- Email: [email protected]
A new correlation of solubilities of azoic compounds and anthraquinone derivatives in supercritical carbon dioxide
J. of Supercritical Fluids 32 (2004) 27–35
A new correlation of solubilities of azoic compounds and anthraquinone derivatives in supercritical carbon dioxide A. Ferri, M. Banchero∗ , L. Manna, S. Sicardi Dipartimento di Scienza dei Materiali e Ingegneria Chimica, Politecnico di Torino, C.so Duca degli Abruzzi, 24, Torino 10129, Italy Received in revised form 2 December 2003; accepted 30 December 2003
Abstract Solubilities of azoic compounds and anthraquinone derivatives in supercritical carbon dioxide were correlated with a new semiempirical equation and five equations taken from literature. All solutes are dyestuffs or compounds with a molecular structure similar to dyestuffs. The equations were applied to literature solubility data [J. Supercrit. Fluids 21 (2001) 1; J. Supercrit. Fluids 13 (1998) 37; Fluid Phase Equilib. 158–160 (1999) 707; J. Supercrit. Fluids 13 (1998) 43; Talanta 48 (1999) 951; Fluid Phase Equilib. 200 (2002) 31; Fluid Phase Equilib. 194–197 (2002) 895; J. Supercrit. Fluids, in press] and to a new data set of solvent brown 1, experimentally measured by us. Altogether, 16 compounds and over 400 solubility data were considered. In the development of the new correlation, which has three fitting parameters, a dimensionless group was defined: this group, which involves solute molar volume and fusion properties, is a function of solvent density over a significant range of pressures and temperatures. The proposed equation is able to correlate solubility data with good agreement. The mean average absolute percent deviation (AA%D) of the new equation was the lowest among the equations with the same number of fitting parameters. © 2003 Elsevier B.V. All rights reserved. Keywords: Solubility; Supercritical carbon dioxide; Dyestuff; Correlation
1. Introduction The knowledge of disperse dyestuffs’ solubility in supercritical carbon dioxide is of great interest for the new dyeing technique that proposes to substitute water with the supercritical fluid in textile processes [10,11]. For the design of this high-pressure process, phase behaviour and dye solubilities should be known as widely as possible. Among the different approaches to correlate solubilities of low-volatile substances in supercritical solvents, empirical and semiempirical equations are commonly used. These equations have a large success because they are easily applied (they are based on simple error minimization using least square functions [12]) and because, for most of them, there is no need to know solute physico-chemical properties. Another important remark is that theoretical based models, such as equation of state [7] or expanded liquid model [13], often do not give better results even though they require more complicated computational procedures. This is due to a lack of
accuracy on estimation of the many solute properties that theoretical models need (critical properties, acentric factor, sublimation pressure etc.). In this work a new semiempirical equation based on the thermodynamic equilibrium equation of the solute between the solid and the supercritical phases is presented. The new equation, which has three adjustable parameters, is applied to our solubility measures [8] and to literature data sets [1–7]. Moreover, five literature equations are applied to the same solubility data. The aims are the comparison between our equation and the literature ones and the analysis of the most frequently used empirical or semiempirical equations in order to find which of them fits better experimental solubilities of disperse dyestuffs or substances with a similar molecular structure. In the following paragraphs a review of the literature equations used in this work and the new correlation are presented.
2. Literature equations ∗
Corresponding author. Tel.: +39-011-5644703; fax: +39-011-5644648. E-mail address: [email protected] (M. Banchero). 0896-8446/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.supflu.2003.12.013
All empirical or semiempirical equations assume a solute (2) solubility dependence on solvent density, pressure
28
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35
Mendez and Teja [15] proposed the expression for solubility shown below:
Nomenclature a, b, c A, B, C B0 –B3 H M0 –M5 P s, t, k T v y
parameters of Bartle equation parameters of Mendez equation parameters of Del Valle equation enthalpy parameters of Jouyban equation pressure parameters of Chrastil equation temperature volume z, number of parameters
Greek letters α, D, β, m, n ρ φ
parameters of the new correlation density fugacity coefficient
Subscripts c obs pred ref 2
critical observed predicted reference state solute
Superscripts m sub S SFC t
melting sublimation solid phase supercritical fluid phase triple point
T ln(y2 P) = A + Bρ + CT
It was derived from the definition of the Henry’s constant for solute dissolved in a supercritical fluid [18] and it was tested on 48 substances with percent deviations from 0.11 to 35.95%. In their work Mendez-Santiago and Teja also proposed a simple test to check the consistency of experimental data. They tested the relationship: T ln E = A + Bρ
where Pref is a standard pressure of 1 bar, ρref is a reference density for which a value of 700 kg m−3 was used for calculation. Bartle applied Eq. (1) to correlate solubility measures of eight dyestuffs and obtained relative standard deviations between 3.3 and 8.2%.
(3)
where E, enhancement factor, is defined as the ratio between observed solubility and the solubility predicted by ideal gas law at the same temperature and pressure: E=
y2 P P2 sub
(4)
A and B appeared to be independent on temperature. In fact, plotting T ln E versus density, solubility data collapse to a straight line. Among equations which provide power dependence on density the most popular is the one proposed by Chrastil [8], which has the following expression: s ln y2 = k lnρ + + t (5) T s, t, k are adjustable parameters and are obtained by fitting experimental data. Chrastil equation assumes that a solvate complex between solvent (S) and solute (W) molecules is formed at equilibrium: W + kS ↔ WSk
and temperature. The majority of empirical equations show a dependence of ln y2 on 1/T because solubility is closely connected to solute sublimation pressure, which can be expressed by a Clausius–Clapeyron equation. Anyway, the most important property for correlation of experimental data is solvent density. Different kinds of dependence have been suggested: some authors propose the dependence of ln(y2 P) on density [14,15], some others assume a linear dependence of ln y2 on ln ρ [9,12,16]. Probably depending on the solute, on the working pressure and temperature one kind of dependence is more suitable than the other one. Bartle et al. [14] and Mendez and Teja [15] expect a dependence of ln(y2 P) on density. Bartle equation, which has also been applied to correlate solubility of dyestuffs in supercritical carbon dioxide [17], has the following expression: y2 P b ln = a + + c(ρ − ρref ) (1) Pref T
(2)
(6)
k is the association factor that represents the average number of solvent molecules in the complex while s depends on the sublimation and solvation enthalpies of the solute and t on the molecular weight of the solute and of the solvent. Del Valle and Aguilera [16] added one term to Chrastil equation, assuming an additional dependence of ln y2 on 1/T2 . The resulting equation is: ln y2 = B0 +
B1 B3 + B2 ln ρ + 2 T T
(7)
where B0 –B3 are model constants. Although ρ is a function of pressure and temperature, both equations do not include a term for explicit dependence of solubility on pressure. Recently Jouyban et al. [12] observed a non linear dependence of solubility on pressure for a great number of published data and proposed the following empirical equation: ln y2 = M0 + M1 P + M2 P 2 + M3 PT +
where M0 –M5 are proper parameters.
