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Surface tension prediction and thermodynamic analysis of the surface for binary solutions
Chemical Engineering Science 60 (2005) 4935 – 4952 www.elsevier.com/locate/ces
Surface tension prediction and thermodynamic analysis of the surface for binary solutions Reza Taherya , Hamid Modarressa,∗ , John Satherleyb a Chemical Engineering Department, Amir Kabir University of Technology, P.O. Box 15875-4413, Tehran, Iran b Department of Chemistry, University of Liverpool, Liverpool L69 7ZD, Merseyside, UK
Received 17 November 2004; received in revised form 21 February 2005; accepted 23 March 2005 Available online 4 June 2005
Abstract The surface tensions of 100 aqueous and 200 non-aqueous binary solutions are correlated by Shereshefsky model and excellent results are obtained. The average percent deviations are about ∼ 1.8% for aqueous and ∼ 0.56% for non-aqueous binary solutions. The free energy change in the surface region is calculated and is used to obtain the excess number of molecular layers in the surface region. Furthermore, the model is used to derive an equation for the standard Gibbs energy of adsorption. Where experimental data is available for the standard Gibbs energy of adsorption, the agreement between the calculated and the experimental data is found to be very good. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Surface tension; Binary solution; Excess number of molecular layer; Standard Gibbs energy of adsorption
1. Introduction The surface of a liquid has interesting properties which appear as the surface tension. The surface tension of liquids can be looked upon as the property which draws a liquid together and forms a liquid–vapour interface. In vapour–liquid equilibrium the effect of surface tension on interface curvature, is very important and should be taken into account. Surface tension has high industrial importance in chemical reactions as the reactions in the surface region are quite different from the bulk region. In various chemical engineering processes such as separation, distillation, extraction and absorption, surface tension has a determining effect. Also in electrochemical reactions, biological membranes operation, environmental engineering and several other processes namely; corrosion, adherency, detergency, floating and lubricating the surface tension plays a significant role. The surface tension of liquids and its variation with composition in liquid solutions must often be taken into account in designing rational chemical process equipment involving ∗ Corresponding author. Tel.: +98 21 64543176; fax: +98 21 6405847.
E-mail address: [email protected] (H. Modarress). 0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2005.03.056
interphase heat and mass transfer. Many methods to calculate the surface tension of binary non-electrolyte mixtures have been proposed. Belton and Evans (1945) developed semi-empirical equations for ideal or nearly ideal solutions in the bulk phase. However, these equations are empirical, and the constant terms have no apparent relation to the properties of the pure components and therefore the calculation of surface tension is complicated. Guggenheim (1945) used a quasicrystalline model to derive an equation for the surface tension of regular solutions as a function of heat of mixing and simplified it for ideal solutions. Guggenheim model was extended by Hildebrand and Scott (1964) for mixtures of different size molecules. A one-parameter equation for binary liquid mixtures was proposed by Eberhart (1966) by assuming that the surface tension is a linear function of surface layer mole fraction. By using a statistical thermodynamic approach, he calculated the parameter of his model and the surface tension of binary liquid mixtures with good accuracy. Winterfeld et al. (1978) derived an expression based on the Fowler–Kirkwood–Buff model (Kirkwood and Buff, 1949) relating the surface tension of multicomponent systems to quantities dependent on the intermolecular pair potentials and pair correlation functions and applied
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R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
it to the surface tension of binary systems. This expression involves a parameter, which is defined as the mixing parameter. However, this mixing parameter is difficult to calculate, since the pair potential and the correlation functions are not generally available. Based on the conformal solution theory of mixtures, Escobedo and Mansoori (1998) derived an expression for surface tension and applied to a variety of binary mixtures. Li et al. (1990) used the UNIFAC group contribution method to calculate the surface tension of binary mixtures. This approach, however, is not recommended for aqueous solutions since the difference between the surface tension of the pure components is large. Subsequently, Li et al. (2000) derived a two-parameter equation for the surface tension of mixtures based on the Wilson equation for excess Gibbs free energy. This model was found to work well for both binary organic and aqueous solutions. Li and Lu (2001) have developed a prediction method for the surface tension of real mixtures based on the Davis theory (Davis, 1975) and tested it against molecular dynamics simulation of the surface tension of the Lennard–Jones fluid. They applied it with a good success to binary and ternary organic solutions and binary aqueous solutions. Very recently, Miqueu et al. (2004) have used the gradient theory of fluid interfaces to compute the surface tension of various binary and ternary mixtures of gas and liquid hydrocarbons with good results. An alternative model which gives knowledge about the surface structure of binary solutions and is able to compute the excess number of molecular layers and free energy change in the surface region was developed by Shereshefsky (1967). This model was applied to a limited number of binary solutions (Shereshefsky, 1967; Cotton, 1969). Unfortunately, researchers dealing with liquid surface properties have not paid enough attention to this model, and have not extended its application to various aqueous and non-aqueous solutions. In this work, the Shereshefsky model is applied to a wide range of organic and aqueous binary solutions and it is shown that a wealth of information can be obtained from this model. In addition, this model is used to derive a relation between the standard Gibbs energy of adsorption, the free energy change in the surface region and the difference between surface tension of pure components. Furthermore the differences between surface tensions of constituents in 300 organic and aqueous binary solutions are calculated. This quantity is used to estimate the surface tension of pure components which are difficult to obtain experimentally.
where the components have a similar size and attractive forces (Fowler and Guggenheim, 1939). For simplicity, however, Shereshefsky (1967) presented his model by assuming that the surface is homogeneous and uniform in composition and the energy of interaction between the molecules in the surface region is less than that of the bulk liquid phase due to its lower density and greater average distance between molecules. Based on these assumptions, Shereshefsky (1967) derived an equation for the surface tension, , of a binary solution as represented by the following equation:
= 1 −
◦ x2b eGs/RT , 1 + x2b (eGs /RT − 1)
(1)
where ◦ = 1 − 2 is the difference between the surface tensions of pure solvent (1 ) and pure solute (2 ), x2b is the mole fraction of solute in the bulk liquid, T is the absolute temperature and R is the gas constant. In Eq. (1), GS is the free energy change of replacing 1 mol of solvent with 1 mol of solute in the surface region. Eq. (1) can be rearranged in the following form: x2b 1 GS /RT x2b = e + (1 − eGS /RT ), ◦ ◦
(2)
where = 1 − is the difference between the surface tension of pure solvent (1 ) and that of solution (). According to Eq. (2) the variation of x2b / versus x2b is linear. Therefore GS can be expressed by the following equation: , (3) GS = RT ln 1 + where = (1 − e−GS /RT )/◦ is the slope, = (e−GS /RT )/◦ is the intercept of Eq. (2) and therefore ◦ can be obtained as
◦ =
1 . +
(4)
The excess number of molecular layers of solute in the surface region in respect to the bulk region E 2 , which has been named as number of molecular layers by Shereshefsky (1967), is redefined here in consistency with the Gibbs equation for adsorption in the following form:
E 2 =
◦ A¯ 2 , GS
(5)
where A¯ 2 is the molar area of solute (2). The molar area of solute (2) is given by
2. Model description
1/3 A¯ 2 = (M2 /2 )2/3 NA ,
The surface region of a binary mixture differs from the bulk phase in several aspects, namely it is not homogeneous, and its density varies continuously in the direction perpendicular to the surface. It may differ in composition from the bulk, as has been shown by Gibbs (1931), except in cases
where M2 and 2 are the molecular weight and the density of solute and NA is Avogadro’s number. A positive and high value of E 2 means that solute (2) is adsorbed in the surface and therefore solute molecules are in excess in the surface with respect to the bulk. Such a case
(6)
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
is observed for binary solutions where on addition of the solute to the solvent the surface tension of binary solution shows a decreasing trend, whereas a negative value of E 2 means that solute (2) is not adsorbed in the surface and it is in excess in the bulk with respect to the surface. Such a case is observed for binary solutions where on addition of the solute to the solvent, the surface tension shows an increasing trend. The sign and variation of E 2 is consistent with the Gibbs equation for adsorption as expressed by the following equation (Adamson and Gast, 1997):
E 2 =−
j 1 , RT j ln c2
(7)
where is the surface tension of solution and c2 is the concentration of solute. The molar surface excess function E 2 is defined as
E 2
nS − nb2 = 2 , A
(8)
where nS2 and nb2 are, respectively, the number of moles of solute in the surface and in the bulk and A is the surface S b area. A positive value of E 2 means that n2 > n2 and soE lute is adsorbed on the surface. For 2 > 0, according to Eq. (7), j/j ln c2 < 0 and addition of solute has a decreasing effect on the surface tension of solution. On the other S b hand, a negative value of E 2 means that n2 < n2 and solute is not adsorbed on the surface. For E 2 < 0, according to Eq. (7), j/j ln c2 > 0 and addition of solute has an increasing effect on the surface tension of solution. The standard Gibbs energy of adsorption, which reflects the energy required to move one molecule of solute from the bulk to the surface, can be expressed as (Calvo et al., 2004)
G◦ = − lim {RT ln (/x2b )}. x2b →0
(9)
Now, by substituting for /x2b from Eq. (2) into Eq. (9) and taking the limit as x2b → 0 we have 1 −GS /RT ◦ G /RT = lim ln e x2b →0 ◦ x2b + (1 − e−GS /RT ) ◦ 1 −GS /RT , e = ln ◦ G◦ GS (10) =− + ln ◦ . RT RT This equation consequently enables the calculation of the standard Gibbs energy of adsorption from GS and ◦ . These terms can be determined from Eqs. (3) and (4). 3. Results The surface tensions of binary solutions were fitted in Eq. (2) for 200 binary organic solutions and 100 binary
4937
aqueous solutions and from the slope and intercept the values of ◦ and GS /RT were evaluated. The R-squared values for linearity of Eq. (2) defined as
2 yi2 − yi /n , (yi − yˆi )2 R2 = 1 − (11) where yi = (x2b /)i is the experimental value of the data point i, yˆi is the regressed value of yi according to Eq. (2) and n is the number of data points (Beyer, 1991). For the studied binary organic solutions reported in Table 1 and binary aqueous solutions reported in Table 2 , the values of R 2 are 0.90 and 0.96, respectively, which indicate good linear plots according to Eq. (2) for the studied solutions. R 2 is defined as R 2 =
N
(R 2 )j /N ,
(12)
j =1
where N is the number of solutions. The results of applying Eqs. (1)–(6) and (10) to 200 binary organic solutions and 100 binary aqueous solutions are given in Tables 1 and 2. In the fifth and sixth columns, the experimental and calculated values of ◦ are given. The values of GS /RT calculated by Eq. (3) and −G◦ /RT calculated by Eq. (10) are tabulated, respectively, in columns 7th and 8th. In the 9th and 10th column, respectively, the molar area of the surface-active component A¯ 2 calculated by Eq. (6) and the excess number of molecular layers E 2 calculated by Eq. (5) are reported. The relative absolute deviation percent (RAD%) in the calculating surface tension of pure solute (2 ) in the binary solution is expressed as ( ) 2 Exp. − (2 )Calc. (13) RAD% = 100 × . (2 )Exp. For fixed and known values of 1 and by the definition ◦ = 1 − 2 we have (2 )Exp. − (2 )Calc. = (◦ )Exp. − (◦ )Calc.
(14)
then the RAD% values for the studied binary solutions can be calculated by the following equation: ( ) ◦ Exp. − (◦ )Calc. (15) RAD% = 100 × . (2 )Exp. The results are reported in 11th column of Tables 1 and 2. The absolute average deviation percent (AAD%) in surface tension are calculated by the following equation: AAD% = 100 ×
n i=1
Exp.
|(i
Exp.
− Calc. )/i i
|/n
(16)
and are tabulated in the 12th column of Tables 1 and 2.
No.
Temp. (K)
1
2
Acetic acid Acetic acid Acetone Aniline Aniline Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzyl alcohol Benzyl alcohol 1-Butanol 1-Butanol 1-Butanol 1-Butanol 2-Butanol Butyric acid Carbon disulfide Carbon disulfide Carbon disulfide CTC Chlorobenzene Chlorobenzene
Ethyl acetate Ethanol Isooctane Benzene Toluene Acetone Cyclohexane Cyclopentane Ethanol Ethyl acetate Ethyl acetate Ethyl ether Ethyl ether Isooctane Hexane Hexane Hexane Hexane Dodecane Dodecane Dodecane Dodecane 1−Propanol Propionic acid Toluene Ethyl acetate Toluene 2-Chlorobutane Hexane 2-M-1-CP Octane 2-M-2-CP Cyclohexane Acetone Benzene Chloroform Cyclopentane Benzene Benzene
298.15 298.15 298.15 293.15 293.15 298.15 293.15 298.15 298.15 293.15 298.15 291.15 291.15 303.15 298.15 303.15 308.15 313.15 298.15 303.15 308.15 313.15 298.15 303.15 291.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 303.15 289.15 298.15 291.15 298.15 283.15 313.15
◦ (mN/m) Exp.
Calc.
5.1 6.6 4.67 15.08 15.45 4.8 4.05 6.35 7.1 5.1 4.5 11 11.5 9.64 10.21 10.05 9.91 9.76 3.46 3.17 2.96 2.72 2.9 1.81 0.35 15.8 11.3 2.42 6.13 2.45 2.85 4.21 1.68 10.2 4.46 4.91 4.28 4.31 4.51
4.82 6.1 4.84 14.99 15.34 5.78 4.12 6.39 7.08 4.95 4.48 10.81 11.43 9.61 9.99 10.07 9.82 9.75 3.5 3.15 2.95 2.75 3.39 1.74 0.35 15.48 11.71 2.55 6.3 2.58 2.94 4.38 1.54 10.42 4.54 4.97 4.33 4.27 4.55
GS /RT −G◦ /RT
A¯ 2 (A˚ 2 )
E 2
RAD%
AAD%
n
Ref.
0.49 −0.25 2.46 0.97 1.27 −0.73 1.06 0.65 0.05 0.27 0.47 0.59 0.5 1.15 1.09 0.97 0.99 0.9 2.6 2.67 2.55 2.63 0.58 0.66 1.02 0.57 0.53 0.31 0.95 0.29 1.28 0.34 0.59 0.57 1.7 1.13 0.06 0.05 0.05
29.9 21.18 42.44 27.92 31.46 24.72 30.71 19 21.18 29.77 29.9 31 31 42.52 36.28 36.45 36.62 36.8 52 52.58 52.74 52.9 24.97 25.02 31.42 29.9 31.57 31.55 36.28 31.46 41.93 32.31 31.56 24.51 28.04 26.26 19 27.7 28.38
0.75 −1.34 0.2 1.07 0.95 −0.39 0.29 0.45 7.52 1.4 0.69 1.44 1.76 0.85 0.82 0.9 0.86 0.93 0.17 0.15 0.14 0.13 0.3 0.16 0.03 2.03 1.64 0.59 0.57 0.64 0.23 0.98 0.22 1.1 0.18 0.28 3.16 5.71 5.93
1.20 2.28 0.93 0.31 0.38 4.17 0.28 0.18 0.09 0.65 0.08 1.12 0.40 0.17 1.23 0.11 0.53 0.06 0.16 0.08 0.04 0.13 1.94 0.27 0.00 1.37 1.47 0.60 0.95 0.60 0.43 0.90 0.59 0.88 0.28 0.22 0.23 0.13 0.15
0.59 0.81 1 0.35 0.4 1.35 0.22 0.13 0.66 0.92 0.52 0.71 0.22 0.25 0.89 0.11 0.36 0.06 0.18 0.09 0.27 0.21 1.18 0.18 0.02 0.67 1.55 0.39 0.76 0.36 0.38 0.5 0.33 0.64 0.21 0.21 0.12 0.08 0.09
6 6 17 5 6 10 11 11 6 5 11 5 7 9 7 5 6 5 5 7 5 6 6 10 7 6 6 13 16 13 19 13 10 5 21 6 10 5 5
Meissner and Michaels (1949) Meissner and Michaels (1949) Papaioannou and Panayiotou (1989) International Critical Table International Critical Table Shipp (1970) Lam and Benson (1970) Lam and Benson (1970) Meissner and Michaels (1949) Meissner and Michaels (1949) Shipp (1970) Meissner and Michaels (1949) International Critical Table Evans and Clever (1964) Schmidt et al. (1966) Schmidt et al. (1966) Schmidt et al. (1966) Schmidt et al. (1966) Schmidt et al. (1966) Schmidt et al. (1966) Schmidt et al. (1966) Schmidt et al. (1966) Michaels et al. (1950) Wright and Akhtar (1970) International Critical Table Michaels et al. (1950) Michaels et al. (1950) Giner et al. (2004) Jimenez et al. (2000) Giner et al. (2004) Segade et al. (2003) Giner et al. (2004) Wright and Akhtar (1970) Meissner and Michaels (1949) Shipp (1970) International Critical Table Lam and Benson (1970) International Critical Table International Critical Table
2.06 1.56 4.04 3.68 4.00 1.02 2.48 2.50 2.01 1.87 1.97 2.97 2.94 3.41 3.39 3.28 3.27 3.18 3.85 3.82 3.63 3.64 1.80 1.21 −0.03 3.31 2.99 1.25 2.79 1.24 2.36 1.82 1.02 2.91 3.21 2.73 1.53 1.50 1.57
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
Mixture Component
4938
Table 1 Experimental and calculated differences of surface tensions of solvent and solute (◦ , Eq. (4)), surface Gibbs energy change (GS /RT , Eq. (3)), standard Gibbs energy of adsorption (−G◦ /RT , Eq. (10)), molar surface area (A¯ 2 , Eq. (6)), excess number of molecular layers (E 2 , Eq. (5)), relative absolute deviation percent (RAD%) in calculating the surface tension of pure solute (Eq. (15)), absolute average deviation percent (AAD%) in calculating the surface tension (Eq. (1)) for several binary organic solutions, the number of experimental data point (n) and the references for the experimental data
Toluene Toluene 2-M-2-P Acetone Ethanol Heptane Heptane Heptane Heptane Heptane Hexane Isooctane Isooctane Isooctane Isooctane Isooctane Isooctane Hexadecane Hexadecane Hexadecane Hexadecane 2-M-1-P 2-Butanol 2-M-2-P 2-Propanol Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol 1-Pentanol Methanol Ethanol 1-Propanol 1-Hexanol 1-Heptanol 1-Octanol 1-Decanol Hexane Heptane Octane Nonane Decane Cyclohexane Cyclohexane Benzene Benzene
283.15 313.15 298.15 291.15 290.65 287.81 297.82 307.86 317.86 327.88 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 313.15 323.15 333.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 293.15 303.15 293.15 303.15
4.82 4.58 3.09 3.6 4.2 4.64 4.57 4.34 4.08 4.03 5.89 6.5 5.9 5.8 5.7 5.5 5.5 3.65 3.81 3.75 3.84 5.9 5.3 8.19 6.12 10.51 10.77 9.25 11.76 8.45 9.69 7.5 10.62 10.92 9.37 6.83 6.06 5.48 4.38 14.58 12.82 11.32 10.21 9.25 8.75 8.35 4.9 4.65
4.8 4.65 2.97 3.71 3.85 4.57 4.48 4.27 4.06 4.12 5.98 6.39 5.92 5.74 5.78 5.55 5.54 3.69 3.77 3.95 3.94 6.01 5.41 8.58 6.46 11.72 10.91 9.32 11.68 8.44 9.62 7.54 11.99 11.14 9.49 6.79 6.04 5.39 4.38 14.29 12.55 11.12 10.07 9.12 8.92 8.37 4.98 4.84
0.16 0.07 0.66 −0.33 −0.89 0.77 0.72 0.71 0.67 0.61 0.68 0.85 0.69 0.72 0.58 0.57 0.62 0.05 −0.26 −0.47 −0.45 −0.7 −0.7 −0.67 −0.67 −0.54 0.22 0.54 0.76 0.85 0.91 1.04 −0.78 −0.06 0.27 0.92 1.08 1.23 1.52 1.83 2.05 2.11 2.21 2.37 0.21 0.64 −0.02 −0.15
1.73 1.61 1.75 0.98 0.46 2.29 2.22 2.16 2.07 2.03 2.47 2.70 2.47 2.47 2.33 2.28 2.33 1.36 1.07 0.90 0.92 1.09 0.99 1.48 1.20 1.92 2.61 2.77 3.22 2.98 3.17 3.06 1.70 2.35 2.52 2.84 2.88 2.91 3.00 4.49 4.58 4.52 4.52 4.58 2.40 2.76 1.59 1.43
31.24 31.92 29.19 24.55 21.07 38.81 39.14 39.45 39.81 40.16 36.11 42.44 42.65 42.81 42.96 43.2 43.34 61.82 62.56 62.95 63.33 28.76 28.64 29.2 25.39 16.58 21.19 24.97 25.36 28.57 28.65 31.93 16.59 21.15 24.97 35.1 38.1 41.02 46.58 36.28 39.14 41.94 44.65 47.30 31.31 31.55 27.92 28.15
2.39 4.77 0.33 −0.67 −0.25 0.59 0.6 0.57 0.55 0.58 0.77 0.79 0.87 0.81 0.98 0.95 0.87 10.52 −2.1 −1.12 −1.19 −0.59 −0.53 −0.86 −0.56 −0.78 2.48 1.03 0.96 0.69 0.74 0.56 −0.55 −9.12 2.14 0.63 0.52 0.44 0.33 0.7 0.6 0.55 0.5 0.45 3.16 0.98 −20.76 −2.12
0.07 0.27 0.59 0.47 1.53 0.34 0.46 0.37 0.11 0.54 0.49 0.59 0.11 0.34 0.47 0.30 0.25 0.16 0.18 0.93 0.49 0.55 0.48 1.93 1.60 5.48 0.64 0.30 0.38 0.04 0.31 0.16 6.19 1.01 0.51 0.16 0.08 0.33 0.00 1.62 1.37 0.94 0.63 0.56 0.68 0.08 0.28 0.69
0.04 0.16 0.4 0.19 0.35 0.28 0.29 0.24 0.18 0.36 0.33 0.37 0.09 0.23 0.29 0.29 0.31 0.08 0.2 0.36 0.27 0.26 0.2 0.65 0.61 1.59 0.41 0.21 0.29 0.1 0.19 0.12 1.49 0.45 0.29 0.09 0.09 0.21 0.06 1.19 1.09 0.8 0.69 0.64 0.37 0.22 0.21 0.32
5 5 13 5 5 11 11 11 11 11 8 21 21 21 21 21 21 5 5 5 5 10 11 10 14 18 16 13 14 16 14 16 14 24 16 15 14 18 14 14 14 14 14 14 8 8 8 8
International Critical Table International Critical Table Giner et al. (2004) Meissner and Michaels (1949) Meissner and Michaels (1949) Kahl et al. (2003a) Kahl et al. (2003a) Kahl et al. (2003a) Kahl et al. (2003a) Kahl et al. (2003a) Ridgway and Butler (1967) Gomez-Diaz et al. (2001) Gomez-Diaz et al. (2001) Gomez-Diaz et al. (2001) Gomez-Diaz et al. (2001) Gomez-Diaz et al. (2001) Gomez-Diaz et al. (2001) Rolo et al. (2002) Rolo et al. (2002) Rolo et al. (2002) Rolo et al. (2002) Lam et al. (1973) Lam et al. (1973) Lam et al. (1973) Postigo et al. (1987) Calvo et al. (2004) Calvo et al. (2004) Calvo et al. (2004) Calvo et al. (2004) Calvo et al. (2004) Calvo et al. (2004) Calvo et al. (2004) Calvo et al. (2001) Calvo et al. (2001) Calvo et al. (2001) Calvo et al. (2001) Calvo et al. (2001) Calvo et al. (2001) Calvo et al. (2001) Calvo et al. (2000) Calvo et al. (2000) Calvo et al. (2000) Calvo et al. (2000) Calvo et al. (2000) Suri and Ramakrishna (1968) Suri and Ramakrishna (1968) Suri and Ramakrishna (1968) Suri and Ramakrishna (1968)
4939
Chlorobenzene Chlorobenzene 1-Chlorobutane Chloroform Chloroform Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Decane Decane Decane Decane 1-Decanol 1-Decanol 1-Decanol DCM 1,3-Dioxolane 1,3-Dioxolane 1,3-Dioxolane 1,3-Dioxolane 1,3-Dioxolane 1,3-Dioxolane 1,3-Dioxolane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87
4940
Table 1 (continued) No.
