangement of JAM. However, this is not the case for eq. (5), as overall AD decreases slightly from five constant terms and then increases again from seven to eight constant terms version of the model. The JAM could be extended for correlating surface tension of ternary solvents as: Ing m ¼ f lng þ f 2 lng 2 þ f 3 lng 3 þ f f 2 2 K i ðf f 2 Þ i þ f f 3 2 K 0 i ðf f 3 Þ i f 2 f 3 2 K 00 i ðf 2 f 3 Þ þ f f 2 f K K 000 i ðf f 2 f 3 Þ i ð8þ where g 3 and f 3 are surface tension of solvent 3 and volume (weight or mole) fraction of solvent three in the mixture and K 0 i,k 00 i and K 000 i are the model constants. The model was applied to the available ternary solvent surface tension data of water glycerin ethanol (Ernst et al. 936), water n-butyl acetate methanol and water n-pentyl acetate methanol (Santos et al. 2003) and ADs obtained were 2.98% (N ¼ 66 and Q ¼ 5), 2.34% (N ¼ 83, Q ¼ 5) and 0.87% (N ¼ 42, Q ¼ 5), respectively, and the overall AD was 2.06%. In our past studies involving the mathematical description of solute solubilities in binary solvents, we noted that it was possible to use the calculated regression parameters determined from binary solvent solubility data to predict the solubility of the solute in ternary solvent mixtures (Jouyban-Gh. et al. 2000b). While there is insufficient ternary mixture surface tension data available in the chemical and pharmaceutical literature to test this possible application, we hypothesize that the ternary mixture form of the JAM should provide reasonably accurate predictions of the surface tensions of ternary mixtures. In conclusion, the JAM is capable of correlating other physico-chemical properties in solvent mixtures, and the results obtained in this study recommend it for correlating surface tension calculations in practice, when an accurate model is needed to screen the experimentally determined surface tensions for detecting possible outliers and/or to predict the surface tension of solvent mixtures at any solvent compositions after training the model using a minimum number of data points, i.e. five points. The best combination of the training set could be considered as: f ¼ 0.00, 0.25, 0.50, 0.75 and.00 for the proposed model. Acknowledgement: The financial support from Drug Applied Research Center, Tabriz University of Medical Sciences is gratefully acknowledged. References Acree Jr WE (992) Mathematical representation of thermodynamic properties. art 2. Derivation of the combined nearly ideal binary solvent (NIBS)/Redlich-Kister mathematical representation from a two-body and three-body interactional mixing model. Thermochim Acta 98: Acree Jr WE (995) olycyclic aromatic hydrocarbons: Binary nonaqueous systems. art (Solutes A-E), IUAC Solubility Data Series, Vol. 58, Oxford University ress, Oxford. Acree Jr WE, Bertrand GL (983) Viscosity, refractive index and surface tension of multicomponent systems: Mathematical representation and estimation from data for binary systems. J Solution Chem 2: Alvarez E, Rendo R, Sanjurjo B, Sanchez-Vilas M, Navaza JM (998) Surface tension of binary mixtures of water þ N-methyldiethanolamine and ternary mixtures of this amine and water with monoethanolamine, diethanolamine, and 2-amino-2-methyl--propanol from 20 to 50 C. J Chem Eng Data 43: harmazie 59 (2004) 2

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