M4 T + M5 ln ρ P (8)
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35
3. A new semiempirical equation The new semiempirical equation results from the equilibrium equation of the solute between the solid and the supercritical fluid phase. Assuming that the solid molar volume is constant with pressure and the supercritical solvent does not dissolve in the solid phase, the resulting equation is the following: vS2 SFC S sub sub φ2 Py2 = φ2 P2 exp (P − P2 ) (9) RT where φ2SFC is dye fugacity in the supercritical phase, φ2S its fugacity in the solid phase, P2sub its sublimation pressure and vS2 is its solid molar volume. Estimation of dye sublimation pressure may be a difficult problem since no experimental values are available under 0.1 Pa [19]. In order to estimate dye sublimation pressure at a temperature T, the Clapeyron relation integrated from the triple point temperature (T2t ) and pressure (P2t ) can be used, assuming a negligible dependence of the sublimation enthalpy with respect to temperature: H2sub 1 P2sub 1 = − ln − (10) R T P2t T2t Triple point temperature can be replaced by normal melting temperature (T2m ); indeed, the difference between these two temperatures is less than 0.1 K for almost all heavy compounds [19]. As shown in Table 1, the analysis of literature data of heavy compounds highlights that the ratio between sublimation and fusion enthalpies is included in a not wide range between 1.2 and 3.8 [19]. Therefore sublimation enthalpy can be expressed by: H2sub = α H2fus
(11)
where α is the ratio between sublimation and fusion enthalpies. Table 1 Literature data of sublimation and fusion enthalpy of heavy compounds [19] Compound
Hsub (J mol−1 )
Hfus (J mol−1 )
Ratio
n-Octacosane n-Triacontane n-Dotriacontane Naphtalene 2,3-m-Naphtalene 2,6-m-Naphtalene 2,7-m-Naphtalene Fluorene Anthracene Phenanthrene Pyrene Hexamethylbenzene Triphenylmethane Biphenyl
245714 264500 283286 31046 35773 36746 84024 36746 36564 40520 40774 43468 35436 32052
64945 70169 75393 19060 25101 25055 23349 19580 28830 16460 17110 20920 18800 20640
3.78 3.77 3.76 1.63 1.43 1.47 3.60 1.88 1.27 2.46 2.38 2.08 1.88 1.55
29
Besides, dye sublimation pressure is so low that it is negligible with respect to working pressure (P − P2sub ≈ P) and that dye fugacity coefficient φ2S at solid–vapour equilibrium of dyestuff is about 1. Then, Eq. (9) can be rewritten in the following way: αH2fus vS2 P y2 P 1 1 1 = t exp − (12) − P2 R T2m T RT φ2SFC In order to avoid estimation of dye triple point pressure, Eq. (12) is multiplied by P2f /Pref , where Pref is the reference pressure of 1 bar. Therefore, a dimensionless group r can be defined: α H2fus P2t vS2 P y2 P 1 1 = exp r= − − Pref R T2m RT T Pref φ2SFC (13) The group involves solute fusion properties, which can be easily evaluated by a DSC analysis, and solute solid molar volume, which is generally obtained by a group-contribution method. Plotting r versus carbon dioxide density, for each dyestuff it is possible to find a α value for which the group r at different pressures and temperatures collapses into a single curve. For example, in Fig. 1 experimental trends of the group r for one of data sets examined in the present paper with two α values are reported: Fig. 1b shows that, when an α value 50% higher than that of Fig. 1a is used, the three isotherms are separated. The next step is to find a simple mathematical representation that fits the experimental trend of r versus carbon dioxide density. In this work two mathematical representations were used, depending on the experimental trend of r, a power or an exponential law: β ρ r=D (14) ρc or: r = men(ρ/ρc )
(15)
The fitting parameters, D and β or m and n, are obtained by minimising least square objective functions. Finally, depending on the experimental trend of r, the predicted solubility has the following expressions: β vS2 P α H2fus 1 Pref ρ 1 exp − m + y2 = D ρc P R T T2 RT (16) or
ρ Pref y2 = m exp n ρc P vS2 P α H2fus 1 1 − m + × exp T T2 R RT
(17)
30
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35 1.0E-01
353.2 K 373.2 K 1.0E-02
r
393.2 K
1.0E-03
1.0E-04 0
0.5
1
1.5
2
1.5
2
ρ / ρc
(a) 1.0E+00
353.2 K 373.2 K 1.0E-01
r
393.2 K
1.0E-02
1.0E-03 0
0.5
(b)
1 ρ / ρc
Fig. 1. (a) Experimental trend of the group r in logarithmic scale for solvent brown 1: (a) α = 2.87. (b) Experimental trend of the group r in logarithmic scale for solvent brown 1: (b) α = 4.31.
We can notice that in Eq. (16) dependence of solubility on solvent density is expressed by a power law (ln y2 on ln ρ) while in Eq. (17) by an exponential law (ln(y2 P) on density). Anyway, both expressions exhibit an explicit dependence of solubility on operative conditions (both pressure and temperature) that is not always present in literature equations. This procedure has the great advantage to include both literature approaches concerning solubility dependence on solvent density in a unique methodology. Compared with literature equations, the new equation shows a greater versatility because it can be adapted to the experimental dependence of solubility on solvent density.
solvent brown 1, listed in Table 2, are also used to test the literature and the newly proposed equations. In Table 3 chemical structure and molecular weight of solvent brown 1 are reported. The experimental technique adopted to obtain Table 2 Solubilities of solvent brown 1 (y2 , mole fraction) in supercritical carbon dioxide T (K)
P (MPa)
ρ (kg/m3 )
106 y2
353.2
20.4 22.0 24.0 28.3 30.4
610.0 650.0 680.0 736.5 758.7
2.83 4.57 6.92 11.8 13.7
373.2
18.1 20.1 22.1 24.4 26.0 28.0 30.0
431.3 487.6 540.0 583.4 609.7 640.0 668.4
1.29 2.45 4.52 7.28 9.80 13.8 16.8
393.2
22.1 24.0 26.0 28.0 30.0
448.0 490.1 530.0 560.0 585.0
3.86 5.70 8.89 15.8 20.8
4. Tested solubility data Among the large amount of substances of which solubilities in supercritical carbon dioxide were measured, dyestuffs or substances with a molecular structure similar to dyestuffs are selected. Altogether, 16 substances and over 400 experimental data are considered. The substances here examined include both literature solubility data [1–7] and our measures published elsewhere [8]. Solubilities of
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35 Table 3 Molecular structure and weight of solvent brown 1 Dye
Molecular structure
Solvent brown 1
Class
Azo
31
function: (yobs − ypred )2 Fobj = 2 yobs
Molecular weight
(18)
Average absolute percent deviations (AA%D) between experimental and calculated solubilities are listed in Table 5. AA%D for each compound was evaluated by the classical expression: 100 |yobs − ypred |i (AA%D)i = (19) Ni ypredi
262.31
i
solvent brown 1 data is the same as the one used by the authors in the previous work [8]. In Table 4 molecular weight, fusion properties and solid molar volume of all tested substances are reported. Fedors’ group-contribution method was used for the estimation of solid molar volume [20]. Melting temperature and fusion enthalpy of disperse blue 79, disperse orange 3, solvent brown 1 and quinizarin were obtained by a DSC analysis. The analysis was performed between 303 and 573 K with a temperature raise of 5 K/min in an inert N2 atmosphere in order to avoid oxidation of the sample. Fusion enthalpies and melting points, not experimentally measured in the present work, were estimated by Marrero-Gani group contribution method [21] or were taken from literature [1,2,22].
