Chen Yao^*, Kazuhiro Tamura, Toshiro Yamada
(Department of Chemistry and Chemical Engineering, Division of Physical Sciences, Kanazawa University, 40-20, Kodatsuno 2-chome, Kanazawa, Ishikawa 920-8667, Japan;    ^*Jointed with the Department of Chemistry, College of Life Science and Technology, Jinan University, Guangzhou, 510632, China )

Received Apr. 30, 2002.

Abstract Two solvation models, single and multi-solvation forms of an extended UNIQUAC associated-solution model, are presented to correlate binary vapor-liquid equilibria and mutual solubilities, furthermore, are employed to predict ternary liquid-liquid equilibria for mixtures including alcohol, acetonitrile and aniline. The models considering reasonably intermolecular association and solvation formed by hydrogen-bonding molecules are able to explain well the thermodynamic properties of multicomponent mixtures. Good calculated results demonstrate that the two solvation models are successful in the accurate representation of binary vapor-liquid and liquid-liquid equilibria as well as ternary liquid-liquid equilibria systems consisting of two associating molecules.
Keywords  Vapor-liquid equilibria, Liquid-liquid equilibria, Ternary mixtures, Associated-solution model

1.  INTRODUCTION           
Hydrogen-bonding molecules such as alcohol, acetonitrile and aniline can interact possibly to form chemical complexes through the association and solvation between like and unlike molecules. The chemical complex formation is not easily characterized, but various procedures and models have been applied to understand these properties. As a whole thermodynamic properties of these mixtures can provide the useful information of the molecular interactions, and the thermodynamic models related to the molecular properties are often used to interpret the bulk properties so far. The results can be often model dependent and sensitive to the assumptions of the model, but the description of liquid-liquid equilibria (LLE) for ternary mixtures of alcohol, acetonitrile and aniline is one of the most powerful probe for the thermodynamic models to account for the chemical complex formation between these hydrogen-bonding molecules.
    An extended form of the UNIQUAC associated-solution model^[1] taking into account the molecular association and solvation between the component molecules was proposed in a previous work to represent accurately the phase equilibria of multicomponent mixtures including one of alcohols, acetonitrile and aniline with non-associating components and the model shows an excellent performance in correlating binary vapor-liquid equilibria (VLE) and mutual solubilities as well as in predicting ternary LLE. Especially this extended model including the association and solvation of acetonitrile improved more successfully the representation of the ternary LLE for the mixtures of acetonitrile with a non-associating component than the UNIQUAC associated-solution model of Nagata.^[2]
    Accordingly, in order to represent ternary LLE for the mixtures formed by two associating molecules of alcohol, acetonitrile and aniline with one non-associating molecule, we assume two solvation models coupled with the extended UNIQUAC associated-solution model and aim at obtaining an understanding of the behavior for these mixtures as well as an accurate description of the ternary LLE. The experimental phase equilibrium data for the binary and ternary mixtures containing alcohol, acetonitrile and aniline examined are available from the literature.

2.  EXTENDED UNIQUAC ASSOCIATED-SOLUTION MODEL                           
The extended UNIQUAC associated-solution model ^[1] was proposed previously for phase equilibria of the multicomponent mixtures containing one alcohol and non-associating component.
    Associating components A and B self-associate to form linear polymers according to the following successive reactions:
            (1)
            (2)
and the association equilibrium constants characterized in terms of the corrected segment fractions of the chemical species existed in the mixtures, are defined by
             (3)
             (4)
K is the association equilibrium constant and independent of the degree of association, and is dependent on temperature and K° is the values of K at T = 323.15K. h is the enthalpy of hydrogen-bond formation and is assumed to be independent of the degree of association and of temperature.
    The associating molecules and can solvate each other. Two solvation models, named by single solvation and multi-solvation are considered in the following sections.