1
2
DMF DMF DMF DMF DMF DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO Dodecane Dodecane Dodecane Dodecane 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol
Toluene Toluene Toluene Toluene Toluene Acetone Benzene Benzene Benzene Bromobenzene Bromobenzene Bromobenzene Butyl acetate Butyl acetate Butyl acetate CTC CTC CTC Chlorobenzene Chlorobenzene Chlorobenzene Chloroform Chloroform Chloroform Toluene Toluene Toluene Hexane Hexane Hexane Hexane Ethanol Ethanol Ethanol Ethanol Ethanol Ethanol Ethanol 1-Propanol 1-Propanol 1-Propanol 1-Propanol 1-Butanol
Temp. (K)
287.81 297.82 307.86 317.86 327.88 303.15 303.15 313.15 323.15 303.15 313.15 323.15 293.15 303.15 313.15 303.15 313.15 323.15 303.15 313.15 323.15 303.15 313.15 323.15 303.15 313.15 323.15 298.15 303.15 308.15 313.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 293.15
◦ (mN/m) Exp.
Calc.
8.03 8.07 8.05 7.91 7.74 19.99 14.92 15.03 15.16 7.32 6.93 7.29 17.9 17.5 17.1 17.09 16.99 17.3 10.43 10.45 10.47 16.58 16.75 17.02 15.09 15.02 15.12 6.75 6.88 6.95 7.04 26.6 26.8 26.7 26.4 26.3 25.9 25.9 23.74 23.81 23.93 23.97 23.01
8.12 8.04 7.99 8 7.84 20.58 15.67 15.97 15.92 7.33 7.2 7.39 17.67 17.33 16.92 17.42 17.12 17.36 10.31 10.53 10.32 16.89 16.92 17.01 15.13 15.22 15.27 6.9 6.83 6.92 6.91 26.74 26.88 26.67 26.46 26.46 26.18 25.91 23.15 23.26 23.31 23.36 22.52
GS /RT
−G◦ /RT
A¯ 2 (A˚ 2 )
E 2
RAD%
AAD%
n
Ref.
0.51 0.53 0.54 0.43 0.36 1.34 0.35 0.33 0.45 0.38 0.36 0.08 1.9 1.84 1.81 0.91 0.9 0.79 0.18 0.09 0.17 0.47 0.46 0.57 0.3 0.28 0.39 −0.36 −0.27 −0.23 −0.16 1.18 1.15 1.15 1.11 1.1 1.06 1.08 1.96 1.92 1.9 1.87 2.54
2.60 2.61 2.62 2.51 2.42 4.36 3.10 3.10 3.22 2.37 2.33 2.08 4.77 4.69 4.64 3.77 3.74 3.64 2.51 2.44 2.50 3.30 3.29 3.40 3.02 3.00 3.12 1.57 1.65 1.70 1.77 4.47 4.44 4.43 4.39 4.38 4.32 4.33 5.10 5.07 5.05 5.02 5.65
31.14 31.46 31.8 32.04 32.26 24.84 28.15 28.39 28.63 31.4 31.59 31.79 36.32 36.6 36.89 29.74 29.99 30.23 30.75 30.96 31.17 26.25 26.43 26.6 31.69 31.92 32.16 36.28 36.45 36.62 36.8 21.11 21.18 21.26 21.34 21.43 21.51 21.6 24.88 24.97 25.05 25.13 28.46
1.24 1.16 1.12 1.33 1.53 0.88 2.86 3.03 2.16 1.44 1.4 6.13 0.85 0.83 0.81 1.34 1.31 1.48 4.22 8.4 4.2 2.23 2.23 1.79 3.84 4.03 2.77 −1.64 −2.18 −2.6 −3.68 1.18 1.2 1.18 1.19 1.19 1.19 1.16 0.75 0.75 0.75 0.76 0.64
0.31 0.11 0.23 0.35 0.41 2.63 2.73 3.60 3.05 0.03 0.79 0.31 0.97 0.74 0.80 1.30 0.54 0.26 0.38 0.26 0.51 1.20 0.70 0.04 0.15 0.76 0.60 0.84 0.29 0.18 0.79 0.63 0.37 0.14 0.28 0.77 1.37 0.05 2.49 2.36 2.71 2.72 2.00
0.25 0.14 0.24 0.24 0.26 1.99 1.42 1.89 1.67 0.07 0.41 0.29 0.78 0.57 0.57 1.13 0.46 0.22 0.26 0.24 0.19 0.88 0.56 0.36 0.16 0.34 0.41 0.32 0.13 0.08 0.34 0.54 0.37 0.38 0.64 0.97 1.23 0.58 1.28 1.16 1.32 1.26 1.61
7 7 7 7 7 7 8 8 8 8 8 8 12 12 12 8 8 8 8 8 8 8 8 8 8 8 8 5 5 5 5 8 8 8 8 8 8 8 16 16 16 16 17
Kahl et al. (2003b) Kahl et al. (2003b) Kahl et al. (2003b) Kahl et al. (2003b) Kahl et al. (2003b) Clever and Snead (1963) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Tsierkezos et al. (2000) Tsierkezos et al. (2000) Tsierkezos et al. (2000) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Schmidt and Clever (1968) Schmidt and Clever (1968) Schmidt and Clever (1968) Schmidt and Clever (1968) Azizian and Hemmati (2003) Azizian and Hemmati (2003) Azizian and Hemmati (2003) Azizian and Hemmati (2003) Azizian and Hemmati (2003) Azizian and Hemmati (2003) Azizian and Hemmati (2003) Jimenez et al. (2001) Jimenez et al. (2001) Jimenez et al. (2001) Jimenez et al. (2001) Jimenez et al. (2001)
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130
Mixture Component
1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol Ethyl butyrate Furfural Furfural Heptane Heptane Heptane Heptane Heptane 1-Heptanol 1-Heptanol 1-Hexanol 1-Hexanol Methyl acetate 2-M-1-CP Nitrobenzene Nitrobenzene Nitrobenzene Nitrobenzene Nitrobenzene Nitrobenzene Nitromethane 1-Octanol 1-Octanol 1-Pentanol 1-Pentanol n-Pentyl acetate Phenol Phenol Phenol 1-Propanol Propionic acid TCET TCET Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene
1-Butanol 1-Butanol 1-Butanol Methanol 2-Propanol Toluene Hexadecane Hexadecane Hexadecane Hexadecane Hexadecane Hexane Octane Hexane Octane Pentane 2-M-2-P Benzene Benzene Cyclohexane Cyclohexane 1,4-Dioxane Toluene Benzene Hexane Octane Hexane Octane Methanol Acetone Benzene Benzene Hexane Cyclohexane Cyclohexane Cyclopentane Acetone Acetone Acetone Acetone Acetone Cyclohexane Cyclopentane Ethyl acetate Heptane Heptane Heptane Heptane
298.15 303.15 308.15 303.15 298.15 298.15 293.15 303.15 313.15 323.15 333.15 298.15 298.15 298.15 298.15 298.15 298.15 293.15 303.15 293.15 303.15 293.15 328.15 298.15 298.15 298.15 298.15 298.15 303.15 293.15 308.15 308.15 298.15 303.15 298.15 298.15 287.81 297.82 307.86 317.86 327.88 298.15 298.15 298.15 287.81 297.82 307.86 317.86
23.12 23.17 23.26 1.72 21.7 15 7.59 7.56 7.76 7.86 7.9 8.58 5.3 7.84 4.56 9.25 1.6 14.55 14.65 18.4 18.35 9.65 14.49 6.9 9.24 5.96 7.08 3.8 3.03 22 12 12.37 5.5 1.89 6.92 9.45 4.99 4.98 5.01 5.13 5.28 3.56 6.09 4.5 8.23 8.13 7.92 7.7
22.62 22.68 22.73 2.16 21.37 14.81 7.54 7.57 8.12 9.44 9.76 9.06 5.33 7.99 4.61 9.71 1.56 14.31 14.06 18.55 18.52 9.71 14.64 6.99 9.51 6.04 7.24 3.8 2.95 22.27 12.02 12.36 5.61 1.78 6.9 9.31 6.73 5.27 5.62 6.5 9.04 3.66 6.07 4.46 8.22 8.11 7.9 7.7
2.51 2.51 2.45 −1.54 1.39 1.03 −0.2 −0.3 −0.54 −1.06 −1.21 0.45 0.92 0.7 0.96 0.52 1.46 0.51 0.7 0.85 1.42 0.04 0.52 1.72 0.53 0.75 0.83 1.23 0.63 0.92 0.74 0.75 1.3 1.34 0.59 0.37 −1.22 −0.35 −0.54 −0.95 −1.62 0.77 0.32 0.2 0.98 0.98 0.97 0.96
5.63 5.63 5.57 −0.77 4.45 3.73 1.82 1.72 1.55 1.18 1.07 2.65 2.59 2.78 2.49 2.79 1.90 3.17 3.34 3.77 4.34 2.31 3.20 3.66 2.78 2.55 2.81 2.57 1.71 4.02 3.23 3.26 3.02 1.92 2.52 2.60 0.69 1.31 1.19 0.92 0.58 2.07 2.12 1.70 3.09 3.07 3.04 3.00
28.57 28.66 28.75 16.65 25.37 31.57 61.82 62.19 62.56 62.95 63.33 36.28 41.93 36.28 41.93 33.37 29.19 27.93 28.15 31.31 31.55 27.15 32.28 28.03 36.28 41.93 36.28 41.93 16.64 24.6 28.26 28.26 36.28 31.56 31.94 19 24.49 24.71 24.98 25.21 25.45 31.94 19 29.9 38.81 39.14 39.45 39.81
0.64 0.63 0.64 −0.04 0.96 1.12 −5.81 −3.7 −2.07 −1.05 −0.9 1.69 0.59 0.98 0.49 1.45 0.08 1.95 1.41 1.67 0.97 17.22 1.98 0.27 1.52 0.81 0.75 0.32 0.19 1.45 1.07 1.1 0.37 0.11 0.9 1.19 −0.25 −0.86 −0.54 −0.31 −0.18 0.36 0.87 1.6 0.82 0.79 0.76 0.73
2.08 2.07 2.28 2.03 1.55 0.68 0.24 0.05 1.95 9.06 11.27 2.68 0.14 0.84 0.24 2.97 0.20 0.83 2.14 0.60 0.71 0.18 0.64 0.31 1.51 0.38 0.89 0.00 0.36 1.17 0.08 0.04 0.61 0.46 0.08 0.64 7.27 1.27 2.83 6.74 19.78 0.41 0.09 0.17 0.05 0.10 0.11 0.00
1.76 1.81 1.81 0.5 1.25 0.38 0.1 0.09 0.62 2.18 2.36 1.49 0.14 0.57 0.21 1.45 0.21 0.52 1.35 0.67 0.66 0.13 0.4 0.34 0.91 0.27 0.67 0.19 0.25 0.66 0.23 0.03 0.6 0.4 0.11 0.33 1.76 0.59 1.08 1.92 3.46 0.31 0.07 0.13 0.16 0.09 0.07 0.08
17 17 17 13 6 5 5 5 5 5 5 17 19 19 19 14 13 11 11 8 8 10 5 6 18 19 18 18 12 5 5 5 17 9 11 11 11 11 11 11 11 13 12 6 6 7 7 7
Jimenez et al. (2001) Jimenez et al. (2001) Jimenez et al. (2001) Kijevcanin et al. (2003) Michaels et al. (1950) Michaels et al. (1950) Rolo et al. (2002) Rolo et al. (2002) Rolo et al. (2002) Rolo et al. (2002) Rolo et al. (2002) Jimenez et al. (2000) Segade et al. (2003) Jimenez et al. (2000) Segade et al. (2003) Postigo et al. (1987) Giner et al. (2004) Suri and Ramakrishna (1968) Suri and Ramakrishna (1968) Suri and Ramakrishna (1968) Suri and Ramakrishna (1968) Suri and Ramakrishna (1968) International Critical Table Meissner and Michaels (1949) Jimenez et al. (2000) Segade et al. (2003) Jimenez et al. (2000) Segade et al. (2003) Santos et al. (2003) Meissner and Michaels (1949) Meissner and Michaels (1949) International Critical Table Jimenez et al. (2000) Wright and Akhtar (1970) Lam and Benson (1970) Lam and Benson (1970) Kahl et al. (2003a) Kahl et al. (2003a) Kahl et al. (2003a) Kahl et al. (2003a) Kahl et al. (2003a) Lam and Benson (1970) Lam and Benson (1970) Michaels et al. (1950) Kahl et al. (2003b) Kahl et al. (2003b) Kahl et al. (2003b) Kahl et al. (2003b)
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178
4941
4942
Table 1 (continued) No.
Overall AAD%
1
2
Toluene TCE TCE o-Xylene o-Xylene o-Xylene o-Xylene o-Xylene o-Xylene o-Xylene m-Xylene m-Xylene m-Xylene m-Xylene m-Xylene m-Xylene p-Xylene p-Xylene p-Xylene p-Xylene p-Xylene p-Xylene
Heptane 1-Propanol 2-Propanol Acetone 2-Butanone Benzene 2-Propanol isoPropyl ether 2-M-2-P MTBE Acetone 2-Butanone 2-Propanol isoPropyl ether 2-M-2-P MTBE Acetone 2-Butanone 2-Propanol isoPropyl ether 2-M-2-P MTBE
Temp. (K)
327.88 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15
◦ (mN/m) Exp.
Calc.
7.61 1.81 3.71 5.34 5.07 1.24 8.67 12.04 9.63 10.1 4.35 4.08 7.43 11.05 8.39 9.11 3.88 3.61 6.96 10.58 7.92 8.64
7.58 2.05 3.73 6.22 5.22 1.3 8.3 11.7 9.35 10.26 5.03 4.05 7.07 10.67 8.14 9.29 4.34 3.58 6.65 10.29 7.8 8.86
GS /RT
0.87 −0.75 −0.6 −1.01 −0.39 0.17 0.52 0.61 0.66 0.41 −0.99 −0.18 0.52 0.59 0.61 0.29 −0.74 −0.18 0.41 0.47 0.44 0.21
−G◦ /RT
2.90 −0.03 0.72 0.82 1.26 0.43 2.64 3.07 2.90 2.74 0.63 1.22 2.48 2.96 2.71 2.52 0.73 1.10 2.30 2.80 2.49 2.39
A¯ 2 (A˚ 2 )
E 2
RAD%
AAD%
n
Ref.