where Ni is the number of data for the compound i. The table also gives a mean value of the percent deviations of all substances. The first five substances in the table are azoic dyes; the others are anthraquinone derivatives. It can be noticed that substances 6, 13 and 14 have deviations larger than the others: this can be caused by polymorphism of the solid state. Concerning substance 6 (quinizarin), in fact, the DSC analysis shows two close peaks between 453 and 468 K associated with two different crystal systems. This phenomenon is quite common among anthraquinone derivatives and is highlighted also by Tuma et al. [23], who analysed 10 anthraquinone dyestuffs and observed polymorphism of the crystal system for seven of them. Comparing results of Eqs. (5) and (7) in the table it can be noticed that the addition of one parameter to Chrastil equation does not give any significant reduction in deviations. Bartle and Mendez–Teja equations show the greatest deviations between observed and predicted data. This seems to suggest that the power dependence between solubility and
5. Results The fitting parameters of Eqs. (1), (2), (5), (7) and (8) are evaluated by minimizing the sum of least square
Table 4 Molecular weight, solid molar volume and fusion properties of the compounds
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 a b c d e f
Compound
M
vs (cm3 /mol)
Hfus (J/mol)
Tm (K)
Disperse blue 79 Disperse orange 3 Solvent brown 1 Disperse yellow 119 Disperse red 153 Quinizarin Anthraquinone 1,4-bis-(n-Octylamino)-9,10-anthraquinone 1,4-bis-(n-Propylamino)-9,10-anthraquinone 1,4-bis-(n-Methylamino)-9,10-anthraquinone 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative Hydroquinone p-Quinone
639.4 242.2 262.3 327.3 404.3 240.2 208.2 462.7 322.4 266.3 240.2 280.3 320.3 320.3 110.1 108.1
477.0f 196.4f 199.6f 211.3f 286.6f 128.8f 83.4f 431.2f 270.2f 205.8f 155.8f 204.7f 234.0f 253.6f 87.8f 66.6f
21000a 15850a 19595a 26190c 31400c 24189a 32570b 55660c 29270c 13820c 35150c 29880c 24610c 30010c 27100b 11838c
413a 468a 427a 540e 440e 467a 560b 349d 406d 493d 459c 441c 421c 490c 445b 386b
DSC analysis. Ullmann’s Encyclopedia [22]. Marrero-Gani group contribution method [21]. [23]. [1]. Fedors group-contribution method [20].
A1 A2 A3 A4
32
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35
Table 5 Average absolute percent deviations of literature equations (AA%D) Compound
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
T (K)
Disperse blue 79 Disperse orange 3 Solvent brown 1 Disperse yellow 119 Disperse red 153 Quinizarin Anthraquinone 1,4-bis-(n-Octylamino)-9,10-anthraquinone 1,4-bis-(n-Propylamino)-9,10-anthraquinone 1,4-bis-(n-Methylamino)-9,10-anthraquinone 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative Hydroquinone p-Quinone
A1 A2 A3 A4
P (MPa)
353.2–393.2 353.2–393.2 353.2–393.2 353.2–393.2 353.2–393.2 353.2–393.2 308.2–333.2 296.0–324.7 305.0–340.0 299.0–340.0 308.2–348.2 308.2–338.2 308.2–348.2 308.2–338.2 333.0–363.0 333.0–363.0
N
16.0–30.0 16.0–30.0 16.0–30.0 15.0–30.0 15.0–30.0 16.0–30.0 15.2–25.3 7.7–32.5 7.9–19.0 6.8–18.8 12.0–36.0 12.0–40.0 12.0–40.0 12.0–40.0 10.0–35.0 10.0–35.0
19 22 17 12 8 15 9 40 69 22 35 31 29 28 33 33
Mean deviation
AA%D
Reference
Eq. (1) (z = 3)
Eq. (2) (z = 3)
Eq. (5) (z = 3)
Eq. (7) (z = 4)
Eq. (8) (z = 6)
10.9 12.3 7.4 18.1 19.0 47.7 5.4 4.8 11.6 16.4 14.5 9.0 31.6 35.2 7.9 10.4
17.5 15.4 10.3 24.3 19.0 53.0 4.4 4.5 15.4 17.3 12.5 7.2 32.1 33.6 9.7 10.6
12.8 5.1 6.8 9.3 15.4 26.3 1.6 9.2 5.5 8.5 10.9 7.3 28.5 34.4 9.9 14.7
12.9 4.5 6.6 7.4 7.7 26.7 1.1 8.7 6.0 13.1 10.7 7.2 28.6 34.8 10.0 14.7
6.5 4.6 3.9 5.4 7.2 15.4 1.6 7.4 6.7 8.2 8.8 4.7 23.6 16.4 8.1 10.1
15.1
16.5
12.5
12.5
9.0
N: number of data points; z: number of parameters. 1.0E-05 333 K 348 K 363 K
r
1.0E-06
1.0E-07
1.0E-08 0
0.5
1
1.5
2
ρ / ρc
Fig. 2. Experimental trend of the group r for hydroquinone in logarithmic scale.
1.0E+00
305 K 1.0E-01
310 K 315 K
r
320 K 1.0E-02
330 K 340 K
1.0E-03
1.0E-04 0
0.5
1
1.5
2
ρ / ρc
Fig. 3. Experimental trend of the group r for 1,4-bis-(n-propylamino)-9,10-anthraquinone in logarithmic scale.
[8] [8] This work [1] [1] [8] [7] [2] [3] [4] [5] [5] [5] [5] [6] [6]
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35
33
Table 6 Parameters of Chrastil equation
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Compound
s (K)
t
k
Disperse blue 79 Disperse orange 3 Solvent brown 1 Disperse yellow 119 Disperse red 153 Quinizarin Anthraquinone 1,4-bis-(n-Octylamino)-9,10-anthraquinone 1,4-bis-(n-Propylamino)-9,10-anthraquinone 1,4-bis-(n-Methylamino)-9,10-anthraquinone 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative Hydroquinone p-Quinone
−12340.9 −7373.7 −6714.1 −8870.0 −8849.3 −5753.4 −5944.2 −9511.9 −6454.3 −5664.9 −5082.1 −5650.0 −7625.4 −6724.1 −2330.9 −2945.0
−41.32 −24.29 −33.40 −26.24 −34.44 −26.85 −9.99 −28.93 −31.5 −35.70 −14.26 −20.58 −2.49 −54.07 −13.17 −12.70
9.89 5.17 6.20 5.77 7.00 5.17 3.22 7.10 6.14 6.07 3.03 4.61 2.47 9.97 1.46 2.65
A1 A2 A3 A4
1.0E-02 296 K 303.2 K 310.1 K
r
324.7 K 1.0E-04
1.0E-06 0
0.5
1
1.5
2
2.5
ρ / ρc
Fig. 4. Experimental trend of the group r for 1,4-bis-(n-octylamino)-9,10-anthraquinone in logarithmic scale. Table 7 α values, regression equations and deviations of the new semiempirical equation α
Compound 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Disperse blue 79 Disperse orange 3 Solvent brown 1 Disperse Yellow 119 Disperse Red 153 Quinizarin Anthraquinone 1,4-bis-(n-Octylamino)-9,10-anthraquinone 1,4-bis-(n-Propylamino)-9,10-anthraquinone 1,4-bis-(n-Methylamino)-9,10-anthraquinone 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative Hydroquinone p-Quinone Mean deviation
A1 A2 A3 A4
3.80 4.05 2.87 3.35 2.26 2.66 1.94 1.26 1.79 2.40 1.17 1.47 2.23 1.10 1.21 3.16
Regression equation r r r r r r r r r r r r r r r r
× 10−4
= = = = = = = = 5.925 × 10−5 × ρr6.110 = 2.112 × 10−3 × ρr5.697 = 2.109 × 10−3 × ρr5.594 = 7.405 × 10−2 × ρr2.649 = 3.556 × 10−2 × ρr3.126 = 1.239 × 10−1 × ρr1.007 = 3.736 × 10−1 × e1.044ρr = 2.856 × 10−3 × e1.834ρr = 1.110 × 10−1 × e3.031ρr 1.452 × ρr6.641 1.649 × 10−2 × ρr4.927 9.712 × 10−4 × ρr5.572 4.978 × 10−2 × ρr3.640 1.505 × 10−2 × ρr6.705 2.014 × 10−1 × ρr5.148 13.85 × e2.685ρr
AA%D 9.4 4.0 5.7 11.0 7.3 29.0 2.1 8.2 7.6 8.2 9.6 14.1 24.0 31.6 5.1 9.2 12.0
34
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35
Table 8 Comparison between Chrastil and the new equations for compounds with experimentally measured fusion properties Compound
AA%D Chrastil equation
New equation
Disperse blue 79 Disperse orange 3 Solvent brown 1 Quinizarin Anthraquinone Hydroquinone
12.8 5.1 6.8 26.3 1.6 9.9
9.4 4.0 5.7 29.0 2.1 5.1
Mean deviation
10.6
8.8