2.1 Single solvation model
The associating molecule species, A_i and B_j, indicated A = alcohol, B = acetonitrile or aniline, solvate each other to form species A_iB_j in the following manner:
(5)
where the suffixes i and j range from unity to infinity. The solvation constant for the above reaction is expressed by
         (6)
The activity coefficient of associating component i (i = A or B) is given by
        (7)
The activity coefficient of non-associating component C is given by
     (8)
where the modified volume parameter, is set to be , segment fraction, , the modified segment fraction, and the surface fraction, , are expressed as follows:
, ,        (9)
and the adjustable binary parameter, t_ji, is defined by
         (10)
The modified area parameter is fixed to be in the model. The modified segment fraction of the monomer of associating component, and are obtained by solving the mass balance equations for two associating components given by
(11)
(12)
The true molar volumes of pure component and ternary mixture, V_A ^0', V_B^0', V ', are individually expressed by
(13)
(14)
(15)
The modified segment fraction of monomer of the self-associating component at the pure-liquid state, and , can be expressed by
(16)
(17)
and for component C.
    When specially K_B=0, the single solvation model is also employed to calculate the binary mixtures containing one associating component and one non-associating component.

2.2 Multi-solvation model                
The pure i-mers and j-mers of two alcohols molecules, A and B, take place successive solvation step by step to form linearly polymer complex multimers (A_iB_j)_k, A_i(B_jA_k)_l, (B_iA_j)_k and B_i(A _jB_k)_l.
                           (18)
                   (19)
......
           (20)
(21)
where the indices i, j, k and l can be any integers from 1 to infinity. We assume that one solvation constant holds for all above solvation reactions. The modified segment fractions of monomer of associating components, and , are obtained from the following mass balance equations:
(22)
(23)
where the sums , , and are defined by
     (24)
     (25)
         (26)
         (27)
The true molar volume of ternary mixture, V ', is expressed by
          (28)

Table 1 Association constants and structural parameters for pure component

r and q were calculated by the method of Vera [7].
q^' was fixed in this work.

3. CALCULATION PROCEDURE
The association constants of aliphatic alcohols at 50^oC were taken from Brandani ^[3]: methanol, 173.9; ethanol, 110.4; 1-propanol, 87.0; 2-propanol, 49.1; 1-butanol, 69.5. A value of h_A= -23.2 kJ·mol^-1 taken from Stokes and Burfitt ^[4] was used as the enthalpy of hydrogen-bonding alcohol molecules and assumed independent of temperature. The association constant of acetonitrile ^[1] and aniline ^[5] is obtained from the previous papers. The enthalpy of hydrogen bond formation in pure aniline ^[5] was set as h_A= -15.4 kJ·mol^-1. The enthalpy of acetonitrile was taken from the reference ^{[1, 6]}. Pure component structural parameters, r and q were calculated by the method of Vera et al. ^[7], listed in Table 1.
    Binary experimental VLE and LLE data reduction were performed according to the following thermodynamic relations:
(29)
(30)
where P is the total pressure, x is the liquid phase mole fraction, y is the vapor phase mole fraction, is the activity coefficient of component i, P_i⁰ is the vapor pressure of pure component i, was calculated using the Antoine equation. V⁰ is the pure liquid molar volume, was obtained by a modified Rackett equation ^[8]. is the fugacity coefficient, was calculated by the eqn. (30), the pure and cross second virial coefficients B were estimated by the method of Hayden and O'Connell ^[9].
    A computation program based on the maximum likelihood principle described by Prausnitz et al ^[10] was used to obtain an optimum set of the model energy parameters by minimizing the objective function:
(31)
where the subscripts cal and exp individually indicate the most probable calculated value corresponding to each measured point and experimental value. The standard deviations in the measured variable were taken as: σ_P = 1 Torr,σ_T = 0.05 K, σ_x = 0.001 and σ_y = 0.003. σ_P for pressure, σ_T for temperature, σ_x for liquid-phase mole fraction, σ_y for vapor-phase mole fraction.
    The energy parameters for partially miscible mixtures at the indicating temperature were obtained by solving thermodynamic eqns. (32) and (33) simultaneously.
(32)
and (33)
where superscripts, I and II, indicate two liquid phases.

Table 2 Solvation equilibrium constants and enthalpies of complex formation used by the single solvation model

Table 3 Solvation equilibrium constants and enthalpies of complex formation used by the multi-solvation model

4. CALCULATED RESULTS
4.1 Binary vapor-liquid equilibria and liquid-liquid equilibria
The solvation equilibrium constant, listed in Tables 2 and 3, estimated by fitting the single and multi-solvation models to reduce well binary VLE and decrease with the increasing the number of carbon atoms in the alcohol. The enthalpies of complex formation were approximately estimated by taking the difference between the enthalpy of infinite dilution of ethanol in saturated hydrocarbons and that of ethanol in active solvents and were assumed to be independent of the number of carbon atoms in alcohol molecules. Table 4 presents the calculated results by using the single solvation model for the 14 binary VLE systems and for the 8 binary LLE systems formed by alcohol, acetonitrile, aniline, whose data are available from the literatures ^[11-28].