40.16 24.97 25.37 24.73 28.2 28.04 25.37 38.21 29.19 34.08 24.73 28.2 25.37 38.21 29.19 34.08 24.73 28.2 25.37 38.21 29.19 34.08
0.78 −0.15 −0.38 −0.32 −0.89 0.49 1.02 1.82 1.03 2.05 −0.26 −1.56 0.88 1.73 0.97 2.6 −0.32 −1.36 1.04 2.09 1.28 3.44
0.18 1.03 0.10 3.67 0.62 0.21 1.77 1.96 1.40 0.83 2.83 0.12 1.72 2.20 1.25 0.94 1.92 0.12 1.48 1.68 0.60 1.14
0.12 0.34 0.17 0.95 0.23 0.13 0.95 1.06 0.78 0.45 0.79 0.06 0.94 1.22 0.74 0.44 0.61 0.05 0.79 0.88 0.34 0.55
7 14 14 11 11 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
Kahl et al. (2003b) Bardavid et al. (1994) Bardavid et al. (1994) Ouyang et al. (2004b) Ouyang et al. (2004b) Lam and Benson (1970) Ouyang et al. (2003) Ouyang et al. (2004a) Ouyang et al. (2003) Ouyang et al. (2004a) Ouyang et al. (2004b) Ouyang et al. (2004b) Ouyang et al. (2003) Ouyang et al. (2004a) Ouyang et al. (2003) Ouyang et al. (2004a) Ouyang et al. (2004b) Ouyang et al. (2004b) Ouyang et al. (2003) Ouyang et al. (2004a) Ouyang et al. (2003) Ouyang et al. (2004a)
0.56
2-M-1-CP: 2-Methyl-1-chloropropane, 2-M-2-CP: 2-Methyl-2-propanol, CTC: Carbon tetrachloride, 2-M-1-P: 2-Methyl-1-propanol, 2-M-2-P: 2-Methyl-2-propanol, DCM: Dichloromethane, DMF: Dimethyl formamide, DMSO: Dimethylsulfoxide, Furfural: 2-Furan carboxaldehyde, TCET: Tetrachloroethylene, TCE: 1,1,1-Trichloroethane, MTBE: Methyl tert-butyl ether.
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
Mixture Component
Table 2 Experimental and calculated differences of surface tensions of solvent and solute (◦ , Eq. (4)), surface Gibbs energy change (GS /RT , Eq. (3)), standard Gibbs energy of adsorption (−G◦ /RT , Eq. (10)), molar surface area (A¯ 2 , Eq. (6)), excess number of molecular layers (E 2 , Eq. (5)), relative absolute deviation percent (RAD%) in calculating the surface tension of pure solute (Eq. (15)), absolute average deviation percent (AAD%) in calculating the surface tension (Eq. (1)) for several binary aqueous solutions, the number of experimental data point (n) and the references for the experimental data (Ref.) No.
2
Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water
MEA MEA MEA MEA MEA MEA DEA DEA DEA DEA DEA DEA TEA TEA TEA TEA TEA TEA Formic acid Formic acid Formic acid Formic acid Formic acid Formic acid Formic acid Acetic acid Acetic acid Acetic acid Acetic acid Acetic acid Acetic acid Acetic acid Propionic acid Propionic acid Propionic acid Propionic acid Propionic acid Propionic acid Propionic acid Methanol Methanol
298.15 303.15 308.15 313.15 318.15 323.15 298.15 303.15 308.15 313.15 318.15 323.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15
◦ (mN/m) Exp.
Calc.
23.06 23.07 23.08 23.09 23.11 23.11 24.8 24.75 24.76 24.77 24.79 24.8 26.06 26.05 26.04 26.04 26.04 26.04 35.17 34.98 34.74 34.48 34.13 33.97 33.58 45.14 44.89 44.58 44.31 43.88 43.71 43.26 46.09 45.84 45.53 45.24 44.83 44.65 44.24 49.8 49.5
21.79 21.79 21.79 21.79 21.83 21.83 23.75 23.7 23.7 23.75 23.75 23.75 26.04 25.97 25.97 25.97 25.97 25.97 34.6 34.48 34.13 33.9 33.56 33.33 33 43.86 43.48 43.29 42.92 42.55 42.37 42.02 45.45 45.25 45.05 44.64 44.25 44.05 43.67 49.5 49.26
GS /RT
−G◦ /RT
˚ 2) A¯ 2 (A
E 2
RAD%
AAD%
n
Ref.
2.18 2.18 2.18 2.18 2.18 2.18 2.33 2.33 2.33 2.33 2.33 2.33 3.12 3.12 3.12 3.12 3.12 3.12 1.75 1.78 1.75 1.76 1.75 1.75 1.74 2.66 2.67 2.67 2.68 2.69 2.69 2.7 3.78 3.79 3.79 3.8 3.81 3.82 3.82 1.98 1.98
5.26 5.26 5.26 5.26 5.26 5.26 5.50 5.50 5.50 5.50 5.50 5.50 6.38 6.38 6.38 6.38 6.38 6.38 5.29 5.32 5.28 5.28 5.26 5.26 5.24 6.44 6.44 6.44 6.44 6.44 6.44 6.44 7.60 7.60 7.60 7.60 7.60 7.61 7.60 5.88 5.88
21.57 21.62 21.7 21.74 21.8 21.87 29.43 29.47 29.56 29.6 29.65 29.73 36.54 36.6 36.67 36.73 36.77 36.86 15.77 15.85 15.89 15.94 16.01 16.07 16.14 20.83 20.89 20.95 21.02 21.08 21.14 21.21 24.86 24.95 25.02 25.1 25.19 25.27 25.35 16.52 16.58
0.55 0.55 0.54 0.53 0.53 0.52 0.76 0.75 0.74 0.73 0.72 0.71 0.74 0.73 0.72 0.71 0.7 0.69 0.78 0.76 0.75 0.74 0.72 0.71 0.7 0.87 0.85 0.84 0.82 0.8 0.78 0.76 0.75 0.73 0.72 0.7 0.69 0.67 0.66 1.03 1.01
2.59 2.66 2.72 2.80 2.80 2.86 2.22 2.26 2.32 2.28 2.36 2.44 0.04 0.18 0.16 0.16 0.16 0.17 1.52 1.35 1.67 1.61 1.61 1.84 1.69 4.64 5.20 4.84 5.32 5.19 5.33 5.03 2.40 2.25 1.87 2.38 2.35 2.48 2.41 1.31 1.07
2.02 2.06 2.09 2.13 2.16 2.21 2.04 2.06 2.09 2.12 2.15 2.19 0.14 0.13 0.14 0.14 0.16 0.16 0.98 1.04 0.95 0.99 0.96 1.01 0.96 3.09 3.09 3.2 3.27 3.38 3.42 3.5 2.38 2.52 2.45 2.47 2.51 2.58 2.67 0.73 0.79
13 13 13 13 13 13 11 11 11 11 11 11 11 11 11 11 11 11 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
Vazquez et al. (1997) Vazquez et al. (1997) Vazquez et al. (1997) Vazquez et al. (1997) Vazquez et al. (1997) Vazquez et al. (1997) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Vazquez et al. (1995) Vazquez et al. (1995)
4943
1
Temp. (K)
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
Mixture Component
4944
Table 2 (continued) No.
1
2
Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water
Methanol Methanol Methanol Methanol Methanol Ethanol Ethanol Ethanol Ethanol Ethanol Ethanol Ethanol 1-Propanol 1-Propanol 1-Propanol 1-Propanol 1-Propanol 1-Propanol 1-Propanol 2-Propanol 2-Propanol 2-Propanol 2-Propanol 2-Propanol 2-Propanol 2-Propanol 1,2-Ethanediol 1,2-Ethanediol 1,2-Propanediol 1,2-Propanediol 1,2-Propanediol 1,2-Propanediol 1,2-Propanediol 1,2-Propanediol 1,2-Propanediol 1,2-Propanediol 1,2-Propanediol 1,3-Propanediol 1,2-Butanediol 2,3-Butanediol 1,3-Butanediol 1,3-Butanediol 1,4-Butanediol 1,4-Butanediol
Temp. (K)
303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 298.15 303.15 298.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 303.15 298.15 298.15 298.15 303.15 298.15 303.15
◦ (mN/m) Exp.
Calc.
49.2 48.9 48.39 48.23 47.71 50.44 50.44 49.8 49.38 48.9 48.62 48.1 49.06 48.73 48.32 47.91 47.41 47.15 46.61 51.01 50.79 50.49 50.19 49.82 49.63 49.23 23.81 24.91 36.41 35.5 34.52 33.82 32.57 31.36 30.39 29.39 28.11 24.2 40.81 39.5 34.88 34.11 26.5 27.36
49.02 49.02 48.08 47.85 47.39 50.25 49.75 49.5 49.02 48.54 48.31 47.85 49.02 48.54 48.08 47.85 47.17 46.95 46.51 50.76 50.51 50.25 50 49.75 49.5 49.02 23.81 24.21 34.97 34.6 33.56 32.79 31.85 30.58 29.67 28.65 27.55 23.64 40.65 39.22 34.01 33.56 25.91 26.67
GS /RT
−G◦ /RT
˚ 2) A¯ 2 (A
E 2
RAD%
AAD%
n
Ref.
1.99 1.99 2.01 2.01 2.02 3.1 3 3.01 3.02 3.03 3.03 3.04 4.62 4.63 4.64 4.65 4.66 4.67 4.68 3.9 3.9 3.91 3.91 3.92 3.92 3.93 1.82 1.9 2.48 2.49 2.52 2.5 2.53 2.53 2.49 2.45 2.49 2.87 3.71 3.06 3.12 3.21 2.78 3.04
5.88 5.88 5.88 5.88 5.88 7.02 6.91 6.91 6.91 6.91 6.91 6.91 8.51 8.51 8.51 8.52 8.51 8.52 8.52 7.83 7.82 7.83 7.82 7.83 7.82 7.82 4.99 5.09 6.03 6.03 6.03 5.99 5.99 5.95 5.88 5.81 5.81 6.03 7.41 6.73 6.65 6.72 6.03 6.32
16.65 16.72 16.79 16.86 16.93 21.11 21.18 21.26 21.34 21.43 21.51 21.6 24.9 24.97 25.06 25.15 25.23 25.32 25.42 25.27 25.36 25.45 25.55 25.65 25.75 25.86 20.5 20.55 24.64 24.67 24.8 24.92 25.05 25.18 25.31 25.46 25.6 24.41 28.2 28.23 28.18 28.2 27.95 28
0.99 0.97 0.94 0.92 0.9 0.85 0.87 0.84 0.82 0.8 0.79 0.77 0.65 0.64 0.62 0.61 0.59 0.58 0.57 0.82 0.8 0.79 0.77 0.75 0.74 0.73 0.65 0.65 0.88 0.84 0.79 0.76 0.7 0.66 0.63 0.61 0.56 0.49 0.75 0.89 0.77 0.72 0.65 0.6
0.82 0.56 1.47 1.84 1.58 0.85 3.16 1.40 1.71 1.75 1.53 1.26 0.17 0.82 1.05 0.27 1.09 0.92 0.47 1.15 1.32 1.16 0.94 0.36 0.68 1.12 0.00 1.51 4.02 2.52 2.74 3.02 2.15 2.36 2.23 2.36 1.82 1.19 0.51 0.86 2.35 1.48 1.30 1.58
0.9 0.98 1.15 1.27 1.43 1.68 1.42 1.47 1.49 1.43 1.49 1.51 1.09 1.1 1.17 1.1 1.07 1.13 1.11 1.46 1.5 1.51 1.55 1.54 1.62 1.64 0.52 1.02 2.65 2.45 2.61 2.72 2.08 2.14 2.04 2.22 1.89 0.97 1.02 0.85 2.21 1.88 1.62 1.91
14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 7 18 8 8 8 8 8 8 8 8 8 18 18 18 18 18 18 18
Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Hoke and Chen (1991) Nakanishi et al. (1971) Hoke and Patton (1992) Hoke and Patton (1992) Hoke and Patton (1992) Hoke and Patton (1992) Hoke and Patton (1992) Hoke and Patton (1992) Hoke and Patton (1992) Hoke and Patton (1992) Hoke and Patton (1992) Nakanishi et al. (1971) Hawrylak et al. (1998) Hawrylak et al. (1998) Hawrylak et al. (1998) Nakanishi et al. (1971) Hawrylak et al. (1998) Nakanishi et al. (1971)
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
Mixture Component
MEA: Monoethanolanine (2-Aminoethanol), DEA: Diethanolamine (2,2-Iminobisethanol), TEA: Triethanolamine (2,2,2-Nitrilotrisethanol), 1-AP: 1-Amino-2-propanol, AMP: 2-Amino-2-methyl-1propanol, 3-AP: 3-Amino-1-propanol, MDEA: N-Methyldiethanolamine, TFE: Trifluoroethanol.
1.8 Overall AAD%
86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water
MDEA MDEA MDEA MDEA MDEA MDEA 3-AP 3-AP 3-AP 3-AP 3-AP 3-AP AMP 1-AP TFE
298.15 303.15 308.15 313.15 318.15 323.15 298.15 303.15 308.15 313.15 318.15 323.15 298.15 298.15 298.15
33.11 33.11 32.8 32.21 31.68 31.04 28.11 28.44 28.81 29.04 29.51 29.76 40.64 34.63 47.5
32.15 32.15 31.85 31.45 30.96 30.58 27.47 27.62 27.86 27.93 28.25 28.41 39.68 33.11 46.95
2.97 2.97 2.98 2.99 3.01 3.08 1.93 2 2.01 2.05 2.11 2.13 3.33 2.41 4.26
6.44 6.44 6.44 6.44 6.44 6.50 5.24 5.32 5.34 5.38 5.45 5.48 7.01 5.91 8.11
32.08 32.16 32.24 32.31 32.42 32.5 25.29 25.39 25.48 25.57 25.67 25.76 20.89 25.7 24.35
0.87 0.86 0.84 0.81 0.78 0.73 0.9 0.86 0.86 0.84 0.82 0.81 0.62 0.9 0.66
2.47 2.52 2.53 2.04 1.94 1.25 1.46 1.92 2.28 2.74 3.20 3.54 3.06 4.07 2.48
3.31 3.35 3.26 2.86 2.37 2.09 1.03 1.42 1.6 1.94 2.26 2.5 3.17 3.34 3.44
14 14 14 14 14 14 12 12 12 12 12 12 14 12 15
Alvarez et al. (1998) Alvarez et al. (1998) Alvarez et al. (1998) Alvarez et al. (1998) Alvarez et al. (1998) Alvarez et al. (1998) Alvarez et al. (2003) Alvarez et al. (2003) Alvarez et al. (2003) Alvarez et al. (2003) Alvarez et al. (2003) Alvarez et al. (2003) Vazquez et al. (1997) Alvarez et al. (2003) Gente and La Mesa (2000)
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
4945
Finally in the 13th and 14th columns of Tables 1 and 2, the number of data points (n) and the references of the experimental data of solutions used in the calculations are given. In Table 3, the standard Gibbs energy of adsorption calculated by applying Eq. (10) to the binary solutions: (1,4dioxane + n-alkanol), (1,4-dioxane + n-alkane) and (1,3dioxolane + n-alkanol) are reported. 4. Discussion In the 5th and 6th columns of Tables 1 and 2, the experimental and calculated values of ◦ are compared. Good agreement in most cases is to be noted. The reported RAD% values in these tables indicate that Eqs. (2) and (4) can accurately calculate the surface tension of a pure solute from the surface tension of its solution in a solvent with known surface tension. This provides a means for obtaining the surface tension of a highly volatile or unstable substance, for which the direct surface tension measurement is very difficult or costly from the surface tension of binary solutions. 4.1. Variation of −G◦ /RT and GS /RT in aqueous solutions of homologues series
GS /RT is reported in 7th column. It is to be noted that generally the free energy change for aqueous solutions is greater than for organic solutions. This may be related to the interactions between the −OH group in water and the −NH2 and –OH groups in the solute and hydrogen bonding, which is formed in these solutions (Papaioannou et al., 1993). In aqueous solutions of monoethanolamine (MEA), diethanolamine (DEA) and triethanolamine (TEA), GS /RT increases from MEA to TEA. This trend is related to the strength of hydrogen bonding on increasing the number of hydroxyl groups from MEA to TEA. In aqueous solutions of aliphatic acids, GS /RT increases from formic to propionic acid. −G◦ /RT and GS /RT both increase with increasing molecular size of the solute within a series of homologous compounds. The increase in −G◦ per −CH2 group at 298.15 K is 2.83 kJ mol−1 for aliphatic acids, 3.27 kJ mol−1 for aliphatic alcohols and 3.01 kJ mol−1 for alkanediols. This consistent variation in the standard Gibbs energy of adsorption (−G◦ ) with regard to methylene addition is analogous to Traube’s rule defined for methylene addition to n-alkanes (Kipling, 1965; Adamson and Gast, 1997). It is also in good agreement with previous observations on the adsorption of hydrocarbons at the air–water interface (Valsaraj, 1994) and long chain anionic surfactants from aqueous solutions (Feurstenau and Healy, 1972). Generally, in aqueous solutions of a homologue series, the free energy change and the standard Gibbs energy of adsorption increase with increasing number of carbon atoms. This trend is linear as can be seen in Figs. 1 and 2.
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R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
Table 3 Surface free energy change, excess number of molecular layers, experimental and calculated standard Gibbs energy of adsorption for binary solutions of 1,4-Dioxane+n-Alkanol, 1,3-Dioxolane+n-Alkanol and 1,4-Dioxane + n-Alkane* Solvent → 1,4-Dioxane Solute ↓
GS /RT
1,3-Dioxolane
E 2
GS /RT E 2
−G◦ /RT This work EL model Exp. Ref.**
Methanol −0.78 Ethanol −0.06 1-Propanol 0.27 2-Propanol 1-Butanol 2-Butanol 1-Pentanol 1-Hexanol 0.92 1-Heptanol 1.08 1-Octanol 1.23 1-Decanol 1.52 Hexane 1.83 Heptane 2.05 Octane 2.11 Nonane 2.21 Decane 2.37
−0.55 1.71 −9.12 2.35 2.14 2.52
0.63 0.52 0.44 0.33 0.70 0.60 0.55 0.50 0.45
2.83 2.88 2.92 3.00 4.49 4.58 4.52 4.52 4.58
1.58 2.26 2.43
2.77 2.83 2.83 2.93 4.51 4.69 4.56 4.61 4.76
−G◦ /RT This work EL model Exp. Ref.**
1.53 Calvo et al. (2002) −0.54 2.24 Calvo et al. (2002) 0.22 2.40 Calvo et al. (2002) 0.54 0.76 0.85 0.91 1.04 2.83 Calvo et al. (2001) 2.96 Calvo et al. (2001) 2.97 Calvo et al. (2001) 3.04 Calvo et al. (2001) 4.45 Calvo et al. (2000) 4.72 Calvo et al. (2000) 4.49 Calvo et al. (2000) 4.54 Calvo et al. (2000) 4.71 Calvo et al. (2000)
−0.78 2.48 1.03 0.96 0.69 0.74 0.56
1.92 2.61 2.78 3.22 2.99 3.17 3.06
1.67 2.47 2.75 3.11 2.98 3.12 3.05
1.61 2.45 2.75 3.09 2.97 3.12 3.04
Calvo Calvo Calvo Calvo Calvo Calvo Calvo
et et et et et et et
al. al. al. al. al. al. al.
(2004) (2004) (2004) (2004) (2004) (2004) (2004)
∗ For all solutions, T = 298.15 K. ∗∗ Reference for experimental and EL model data of −G◦ /RT .