density, proposed by Chrastil, is more correct than exponential dependence, proposed by Bartle and Mendez–Teja. Jouyban equation, which involves six adjustable parameters, gives the smallest deviation but this equation is recommended only when the number of data points is high enough. In Table 6, the values of parameters of Chrastil equation are reported. One can see that the k values are in most cases larger for dyestuffs with more complex chemical structure. This is in line with the physical meaning of k. The new semiempirical correlation proposed in this work was applied to the same data to which literature equations were applied. Figs. 2 and 3 show the trends of the group r versus solvent density in logarithmic scale for hydroquinone and 1,4-bis-(n-propylamino)-9,10-anthraquinone: these two figures are examples of the possible trends of r. In Fig. 4 the group r for 1,4-bis-(n-octylamino)-9,10anthraquinone is reported. It can be noticed that r exhibits a maximum at high reduced densities. Anyway the isotherm at which this phenomenon appears is lower than the critical temperature of carbon dioxide. The new equation was applied for a supercritical system where the trend of group r versus solvent reduced density is monotone. For this reason this isotherm was excluded from the regression. In Table 7 the regression functions of r(ρ), α values and the deviations between observed and predicted solubilities are reported: it can be noticed that α values are generally included in the same range of those of the heavy compounds listed in Table 1. Compared with the other empirical equations with three fitting parameters, the new one gives in the most cases better results with respect to those of Mendez and Bartle and for 10 substances on 16 also with respect to Chrastil equation, that showed to be the best three fitting parameters literature equation. Indeed, mean deviation of the new equation (12.0%) is about equal to Chrastil one (12.5%). However, if the comparison is limited to substances whose fusion properties are experimentally measured (substances 1, 2, 3, 6, 7, 15 in Tables 5 and 7) the reduction in mean deviation between Chrastil and the new correlation becomes more evident. As shown in Table 8, in these cases mean deviation of the new correlation becomes 8.8% while Chrastil mean deviation is 10.6%.
6. Conclusions Solubilities of 16 compounds were correlated with five literature equations and with a newly proposed semiempirical equation. Among literature correlation, Chrastil equation gave the best results in relation to the number of fitting parameters involved. The new correlation was successfully applied and the agreement with experimental data was found to improve if fusion properties of the solute are experimentally measured. Moreover the use of the new correlation is recommended when data with high experimental accuracy are available. Its application requires a greater effort because the knowledge of some dye physical properties is necessary but, if these properties are experimentally measured, the results justify this choice.
References [1] H. Lin, C. Liu, C. Cheng, Y. Chen, M. Lee, Solubilities of disperse dyes of blue79, red 153, and yellow 119 in supercritical carbon dioxide, J. Supercrit. Fluids 21 (2001) 1. [2] D. Tuma, G.M. Schneider, High pressure solubility of disperse dyes in near- and supercritical fluids: measurements up to 100 MPa by a static method, J. Supercrit. Fluids 13 (1998) 37. [3] B. Wagner, C.B. Kautz, G.M. Schneider, Investigations on the solubility of anthraquinone dyes in supercritical carbon dioxide by a flow method, Fluid Phase Equilib. 158–160 (1999) 707. [4] C.B. Kautz, B. Wagner, G.M. Schneider, High pressure solubility of 1,4-bis-(n-alkylamino)-9,10-anthraquinone derivatives in supercritical carbon dioxide, J. Supercrit. Fluids 13 (1998) 43. [5] M-R. Fat’hi, Y. Yamiri, H. Sharghi, M. Shamsipur, Solubilities of some recently synthesized 1,8-dihydroxy-9,10-anthraquinone derivatives in supercritical carbon dioxide, Talanta 48 (1999) 951. [6] J. Garcia-Gonzales, M.J. Molina, F. Rodriguez, F. Mirada, Solubilities of hydroquinone and p-quinone in supercritical carbon dioxide, Fluid Phase Equilib. 200 (2002) 31. [7] K. Mishima, K. Matsuyama, H. Ishikawa, K. Hayashi, S. Maeda, Measurement and correlation of solubilities of azo dyes and anthraquinone in supercritical carbon dioxide, Fluid Phase Equilib. 194-197 (2002) 895. [8] A. Ferri, M. Banchero, L. Manna, S. Sicardi, An experimental technique for measuring high solubilities of dyes in supercritical carbon dioxide, J. Supercrit. Fluids, in press. [9] J. Chrastil, Solubility of solids and liquids in supercritical gases, J. Phys. Chem. 86 (1982) 3016. [10] D. Knittel, W. Saus, E. Schollmeyer, Application of supercritical carbon dioxide in finishing processes, J. Textile Inst. 84 (1993) 534. [11] D. Knittel, W. Saus, E. Schollmeyer, Prevention of water pollution in dyeing processes of synthetic textiles, Eur. Water Pollut. Control 6 (1996) 6. [12] A. Jouyban, H. Chan, N.R. Foster, Mathematical representation of solute solubility in supercritical carbon dioxide using empirical expressions, J. Supercrit. Fluids 24 (2002) 19. [13] J.W. Lee, M.W. Park, H.K. Bae, Measurement and correlation of dye solubility in supercritical carbon dioxide, Fluid Phase Equilib. 173 (2000) 277. [14] K. Bartle, A.A. Clifford, S. Jafar, Solubility of solids and liquids of low volatility in supercritical carbon dioxide, J. Phys. Chem. Ref. Data 20 (1991) 713. [15] J. Mendez-Santiago, A.S. Teja, The solubility of solids in supercritical fluids, Fluid Phase Equilib. 158–160 (1999) 501.
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35 [16] J.M. del Valle, J.M. Aguilera, An improved equation for predicting the solubility of vegetable oils in supercritical CO2 , Ind. Eng. Chem. Res. 27 (1988) 1551. [17] A. Oczan, A.A. Clifford, K. Bartle, Solubility of disperse dyes in supercritical carbon dioxide, J. Chem. Eng. Data 42 (1997) 590. [18] A.H. Harvey, Applications of near-critical dilute-solution thermodynamics, Ind. Eng. Chem. Res. 37 (1998) 3080. [19] E. Neau, S. Garnier, L. Avaullée, A consistent estimation of sublimation pressure using a cubic equation of state and fusion properties, Fluid Phase Equilib. 164 (1999) 173.
35
[20] Fedors, A method for estimating both the solubility parameters and molar volumes of liquids, Polym. Eng. Sci. 14 (1974) 147. [21] J. Marrero, R. Gani, Group-contribution based estimation of pure component properties, Fluid Phase Equilib. 183–184 (2001) 183. [22] Ullmann’s Encyclopedia, sixth ed. [23] D. Tuma, B. Wagner, G. Schneider, Comparative solubility investigations of anthraquinone disperse dyes in near- and supercritical carbon dioxide, Fluid Phase Equilib. 182 (2001) 133.