Table 4 Calculated results of binary phase equilibrium data reduction by using the single solvation model

System (1+2)	Temp. /K	Na	a12 /K	a21 /K	dP /kPa	dT /K	dx ×103	dy ×103	Ref.
Acetonitrile+ 1-butanol	333.15	8	-54.19	646.66	0.29	0.1	0.7	5.2	[11]
Acetonitrile+ ethanol	313.15	14	59.45	265.32	0.10	0.0	0.8	4.5	[12]
Acetonitrile+ cyclohexane	298.15	MSb	157.12	465.48					[13]
Acetonitrile+ n-heptane	298.15	MS	109.63	447.37					[14]
Acetonitrile+ n-hexane	298.15	MS	103.19	455.73					[14]
Acetonitrile+ methanol	298.15	10	-15.89	110.59	0.10	0.0	0.9	6.0	[14]
Acetonitrile+ 1-propanol	318.15	9	35.46	423.88	0.13	0.0	0.5	4.4	[15]
Acetonitrile+ 2-propanol	323.15	15	412.13	166.92	0.05	0.0	0.4	2.8	[16]
Aniline+ ethanol	313.15	13	71.82	24.72	0.04	0.0	0.1	1.4	[17]
Aniline+ cyclohexane	298.15	MS	371.57	104.54					[18]
Aniline+ n-heptane	298.15	MS	469.60	179.53					[19]
1-Butanol+ n-heptane	333.15	19	243.88	-37.61	0.10	0.0	0.5	4.6	[20]
Ethanol+ cyclohexane	293.15	7	184.98	25.91	0.09	0.0	0.2	2.8	[21]
Ethanol+ n-heptane	303.15	22	164.41	53.37	0.05	0.0	0.1		[22]
Methanol+ cyclohexane	298.15	MS	141.41	82.31					[23]
Methanol+ n-heptane	298.15	MS	148.50	89.21					[24]
Methanol+ n-hexane	298.15	MS	166.09	75.53					[24]
1-Propanol+ cyclohexane	298.15	27	326.47	-67.00	0.08	0.0	0.1		[25]
1-Propanol+ n-heptane	298.15	14	16.41	156.01	0.03	0.0	0.0		[26]
1-Propanol+ n-hexane	298.15	25	350.82	-30.01	0.08	0.0	0.1		[25]
2-Propanol+ |cyclohexane	323.15	9	225.25	-40.43	0.11	0.0	0.5	4.3	[27]
2-Propanol+ n-hexane	328.21	24	241.86	-23.54	0.20	0.1	2.9	4.1	[28]

a Number of data points; ^b Mutual solubilities.

    Table 5 presents the calculated results derived from the multi-solvation model for the 3 binary VLE systems formed by two alcohols molecules, whose data are available from the literatures ^[29-31]. The calculated results shown in Table 5 were compared with those of the UNIQUAC associated-solution model of Nagata.^[2] The present model works better than the Nagata model.　

Table 5  Calculated results of binary phase equilibrium data reduction by using the multi-solvation model

System (1+2)	Temp. /K	Na	a12 /K	a21 /K	d P   /kPa	d T /K	d x ×103	d y ×103	Ref.
Methanol+Ethanol	298.15	11	362.76	-173.06	0.03b 0.39c	0.0 0.0	0.0 1.7	4.8 10.9	[29]
Methanol+1-propanol	333.15	24	-97.01	256.68	0.05 b	0.0	0.3	1.4	[30]
Methanol+2-propanol	328.15	20	-122.33	261.68	0.18 b 0.49c	0.1 0.1	0.9 2.2	4.2 11.6	[31]

a Number of data points; ^b Extended UNIQUAC associated-solution model; ^c UNIQUAC associated-solution model.