The results of calculations for isomeric butanediols at 298.15 K show the following trend for the standard Gibbs energy of adsorption (−G◦ ): 1,2-butanediol > 2,3-butanediol > 1,3-butanediol > 1,4-butanediol. Experimental data for −G◦ shows the same trend as for the aqueous solutions of isomeric butanediols (Zagorska et al., 1994). This relationship reflects a higher surface activity and a higher degree of hydrophobicity for both 1,2-butanediol and 2,3-butanediol. This observation can be explained by hydrogen bonding operating between solute molecules (Buc, 1963; Japaridze, 1977). Also this behaviour may be associated with the ability of neighbouring −OH groups to form intermolecular hydrogen bonds, which would reduce the capability of these molecules from interacting with the solvent. This in turn would lead to a higher adsorbability of both 1,2- and 2,3-butanediol than 1,3- and 1,4-butanediol. Since the −OH groups are farther apart in 1,3- and 1,4butanediol, these molecules form hydrogen bonding with water molecules only. In fact the difference between GS and −G◦ for 2,3-butanediol and 1,3-butanediol is not significant and this matter is puzzling and cannot easily be explained in terms of mixed behaviour. 4.2. Variation of −G◦ /RT and GS /RT in organic solutions of homologues series First we examine the 1,4-dioxane + n-alkanol from methanol to 1-decanol. As is seen in Table 3, GS is nega-
tive for 1,4-dioxane + methanol and 1,4-dioxane + ethanol solutions. The transfer of alcohol molecules from the bulk to the surface depends on their interactions in the bulk. Several authors (Letcher and Govender, 1995; Papanastasiou et al., 1987; Papanastasiou and Ziogas, 1992) have provided evidence that methanol and ethanol molecules form hydrogen-bonded complexes with 1,4-dioxane and these interactions partially replace alcohol–alcohol hydrogen bonding. This formation of hydrogen–hydrogen complexes in the bulk counteracts the tendency of the alcohol (the component with the lower surface tension) to segregate at the surface and explains why ethanol and methanol have negative GS and consequently negative the excess number of molecular layers. For the case of short-chain length alcohols, the strong interactions between the cyclic ether and alcohol give rise to an increase in surface tension (Calvo et al., 2004). For example for the binary solution (1,4-dioxane + methanol), the excess surface tension (E = − 1 x1b − 2 x2b ) is positive. When the alcohol is ethanol, E fluctuates near zero and takes both positive and negative sign, for this reason GS and E 2 are negative for methanol and ethanol. For alcohols with longer chain length, the excess surface tension is negative this means that for the longer chain length alcohol mixtures, the surface concentration of the alcohol is greater than that of cyclic ether. In longer chain length alcohols, lyophobicity is the factor which has the greatest influence on the surface tension and adsorption hence GS and −G◦ both increase from (1,4-dioxane + methanol) to (1,4-dioxane + 1-decanol). The trend of variation of GS /RT in these solutions is shown in Fig. 1. For the mixtures of (1,3-dioxolane
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
5
4
∆GS/RT
3
2
1
0 0
4
2
6
8
10
12
-1 Number of Carbon Atoms 1,4-Dioxane +n-Alkane 1,3-Dioxolane +n-Alkanol Water +n-Alkanol
1,4-Dioxane + n-Alkanol Water +Aliphatic acid Water +n-Alkanediol
Fig. 1. Dimensionless surface free energy change (GS /RT ) for binary mixtures versus number of carbon atoms.
9
7
-∆G˚ /RT
+ n-alkanol), similar behaviour to (1,4-dioxane + alcohol) is observed, as is seen from Table 3 and Fig. 1. For (1,3dioxolane + methanol) the excess surface tension is positive hence both GS and E 2 are negative while for other are positive. Comparing GS for n-alkanols, GS and E 2 (1-propanol and 2-propanol) and (1-butanol and 2-butanol) shows that if the −OH group is in the 2 position; there will be an increase in lyophobicity. In Table 3 the results of calculations for (1,4-dioxane + nalkane) are also listed. With increasing the number of carbon atoms in the alkane, the lyophobicity of the solute increases and consequently the tendency of the alkane to adsorb at the surface layer increases from hexane to decane therefore GS increases from hexane to decane. This trend is linear as is shown in Fig. 1. Fig. 1 shows the dependence of GS /RT on the number of carbon atoms. It is clear that the dependence of GS /RT on the number of carbon atoms in (1,4-dioxane + n-alkane) is less than for (1,4-dioxane + n-alkanol). This indicates that in 1,4-dioxane the length of the hydrocarbon chain in the alcohols does not have a very strong influence on the surface activity. Presumably, the interactions between the −CH2 group and 1,4-dioxane are less effective than the interactions between the −OH group and 1,4-dioxane. As a consequence, GS /RT depends less on the number −CH2 groups. By comparing the results of calculations for (1,4-dioxane + n-alkane) and (1,4-dioxane + n-alkanol) it can be seen that GS /RT and −G◦ /RT for the n-alkane solution are greater than for the n-alkanol solution. This indicates that 1,4-dioxane repels alkanes from the bulk much more than n-alkanols. This effect is in agreement with earlier measurements (Calvo et al., 2002) which this behaviour has been attributed to the weaker interactions between alkane-ether interactions than alkanol-ether.
4947
5
4.3. Dependence of GS /RT on temperature in aqueous and organic solutions 3
An important feature of GS is its temperature dependence. For all the aqueous solutions, GS increases linearly with increasing temperature. However, GS /RT in most cases is independent of temperature as is seen in Fig. 3. With increasing temperature, the calculated standard Gibbs energy of adsorption for aqueous solutions also increases, showing that higher temperatures favour transfer of solute from bulk to surface (Calvo et al., 2002) with a concomitant reduction in the surface tension. For the organic solutions it would be expected that with increasing temperature, GS /RT would increase since surface tension decreases with increasing temperature. In general this is the case for (dodecane + hexane), (DMSO + benzene), (DMSO + chloroform), (DMSO + toluene), (nitrobenzene + benzene) and (nitrobenzene + cyclohexane) as examples. However, for some organic solutions a different
1 0
2
4 Water +n-Alkanol Water +Aliphatic acid 1,4-Dioxane + n-Alkane
6
8
10
12
Water +n-Alkanediol 1,3-Dioxolane +n-Alkane 1,4-Dioxane +n-Alkanol
Fig. 2. Dimensionless standard Gibbs energy of adsorption (−G◦ /RT ) for binary mixtures versus number of carbon atoms.
behaviour is observed for example, (benzene + hexane), and (DMSO + chlorobenzene). It is likely that these deviations are related to experimental errors in the surface tension measurements. However, it should be noted that the vapour pressure of the solute is lower than the solvent. These, together
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R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
5.0
∆GS/RT
4.1
3.2
2.3
1.4 290
300 3-Amino-1-propanol TEA Propionic acid 1-Propanol
310 T/ K MEA Formic acid Methanol 2-Propanol
320
330 DEA Acetic acid Ethanol MDEA
Fig. 3. Variation of dimensionless surface free energy change for aqueous solutions versus temperature. The points are calculated values and the solid lines are fitted lines.
with the cases where the vapour pressure of the solute and the solvent are comparable would give rise to the observed deviation. For some mixtures, GS /RT decreases with increasing temperature. 4.4. The sign of GS For most mixtures GS is positive which means that solute (2) has a tendency to adsorb at the surface layer. However, for some mixtures such as [benzene (1) + acetone (2)], [chloroform (1) + acetone (2)], [toluene (1) + acetone (2)], [1,3-dioxolane (1) + methanol (1)] and [o-xylene (1) + acetone (2)], GS is negative, indicating that the solute molecules are restrained from entering the surface layer. Most of these mixtures are highly polar and in most cases the solute is acetone. The explanation for this behaviour is either the high intermolecular interactions between solute and solvent (Benson and Lam, 1972) or the volatility of the solute. The strong molecular interactions between the solute and the solvent in the bulk counteract the tendency of the solute to adsorb at the surface while the more volatile component has a tendency to enrich the vapour phase and thus escape from the surface layer (Papaioannou and Panayiotou, 1989). For [decane (1) + hexadecane (2)] and [heptane (1) + hexadecane (2)] solutions GS is also negative. This may be related to the very unsymmetrical structure of hexadecane and hence the possibility of different orientations of the component at the surface and bulk region. For [dodecane (1) + hexane (2)] the negative GS which results in negative E 2
is related to the higher vapour pressure and higher volatility of hexane in contrast to dodecane. Hexane has a higher vapour pressure and escapes from the interface and enriches the vapour phase. For this system two arrangements are possible (Schmidt and Clever, 1968): the surface layer is multimolecular with respect to hexane (Fig. 4A) or monomolecular with a substantial part of the dodecane above the nominal surface (Fig. 4B). The first case would lead to a convex composite isotherm and a negative excess surface tension (E = − 1 x1b − 2 x2b ). The second case would mean an enhanced number of dodecane molecules per unit area in the surface region and hence greater dodecane–dodecane interactions with increasing concentration of dodecane. This would give rise to a corresponding reduction in the surface tension and a positive excess surface tension. Both of these are observed. Furthermore, it is observed that for all systems with negative GS , the excess surface tension is positive and the surface tension vs. composition curve lies above the straight line of an ideal mixture. This observation indicates that the concentration of the solute (the component with the lower surface tension) is less than the solvent in these solutions. It is to be noted that for some mixtures, e.g. (1,4-dioxane + benzene, 293.15 K), (carbon tetrachloride + cyclopentane, 298.15 K), (chlorobenzene + toluene, 313.15 K), (decane + hexadecane, 293.15 K), (DMSO + bromobenzene, 323.15 K) and (nitrobenzene + 1,4-dioxane, 293.15 K), GS /RT is nearly equal to zero. For these solutions the components are approximately of the same size and the solvent–solvent and solute–solute intermolecular attractive forces and the distribution of each component between the surface region and the bulk is nearly the same. For these mixtures, the additivity law is a good approximation for the surface tension as given in Eq. (1):
= 1 x1b + 2 x2b .
(17)
For the above-mentioned systems, the calculated surface tension using Eq. (17) are compared with experimental data in Fig. 5. It is clear for these systems that the additivity law is a good approximation to the surface tension. 4.5. The excess number of molecular layers in binary aqueous and organic solutions As can be seen from Table 2, for all of the aqueous solutions the E 2 is positive which indicates the excess number of molecular layers of solute in the surface with respect to the bulk. In these solutions the solute is adsorbed in the surface and had a decreasing effect on the surface tension of solution. The calculated non integer values of E 2 can be attributed to the differences in orientation of solute in the surface and bulk regions (Langmuir, 1932; Ward, 1946; Hartkopf and Karger, 1973). Some authors have known other effects responsible for obtaining non-integer values of E 2 , such as significant escaping tendency of both
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
4949
NORMAL SURFACE H
H C-H C-H H-C H-C
H-C C-H
H
H-C
C-H
C-H
H-C C-H
H-C
H-C C-H
H-C H
C-H
C-H
H-C C-H
H-C
H-C C-H
H-C C-H
C-H
C-H
C-H H-C
C-H
H
H
H C-H
H-C
H-C
H-C
C-H H-C
C-H
H-C
C-H
H-C
H-C C-H
H-C
H-C H
H
(A)
H-C
H
C-H C-H
H-C
C-H
H-C
C-H
H-C
C-H C-H
H-C H
H
(B)
Fig. 4. Surface layer configuration for hexane + dodecane mixture, (A) multimolecular layer, (B) monomolecular layer with respect to hexane.
[1,4-dioxane (1) + decane (2)] where the non-integer values of E 2 are obtained, as reported in Table 1, it seems that for these solutions the differences in structural orientations of solute molecules in the surface and bulk regions should have a decisive effect on determining the non-integer values of E 2. But in the case of binary solutions of [cyclohexane (1) + heptane (2)], [benzene (1) + hexane (2)] and [toluene (1) + heptane (2)] where both components are volatile and then have a considerable escaping tendency from surface region, the excess number of molecular layers has a large deviation from an integer value. This tendency of both components cannot balance the low surface tension solute enriching the interfacial region. Thus for these solutions the excess number of molecular layer has a large deviation from an integer value.
45
Surface Tension / mN.m-1
40
35
30
25
20 0
0.2
0.4
1,4-Dioxane + Benzene (293.15 K) Nitrobenzene + 1,4-Dioxane (293.15 K) DMSO + Bromobenzene (323.15 K)
x2
0.6
0.8
1
Chlorobenzene + Toluene (313.15 K) Decane + Hexadecane (293.15 K) Carbon tetrachloride + Cyclopentane (298.15 K)
Fig. 5. Calculated and experimental surface tension values of binary organic solutions. The solid lines are calculated surface tension based on Eq. (17) and the points are experimental.
solvent and solute molecules (Papaioannou and Panayiotou, 1989). In the studied organic binary solutions, the values of E 2, as reported in Table 1, in most cases are positive and with the same argument as presented above for the aqueous binary solutions this behaviour can be ascribed to the adsorption of solute in the surface region and its decreasing effect on the surface tension of the binary solutions. As it is seen from Table 1, the calculated E 2 is negative for a number of binary organic solutions. In these solutions the solute is not adsorbed in the surface region and according to Gibbs equation (Eq. (7)) has an increasing effect on the surface tension of these solutions. However, considering the unsymmetrical solute molecules (2) in relatively non-volatile binary solutions of [1,4-dioxane (1) + nonane (2)], [1-butanol (1) + 2-chlorobutane (2)] and
4.6. Variation of −G◦ in organic solutions of homologue series The standard Gibbs energy of adsorption has been computed by using Eq. (10) and the results obtained in this study. However, experimental data for the standard Gibbs energy of adsorption is not available for all the solutions. Table 3 lists only the mixtures for which the experimental data is available. In Table 3, the calculated standard Gibbs energy of adsorption is compared with the results of applying the extended Langmuir (EL) model (Calvo et al., 2004) and the experimental data in Table 3. It can be seen that the calculated standard Gibbs energy of adsorption is in good agreement with experimental data. The values of calculated standard Gibbs energy of adsorption for solutions of 1,4-dioxane with methanol, ethanol and 1-propanol are small compared with adsorption from aqueous solutions. This can be related to the high affinity of 1,4-dioxane for alcohol molecules since these can be solvated both by interactions with the hydrophilic group of 1,4-dioxane, and by the hydrophobic interaction of the hydrocarbon chain with the methyl groups of 1,4-dioxane. Thus, alcohol molecules have little tendency to leave the 1,4-dioxane solution and explains why the values of −G◦ for aqueous solutions of alcohols are greater than alcohol solutions with 1,4-dioxane.
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R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
4.7. Surface tension prediction results for aqueous and organic solutions Surface tension of aqueous and organic solutions can be calculated by using Eq. (4). The AAD% in calculating surface tension has been reported in Tables 1 and 2. According to the results in Tables 1 and 2, the capability of this model for prediction of surface tension for binary solutions is remarkably good.
Subscripts 1 2 b S
Superscript E
5. Conclusions A model for calculating the surface tension of both organic and aqueous binary solutions has been presented. It is shown that this model can give knowledge about the surface structure of a wide range of binary solutions. However, for physically meaningful results about the surface, it is necessary that the solutions conform to the assumptions used in deriving the equation and that accurate surface tension data for the studied solutions are available. The equation used for the surface tension calculation in this work generates more detailed information about surface region structure. Furthermore, it has also been used to calculate the free energy change in the surface region, excess number of molecular layers, the difference between surface tension of pure components and the standard Gibbs energy of adsorption. The calculated values of surface tension and the standard Gibbs energy of adsorption compare remarkably well with experimental data.
Notation A¯ A c G M n N NA R R 2 T x
molar area surface area concentration Gibbs free energy molecular weight number of data point number of solutions Avogadro’s number gas constant mean squared linearity coefficient for Eq. (2) temperature, K mole fraction
Greek letters
slope of Eq. (2) intercept of Eq. (2) surface tension molar surface excess function excess number of molecular layers density
solvent solute bulk surface region
Excess
Acknowledgements RT would like to thank both the British Council and the Iranian Ministry of Science, Research and Technology for support while visiting the United Kingdom. References Adamson, A.W., Gast, A.P., 1997. Physical Chemistry of Surfaces. sixth ed. Wiley, New York. Agarwal, D.K., Gopal, R., Agarwal, S., 1979. Surface tensions of binaryliquid mixtures of some polar and non-polar liquids with dimethylsulfoxide (Me2 SO). Journal of Chemical and Engineering Data 24, 181–183. Alvarez, E., Vazquez, G., Sanchez, V.M., Sanjurjo, B., Navaza, J.M., 1997. Surface tension of organic acids plus water binary mixtures from 20 to 50 ◦ C. Journal of Chemical and Engineering Data 42, 957–960. Alvarez, E., Rendo, R., Sanjurjo, B., Sanchez, V.M., Navaza, J.M., 1998. Surface tension of binary mixtures of water plus Nmethyldiethanolamine and ternary mixtures of this amine and water with monoethanolamine, diethanolamine, and 2-amino-2-methyl-1propanol from 25 ◦ C to 50 ◦ C. Journal of Chemical and Engineering Data 43, 1027–1029. Alvarez, E., Cancela, A., Maceiras, R., Navaza, J.M., Taboas, R., 2003. Surface tension of aqueous binary mixtures of 1-amino-2propanol and 3-amino-1-propanol, and aqueous ternary mixtures of these amines with diethanolamine, triethanolamine, and 2-amino-2methyl-1-propanol from 298.15 to 323.15 K. Journal of Chemical and Engineering Data 48, 32–35. Azizian, S., Hemmati, M., 2003. Surface tension of binary mixtures of ethanol plus ethylene glycol from 20 to 50 ◦ C. Journal of Chemical and Engineering Data 48, 662–663. Bardavid, S.M., Pedrosa, G.C., Katz, M., 1994. Surface tensions of some nonelectrolyte binary liquid mixtures. Journal of Colloid and Interface Science 165, 264–268. Belton, J.W., Evans, M.G., 1945. Studies in the molecular forces involved in surface formation. 2. The surface free energies of simple liquid mixtures. Transactions of the Faraday Society 41, 1–12. Benson, G.C., Lam, V.T., 1972. Surface tensions of binary liquid systems. 2. Mixtures of alcohols. Journal of Colloid and Interface Science 38, 294–301. Beyer, W.H., 1991. CRC Standard Mathematical Tables and formulae. 29th ed. CRC Press, London. Buc, H., 1963. Influence Des Liaisons Hydrogene Intramoleculaires Sur Les Conformations Prises En Solution Par Les Molecules De Beta- Diols Et Dalcool Polyvinylique. Annales De Chimie France 8, 431–456. Calvo, E., Penas, A., Pintos, M., Bravo, R., Amigo, A., 2001. Refractive indices and surface tensions of binary mixtures of 1,4-dioxane + 1alkanols at 298.15 K. Journal of Chemical and Engineering Data 46, 692–695.
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Valsaraj, K.T., 1994. Hydrophobic compounds in the environment: adsorption equilibrium at the air-water interface. Water Research 28, 819–830. Vazquez, G., Alvarez, E., Navaza, J.M., 1995. Surface tension of alcohol + water from 20 to 50 ◦ C. Journal of Chemical and Engineering Data 40, 611–614. Vazquez, G., Alvarez, E., Rendo, R., Romero, E., Navaza, J.M., 1996. Surface tension of aqueous solutions of diethanolamine and triethanolamine from 25 to 50 ◦ C. Journal of Chemical and Engineering Data 41, 806–808. Vazquez, G., Alvarez, E., Navaza, J.M., Rendo, R., Romero, E., 1997. Surface tension of binary mixtures of water + monoethanolamine and water + 2-amino-2-methyl-1-propanol and tertiary mixtures of these amines with water from 25 to 50 ◦ C. Journal of Chemical and Engineering Data 42, 57–59. Ward, A.F.H., 1946. Thermodynamics of monolayers on solutions. 1. The theoretical significance of Traubes rule. Transactions of the Faraday Society 42, 399–407. Winterfeld, P.H., Scriven, L.E., Davis, H.T., 1978. An approximate theory of interfacial tensions of multicomponent systems: applications to binary liquid–vapor tensions. A.I.Ch.E. Journal 24, 1010–1014. Wright, E.H.M., Akhtar, B.A., 1970. Equilibrium studies of soluble films of short-chain monocarboxylic fatty acids at organoliquid-vapour phase boundary. Transactions of the Faraday Society 66, 990–1003. Zagorska, I., Trasatti, S., Koczorowski, Z., 1994. Surface and interfacial behavior of isomeric butanediols. Journal of Electroanalytical Chemistry 366, 211–218.