A new correlation of solubilities of azoic compounds and anthraquinone derivatives in supercritical carbon dioxide A. Ferri, M. Banchero∗ , L. Manna, S. Sicardi Dipartimento di Scienza dei Materiali e Ingegneria Chimica, Politecnico di Torino, C.so Duca degli Abruzzi, 24, Torino 10129, Italy Received in revised form 2 December 2003; accepted 30 December 2003
Abstract Solubilities of azoic compounds and anthraquinone derivatives in supercritical carbon dioxide were correlated with a new semiempirical equation and five equations taken from literature. All solutes are dyestuffs or compounds with a molecular structure similar to dyestuffs. The equations were applied to literature solubility data [J. Supercrit. Fluids 21 (2001) 1; J. Supercrit. Fluids 13 (1998) 37; Fluid Phase Equilib. 158–160 (1999) 707; J. Supercrit. Fluids 13 (1998) 43; Talanta 48 (1999) 951; Fluid Phase Equilib. 200 (2002) 31; Fluid Phase Equilib. 194–197 (2002) 895; J. Supercrit. Fluids, in press] and to a new data set of solvent brown 1, experimentally measured by us. Altogether, 16 compounds and over 400 solubility data were considered. In the development of the new correlation, which has three fitting parameters, a dimensionless group was defined: this group, which involves solute molar volume and fusion properties, is a function of solvent density over a significant range of pressures and temperatures. The proposed equation is able to correlate solubility data with good agreement. The mean average absolute percent deviation (AA%D) of the new equation was the lowest among the equations with the same number of fitting parameters. © 2003 Elsevier B.V. All rights reserved. Keywords: Solubility; Supercritical carbon dioxide; Dyestuff; Correlation
1. Introduction The knowledge of disperse dyestuffs’ solubility in supercritical carbon dioxide is of great interest for the new dyeing technique that proposes to substitute water with the supercritical fluid in textile processes [10,11]. For the design of this high-pressure process, phase behaviour and dye solubilities should be known as widely as possible. Among the different approaches to correlate solubilities of low-volatile substances in supercritical solvents, empirical and semiempirical equations are commonly used. These equations have a large success because they are easily applied (they are based on simple error minimization using least square functions [12]) and because, for most of them, there is no need to know solute physico-chemical properties. Another important remark is that theoretical based models, such as equation of state [7] or expanded liquid model [13], often do not give better results even though they require more complicated computational procedures. This is due to a lack of
accuracy on estimation of the many solute properties that theoretical models need (critical properties, acentric factor, sublimation pressure etc.). In this work a new semiempirical equation based on the thermodynamic equilibrium equation of the solute between the solid and the supercritical phases is presented. The new equation, which has three adjustable parameters, is applied to our solubility measures [8] and to literature data sets [1–7]. Moreover, five literature equations are applied to the same solubility data. The aims are the comparison between our equation and the literature ones and the analysis of the most frequently used empirical or semiempirical equations in order to find which of them fits better experimental solubilities of disperse dyestuffs or substances with a similar molecular structure. In the following paragraphs a review of the literature equations used in this work and the new correlation are presented.
2. Literature equations ∗
Corresponding author. Tel.: +39-011-5644703; fax: +39-011-5644648. E-mail address: [email protected] (M. Banchero). 0896-8446/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.supflu.2003.12.013
All empirical or semiempirical equations assume a solute (2) solubility dependence on solvent density, pressure
28
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35
Mendez and Teja [15] proposed the expression for solubility shown below:
Nomenclature a, b, c A, B, C B0 –B3 H M0 –M5 P s, t, k T v y
parameters of Bartle equation parameters of Mendez equation parameters of Del Valle equation enthalpy parameters of Jouyban equation pressure parameters of Chrastil equation temperature volume z, number of parameters
Greek letters α, D, β, m, n ρ φ
parameters of the new correlation density fugacity coefficient
Subscripts c obs pred ref 2
critical observed predicted reference state solute
Superscripts m sub S SFC t
melting sublimation solid phase supercritical fluid phase triple point
T ln(y2 P) = A + Bρ + CT
It was derived from the definition of the Henry’s constant for solute dissolved in a supercritical fluid [18] and it was tested on 48 substances with percent deviations from 0.11 to 35.95%. In their work Mendez-Santiago and Teja also proposed a simple test to check the consistency of experimental data. They tested the relationship: T ln E = A + Bρ
where Pref is a standard pressure of 1 bar, ρref is a reference density for which a value of 700 kg m−3 was used for calculation. Bartle applied Eq. (1) to correlate solubility measures of eight dyestuffs and obtained relative standard deviations between 3.3 and 8.2%.
(3)
where E, enhancement factor, is defined as the ratio between observed solubility and the solubility predicted by ideal gas law at the same temperature and pressure: E=
y2 P P2 sub
(4)
A and B appeared to be independent on temperature. In fact, plotting T ln E versus density, solubility data collapse to a straight line. Among equations which provide power dependence on density the most popular is the one proposed by Chrastil [8], which has the following expression: s ln y2 = k lnρ + + t (5) T s, t, k are adjustable parameters and are obtained by fitting experimental data. Chrastil equation assumes that a solvate complex between solvent (S) and solute (W) molecules is formed at equilibrium: W + kS ↔ WSk
and temperature. The majority of empirical equations show a dependence of ln y2 on 1/T because solubility is closely connected to solute sublimation pressure, which can be expressed by a Clausius–Clapeyron equation. Anyway, the most important property for correlation of experimental data is solvent density. Different kinds of dependence have been suggested: some authors propose the dependence of ln(y2 P) on density [14,15], some others assume a linear dependence of ln y2 on ln ρ [9,12,16]. Probably depending on the solute, on the working pressure and temperature one kind of dependence is more suitable than the other one. Bartle et al. [14] and Mendez and Teja [15] expect a dependence of ln(y2 P) on density. Bartle equation, which has also been applied to correlate solubility of dyestuffs in supercritical carbon dioxide [17], has the following expression: y2 P b ln = a + + c(ρ − ρref ) (1) Pref T
(2)
(6)
k is the association factor that represents the average number of solvent molecules in the complex while s depends on the sublimation and solvation enthalpies of the solute and t on the molecular weight of the solute and of the solvent. Del Valle and Aguilera [16] added one term to Chrastil equation, assuming an additional dependence of ln y2 on 1/T2 . The resulting equation is: ln y2 = B0 +
B1 B3 + B2 ln ρ + 2 T T
(7)
where B0 –B3 are model constants. Although ρ is a function of pressure and temperature, both equations do not include a term for explicit dependence of solubility on pressure. Recently Jouyban et al. [12] observed a non linear dependence of solubility on pressure for a great number of published data and proposed the following empirical equation: ln y2 = M0 + M1 P + M2 P 2 + M3 PT +
where M0 –M5 are proper parameters.