4.2 Ternary liquid-liquid equilibria
The binary parameters, shown in Tables 4 and 5, obtained from the binary phase equilibrium data reproduction were used to predict ternary LLE for many representative ternary mixtures without any additional ternary parameters. We used the binary parameters that were obtained from the experimental binary data at the temperature as close as the ternary ones. The binary parameters obtained slightly depend on the temperature, but the model can predict well the ternary LLE using the temperature-independent binary parameters listed in Tables 4 and 5. The ternary predicted results and experimental values were plotted in Figures 1 and 2 for some ternary systems. Figure 1(a) for type II systems, where two binaries are partially miscible and the third binary is completely miscible; Figure 1 (b) to (d) and Figure 2 (a) to (c) for type I systems, where only one binary is partially miscible. Fig. 1 shows the ternary LLE systems of one alcohol and one acetonitrile or aniline mixtures predicted by the single solvation model having the only binary parameters taken from Table 4. Fig. 2 shows the ternary LLE systems of two alcohol mixtures predicted by the multi-solvation model using the binary parameters given in Table 5. The experimental tie-line data for the ternary systems investigated here are available from the literatures ^{[13,14,32-34]}. Furthermore Figure 1 and 2 shows comparison of the predicted results of the extended UNIQUAC associated-model with those of the UNIUAC model. Good agreement between the results calculated by the present model for the ternary LLE with the experimental ones was obtained, as demonstrated in Figures 1 and 2.

Fig.1 Liquid-liquid equilibria for the ternary systems consisting of one alcohol and one acetonitrile or aniline mixtures; Experimental tie-line: ● - ●; Predicted lines: ——, Extended UNIQUAC associated-solution model; - - - - - , UNIQUAC model.
(a). Acetonitrile + methanol + cyclohexane at 25^oC ^[14];(b). Acetonitrile + 2-propanol + cyclohexane at 25^oC ^[32];(c). Acetonitrile + 1-butanol + n-heptane at 25^oC ^[14]; (d). Aniline + ethanol + cyclohexane at 25^oC ^[33].

Fig.2 Liquid-liquid equilibria for the ternary systems consisting of two alcohol mixtures; Experimental tie-line: ● -  ●; Predicted lines: ——, Extended UNIQUAC associated-solution model; - - - - - , UNIQUAC model.
(a). Methanol + ethanol + cyclohexane at 25^oC ^[13]; (b). Methanol + 1-propanol + n-heptane at 25^oC ^[34];(c). Methanol + 2-propanol + cyclohexane at 25^oC ^[23].

5. CONCLUSION
The single and multi-solvation forms of the extended UNIQUAC associated-solution model are able to correlate well binary VLE and LLE and to predict ternary LLE for the mixtures containing two associating molecules of alcohol, acetonitrile and aniline. The models involving association and solvation constants fixed in this work are successful in the accurate description of thermodynamic properties of the multicomponent mixtures. The calculated results confirm fully good working abilities of the solvation models in correlating binary VLE and LLE and in predicting ternary LLE of two associating molecules by using binary parameters alone with association and solvation constants.

LIST  OF SYMBOLS

aij	binary interaction parameters
gE	excess Gibbs free energy
hA	molar enthalpy of hydrogen-bond formation
hAB	enthalpies of formation of chemical complexes AiBj
KA , KB	association equilibrium constants
KAB	solvation equilibrium constant of formation of chemical complexes AiBj
P	total pressure
Pi0	saturated vapor pressure of pure component i
	area parameter of pure component i
	modified area parameter of pure component i
	volume parameter of pure component i
	modified volume parameter of pure component i
R	universal gas constant
	sums as defined by eqns. (24) and (25)
	sums as defined by eqns. (26) and (27)

T	absolute temperature
	true molar volume of the ternary mixture
	true molar volume of pure component i
xi	liquid-phase mole fraction of component i
yi	vapor-phase mole fraction of component i
Z	lattice coordination number

Greek letters

gi	activity coefficient of component i
qi	surface fraction of component i
sP, sT, sx, sy,	standard deviations in pressure, temperature, liquid mole fraction and vapor mole fraction
τij	adjustable binary parameters
Fi	segment fraction of component i
F ' i	modified segment fraction of component i
F 'A1,F 'B1	monomer segment fractions of associating components
F '0C	monomer segment fraction of non-associating component
i	vapor phase fugacity coefficient of component i
i0	vapor phase fugacity coefficient of pure component i

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