Further reading International Critical Table, 2003, vol. IV. McGraw-Hill, New York, pp. 471–474. Penas, A., Calvo, E., Pintos, M., Amigo, A., Bravo, R., 2000. Refractive indices and surface tensions of binary mixtures of 1,4-dioxane plus n-alkanes at 298.15 K. Journal of Chemical and Engineering Data 45, 682–685. Ramakrishna, V., Suri, S.K., 1967. Surface tension of liquid mixtures. Indian Journal of Chemistry 5, 310.
Surface tension prediction and thermodynamic analysis of the surface for binary solutions Reza Taherya , Hamid Modarressa,∗ , John Satherleyb a Chemical Engineering Department, Amir Kabir University of Technology, P.O. Box 15875-4413, Tehran, Iran b Department of Chemistry, University of Liverpool, Liverpool L69 7ZD, Merseyside, UK
Received 17 November 2004; received in revised form 21 February 2005; accepted 23 March 2005 Available online 4 June 2005
Abstract The surface tensions of 100 aqueous and 200 non-aqueous binary solutions are correlated by Shereshefsky model and excellent results are obtained. The average percent deviations are about ∼ 1.8% for aqueous and ∼ 0.56% for non-aqueous binary solutions. The free energy change in the surface region is calculated and is used to obtain the excess number of molecular layers in the surface region. Furthermore, the model is used to derive an equation for the standard Gibbs energy of adsorption. Where experimental data is available for the standard Gibbs energy of adsorption, the agreement between the calculated and the experimental data is found to be very good. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Surface tension; Binary solution; Excess number of molecular layer; Standard Gibbs energy of adsorption
1. Introduction The surface of a liquid has interesting properties which appear as the surface tension. The surface tension of liquids can be looked upon as the property which draws a liquid together and forms a liquid–vapour interface. In vapour–liquid equilibrium the effect of surface tension on interface curvature, is very important and should be taken into account. Surface tension has high industrial importance in chemical reactions as the reactions in the surface region are quite different from the bulk region. In various chemical engineering processes such as separation, distillation, extraction and absorption, surface tension has a determining effect. Also in electrochemical reactions, biological membranes operation, environmental engineering and several other processes namely; corrosion, adherency, detergency, floating and lubricating the surface tension plays a significant role. The surface tension of liquids and its variation with composition in liquid solutions must often be taken into account in designing rational chemical process equipment involving ∗ Corresponding author. Tel.: +98 21 64543176; fax: +98 21 6405847.
E-mail address: [email protected] (H. Modarress). 0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2005.03.056
interphase heat and mass transfer. Many methods to calculate the surface tension of binary non-electrolyte mixtures have been proposed. Belton and Evans (1945) developed semi-empirical equations for ideal or nearly ideal solutions in the bulk phase. However, these equations are empirical, and the constant terms have no apparent relation to the properties of the pure components and therefore the calculation of surface tension is complicated. Guggenheim (1945) used a quasicrystalline model to derive an equation for the surface tension of regular solutions as a function of heat of mixing and simplified it for ideal solutions. Guggenheim model was extended by Hildebrand and Scott (1964) for mixtures of different size molecules. A one-parameter equation for binary liquid mixtures was proposed by Eberhart (1966) by assuming that the surface tension is a linear function of surface layer mole fraction. By using a statistical thermodynamic approach, he calculated the parameter of his model and the surface tension of binary liquid mixtures with good accuracy. Winterfeld et al. (1978) derived an expression based on the Fowler–Kirkwood–Buff model (Kirkwood and Buff, 1949) relating the surface tension of multicomponent systems to quantities dependent on the intermolecular pair potentials and pair correlation functions and applied
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it to the surface tension of binary systems. This expression involves a parameter, which is defined as the mixing parameter. However, this mixing parameter is difficult to calculate, since the pair potential and the correlation functions are not generally available. Based on the conformal solution theory of mixtures, Escobedo and Mansoori (1998) derived an expression for surface tension and applied to a variety of binary mixtures. Li et al. (1990) used the UNIFAC group contribution method to calculate the surface tension of binary mixtures. This approach, however, is not recommended for aqueous solutions since the difference between the surface tension of the pure components is large. Subsequently, Li et al. (2000) derived a two-parameter equation for the surface tension of mixtures based on the Wilson equation for excess Gibbs free energy. This model was found to work well for both binary organic and aqueous solutions. Li and Lu (2001) have developed a prediction method for the surface tension of real mixtures based on the Davis theory (Davis, 1975) and tested it against molecular dynamics simulation of the surface tension of the Lennard–Jones fluid. They applied it with a good success to binary and ternary organic solutions and binary aqueous solutions. Very recently, Miqueu et al. (2004) have used the gradient theory of fluid interfaces to compute the surface tension of various binary and ternary mixtures of gas and liquid hydrocarbons with good results. An alternative model which gives knowledge about the surface structure of binary solutions and is able to compute the excess number of molecular layers and free energy change in the surface region was developed by Shereshefsky (1967). This model was applied to a limited number of binary solutions (Shereshefsky, 1967; Cotton, 1969). Unfortunately, researchers dealing with liquid surface properties have not paid enough attention to this model, and have not extended its application to various aqueous and non-aqueous solutions. In this work, the Shereshefsky model is applied to a wide range of organic and aqueous binary solutions and it is shown that a wealth of information can be obtained from this model. In addition, this model is used to derive a relation between the standard Gibbs energy of adsorption, the free energy change in the surface region and the difference between surface tension of pure components. Furthermore the differences between surface tensions of constituents in 300 organic and aqueous binary solutions are calculated. This quantity is used to estimate the surface tension of pure components which are difficult to obtain experimentally.
where the components have a similar size and attractive forces (Fowler and Guggenheim, 1939). For simplicity, however, Shereshefsky (1967) presented his model by assuming that the surface is homogeneous and uniform in composition and the energy of interaction between the molecules in the surface region is less than that of the bulk liquid phase due to its lower density and greater average distance between molecules. Based on these assumptions, Shereshefsky (1967) derived an equation for the surface tension, , of a binary solution as represented by the following equation:
= 1 −
◦ x2b eGs/RT , 1 + x2b (eGs /RT − 1)
(1)
where ◦ = 1 − 2 is the difference between the surface tensions of pure solvent (1 ) and pure solute (2 ), x2b is the mole fraction of solute in the bulk liquid, T is the absolute temperature and R is the gas constant. In Eq. (1), GS is the free energy change of replacing 1 mol of solvent with 1 mol of solute in the surface region. Eq. (1) can be rearranged in the following form: x2b 1 GS /RT x2b = e + (1 − eGS /RT ), ◦ ◦
(2)
where = 1 − is the difference between the surface tension of pure solvent (1 ) and that of solution (). According to Eq. (2) the variation of x2b / versus x2b is linear. Therefore GS can be expressed by the following equation: , (3) GS = RT ln 1 + where = (1 − e−GS /RT )/◦ is the slope, = (e−GS /RT )/◦ is the intercept of Eq. (2) and therefore ◦ can be obtained as
◦ =
1 . +
(4)
The excess number of molecular layers of solute in the surface region in respect to the bulk region E 2 , which has been named as number of molecular layers by Shereshefsky (1967), is redefined here in consistency with the Gibbs equation for adsorption in the following form:
E 2 =
◦ A¯ 2 , GS
(5)
where A¯ 2 is the molar area of solute (2). The molar area of solute (2) is given by
2. Model description
1/3 A¯ 2 = (M2 /2 )2/3 NA ,
The surface region of a binary mixture differs from the bulk phase in several aspects, namely it is not homogeneous, and its density varies continuously in the direction perpendicular to the surface. It may differ in composition from the bulk, as has been shown by Gibbs (1931), except in cases
where M2 and 2 are the molecular weight and the density of solute and NA is Avogadro’s number. A positive and high value of E 2 means that solute (2) is adsorbed in the surface and therefore solute molecules are in excess in the surface with respect to the bulk. Such a case
(6)
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
is observed for binary solutions where on addition of the solute to the solvent the surface tension of binary solution shows a decreasing trend, whereas a negative value of E 2 means that solute (2) is not adsorbed in the surface and it is in excess in the bulk with respect to the surface. Such a case is observed for binary solutions where on addition of the solute to the solvent, the surface tension shows an increasing trend. The sign and variation of E 2 is consistent with the Gibbs equation for adsorption as expressed by the following equation (Adamson and Gast, 1997):
E 2 =−
j 1 , RT j ln c2
(7)
where is the surface tension of solution and c2 is the concentration of solute. The molar surface excess function E 2 is defined as
E 2
nS − nb2 = 2 , A
(8)
where nS2 and nb2 are, respectively, the number of moles of solute in the surface and in the bulk and A is the surface S b area. A positive value of E 2 means that n2 > n2 and soE lute is adsorbed on the surface. For 2 > 0, according to Eq. (7), j/j ln c2 < 0 and addition of solute has a decreasing effect on the surface tension of solution. On the other S b hand, a negative value of E 2 means that n2 < n2 and solute is not adsorbed on the surface. For E 2 < 0, according to Eq. (7), j/j ln c2 > 0 and addition of solute has an increasing effect on the surface tension of solution. The standard Gibbs energy of adsorption, which reflects the energy required to move one molecule of solute from the bulk to the surface, can be expressed as (Calvo et al., 2004)
G◦ = − lim {RT ln (/x2b )}. x2b →0
(9)
Now, by substituting for /x2b from Eq. (2) into Eq. (9) and taking the limit as x2b → 0 we have 1 −GS /RT ◦ G /RT = lim ln e x2b →0 ◦ x2b + (1 − e−GS /RT ) ◦ 1 −GS /RT , e = ln ◦ G◦ GS (10) =− + ln ◦ . RT RT This equation consequently enables the calculation of the standard Gibbs energy of adsorption from GS and ◦ . These terms can be determined from Eqs. (3) and (4). 3. Results The surface tensions of binary solutions were fitted in Eq. (2) for 200 binary organic solutions and 100 binary
4937
aqueous solutions and from the slope and intercept the values of ◦ and GS /RT were evaluated. The R-squared values for linearity of Eq. (2) defined as
2 yi2 − yi /n , (yi − yˆi )2 R2 = 1 − (11) where yi = (x2b /)i is the experimental value of the data point i, yˆi is the regressed value of yi according to Eq. (2) and n is the number of data points (Beyer, 1991). For the studied binary organic solutions reported in Table 1 and binary aqueous solutions reported in Table 2 , the values of R 2 are 0.90 and 0.96, respectively, which indicate good linear plots according to Eq. (2) for the studied solutions. R 2 is defined as R 2 =
N
(R 2 )j /N ,
(12)
j =1
where N is the number of solutions. The results of applying Eqs. (1)–(6) and (10) to 200 binary organic solutions and 100 binary aqueous solutions are given in Tables 1 and 2. In the fifth and sixth columns, the experimental and calculated values of ◦ are given. The values of GS /RT calculated by Eq. (3) and −G◦ /RT calculated by Eq. (10) are tabulated, respectively, in columns 7th and 8th. In the 9th and 10th column, respectively, the molar area of the surface-active component A¯ 2 calculated by Eq. (6) and the excess number of molecular layers E 2 calculated by Eq. (5) are reported. The relative absolute deviation percent (RAD%) in the calculating surface tension of pure solute (2 ) in the binary solution is expressed as ( ) 2 Exp. − (2 )Calc. (13) RAD% = 100 × . (2 )Exp. For fixed and known values of 1 and by the definition ◦ = 1 − 2 we have (2 )Exp. − (2 )Calc. = (◦ )Exp. − (◦ )Calc.
(14)
then the RAD% values for the studied binary solutions can be calculated by the following equation: ( ) ◦ Exp. − (◦ )Calc. (15) RAD% = 100 × . (2 )Exp. The results are reported in 11th column of Tables 1 and 2. The absolute average deviation percent (AAD%) in surface tension are calculated by the following equation: AAD% = 100 ×
n i=1
Exp.
|(i
Exp.
− Calc. )/i i
|/n
(16)
and are tabulated in the 12th column of Tables 1 and 2.
No.
Temp. (K)
1
2
Acetic acid Acetic acid Acetone Aniline Aniline Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzyl alcohol Benzyl alcohol 1-Butanol 1-Butanol 1-Butanol 1-Butanol 2-Butanol Butyric acid Carbon disulfide Carbon disulfide Carbon disulfide CTC Chlorobenzene Chlorobenzene
Ethyl acetate Ethanol Isooctane Benzene Toluene Acetone Cyclohexane Cyclopentane Ethanol Ethyl acetate Ethyl acetate Ethyl ether Ethyl ether Isooctane Hexane Hexane Hexane Hexane Dodecane Dodecane Dodecane Dodecane 1−Propanol Propionic acid Toluene Ethyl acetate Toluene 2-Chlorobutane Hexane 2-M-1-CP Octane 2-M-2-CP Cyclohexane Acetone Benzene Chloroform Cyclopentane Benzene Benzene
298.15 298.15 298.15 293.15 293.15 298.15 293.15 298.15 298.15 293.15 298.15 291.15 291.15 303.15 298.15 303.15 308.15 313.15 298.15 303.15 308.15 313.15 298.15 303.15 291.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 303.15 289.15 298.15 291.15 298.15 283.15 313.15
◦ (mN/m) Exp.
Calc.
5.1 6.6 4.67 15.08 15.45 4.8 4.05 6.35 7.1 5.1 4.5 11 11.5 9.64 10.21 10.05 9.91 9.76 3.46 3.17 2.96 2.72 2.9 1.81 0.35 15.8 11.3 2.42 6.13 2.45 2.85 4.21 1.68 10.2 4.46 4.91 4.28 4.31 4.51
4.82 6.1 4.84 14.99 15.34 5.78 4.12 6.39 7.08 4.95 4.48 10.81 11.43 9.61 9.99 10.07 9.82 9.75 3.5 3.15 2.95 2.75 3.39 1.74 0.35 15.48 11.71 2.55 6.3 2.58 2.94 4.38 1.54 10.42 4.54 4.97 4.33 4.27 4.55
GS /RT −G◦ /RT
A¯ 2 (A˚ 2 )
E 2
RAD%
AAD%
n
Ref.