M4 T + M5 ln ρ P (8)
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35
3. A new semiempirical equation The new semiempirical equation results from the equilibrium equation of the solute between the solid and the supercritical fluid phase. Assuming that the solid molar volume is constant with pressure and the supercritical solvent does not dissolve in the solid phase, the resulting equation is the following: vS2 SFC S sub sub φ2 Py2 = φ2 P2 exp (P − P2 ) (9) RT where φ2SFC is dye fugacity in the supercritical phase, φ2S its fugacity in the solid phase, P2sub its sublimation pressure and vS2 is its solid molar volume. Estimation of dye sublimation pressure may be a difficult problem since no experimental values are available under 0.1 Pa [19]. In order to estimate dye sublimation pressure at a temperature T, the Clapeyron relation integrated from the triple point temperature (T2t ) and pressure (P2t ) can be used, assuming a negligible dependence of the sublimation enthalpy with respect to temperature: H2sub 1 P2sub 1 = − ln − (10) R T P2t T2t Triple point temperature can be replaced by normal melting temperature (T2m ); indeed, the difference between these two temperatures is less than 0.1 K for almost all heavy compounds [19]. As shown in Table 1, the analysis of literature data of heavy compounds highlights that the ratio between sublimation and fusion enthalpies is included in a not wide range between 1.2 and 3.8 [19]. Therefore sublimation enthalpy can be expressed by: H2sub = α H2fus
(11)
where α is the ratio between sublimation and fusion enthalpies. Table 1 Literature data of sublimation and fusion enthalpy of heavy compounds [19] Compound
Hsub (J mol−1 )
Hfus (J mol−1 )
Ratio
n-Octacosane n-Triacontane n-Dotriacontane Naphtalene 2,3-m-Naphtalene 2,6-m-Naphtalene 2,7-m-Naphtalene Fluorene Anthracene Phenanthrene Pyrene Hexamethylbenzene Triphenylmethane Biphenyl
245714 264500 283286 31046 35773 36746 84024 36746 36564 40520 40774 43468 35436 32052
64945 70169 75393 19060 25101 25055 23349 19580 28830 16460 17110 20920 18800 20640
3.78 3.77 3.76 1.63 1.43 1.47 3.60 1.88 1.27 2.46 2.38 2.08 1.88 1.55
29
Besides, dye sublimation pressure is so low that it is negligible with respect to working pressure (P − P2sub ≈ P) and that dye fugacity coefficient φ2S at solid–vapour equilibrium of dyestuff is about 1. Then, Eq. (9) can be rewritten in the following way: αH2fus vS2 P y2 P 1 1 1 = t exp − (12) − P2 R T2m T RT φ2SFC In order to avoid estimation of dye triple point pressure, Eq. (12) is multiplied by P2f /Pref , where Pref is the reference pressure of 1 bar. Therefore, a dimensionless group r can be defined: α H2fus P2t vS2 P y2 P 1 1 = exp r= − − Pref R T2m RT T Pref φ2SFC (13) The group involves solute fusion properties, which can be easily evaluated by a DSC analysis, and solute solid molar volume, which is generally obtained by a group-contribution method. Plotting r versus carbon dioxide density, for each dyestuff it is possible to find a α value for which the group r at different pressures and temperatures collapses into a single curve. For example, in Fig. 1 experimental trends of the group r for one of data sets examined in the present paper with two α values are reported: Fig. 1b shows that, when an α value 50% higher than that of Fig. 1a is used, the three isotherms are separated. The next step is to find a simple mathematical representation that fits the experimental trend of r versus carbon dioxide density. In this work two mathematical representations were used, depending on the experimental trend of r, a power or an exponential law: β ρ r=D (14) ρc or: r = men(ρ/ρc )
(15)
The fitting parameters, D and β or m and n, are obtained by minimising least square objective functions. Finally, depending on the experimental trend of r, the predicted solubility has the following expressions: β vS2 P α H2fus 1 Pref ρ 1 exp − m + y2 = D ρc P R T T2 RT (16) or
ρ Pref y2 = m exp n ρc P vS2 P α H2fus 1 1 − m + × exp T T2 R RT
(17)
30
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35 1.0E-01
353.2 K 373.2 K 1.0E-02
r
393.2 K
1.0E-03
1.0E-04 0
0.5
1
1.5
2
1.5
2
ρ / ρc
(a) 1.0E+00
353.2 K 373.2 K 1.0E-01
r
393.2 K
1.0E-02
1.0E-03 0
0.5
(b)
1 ρ / ρc
Fig. 1. (a) Experimental trend of the group r in logarithmic scale for solvent brown 1: (a) α = 2.87. (b) Experimental trend of the group r in logarithmic scale for solvent brown 1: (b) α = 4.31.
We can notice that in Eq. (16) dependence of solubility on solvent density is expressed by a power law (ln y2 on ln ρ) while in Eq. (17) by an exponential law (ln(y2 P) on density). Anyway, both expressions exhibit an explicit dependence of solubility on operative conditions (both pressure and temperature) that is not always present in literature equations. This procedure has the great advantage to include both literature approaches concerning solubility dependence on solvent density in a unique methodology. Compared with literature equations, the new equation shows a greater versatility because it can be adapted to the experimental dependence of solubility on solvent density.
solvent brown 1, listed in Table 2, are also used to test the literature and the newly proposed equations. In Table 3 chemical structure and molecular weight of solvent brown 1 are reported. The experimental technique adopted to obtain Table 2 Solubilities of solvent brown 1 (y2 , mole fraction) in supercritical carbon dioxide T (K)
P (MPa)
ρ (kg/m3 )
106 y2
353.2
20.4 22.0 24.0 28.3 30.4
610.0 650.0 680.0 736.5 758.7
2.83 4.57 6.92 11.8 13.7
373.2
18.1 20.1 22.1 24.4 26.0 28.0 30.0
431.3 487.6 540.0 583.4 609.7 640.0 668.4
1.29 2.45 4.52 7.28 9.80 13.8 16.8
393.2
22.1 24.0 26.0 28.0 30.0
448.0 490.1 530.0 560.0 585.0
3.86 5.70 8.89 15.8 20.8
4. Tested solubility data Among the large amount of substances of which solubilities in supercritical carbon dioxide were measured, dyestuffs or substances with a molecular structure similar to dyestuffs are selected. Altogether, 16 substances and over 400 experimental data are considered. The substances here examined include both literature solubility data [1–7] and our measures published elsewhere [8]. Solubilities of
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35 Table 3 Molecular structure and weight of solvent brown 1 Dye
Molecular structure
Solvent brown 1
Class
Azo
31
function: (yobs − ypred )2 Fobj = 2 yobs
Molecular weight
(18)
Average absolute percent deviations (AA%D) between experimental and calculated solubilities are listed in Table 5. AA%D for each compound was evaluated by the classical expression: 100 |yobs − ypred |i (AA%D)i = (19) Ni ypredi
262.31
i
solvent brown 1 data is the same as the one used by the authors in the previous work [8]. In Table 4 molecular weight, fusion properties and solid molar volume of all tested substances are reported. Fedors’ group-contribution method was used for the estimation of solid molar volume [20]. Melting temperature and fusion enthalpy of disperse blue 79, disperse orange 3, solvent brown 1 and quinizarin were obtained by a DSC analysis. The analysis was performed between 303 and 573 K with a temperature raise of 5 K/min in an inert N2 atmosphere in order to avoid oxidation of the sample. Fusion enthalpies and melting points, not experimentally measured in the present work, were estimated by Marrero-Gani group contribution method [21] or were taken from literature [1,2,22].