0.49 −0.25 2.46 0.97 1.27 −0.73 1.06 0.65 0.05 0.27 0.47 0.59 0.5 1.15 1.09 0.97 0.99 0.9 2.6 2.67 2.55 2.63 0.58 0.66 1.02 0.57 0.53 0.31 0.95 0.29 1.28 0.34 0.59 0.57 1.7 1.13 0.06 0.05 0.05
29.9 21.18 42.44 27.92 31.46 24.72 30.71 19 21.18 29.77 29.9 31 31 42.52 36.28 36.45 36.62 36.8 52 52.58 52.74 52.9 24.97 25.02 31.42 29.9 31.57 31.55 36.28 31.46 41.93 32.31 31.56 24.51 28.04 26.26 19 27.7 28.38
0.75 −1.34 0.2 1.07 0.95 −0.39 0.29 0.45 7.52 1.4 0.69 1.44 1.76 0.85 0.82 0.9 0.86 0.93 0.17 0.15 0.14 0.13 0.3 0.16 0.03 2.03 1.64 0.59 0.57 0.64 0.23 0.98 0.22 1.1 0.18 0.28 3.16 5.71 5.93
1.20 2.28 0.93 0.31 0.38 4.17 0.28 0.18 0.09 0.65 0.08 1.12 0.40 0.17 1.23 0.11 0.53 0.06 0.16 0.08 0.04 0.13 1.94 0.27 0.00 1.37 1.47 0.60 0.95 0.60 0.43 0.90 0.59 0.88 0.28 0.22 0.23 0.13 0.15
0.59 0.81 1 0.35 0.4 1.35 0.22 0.13 0.66 0.92 0.52 0.71 0.22 0.25 0.89 0.11 0.36 0.06 0.18 0.09 0.27 0.21 1.18 0.18 0.02 0.67 1.55 0.39 0.76 0.36 0.38 0.5 0.33 0.64 0.21 0.21 0.12 0.08 0.09
6 6 17 5 6 10 11 11 6 5 11 5 7 9 7 5 6 5 5 7 5 6 6 10 7 6 6 13 16 13 19 13 10 5 21 6 10 5 5
Meissner and Michaels (1949) Meissner and Michaels (1949) Papaioannou and Panayiotou (1989) International Critical Table International Critical Table Shipp (1970) Lam and Benson (1970) Lam and Benson (1970) Meissner and Michaels (1949) Meissner and Michaels (1949) Shipp (1970) Meissner and Michaels (1949) International Critical Table Evans and Clever (1964) Schmidt et al. (1966) Schmidt et al. (1966) Schmidt et al. (1966) Schmidt et al. (1966) Schmidt et al. (1966) Schmidt et al. (1966) Schmidt et al. (1966) Schmidt et al. (1966) Michaels et al. (1950) Wright and Akhtar (1970) International Critical Table Michaels et al. (1950) Michaels et al. (1950) Giner et al. (2004) Jimenez et al. (2000) Giner et al. (2004) Segade et al. (2003) Giner et al. (2004) Wright and Akhtar (1970) Meissner and Michaels (1949) Shipp (1970) International Critical Table Lam and Benson (1970) International Critical Table International Critical Table
2.06 1.56 4.04 3.68 4.00 1.02 2.48 2.50 2.01 1.87 1.97 2.97 2.94 3.41 3.39 3.28 3.27 3.18 3.85 3.82 3.63 3.64 1.80 1.21 −0.03 3.31 2.99 1.25 2.79 1.24 2.36 1.82 1.02 2.91 3.21 2.73 1.53 1.50 1.57
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
Mixture Component
4938
Table 1 Experimental and calculated differences of surface tensions of solvent and solute (◦ , Eq. (4)), surface Gibbs energy change (GS /RT , Eq. (3)), standard Gibbs energy of adsorption (−G◦ /RT , Eq. (10)), molar surface area (A¯ 2 , Eq. (6)), excess number of molecular layers (E 2 , Eq. (5)), relative absolute deviation percent (RAD%) in calculating the surface tension of pure solute (Eq. (15)), absolute average deviation percent (AAD%) in calculating the surface tension (Eq. (1)) for several binary organic solutions, the number of experimental data point (n) and the references for the experimental data
Toluene Toluene 2-M-2-P Acetone Ethanol Heptane Heptane Heptane Heptane Heptane Hexane Isooctane Isooctane Isooctane Isooctane Isooctane Isooctane Hexadecane Hexadecane Hexadecane Hexadecane 2-M-1-P 2-Butanol 2-M-2-P 2-Propanol Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol 1-Pentanol Methanol Ethanol 1-Propanol 1-Hexanol 1-Heptanol 1-Octanol 1-Decanol Hexane Heptane Octane Nonane Decane Cyclohexane Cyclohexane Benzene Benzene
283.15 313.15 298.15 291.15 290.65 287.81 297.82 307.86 317.86 327.88 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 313.15 323.15 333.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 293.15 303.15 293.15 303.15
4.82 4.58 3.09 3.6 4.2 4.64 4.57 4.34 4.08 4.03 5.89 6.5 5.9 5.8 5.7 5.5 5.5 3.65 3.81 3.75 3.84 5.9 5.3 8.19 6.12 10.51 10.77 9.25 11.76 8.45 9.69 7.5 10.62 10.92 9.37 6.83 6.06 5.48 4.38 14.58 12.82 11.32 10.21 9.25 8.75 8.35 4.9 4.65
4.8 4.65 2.97 3.71 3.85 4.57 4.48 4.27 4.06 4.12 5.98 6.39 5.92 5.74 5.78 5.55 5.54 3.69 3.77 3.95 3.94 6.01 5.41 8.58 6.46 11.72 10.91 9.32 11.68 8.44 9.62 7.54 11.99 11.14 9.49 6.79 6.04 5.39 4.38 14.29 12.55 11.12 10.07 9.12 8.92 8.37 4.98 4.84
0.16 0.07 0.66 −0.33 −0.89 0.77 0.72 0.71 0.67 0.61 0.68 0.85 0.69 0.72 0.58 0.57 0.62 0.05 −0.26 −0.47 −0.45 −0.7 −0.7 −0.67 −0.67 −0.54 0.22 0.54 0.76 0.85 0.91 1.04 −0.78 −0.06 0.27 0.92 1.08 1.23 1.52 1.83 2.05 2.11 2.21 2.37 0.21 0.64 −0.02 −0.15
1.73 1.61 1.75 0.98 0.46 2.29 2.22 2.16 2.07 2.03 2.47 2.70 2.47 2.47 2.33 2.28 2.33 1.36 1.07 0.90 0.92 1.09 0.99 1.48 1.20 1.92 2.61 2.77 3.22 2.98 3.17 3.06 1.70 2.35 2.52 2.84 2.88 2.91 3.00 4.49 4.58 4.52 4.52 4.58 2.40 2.76 1.59 1.43
31.24 31.92 29.19 24.55 21.07 38.81 39.14 39.45 39.81 40.16 36.11 42.44 42.65 42.81 42.96 43.2 43.34 61.82 62.56 62.95 63.33 28.76 28.64 29.2 25.39 16.58 21.19 24.97 25.36 28.57 28.65 31.93 16.59 21.15 24.97 35.1 38.1 41.02 46.58 36.28 39.14 41.94 44.65 47.30 31.31 31.55 27.92 28.15
2.39 4.77 0.33 −0.67 −0.25 0.59 0.6 0.57 0.55 0.58 0.77 0.79 0.87 0.81 0.98 0.95 0.87 10.52 −2.1 −1.12 −1.19 −0.59 −0.53 −0.86 −0.56 −0.78 2.48 1.03 0.96 0.69 0.74 0.56 −0.55 −9.12 2.14 0.63 0.52 0.44 0.33 0.7 0.6 0.55 0.5 0.45 3.16 0.98 −20.76 −2.12
0.07 0.27 0.59 0.47 1.53 0.34 0.46 0.37 0.11 0.54 0.49 0.59 0.11 0.34 0.47 0.30 0.25 0.16 0.18 0.93 0.49 0.55 0.48 1.93 1.60 5.48 0.64 0.30 0.38 0.04 0.31 0.16 6.19 1.01 0.51 0.16 0.08 0.33 0.00 1.62 1.37 0.94 0.63 0.56 0.68 0.08 0.28 0.69
0.04 0.16 0.4 0.19 0.35 0.28 0.29 0.24 0.18 0.36 0.33 0.37 0.09 0.23 0.29 0.29 0.31 0.08 0.2 0.36 0.27 0.26 0.2 0.65 0.61 1.59 0.41 0.21 0.29 0.1 0.19 0.12 1.49 0.45 0.29 0.09 0.09 0.21 0.06 1.19 1.09 0.8 0.69 0.64 0.37 0.22 0.21 0.32
5 5 13 5 5 11 11 11 11 11 8 21 21 21 21 21 21 5 5 5 5 10 11 10 14 18 16 13 14 16 14 16 14 24 16 15 14 18 14 14 14 14 14 14 8 8 8 8
International Critical Table International Critical Table Giner et al. (2004) Meissner and Michaels (1949) Meissner and Michaels (1949) Kahl et al. (2003a) Kahl et al. (2003a) Kahl et al. (2003a) Kahl et al. (2003a) Kahl et al. (2003a) Ridgway and Butler (1967) Gomez-Diaz et al. (2001) Gomez-Diaz et al. (2001) Gomez-Diaz et al. (2001) Gomez-Diaz et al. (2001) Gomez-Diaz et al. (2001) Gomez-Diaz et al. (2001) Rolo et al. (2002) Rolo et al. (2002) Rolo et al. (2002) Rolo et al. (2002) Lam et al. (1973) Lam et al. (1973) Lam et al. (1973) Postigo et al. (1987) Calvo et al. (2004) Calvo et al. (2004) Calvo et al. (2004) Calvo et al. (2004) Calvo et al. (2004) Calvo et al. (2004) Calvo et al. (2004) Calvo et al. (2001) Calvo et al. (2001) Calvo et al. (2001) Calvo et al. (2001) Calvo et al. (2001) Calvo et al. (2001) Calvo et al. (2001) Calvo et al. (2000) Calvo et al. (2000) Calvo et al. (2000) Calvo et al. (2000) Calvo et al. (2000) Suri and Ramakrishna (1968) Suri and Ramakrishna (1968) Suri and Ramakrishna (1968) Suri and Ramakrishna (1968)
4939
Chlorobenzene Chlorobenzene 1-Chlorobutane Chloroform Chloroform Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Decane Decane Decane Decane 1-Decanol 1-Decanol 1-Decanol DCM 1,3-Dioxolane 1,3-Dioxolane 1,3-Dioxolane 1,3-Dioxolane 1,3-Dioxolane 1,3-Dioxolane 1,3-Dioxolane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane 1,4-Dioxane
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87
4940
Table 1 (continued) No.
1
2
DMF DMF DMF DMF DMF DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO DMSO Dodecane Dodecane Dodecane Dodecane 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol
Toluene Toluene Toluene Toluene Toluene Acetone Benzene Benzene Benzene Bromobenzene Bromobenzene Bromobenzene Butyl acetate Butyl acetate Butyl acetate CTC CTC CTC Chlorobenzene Chlorobenzene Chlorobenzene Chloroform Chloroform Chloroform Toluene Toluene Toluene Hexane Hexane Hexane Hexane Ethanol Ethanol Ethanol Ethanol Ethanol Ethanol Ethanol 1-Propanol 1-Propanol 1-Propanol 1-Propanol 1-Butanol
Temp. (K)
287.81 297.82 307.86 317.86 327.88 303.15 303.15 313.15 323.15 303.15 313.15 323.15 293.15 303.15 313.15 303.15 313.15 323.15 303.15 313.15 323.15 303.15 313.15 323.15 303.15 313.15 323.15 298.15 303.15 308.15 313.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 293.15
◦ (mN/m) Exp.
Calc.
8.03 8.07 8.05 7.91 7.74 19.99 14.92 15.03 15.16 7.32 6.93 7.29 17.9 17.5 17.1 17.09 16.99 17.3 10.43 10.45 10.47 16.58 16.75 17.02 15.09 15.02 15.12 6.75 6.88 6.95 7.04 26.6 26.8 26.7 26.4 26.3 25.9 25.9 23.74 23.81 23.93 23.97 23.01
8.12 8.04 7.99 8 7.84 20.58 15.67 15.97 15.92 7.33 7.2 7.39 17.67 17.33 16.92 17.42 17.12 17.36 10.31 10.53 10.32 16.89 16.92 17.01 15.13 15.22 15.27 6.9 6.83 6.92 6.91 26.74 26.88 26.67 26.46 26.46 26.18 25.91 23.15 23.26 23.31 23.36 22.52
GS /RT
−G◦ /RT
A¯ 2 (A˚ 2 )
E 2
RAD%
AAD%
n
Ref.
0.51 0.53 0.54 0.43 0.36 1.34 0.35 0.33 0.45 0.38 0.36 0.08 1.9 1.84 1.81 0.91 0.9 0.79 0.18 0.09 0.17 0.47 0.46 0.57 0.3 0.28 0.39 −0.36 −0.27 −0.23 −0.16 1.18 1.15 1.15 1.11 1.1 1.06 1.08 1.96 1.92 1.9 1.87 2.54
2.60 2.61 2.62 2.51 2.42 4.36 3.10 3.10 3.22 2.37 2.33 2.08 4.77 4.69 4.64 3.77 3.74 3.64 2.51 2.44 2.50 3.30 3.29 3.40 3.02 3.00 3.12 1.57 1.65 1.70 1.77 4.47 4.44 4.43 4.39 4.38 4.32 4.33 5.10 5.07 5.05 5.02 5.65
31.14 31.46 31.8 32.04 32.26 24.84 28.15 28.39 28.63 31.4 31.59 31.79 36.32 36.6 36.89 29.74 29.99 30.23 30.75 30.96 31.17 26.25 26.43 26.6 31.69 31.92 32.16 36.28 36.45 36.62 36.8 21.11 21.18 21.26 21.34 21.43 21.51 21.6 24.88 24.97 25.05 25.13 28.46
1.24 1.16 1.12 1.33 1.53 0.88 2.86 3.03 2.16 1.44 1.4 6.13 0.85 0.83 0.81 1.34 1.31 1.48 4.22 8.4 4.2 2.23 2.23 1.79 3.84 4.03 2.77 −1.64 −2.18 −2.6 −3.68 1.18 1.2 1.18 1.19 1.19 1.19 1.16 0.75 0.75 0.75 0.76 0.64
0.31 0.11 0.23 0.35 0.41 2.63 2.73 3.60 3.05 0.03 0.79 0.31 0.97 0.74 0.80 1.30 0.54 0.26 0.38 0.26 0.51 1.20 0.70 0.04 0.15 0.76 0.60 0.84 0.29 0.18 0.79 0.63 0.37 0.14 0.28 0.77 1.37 0.05 2.49 2.36 2.71 2.72 2.00
0.25 0.14 0.24 0.24 0.26 1.99 1.42 1.89 1.67 0.07 0.41 0.29 0.78 0.57 0.57 1.13 0.46 0.22 0.26 0.24 0.19 0.88 0.56 0.36 0.16 0.34 0.41 0.32 0.13 0.08 0.34 0.54 0.37 0.38 0.64 0.97 1.23 0.58 1.28 1.16 1.32 1.26 1.61
7 7 7 7 7 7 8 8 8 8 8 8 12 12 12 8 8 8 8 8 8 8 8 8 8 8 8 5 5 5 5 8 8 8 8 8 8 8 16 16 16 16 17
Kahl et al. (2003b) Kahl et al. (2003b) Kahl et al. (2003b) Kahl et al. (2003b) Kahl et al. (2003b) Clever and Snead (1963) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Tsierkezos et al. (2000) Tsierkezos et al. (2000) Tsierkezos et al. (2000) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Agarwal et al. (1979) Schmidt and Clever (1968) Schmidt and Clever (1968) Schmidt and Clever (1968) Schmidt and Clever (1968) Azizian and Hemmati (2003) Azizian and Hemmati (2003) Azizian and Hemmati (2003) Azizian and Hemmati (2003) Azizian and Hemmati (2003) Azizian and Hemmati (2003) Azizian and Hemmati (2003) Jimenez et al. (2001) Jimenez et al. (2001) Jimenez et al. (2001) Jimenez et al. (2001) Jimenez et al. (2001)
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130
Mixture Component
1,2-Ethanediol 1,2-Ethanediol 1,2-Ethanediol Ethyl butyrate Furfural Furfural Heptane Heptane Heptane Heptane Heptane 1-Heptanol 1-Heptanol 1-Hexanol 1-Hexanol Methyl acetate 2-M-1-CP Nitrobenzene Nitrobenzene Nitrobenzene Nitrobenzene Nitrobenzene Nitrobenzene Nitromethane 1-Octanol 1-Octanol 1-Pentanol 1-Pentanol n-Pentyl acetate Phenol Phenol Phenol 1-Propanol Propionic acid TCET TCET Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene
1-Butanol 1-Butanol 1-Butanol Methanol 2-Propanol Toluene Hexadecane Hexadecane Hexadecane Hexadecane Hexadecane Hexane Octane Hexane Octane Pentane 2-M-2-P Benzene Benzene Cyclohexane Cyclohexane 1,4-Dioxane Toluene Benzene Hexane Octane Hexane Octane Methanol Acetone Benzene Benzene Hexane Cyclohexane Cyclohexane Cyclopentane Acetone Acetone Acetone Acetone Acetone Cyclohexane Cyclopentane Ethyl acetate Heptane Heptane Heptane Heptane
298.15 303.15 308.15 303.15 298.15 298.15 293.15 303.15 313.15 323.15 333.15 298.15 298.15 298.15 298.15 298.15 298.15 293.15 303.15 293.15 303.15 293.15 328.15 298.15 298.15 298.15 298.15 298.15 303.15 293.15 308.15 308.15 298.15 303.15 298.15 298.15 287.81 297.82 307.86 317.86 327.88 298.15 298.15 298.15 287.81 297.82 307.86 317.86
23.12 23.17 23.26 1.72 21.7 15 7.59 7.56 7.76 7.86 7.9 8.58 5.3 7.84 4.56 9.25 1.6 14.55 14.65 18.4 18.35 9.65 14.49 6.9 9.24 5.96 7.08 3.8 3.03 22 12 12.37 5.5 1.89 6.92 9.45 4.99 4.98 5.01 5.13 5.28 3.56 6.09 4.5 8.23 8.13 7.92 7.7
22.62 22.68 22.73 2.16 21.37 14.81 7.54 7.57 8.12 9.44 9.76 9.06 5.33 7.99 4.61 9.71 1.56 14.31 14.06 18.55 18.52 9.71 14.64 6.99 9.51 6.04 7.24 3.8 2.95 22.27 12.02 12.36 5.61 1.78 6.9 9.31 6.73 5.27 5.62 6.5 9.04 3.66 6.07 4.46 8.22 8.11 7.9 7.7
2.51 2.51 2.45 −1.54 1.39 1.03 −0.2 −0.3 −0.54 −1.06 −1.21 0.45 0.92 0.7 0.96 0.52 1.46 0.51 0.7 0.85 1.42 0.04 0.52 1.72 0.53 0.75 0.83 1.23 0.63 0.92 0.74 0.75 1.3 1.34 0.59 0.37 −1.22 −0.35 −0.54 −0.95 −1.62 0.77 0.32 0.2 0.98 0.98 0.97 0.96
5.63 5.63 5.57 −0.77 4.45 3.73 1.82 1.72 1.55 1.18 1.07 2.65 2.59 2.78 2.49 2.79 1.90 3.17 3.34 3.77 4.34 2.31 3.20 3.66 2.78 2.55 2.81 2.57 1.71 4.02 3.23 3.26 3.02 1.92 2.52 2.60 0.69 1.31 1.19 0.92 0.58 2.07 2.12 1.70 3.09 3.07 3.04 3.00
28.57 28.66 28.75 16.65 25.37 31.57 61.82 62.19 62.56 62.95 63.33 36.28 41.93 36.28 41.93 33.37 29.19 27.93 28.15 31.31 31.55 27.15 32.28 28.03 36.28 41.93 36.28 41.93 16.64 24.6 28.26 28.26 36.28 31.56 31.94 19 24.49 24.71 24.98 25.21 25.45 31.94 19 29.9 38.81 39.14 39.45 39.81
0.64 0.63 0.64 −0.04 0.96 1.12 −5.81 −3.7 −2.07 −1.05 −0.9 1.69 0.59 0.98 0.49 1.45 0.08 1.95 1.41 1.67 0.97 17.22 1.98 0.27 1.52 0.81 0.75 0.32 0.19 1.45 1.07 1.1 0.37 0.11 0.9 1.19 −0.25 −0.86 −0.54 −0.31 −0.18 0.36 0.87 1.6 0.82 0.79 0.76 0.73
2.08 2.07 2.28 2.03 1.55 0.68 0.24 0.05 1.95 9.06 11.27 2.68 0.14 0.84 0.24 2.97 0.20 0.83 2.14 0.60 0.71 0.18 0.64 0.31 1.51 0.38 0.89 0.00 0.36 1.17 0.08 0.04 0.61 0.46 0.08 0.64 7.27 1.27 2.83 6.74 19.78 0.41 0.09 0.17 0.05 0.10 0.11 0.00
1.76 1.81 1.81 0.5 1.25 0.38 0.1 0.09 0.62 2.18 2.36 1.49 0.14 0.57 0.21 1.45 0.21 0.52 1.35 0.67 0.66 0.13 0.4 0.34 0.91 0.27 0.67 0.19 0.25 0.66 0.23 0.03 0.6 0.4 0.11 0.33 1.76 0.59 1.08 1.92 3.46 0.31 0.07 0.13 0.16 0.09 0.07 0.08
17 17 17 13 6 5 5 5 5 5 5 17 19 19 19 14 13 11 11 8 8 10 5 6 18 19 18 18 12 5 5 5 17 9 11 11 11 11 11 11 11 13 12 6 6 7 7 7
Jimenez et al. (2001) Jimenez et al. (2001) Jimenez et al. (2001) Kijevcanin et al. (2003) Michaels et al. (1950) Michaels et al. (1950) Rolo et al. (2002) Rolo et al. (2002) Rolo et al. (2002) Rolo et al. (2002) Rolo et al. (2002) Jimenez et al. (2000) Segade et al. (2003) Jimenez et al. (2000) Segade et al. (2003) Postigo et al. (1987) Giner et al. (2004) Suri and Ramakrishna (1968) Suri and Ramakrishna (1968) Suri and Ramakrishna (1968) Suri and Ramakrishna (1968) Suri and Ramakrishna (1968) International Critical Table Meissner and Michaels (1949) Jimenez et al. (2000) Segade et al. (2003) Jimenez et al. (2000) Segade et al. (2003) Santos et al. (2003) Meissner and Michaels (1949) Meissner and Michaels (1949) International Critical Table Jimenez et al. (2000) Wright and Akhtar (1970) Lam and Benson (1970) Lam and Benson (1970) Kahl et al. (2003a) Kahl et al. (2003a) Kahl et al. (2003a) Kahl et al. (2003a) Kahl et al. (2003a) Lam and Benson (1970) Lam and Benson (1970) Michaels et al. (1950) Kahl et al. (2003b) Kahl et al. (2003b) Kahl et al. (2003b) Kahl et al. (2003b)
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178
4941
4942
Table 1 (continued) No.
Overall AAD%
1
2
Toluene TCE TCE o-Xylene o-Xylene o-Xylene o-Xylene o-Xylene o-Xylene o-Xylene m-Xylene m-Xylene m-Xylene m-Xylene m-Xylene m-Xylene p-Xylene p-Xylene p-Xylene p-Xylene p-Xylene p-Xylene
Heptane 1-Propanol 2-Propanol Acetone 2-Butanone Benzene 2-Propanol isoPropyl ether 2-M-2-P MTBE Acetone 2-Butanone 2-Propanol isoPropyl ether 2-M-2-P MTBE Acetone 2-Butanone 2-Propanol isoPropyl ether 2-M-2-P MTBE
Temp. (K)
327.88 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15
◦ (mN/m) Exp.
Calc.
7.61 1.81 3.71 5.34 5.07 1.24 8.67 12.04 9.63 10.1 4.35 4.08 7.43 11.05 8.39 9.11 3.88 3.61 6.96 10.58 7.92 8.64
7.58 2.05 3.73 6.22 5.22 1.3 8.3 11.7 9.35 10.26 5.03 4.05 7.07 10.67 8.14 9.29 4.34 3.58 6.65 10.29 7.8 8.86
GS /RT
0.87 −0.75 −0.6 −1.01 −0.39 0.17 0.52 0.61 0.66 0.41 −0.99 −0.18 0.52 0.59 0.61 0.29 −0.74 −0.18 0.41 0.47 0.44 0.21
−G◦ /RT
2.90 −0.03 0.72 0.82 1.26 0.43 2.64 3.07 2.90 2.74 0.63 1.22 2.48 2.96 2.71 2.52 0.73 1.10 2.30 2.80 2.49 2.39
A¯ 2 (A˚ 2 )
E 2
RAD%
AAD%
n
Ref.
40.16 24.97 25.37 24.73 28.2 28.04 25.37 38.21 29.19 34.08 24.73 28.2 25.37 38.21 29.19 34.08 24.73 28.2 25.37 38.21 29.19 34.08
0.78 −0.15 −0.38 −0.32 −0.89 0.49 1.02 1.82 1.03 2.05 −0.26 −1.56 0.88 1.73 0.97 2.6 −0.32 −1.36 1.04 2.09 1.28 3.44
0.18 1.03 0.10 3.67 0.62 0.21 1.77 1.96 1.40 0.83 2.83 0.12 1.72 2.20 1.25 0.94 1.92 0.12 1.48 1.68 0.60 1.14
0.12 0.34 0.17 0.95 0.23 0.13 0.95 1.06 0.78 0.45 0.79 0.06 0.94 1.22 0.74 0.44 0.61 0.05 0.79 0.88 0.34 0.55
7 14 14 11 11 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
Kahl et al. (2003b) Bardavid et al. (1994) Bardavid et al. (1994) Ouyang et al. (2004b) Ouyang et al. (2004b) Lam and Benson (1970) Ouyang et al. (2003) Ouyang et al. (2004a) Ouyang et al. (2003) Ouyang et al. (2004a) Ouyang et al. (2004b) Ouyang et al. (2004b) Ouyang et al. (2003) Ouyang et al. (2004a) Ouyang et al. (2003) Ouyang et al. (2004a) Ouyang et al. (2004b) Ouyang et al. (2004b) Ouyang et al. (2003) Ouyang et al. (2004a) Ouyang et al. (2003) Ouyang et al. (2004a)
0.56
2-M-1-CP: 2-Methyl-1-chloropropane, 2-M-2-CP: 2-Methyl-2-propanol, CTC: Carbon tetrachloride, 2-M-1-P: 2-Methyl-1-propanol, 2-M-2-P: 2-Methyl-2-propanol, DCM: Dichloromethane, DMF: Dimethyl formamide, DMSO: Dimethylsulfoxide, Furfural: 2-Furan carboxaldehyde, TCET: Tetrachloroethylene, TCE: 1,1,1-Trichloroethane, MTBE: Methyl tert-butyl ether.
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
Mixture Component
Table 2 Experimental and calculated differences of surface tensions of solvent and solute (◦ , Eq. (4)), surface Gibbs energy change (GS /RT , Eq. (3)), standard Gibbs energy of adsorption (−G◦ /RT , Eq. (10)), molar surface area (A¯ 2 , Eq. (6)), excess number of molecular layers (E 2 , Eq. (5)), relative absolute deviation percent (RAD%) in calculating the surface tension of pure solute (Eq. (15)), absolute average deviation percent (AAD%) in calculating the surface tension (Eq. (1)) for several binary aqueous solutions, the number of experimental data point (n) and the references for the experimental data (Ref.) No.
2
Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water
MEA MEA MEA MEA MEA MEA DEA DEA DEA DEA DEA DEA TEA TEA TEA TEA TEA TEA Formic acid Formic acid Formic acid Formic acid Formic acid Formic acid Formic acid Acetic acid Acetic acid Acetic acid Acetic acid Acetic acid Acetic acid Acetic acid Propionic acid Propionic acid Propionic acid Propionic acid Propionic acid Propionic acid Propionic acid Methanol Methanol
298.15 303.15 308.15 313.15 318.15 323.15 298.15 303.15 308.15 313.15 318.15 323.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15
◦ (mN/m) Exp.
Calc.
23.06 23.07 23.08 23.09 23.11 23.11 24.8 24.75 24.76 24.77 24.79 24.8 26.06 26.05 26.04 26.04 26.04 26.04 35.17 34.98 34.74 34.48 34.13 33.97 33.58 45.14 44.89 44.58 44.31 43.88 43.71 43.26 46.09 45.84 45.53 45.24 44.83 44.65 44.24 49.8 49.5
21.79 21.79 21.79 21.79 21.83 21.83 23.75 23.7 23.7 23.75 23.75 23.75 26.04 25.97 25.97 25.97 25.97 25.97 34.6 34.48 34.13 33.9 33.56 33.33 33 43.86 43.48 43.29 42.92 42.55 42.37 42.02 45.45 45.25 45.05 44.64 44.25 44.05 43.67 49.5 49.26
GS /RT
−G◦ /RT
˚ 2) A¯ 2 (A
E 2
RAD%
AAD%
n
Ref.
2.18 2.18 2.18 2.18 2.18 2.18 2.33 2.33 2.33 2.33 2.33 2.33 3.12 3.12 3.12 3.12 3.12 3.12 1.75 1.78 1.75 1.76 1.75 1.75 1.74 2.66 2.67 2.67 2.68 2.69 2.69 2.7 3.78 3.79 3.79 3.8 3.81 3.82 3.82 1.98 1.98
5.26 5.26 5.26 5.26 5.26 5.26 5.50 5.50 5.50 5.50 5.50 5.50 6.38 6.38 6.38 6.38 6.38 6.38 5.29 5.32 5.28 5.28 5.26 5.26 5.24 6.44 6.44 6.44 6.44 6.44 6.44 6.44 7.60 7.60 7.60 7.60 7.60 7.61 7.60 5.88 5.88
21.57 21.62 21.7 21.74 21.8 21.87 29.43 29.47 29.56 29.6 29.65 29.73 36.54 36.6 36.67 36.73 36.77 36.86 15.77 15.85 15.89 15.94 16.01 16.07 16.14 20.83 20.89 20.95 21.02 21.08 21.14 21.21 24.86 24.95 25.02 25.1 25.19 25.27 25.35 16.52 16.58
0.55 0.55 0.54 0.53 0.53 0.52 0.76 0.75 0.74 0.73 0.72 0.71 0.74 0.73 0.72 0.71 0.7 0.69 0.78 0.76 0.75 0.74 0.72 0.71 0.7 0.87 0.85 0.84 0.82 0.8 0.78 0.76 0.75 0.73 0.72 0.7 0.69 0.67 0.66 1.03 1.01
2.59 2.66 2.72 2.80 2.80 2.86 2.22 2.26 2.32 2.28 2.36 2.44 0.04 0.18 0.16 0.16 0.16 0.17 1.52 1.35 1.67 1.61 1.61 1.84 1.69 4.64 5.20 4.84 5.32 5.19 5.33 5.03 2.40 2.25 1.87 2.38 2.35 2.48 2.41 1.31 1.07
2.02 2.06 2.09 2.13 2.16 2.21 2.04 2.06 2.09 2.12 2.15 2.19 0.14 0.13 0.14 0.14 0.16 0.16 0.98 1.04 0.95 0.99 0.96 1.01 0.96 3.09 3.09 3.2 3.27 3.38 3.42 3.5 2.38 2.52 2.45 2.47 2.51 2.58 2.67 0.73 0.79
13 13 13 13 13 13 11 11 11 11 11 11 11 11 11 11 11 11 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
Vazquez et al. (1997) Vazquez et al. (1997) Vazquez et al. (1997) Vazquez et al. (1997) Vazquez et al. (1997) Vazquez et al. (1997) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Vazquez et al. (1996) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Alvarez et al. (1997) Vazquez et al. (1995) Vazquez et al. (1995)
4943
1
Temp. (K)
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
Mixture Component
4944
Table 2 (continued) No.
1
2
Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water
Methanol Methanol Methanol Methanol Methanol Ethanol Ethanol Ethanol Ethanol Ethanol Ethanol Ethanol 1-Propanol 1-Propanol 1-Propanol 1-Propanol 1-Propanol 1-Propanol 1-Propanol 2-Propanol 2-Propanol 2-Propanol 2-Propanol 2-Propanol 2-Propanol 2-Propanol 1,2-Ethanediol 1,2-Ethanediol 1,2-Propanediol 1,2-Propanediol 1,2-Propanediol 1,2-Propanediol 1,2-Propanediol 1,2-Propanediol 1,2-Propanediol 1,2-Propanediol 1,2-Propanediol 1,3-Propanediol 1,2-Butanediol 2,3-Butanediol 1,3-Butanediol 1,3-Butanediol 1,4-Butanediol 1,4-Butanediol
Temp. (K)
303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 298.15 303.15 298.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 303.15 298.15 298.15 298.15 303.15 298.15 303.15
◦ (mN/m) Exp.
Calc.
49.2 48.9 48.39 48.23 47.71 50.44 50.44 49.8 49.38 48.9 48.62 48.1 49.06 48.73 48.32 47.91 47.41 47.15 46.61 51.01 50.79 50.49 50.19 49.82 49.63 49.23 23.81 24.91 36.41 35.5 34.52 33.82 32.57 31.36 30.39 29.39 28.11 24.2 40.81 39.5 34.88 34.11 26.5 27.36
49.02 49.02 48.08 47.85 47.39 50.25 49.75 49.5 49.02 48.54 48.31 47.85 49.02 48.54 48.08 47.85 47.17 46.95 46.51 50.76 50.51 50.25 50 49.75 49.5 49.02 23.81 24.21 34.97 34.6 33.56 32.79 31.85 30.58 29.67 28.65 27.55 23.64 40.65 39.22 34.01 33.56 25.91 26.67
GS /RT
−G◦ /RT
˚ 2) A¯ 2 (A
E 2
RAD%
AAD%
n
Ref.
1.99 1.99 2.01 2.01 2.02 3.1 3 3.01 3.02 3.03 3.03 3.04 4.62 4.63 4.64 4.65 4.66 4.67 4.68 3.9 3.9 3.91 3.91 3.92 3.92 3.93 1.82 1.9 2.48 2.49 2.52 2.5 2.53 2.53 2.49 2.45 2.49 2.87 3.71 3.06 3.12 3.21 2.78 3.04
5.88 5.88 5.88 5.88 5.88 7.02 6.91 6.91 6.91 6.91 6.91 6.91 8.51 8.51 8.51 8.52 8.51 8.52 8.52 7.83 7.82 7.83 7.82 7.83 7.82 7.82 4.99 5.09 6.03 6.03 6.03 5.99 5.99 5.95 5.88 5.81 5.81 6.03 7.41 6.73 6.65 6.72 6.03 6.32
16.65 16.72 16.79 16.86 16.93 21.11 21.18 21.26 21.34 21.43 21.51 21.6 24.9 24.97 25.06 25.15 25.23 25.32 25.42 25.27 25.36 25.45 25.55 25.65 25.75 25.86 20.5 20.55 24.64 24.67 24.8 24.92 25.05 25.18 25.31 25.46 25.6 24.41 28.2 28.23 28.18 28.2 27.95 28
0.99 0.97 0.94 0.92 0.9 0.85 0.87 0.84 0.82 0.8 0.79 0.77 0.65 0.64 0.62 0.61 0.59 0.58 0.57 0.82 0.8 0.79 0.77 0.75 0.74 0.73 0.65 0.65 0.88 0.84 0.79 0.76 0.7 0.66 0.63 0.61 0.56 0.49 0.75 0.89 0.77 0.72 0.65 0.6
0.82 0.56 1.47 1.84 1.58 0.85 3.16 1.40 1.71 1.75 1.53 1.26 0.17 0.82 1.05 0.27 1.09 0.92 0.47 1.15 1.32 1.16 0.94 0.36 0.68 1.12 0.00 1.51 4.02 2.52 2.74 3.02 2.15 2.36 2.23 2.36 1.82 1.19 0.51 0.86 2.35 1.48 1.30 1.58
0.9 0.98 1.15 1.27 1.43 1.68 1.42 1.47 1.49 1.43 1.49 1.51 1.09 1.1 1.17 1.1 1.07 1.13 1.11 1.46 1.5 1.51 1.55 1.54 1.62 1.64 0.52 1.02 2.65 2.45 2.61 2.72 2.08 2.14 2.04 2.22 1.89 0.97 1.02 0.85 2.21 1.88 1.62 1.91
14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 7 18 8 8 8 8 8 8 8 8 8 18 18 18 18 18 18 18
Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Vazquez et al. (1995) Hoke and Chen (1991) Nakanishi et al. (1971) Hoke and Patton (1992) Hoke and Patton (1992) Hoke and Patton (1992) Hoke and Patton (1992) Hoke and Patton (1992) Hoke and Patton (1992) Hoke and Patton (1992) Hoke and Patton (1992) Hoke and Patton (1992) Nakanishi et al. (1971) Hawrylak et al. (1998) Hawrylak et al. (1998) Hawrylak et al. (1998) Nakanishi et al. (1971) Hawrylak et al. (1998) Nakanishi et al. (1971)
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
Mixture Component
MEA: Monoethanolanine (2-Aminoethanol), DEA: Diethanolamine (2,2-Iminobisethanol), TEA: Triethanolamine (2,2,2-Nitrilotrisethanol), 1-AP: 1-Amino-2-propanol, AMP: 2-Amino-2-methyl-1propanol, 3-AP: 3-Amino-1-propanol, MDEA: N-Methyldiethanolamine, TFE: Trifluoroethanol.
1.8 Overall AAD%
86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
Water Water Water Water Water Water Water Water Water Water Water Water Water Water Water
MDEA MDEA MDEA MDEA MDEA MDEA 3-AP 3-AP 3-AP 3-AP 3-AP 3-AP AMP 1-AP TFE
298.15 303.15 308.15 313.15 318.15 323.15 298.15 303.15 308.15 313.15 318.15 323.15 298.15 298.15 298.15
33.11 33.11 32.8 32.21 31.68 31.04 28.11 28.44 28.81 29.04 29.51 29.76 40.64 34.63 47.5
32.15 32.15 31.85 31.45 30.96 30.58 27.47 27.62 27.86 27.93 28.25 28.41 39.68 33.11 46.95
2.97 2.97 2.98 2.99 3.01 3.08 1.93 2 2.01 2.05 2.11 2.13 3.33 2.41 4.26
6.44 6.44 6.44 6.44 6.44 6.50 5.24 5.32 5.34 5.38 5.45 5.48 7.01 5.91 8.11
32.08 32.16 32.24 32.31 32.42 32.5 25.29 25.39 25.48 25.57 25.67 25.76 20.89 25.7 24.35
0.87 0.86 0.84 0.81 0.78 0.73 0.9 0.86 0.86 0.84 0.82 0.81 0.62 0.9 0.66
2.47 2.52 2.53 2.04 1.94 1.25 1.46 1.92 2.28 2.74 3.20 3.54 3.06 4.07 2.48
3.31 3.35 3.26 2.86 2.37 2.09 1.03 1.42 1.6 1.94 2.26 2.5 3.17 3.34 3.44
14 14 14 14 14 14 12 12 12 12 12 12 14 12 15
Alvarez et al. (1998) Alvarez et al. (1998) Alvarez et al. (1998) Alvarez et al. (1998) Alvarez et al. (1998) Alvarez et al. (1998) Alvarez et al. (2003) Alvarez et al. (2003) Alvarez et al. (2003) Alvarez et al. (2003) Alvarez et al. (2003) Alvarez et al. (2003) Vazquez et al. (1997) Alvarez et al. (2003) Gente and La Mesa (2000)
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
4945
Finally in the 13th and 14th columns of Tables 1 and 2, the number of data points (n) and the references of the experimental data of solutions used in the calculations are given. In Table 3, the standard Gibbs energy of adsorption calculated by applying Eq. (10) to the binary solutions: (1,4dioxane + n-alkanol), (1,4-dioxane + n-alkane) and (1,3dioxolane + n-alkanol) are reported. 4. Discussion In the 5th and 6th columns of Tables 1 and 2, the experimental and calculated values of ◦ are compared. Good agreement in most cases is to be noted. The reported RAD% values in these tables indicate that Eqs. (2) and (4) can accurately calculate the surface tension of a pure solute from the surface tension of its solution in a solvent with known surface tension. This provides a means for obtaining the surface tension of a highly volatile or unstable substance, for which the direct surface tension measurement is very difficult or costly from the surface tension of binary solutions. 4.1. Variation of −G◦ /RT and GS /RT in aqueous solutions of homologues series
GS /RT is reported in 7th column. It is to be noted that generally the free energy change for aqueous solutions is greater than for organic solutions. This may be related to the interactions between the −OH group in water and the −NH2 and –OH groups in the solute and hydrogen bonding, which is formed in these solutions (Papaioannou et al., 1993). In aqueous solutions of monoethanolamine (MEA), diethanolamine (DEA) and triethanolamine (TEA), GS /RT increases from MEA to TEA. This trend is related to the strength of hydrogen bonding on increasing the number of hydroxyl groups from MEA to TEA. In aqueous solutions of aliphatic acids, GS /RT increases from formic to propionic acid. −G◦ /RT and GS /RT both increase with increasing molecular size of the solute within a series of homologous compounds. The increase in −G◦ per −CH2 group at 298.15 K is 2.83 kJ mol−1 for aliphatic acids, 3.27 kJ mol−1 for aliphatic alcohols and 3.01 kJ mol−1 for alkanediols. This consistent variation in the standard Gibbs energy of adsorption (−G◦ ) with regard to methylene addition is analogous to Traube’s rule defined for methylene addition to n-alkanes (Kipling, 1965; Adamson and Gast, 1997). It is also in good agreement with previous observations on the adsorption of hydrocarbons at the air–water interface (Valsaraj, 1994) and long chain anionic surfactants from aqueous solutions (Feurstenau and Healy, 1972). Generally, in aqueous solutions of a homologue series, the free energy change and the standard Gibbs energy of adsorption increase with increasing number of carbon atoms. This trend is linear as can be seen in Figs. 1 and 2.
4946
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
Table 3 Surface free energy change, excess number of molecular layers, experimental and calculated standard Gibbs energy of adsorption for binary solutions of 1,4-Dioxane+n-Alkanol, 1,3-Dioxolane+n-Alkanol and 1,4-Dioxane + n-Alkane* Solvent → 1,4-Dioxane Solute ↓
GS /RT
1,3-Dioxolane
E 2
GS /RT E 2
−G◦ /RT This work EL model Exp. Ref.**
Methanol −0.78 Ethanol −0.06 1-Propanol 0.27 2-Propanol 1-Butanol 2-Butanol 1-Pentanol 1-Hexanol 0.92 1-Heptanol 1.08 1-Octanol 1.23 1-Decanol 1.52 Hexane 1.83 Heptane 2.05 Octane 2.11 Nonane 2.21 Decane 2.37
−0.55 1.71 −9.12 2.35 2.14 2.52
0.63 0.52 0.44 0.33 0.70 0.60 0.55 0.50 0.45
2.83 2.88 2.92 3.00 4.49 4.58 4.52 4.52 4.58
1.58 2.26 2.43
2.77 2.83 2.83 2.93 4.51 4.69 4.56 4.61 4.76
−G◦ /RT This work EL model Exp. Ref.**
1.53 Calvo et al. (2002) −0.54 2.24 Calvo et al. (2002) 0.22 2.40 Calvo et al. (2002) 0.54 0.76 0.85 0.91 1.04 2.83 Calvo et al. (2001) 2.96 Calvo et al. (2001) 2.97 Calvo et al. (2001) 3.04 Calvo et al. (2001) 4.45 Calvo et al. (2000) 4.72 Calvo et al. (2000) 4.49 Calvo et al. (2000) 4.54 Calvo et al. (2000) 4.71 Calvo et al. (2000)
−0.78 2.48 1.03 0.96 0.69 0.74 0.56
1.92 2.61 2.78 3.22 2.99 3.17 3.06
1.67 2.47 2.75 3.11 2.98 3.12 3.05
1.61 2.45 2.75 3.09 2.97 3.12 3.04
Calvo Calvo Calvo Calvo Calvo Calvo Calvo
et et et et et et et
al. al. al. al. al. al. al.