where Ni is the number of data for the compound i. The table also gives a mean value of the percent deviations of all substances. The first five substances in the table are azoic dyes; the others are anthraquinone derivatives. It can be noticed that substances 6, 13 and 14 have deviations larger than the others: this can be caused by polymorphism of the solid state. Concerning substance 6 (quinizarin), in fact, the DSC analysis shows two close peaks between 453 and 468 K associated with two different crystal systems. This phenomenon is quite common among anthraquinone derivatives and is highlighted also by Tuma et al. [23], who analysed 10 anthraquinone dyestuffs and observed polymorphism of the crystal system for seven of them. Comparing results of Eqs. (5) and (7) in the table it can be noticed that the addition of one parameter to Chrastil equation does not give any significant reduction in deviations. Bartle and Mendez–Teja equations show the greatest deviations between observed and predicted data. This seems to suggest that the power dependence between solubility and
5. Results The fitting parameters of Eqs. (1), (2), (5), (7) and (8) are evaluated by minimizing the sum of least square
Table 4 Molecular weight, solid molar volume and fusion properties of the compounds
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 a b c d e f
Compound
M
vs (cm3 /mol)
Hfus (J/mol)
Tm (K)
Disperse blue 79 Disperse orange 3 Solvent brown 1 Disperse yellow 119 Disperse red 153 Quinizarin Anthraquinone 1,4-bis-(n-Octylamino)-9,10-anthraquinone 1,4-bis-(n-Propylamino)-9,10-anthraquinone 1,4-bis-(n-Methylamino)-9,10-anthraquinone 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative Hydroquinone p-Quinone
639.4 242.2 262.3 327.3 404.3 240.2 208.2 462.7 322.4 266.3 240.2 280.3 320.3 320.3 110.1 108.1
477.0f 196.4f 199.6f 211.3f 286.6f 128.8f 83.4f 431.2f 270.2f 205.8f 155.8f 204.7f 234.0f 253.6f 87.8f 66.6f
21000a 15850a 19595a 26190c 31400c 24189a 32570b 55660c 29270c 13820c 35150c 29880c 24610c 30010c 27100b 11838c
413a 468a 427a 540e 440e 467a 560b 349d 406d 493d 459c 441c 421c 490c 445b 386b
DSC analysis. Ullmann’s Encyclopedia [22]. Marrero-Gani group contribution method [21]. [23]. [1]. Fedors group-contribution method [20].
A1 A2 A3 A4
32
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35
Table 5 Average absolute percent deviations of literature equations (AA%D) Compound
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
T (K)
Disperse blue 79 Disperse orange 3 Solvent brown 1 Disperse yellow 119 Disperse red 153 Quinizarin Anthraquinone 1,4-bis-(n-Octylamino)-9,10-anthraquinone 1,4-bis-(n-Propylamino)-9,10-anthraquinone 1,4-bis-(n-Methylamino)-9,10-anthraquinone 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative Hydroquinone p-Quinone
A1 A2 A3 A4
P (MPa)
353.2–393.2 353.2–393.2 353.2–393.2 353.2–393.2 353.2–393.2 353.2–393.2 308.2–333.2 296.0–324.7 305.0–340.0 299.0–340.0 308.2–348.2 308.2–338.2 308.2–348.2 308.2–338.2 333.0–363.0 333.0–363.0
N
16.0–30.0 16.0–30.0 16.0–30.0 15.0–30.0 15.0–30.0 16.0–30.0 15.2–25.3 7.7–32.5 7.9–19.0 6.8–18.8 12.0–36.0 12.0–40.0 12.0–40.0 12.0–40.0 10.0–35.0 10.0–35.0
19 22 17 12 8 15 9 40 69 22 35 31 29 28 33 33
Mean deviation
AA%D
Reference
Eq. (1) (z = 3)
Eq. (2) (z = 3)
Eq. (5) (z = 3)
Eq. (7) (z = 4)
Eq. (8) (z = 6)
10.9 12.3 7.4 18.1 19.0 47.7 5.4 4.8 11.6 16.4 14.5 9.0 31.6 35.2 7.9 10.4
17.5 15.4 10.3 24.3 19.0 53.0 4.4 4.5 15.4 17.3 12.5 7.2 32.1 33.6 9.7 10.6
12.8 5.1 6.8 9.3 15.4 26.3 1.6 9.2 5.5 8.5 10.9 7.3 28.5 34.4 9.9 14.7
12.9 4.5 6.6 7.4 7.7 26.7 1.1 8.7 6.0 13.1 10.7 7.2 28.6 34.8 10.0 14.7
6.5 4.6 3.9 5.4 7.2 15.4 1.6 7.4 6.7 8.2 8.8 4.7 23.6 16.4 8.1 10.1
15.1
16.5
12.5
12.5
9.0
N: number of data points; z: number of parameters. 1.0E-05 333 K 348 K 363 K
r
1.0E-06
1.0E-07
1.0E-08 0
0.5
1
1.5
2
ρ / ρc
Fig. 2. Experimental trend of the group r for hydroquinone in logarithmic scale.
1.0E+00
305 K 1.0E-01
310 K 315 K
r
320 K 1.0E-02
330 K 340 K
1.0E-03
1.0E-04 0
0.5
1
1.5
2
ρ / ρc
Fig. 3. Experimental trend of the group r for 1,4-bis-(n-propylamino)-9,10-anthraquinone in logarithmic scale.
[8] [8] This work [1] [1] [8] [7] [2] [3] [4] [5] [5] [5] [5] [6] [6]
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35
33
Table 6 Parameters of Chrastil equation
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Compound
s (K)
t
k
Disperse blue 79 Disperse orange 3 Solvent brown 1 Disperse yellow 119 Disperse red 153 Quinizarin Anthraquinone 1,4-bis-(n-Octylamino)-9,10-anthraquinone 1,4-bis-(n-Propylamino)-9,10-anthraquinone 1,4-bis-(n-Methylamino)-9,10-anthraquinone 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative Hydroquinone p-Quinone
−12340.9 −7373.7 −6714.1 −8870.0 −8849.3 −5753.4 −5944.2 −9511.9 −6454.3 −5664.9 −5082.1 −5650.0 −7625.4 −6724.1 −2330.9 −2945.0
−41.32 −24.29 −33.40 −26.24 −34.44 −26.85 −9.99 −28.93 −31.5 −35.70 −14.26 −20.58 −2.49 −54.07 −13.17 −12.70
9.89 5.17 6.20 5.77 7.00 5.17 3.22 7.10 6.14 6.07 3.03 4.61 2.47 9.97 1.46 2.65
A1 A2 A3 A4
1.0E-02 296 K 303.2 K 310.1 K
r
324.7 K 1.0E-04
1.0E-06 0
0.5
1
1.5
2
2.5
ρ / ρc
Fig. 4. Experimental trend of the group r for 1,4-bis-(n-octylamino)-9,10-anthraquinone in logarithmic scale. Table 7 α values, regression equations and deviations of the new semiempirical equation α
Compound 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Disperse blue 79 Disperse orange 3 Solvent brown 1 Disperse Yellow 119 Disperse Red 153 Quinizarin Anthraquinone 1,4-bis-(n-Octylamino)-9,10-anthraquinone 1,4-bis-(n-Propylamino)-9,10-anthraquinone 1,4-bis-(n-Methylamino)-9,10-anthraquinone 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative 1,8-Dihydroxy-9,10-anthraquinone derivative Hydroquinone p-Quinone Mean deviation
A1 A2 A3 A4
3.80 4.05 2.87 3.35 2.26 2.66 1.94 1.26 1.79 2.40 1.17 1.47 2.23 1.10 1.21 3.16
Regression equation r r r r r r r r r r r r r r r r
× 10−4
= = = = = = = = 5.925 × 10−5 × ρr6.110 = 2.112 × 10−3 × ρr5.697 = 2.109 × 10−3 × ρr5.594 = 7.405 × 10−2 × ρr2.649 = 3.556 × 10−2 × ρr3.126 = 1.239 × 10−1 × ρr1.007 = 3.736 × 10−1 × e1.044ρr = 2.856 × 10−3 × e1.834ρr = 1.110 × 10−1 × e3.031ρr 1.452 × ρr6.641 1.649 × 10−2 × ρr4.927 9.712 × 10−4 × ρr5.572 4.978 × 10−2 × ρr3.640 1.505 × 10−2 × ρr6.705 2.014 × 10−1 × ρr5.148 13.85 × e2.685ρr
AA%D 9.4 4.0 5.7 11.0 7.3 29.0 2.1 8.2 7.6 8.2 9.6 14.1 24.0 31.6 5.1 9.2 12.0
34
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35
Table 8 Comparison between Chrastil and the new equations for compounds with experimentally measured fusion properties Compound
AA%D Chrastil equation
New equation
Disperse blue 79 Disperse orange 3 Solvent brown 1 Quinizarin Anthraquinone Hydroquinone
12.8 5.1 6.8 26.3 1.6 9.9
9.4 4.0 5.7 29.0 2.1 5.1
Mean deviation
10.6
8.8