(2004) (2004) (2004) (2004) (2004) (2004) (2004)
∗ For all solutions, T = 298.15 K. ∗∗ Reference for experimental and EL model data of −G◦ /RT .
The results of calculations for isomeric butanediols at 298.15 K show the following trend for the standard Gibbs energy of adsorption (−G◦ ): 1,2-butanediol > 2,3-butanediol > 1,3-butanediol > 1,4-butanediol. Experimental data for −G◦ shows the same trend as for the aqueous solutions of isomeric butanediols (Zagorska et al., 1994). This relationship reflects a higher surface activity and a higher degree of hydrophobicity for both 1,2-butanediol and 2,3-butanediol. This observation can be explained by hydrogen bonding operating between solute molecules (Buc, 1963; Japaridze, 1977). Also this behaviour may be associated with the ability of neighbouring −OH groups to form intermolecular hydrogen bonds, which would reduce the capability of these molecules from interacting with the solvent. This in turn would lead to a higher adsorbability of both 1,2- and 2,3-butanediol than 1,3- and 1,4-butanediol. Since the −OH groups are farther apart in 1,3- and 1,4butanediol, these molecules form hydrogen bonding with water molecules only. In fact the difference between GS and −G◦ for 2,3-butanediol and 1,3-butanediol is not significant and this matter is puzzling and cannot easily be explained in terms of mixed behaviour. 4.2. Variation of −G◦ /RT and GS /RT in organic solutions of homologues series First we examine the 1,4-dioxane + n-alkanol from methanol to 1-decanol. As is seen in Table 3, GS is nega-
tive for 1,4-dioxane + methanol and 1,4-dioxane + ethanol solutions. The transfer of alcohol molecules from the bulk to the surface depends on their interactions in the bulk. Several authors (Letcher and Govender, 1995; Papanastasiou et al., 1987; Papanastasiou and Ziogas, 1992) have provided evidence that methanol and ethanol molecules form hydrogen-bonded complexes with 1,4-dioxane and these interactions partially replace alcohol–alcohol hydrogen bonding. This formation of hydrogen–hydrogen complexes in the bulk counteracts the tendency of the alcohol (the component with the lower surface tension) to segregate at the surface and explains why ethanol and methanol have negative GS and consequently negative the excess number of molecular layers. For the case of short-chain length alcohols, the strong interactions between the cyclic ether and alcohol give rise to an increase in surface tension (Calvo et al., 2004). For example for the binary solution (1,4-dioxane + methanol), the excess surface tension (E = − 1 x1b − 2 x2b ) is positive. When the alcohol is ethanol, E fluctuates near zero and takes both positive and negative sign, for this reason GS and E 2 are negative for methanol and ethanol. For alcohols with longer chain length, the excess surface tension is negative this means that for the longer chain length alcohol mixtures, the surface concentration of the alcohol is greater than that of cyclic ether. In longer chain length alcohols, lyophobicity is the factor which has the greatest influence on the surface tension and adsorption hence GS and −G◦ both increase from (1,4-dioxane + methanol) to (1,4-dioxane + 1-decanol). The trend of variation of GS /RT in these solutions is shown in Fig. 1. For the mixtures of (1,3-dioxolane
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
5
4
∆GS/RT
3
2
1
0 0
4
2
6
8
10
12
-1 Number of Carbon Atoms 1,4-Dioxane +n-Alkane 1,3-Dioxolane +n-Alkanol Water +n-Alkanol
1,4-Dioxane + n-Alkanol Water +Aliphatic acid Water +n-Alkanediol
Fig. 1. Dimensionless surface free energy change (GS /RT ) for binary mixtures versus number of carbon atoms.
9
7
-∆G˚ /RT
+ n-alkanol), similar behaviour to (1,4-dioxane + alcohol) is observed, as is seen from Table 3 and Fig. 1. For (1,3dioxolane + methanol) the excess surface tension is positive hence both GS and E 2 are negative while for other are positive. Comparing GS for n-alkanols, GS and E 2 (1-propanol and 2-propanol) and (1-butanol and 2-butanol) shows that if the −OH group is in the 2 position; there will be an increase in lyophobicity. In Table 3 the results of calculations for (1,4-dioxane + nalkane) are also listed. With increasing the number of carbon atoms in the alkane, the lyophobicity of the solute increases and consequently the tendency of the alkane to adsorb at the surface layer increases from hexane to decane therefore GS increases from hexane to decane. This trend is linear as is shown in Fig. 1. Fig. 1 shows the dependence of GS /RT on the number of carbon atoms. It is clear that the dependence of GS /RT on the number of carbon atoms in (1,4-dioxane + n-alkane) is less than for (1,4-dioxane + n-alkanol). This indicates that in 1,4-dioxane the length of the hydrocarbon chain in the alcohols does not have a very strong influence on the surface activity. Presumably, the interactions between the −CH2 group and 1,4-dioxane are less effective than the interactions between the −OH group and 1,4-dioxane. As a consequence, GS /RT depends less on the number −CH2 groups. By comparing the results of calculations for (1,4-dioxane + n-alkane) and (1,4-dioxane + n-alkanol) it can be seen that GS /RT and −G◦ /RT for the n-alkane solution are greater than for the n-alkanol solution. This indicates that 1,4-dioxane repels alkanes from the bulk much more than n-alkanols. This effect is in agreement with earlier measurements (Calvo et al., 2002) which this behaviour has been attributed to the weaker interactions between alkane-ether interactions than alkanol-ether.
4947
5
4.3. Dependence of GS /RT on temperature in aqueous and organic solutions 3
An important feature of GS is its temperature dependence. For all the aqueous solutions, GS increases linearly with increasing temperature. However, GS /RT in most cases is independent of temperature as is seen in Fig. 3. With increasing temperature, the calculated standard Gibbs energy of adsorption for aqueous solutions also increases, showing that higher temperatures favour transfer of solute from bulk to surface (Calvo et al., 2002) with a concomitant reduction in the surface tension. For the organic solutions it would be expected that with increasing temperature, GS /RT would increase since surface tension decreases with increasing temperature. In general this is the case for (dodecane + hexane), (DMSO + benzene), (DMSO + chloroform), (DMSO + toluene), (nitrobenzene + benzene) and (nitrobenzene + cyclohexane) as examples. However, for some organic solutions a different
1 0
2
4 Water +n-Alkanol Water +Aliphatic acid 1,4-Dioxane + n-Alkane
6
8
10
12
Water +n-Alkanediol 1,3-Dioxolane +n-Alkane 1,4-Dioxane +n-Alkanol
Fig. 2. Dimensionless standard Gibbs energy of adsorption (−G◦ /RT ) for binary mixtures versus number of carbon atoms.
behaviour is observed for example, (benzene + hexane), and (DMSO + chlorobenzene). It is likely that these deviations are related to experimental errors in the surface tension measurements. However, it should be noted that the vapour pressure of the solute is lower than the solvent. These, together
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5.0
∆GS/RT
4.1
3.2
2.3
1.4 290
300 3-Amino-1-propanol TEA Propionic acid 1-Propanol
310 T/ K MEA Formic acid Methanol 2-Propanol
320
330 DEA Acetic acid Ethanol MDEA
Fig. 3. Variation of dimensionless surface free energy change for aqueous solutions versus temperature. The points are calculated values and the solid lines are fitted lines.
with the cases where the vapour pressure of the solute and the solvent are comparable would give rise to the observed deviation. For some mixtures, GS /RT decreases with increasing temperature. 4.4. The sign of GS For most mixtures GS is positive which means that solute (2) has a tendency to adsorb at the surface layer. However, for some mixtures such as [benzene (1) + acetone (2)], [chloroform (1) + acetone (2)], [toluene (1) + acetone (2)], [1,3-dioxolane (1) + methanol (1)] and [o-xylene (1) + acetone (2)], GS is negative, indicating that the solute molecules are restrained from entering the surface layer. Most of these mixtures are highly polar and in most cases the solute is acetone. The explanation for this behaviour is either the high intermolecular interactions between solute and solvent (Benson and Lam, 1972) or the volatility of the solute. The strong molecular interactions between the solute and the solvent in the bulk counteract the tendency of the solute to adsorb at the surface while the more volatile component has a tendency to enrich the vapour phase and thus escape from the surface layer (Papaioannou and Panayiotou, 1989). For [decane (1) + hexadecane (2)] and [heptane (1) + hexadecane (2)] solutions GS is also negative. This may be related to the very unsymmetrical structure of hexadecane and hence the possibility of different orientations of the component at the surface and bulk region. For [dodecane (1) + hexane (2)] the negative GS which results in negative E 2
is related to the higher vapour pressure and higher volatility of hexane in contrast to dodecane. Hexane has a higher vapour pressure and escapes from the interface and enriches the vapour phase. For this system two arrangements are possible (Schmidt and Clever, 1968): the surface layer is multimolecular with respect to hexane (Fig. 4A) or monomolecular with a substantial part of the dodecane above the nominal surface (Fig. 4B). The first case would lead to a convex composite isotherm and a negative excess surface tension (E = − 1 x1b − 2 x2b ). The second case would mean an enhanced number of dodecane molecules per unit area in the surface region and hence greater dodecane–dodecane interactions with increasing concentration of dodecane. This would give rise to a corresponding reduction in the surface tension and a positive excess surface tension. Both of these are observed. Furthermore, it is observed that for all systems with negative GS , the excess surface tension is positive and the surface tension vs. composition curve lies above the straight line of an ideal mixture. This observation indicates that the concentration of the solute (the component with the lower surface tension) is less than the solvent in these solutions. It is to be noted that for some mixtures, e.g. (1,4-dioxane + benzene, 293.15 K), (carbon tetrachloride + cyclopentane, 298.15 K), (chlorobenzene + toluene, 313.15 K), (decane + hexadecane, 293.15 K), (DMSO + bromobenzene, 323.15 K) and (nitrobenzene + 1,4-dioxane, 293.15 K), GS /RT is nearly equal to zero. For these solutions the components are approximately of the same size and the solvent–solvent and solute–solute intermolecular attractive forces and the distribution of each component between the surface region and the bulk is nearly the same. For these mixtures, the additivity law is a good approximation for the surface tension as given in Eq. (1):
= 1 x1b + 2 x2b .
(17)
For the above-mentioned systems, the calculated surface tension using Eq. (17) are compared with experimental data in Fig. 5. It is clear for these systems that the additivity law is a good approximation to the surface tension. 4.5. The excess number of molecular layers in binary aqueous and organic solutions As can be seen from Table 2, for all of the aqueous solutions the E 2 is positive which indicates the excess number of molecular layers of solute in the surface with respect to the bulk. In these solutions the solute is adsorbed in the surface and had a decreasing effect on the surface tension of solution. The calculated non integer values of E 2 can be attributed to the differences in orientation of solute in the surface and bulk regions (Langmuir, 1932; Ward, 1946; Hartkopf and Karger, 1973). Some authors have known other effects responsible for obtaining non-integer values of E 2 , such as significant escaping tendency of both
R. Tahery et al. / Chemical Engineering Science 60 (2005) 4935 – 4952
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NORMAL SURFACE H
H C-H C-H H-C H-C
H-C C-H
H
H-C
C-H
C-H
H-C C-H
H-C
H-C C-H
H-C H
C-H
C-H
H-C C-H
H-C
H-C C-H
H-C C-H
C-H
C-H
C-H H-C
C-H
H
H
H C-H
H-C
H-C
H-C
C-H H-C
C-H
H-C
C-H
H-C
H-C C-H
H-C
H-C H
H
(A)
H-C
H
C-H C-H
H-C
C-H
H-C
C-H
H-C
C-H C-H
H-C H
H
(B)
Fig. 4. Surface layer configuration for hexane + dodecane mixture, (A) multimolecular layer, (B) monomolecular layer with respect to hexane.
[1,4-dioxane (1) + decane (2)] where the non-integer values of E 2 are obtained, as reported in Table 1, it seems that for these solutions the differences in structural orientations of solute molecules in the surface and bulk regions should have a decisive effect on determining the non-integer values of E 2. But in the case of binary solutions of [cyclohexane (1) + heptane (2)], [benzene (1) + hexane (2)] and [toluene (1) + heptane (2)] where both components are volatile and then have a considerable escaping tendency from surface region, the excess number of molecular layers has a large deviation from an integer value. This tendency of both components cannot balance the low surface tension solute enriching the interfacial region. Thus for these solutions the excess number of molecular layer has a large deviation from an integer value.
45
Surface Tension / mN.m-1
40
35
30
25
20 0
0.2
0.4
1,4-Dioxane + Benzene (293.15 K) Nitrobenzene + 1,4-Dioxane (293.15 K) DMSO + Bromobenzene (323.15 K)
x2
0.6
0.8
1
Chlorobenzene + Toluene (313.15 K) Decane + Hexadecane (293.15 K) Carbon tetrachloride + Cyclopentane (298.15 K)
Fig. 5. Calculated and experimental surface tension values of binary organic solutions. The solid lines are calculated surface tension based on Eq. (17) and the points are experimental.
solvent and solute molecules (Papaioannou and Panayiotou, 1989). In the studied organic binary solutions, the values of E 2, as reported in Table 1, in most cases are positive and with the same argument as presented above for the aqueous binary solutions this behaviour can be ascribed to the adsorption of solute in the surface region and its decreasing effect on the surface tension of the binary solutions. As it is seen from Table 1, the calculated E 2 is negative for a number of binary organic solutions. In these solutions the solute is not adsorbed in the surface region and according to Gibbs equation (Eq. (7)) has an increasing effect on the surface tension of these solutions. However, considering the unsymmetrical solute molecules (2) in relatively non-volatile binary solutions of [1,4-dioxane (1) + nonane (2)], [1-butanol (1) + 2-chlorobutane (2)] and
4.6. Variation of −G◦ in organic solutions of homologue series The standard Gibbs energy of adsorption has been computed by using Eq. (10) and the results obtained in this study. However, experimental data for the standard Gibbs energy of adsorption is not available for all the solutions. Table 3 lists only the mixtures for which the experimental data is available. In Table 3, the calculated standard Gibbs energy of adsorption is compared with the results of applying the extended Langmuir (EL) model (Calvo et al., 2004) and the experimental data in Table 3. It can be seen that the calculated standard Gibbs energy of adsorption is in good agreement with experimental data. The values of calculated standard Gibbs energy of adsorption for solutions of 1,4-dioxane with methanol, ethanol and 1-propanol are small compared with adsorption from aqueous solutions. This can be related to the high affinity of 1,4-dioxane for alcohol molecules since these can be solvated both by interactions with the hydrophilic group of 1,4-dioxane, and by the hydrophobic interaction of the hydrocarbon chain with the methyl groups of 1,4-dioxane. Thus, alcohol molecules have little tendency to leave the 1,4-dioxane solution and explains why the values of −G◦ for aqueous solutions of alcohols are greater than alcohol solutions with 1,4-dioxane.
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4.7. Surface tension prediction results for aqueous and organic solutions Surface tension of aqueous and organic solutions can be calculated by using Eq. (4). The AAD% in calculating surface tension has been reported in Tables 1 and 2. According to the results in Tables 1 and 2, the capability of this model for prediction of surface tension for binary solutions is remarkably good.
Subscripts 1 2 b S
Superscript E
5. Conclusions A model for calculating the surface tension of both organic and aqueous binary solutions has been presented. It is shown that this model can give knowledge about the surface structure of a wide range of binary solutions. However, for physically meaningful results about the surface, it is necessary that the solutions conform to the assumptions used in deriving the equation and that accurate surface tension data for the studied solutions are available. The equation used for the surface tension calculation in this work generates more detailed information about surface region structure. Furthermore, it has also been used to calculate the free energy change in the surface region, excess number of molecular layers, the difference between surface tension of pure components and the standard Gibbs energy of adsorption. The calculated values of surface tension and the standard Gibbs energy of adsorption compare remarkably well with experimental data.
Notation A¯ A c G M n N NA R R 2 T x
molar area surface area concentration Gibbs free energy molecular weight number of data point number of solutions Avogadro’s number gas constant mean squared linearity coefficient for Eq. (2) temperature, K mole fraction
Greek letters
slope of Eq. (2) intercept of Eq. (2) surface tension molar surface excess function excess number of molecular layers density
solvent solute bulk surface region
Excess
Acknowledgements RT would like to thank both the British Council and the Iranian Ministry of Science, Research and Technology for support while visiting the United Kingdom. References Adamson, A.W., Gast, A.P., 1997. Physical Chemistry of Surfaces. sixth ed. Wiley, New York. Agarwal, D.K., Gopal, R., Agarwal, S., 1979. Surface tensions of binaryliquid mixtures of some polar and non-polar liquids with dimethylsulfoxide (Me2 SO). Journal of Chemical and Engineering Data 24, 181–183. Alvarez, E., Vazquez, G., Sanchez, V.M., Sanjurjo, B., Navaza, J.M., 1997. Surface tension of organic acids plus water binary mixtures from 20 to 50 ◦ C. Journal of Chemical and Engineering Data 42, 957–960. Alvarez, E., Rendo, R., Sanjurjo, B., Sanchez, V.M., Navaza, J.M., 1998. Surface tension of binary mixtures of water plus Nmethyldiethanolamine and ternary mixtures of this amine and water with monoethanolamine, diethanolamine, and 2-amino-2-methyl-1propanol from 25 ◦ C to 50 ◦ C. Journal of Chemical and Engineering Data 43, 1027–1029. Alvarez, E., Cancela, A., Maceiras, R., Navaza, J.M., Taboas, R., 2003. Surface tension of aqueous binary mixtures of 1-amino-2propanol and 3-amino-1-propanol, and aqueous ternary mixtures of these amines with diethanolamine, triethanolamine, and 2-amino-2methyl-1-propanol from 298.15 to 323.15 K. Journal of Chemical and Engineering Data 48, 32–35. Azizian, S., Hemmati, M., 2003. Surface tension of binary mixtures of ethanol plus ethylene glycol from 20 to 50 ◦ C. Journal of Chemical and Engineering Data 48, 662–663. Bardavid, S.M., Pedrosa, G.C., Katz, M., 1994. Surface tensions of some nonelectrolyte binary liquid mixtures. Journal of Colloid and Interface Science 165, 264–268. Belton, J.W., Evans, M.G., 1945. Studies in the molecular forces involved in surface formation. 2. The surface free energies of simple liquid mixtures. Transactions of the Faraday Society 41, 1–12. Benson, G.C., Lam, V.T., 1972. Surface tensions of binary liquid systems. 2. Mixtures of alcohols. Journal of Colloid and Interface Science 38, 294–301. Beyer, W.H., 1991. CRC Standard Mathematical Tables and formulae. 29th ed. CRC Press, London. Buc, H., 1963. Influence Des Liaisons Hydrogene Intramoleculaires Sur Les Conformations Prises En Solution Par Les Molecules De Beta- Diols Et Dalcool Polyvinylique. Annales De Chimie France 8, 431–456. Calvo, E., Penas, A., Pintos, M., Bravo, R., Amigo, A., 2001. Refractive indices and surface tensions of binary mixtures of 1,4-dioxane + 1alkanols at 298.15 K. Journal of Chemical and Engineering Data 46, 692–695.
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Further reading International Critical Table, 2003, vol. IV. McGraw-Hill, New York, pp. 471–474. Penas, A., Calvo, E., Pintos, M., Amigo, A., Bravo, R., 2000. Refractive indices and surface tensions of binary mixtures of 1,4-dioxane plus n-alkanes at 298.15 K. Journal of Chemical and Engineering Data 45, 682–685. Ramakrishna, V., Suri, S.K., 1967. Surface tension of liquid mixtures. Indian Journal of Chemistry 5, 310.