density, proposed by Chrastil, is more correct than exponential dependence, proposed by Bartle and Mendez–Teja. Jouyban equation, which involves six adjustable parameters, gives the smallest deviation but this equation is recommended only when the number of data points is high enough. In Table 6, the values of parameters of Chrastil equation are reported. One can see that the k values are in most cases larger for dyestuffs with more complex chemical structure. This is in line with the physical meaning of k. The new semiempirical correlation proposed in this work was applied to the same data to which literature equations were applied. Figs. 2 and 3 show the trends of the group r versus solvent density in logarithmic scale for hydroquinone and 1,4-bis-(n-propylamino)-9,10-anthraquinone: these two figures are examples of the possible trends of r. In Fig. 4 the group r for 1,4-bis-(n-octylamino)-9,10anthraquinone is reported. It can be noticed that r exhibits a maximum at high reduced densities. Anyway the isotherm at which this phenomenon appears is lower than the critical temperature of carbon dioxide. The new equation was applied for a supercritical system where the trend of group r versus solvent reduced density is monotone. For this reason this isotherm was excluded from the regression. In Table 7 the regression functions of r(ρ), α values and the deviations between observed and predicted solubilities are reported: it can be noticed that α values are generally included in the same range of those of the heavy compounds listed in Table 1. Compared with the other empirical equations with three fitting parameters, the new one gives in the most cases better results with respect to those of Mendez and Bartle and for 10 substances on 16 also with respect to Chrastil equation, that showed to be the best three fitting parameters literature equation. Indeed, mean deviation of the new equation (12.0%) is about equal to Chrastil one (12.5%). However, if the comparison is limited to substances whose fusion properties are experimentally measured (substances 1, 2, 3, 6, 7, 15 in Tables 5 and 7) the reduction in mean deviation between Chrastil and the new correlation becomes more evident. As shown in Table 8, in these cases mean deviation of the new correlation becomes 8.8% while Chrastil mean deviation is 10.6%.
6. Conclusions Solubilities of 16 compounds were correlated with five literature equations and with a newly proposed semiempirical equation. Among literature correlation, Chrastil equation gave the best results in relation to the number of fitting parameters involved. The new correlation was successfully applied and the agreement with experimental data was found to improve if fusion properties of the solute are experimentally measured. Moreover the use of the new correlation is recommended when data with high experimental accuracy are available. Its application requires a greater effort because the knowledge of some dye physical properties is necessary but, if these properties are experimentally measured, the results justify this choice.
References [1] H. Lin, C. Liu, C. Cheng, Y. Chen, M. Lee, Solubilities of disperse dyes of blue79, red 153, and yellow 119 in supercritical carbon dioxide, J. Supercrit. Fluids 21 (2001) 1. [2] D. Tuma, G.M. Schneider, High pressure solubility of disperse dyes in near- and supercritical fluids: measurements up to 100 MPa by a static method, J. Supercrit. Fluids 13 (1998) 37. [3] B. Wagner, C.B. Kautz, G.M. Schneider, Investigations on the solubility of anthraquinone dyes in supercritical carbon dioxide by a flow method, Fluid Phase Equilib. 158–160 (1999) 707. [4] C.B. Kautz, B. Wagner, G.M. Schneider, High pressure solubility of 1,4-bis-(n-alkylamino)-9,10-anthraquinone derivatives in supercritical carbon dioxide, J. Supercrit. Fluids 13 (1998) 43. [5] M-R. Fat’hi, Y. Yamiri, H. Sharghi, M. Shamsipur, Solubilities of some recently synthesized 1,8-dihydroxy-9,10-anthraquinone derivatives in supercritical carbon dioxide, Talanta 48 (1999) 951. [6] J. Garcia-Gonzales, M.J. Molina, F. Rodriguez, F. Mirada, Solubilities of hydroquinone and p-quinone in supercritical carbon dioxide, Fluid Phase Equilib. 200 (2002) 31. [7] K. Mishima, K. Matsuyama, H. Ishikawa, K. Hayashi, S. Maeda, Measurement and correlation of solubilities of azo dyes and anthraquinone in supercritical carbon dioxide, Fluid Phase Equilib. 194-197 (2002) 895. [8] A. Ferri, M. Banchero, L. Manna, S. Sicardi, An experimental technique for measuring high solubilities of dyes in supercritical carbon dioxide, J. Supercrit. Fluids, in press. [9] J. Chrastil, Solubility of solids and liquids in supercritical gases, J. Phys. Chem. 86 (1982) 3016. [10] D. Knittel, W. Saus, E. Schollmeyer, Application of supercritical carbon dioxide in finishing processes, J. Textile Inst. 84 (1993) 534. [11] D. Knittel, W. Saus, E. Schollmeyer, Prevention of water pollution in dyeing processes of synthetic textiles, Eur. Water Pollut. Control 6 (1996) 6. [12] A. Jouyban, H. Chan, N.R. Foster, Mathematical representation of solute solubility in supercritical carbon dioxide using empirical expressions, J. Supercrit. Fluids 24 (2002) 19. [13] J.W. Lee, M.W. Park, H.K. Bae, Measurement and correlation of dye solubility in supercritical carbon dioxide, Fluid Phase Equilib. 173 (2000) 277. [14] K. Bartle, A.A. Clifford, S. Jafar, Solubility of solids and liquids of low volatility in supercritical carbon dioxide, J. Phys. Chem. Ref. Data 20 (1991) 713. [15] J. Mendez-Santiago, A.S. Teja, The solubility of solids in supercritical fluids, Fluid Phase Equilib. 158–160 (1999) 501.
A. Ferri et al. / J. of Supercritical Fluids 32 (2004) 27–35 [16] J.M. del Valle, J.M. Aguilera, An improved equation for predicting the solubility of vegetable oils in supercritical CO2 , Ind. Eng. Chem. Res. 27 (1988) 1551. [17] A. Oczan, A.A. Clifford, K. Bartle, Solubility of disperse dyes in supercritical carbon dioxide, J. Chem. Eng. Data 42 (1997) 590. [18] A.H. Harvey, Applications of near-critical dilute-solution thermodynamics, Ind. Eng. Chem. Res. 37 (1998) 3080. [19] E. Neau, S. Garnier, L. Avaullée, A consistent estimation of sublimation pressure using a cubic equation of state and fusion properties, Fluid Phase Equilib. 164 (1999) 173.
35
[20] Fedors, A method for estimating both the solubility parameters and molar volumes of liquids, Polym. Eng. Sci. 14 (1974) 147. [21] J. Marrero, R. Gani, Group-contribution based estimation of pure component properties, Fluid Phase Equilib. 183–184 (2001) 183. [22] Ullmann’s Encyclopedia, sixth ed. [23] D. Tuma, B. Wagner, G. Schneider, Comparative solubility investigations of anthraquinone disperse dyes in near- and supercritical carbon dioxide, Fluid Phase Equilib. 182 (2001) 133.