Abstract
Proper measurement and correlation/prediction of solubility data of dye compounds (azobenzene and anthraquinone derivatives) in supercritical carbon dioxide (ScCO2) are essential in the development supercritical dyeing technology. Ample data are available for several dye compounds in the literature, but models that are satisfactorily correlating/predicting solubility data are rare. Therefore, in this study, a simple model is developed for the solubility (\(y_{2}\)) in terms of reduced temperature (\(T_{{\text{r}}}\)) and reduced density (\(\rho_{{\text{r}}}\)) to correlate industrially important dye compounds solubility in ScCO2. The proposed model is \( y_{2} = A + \left( {B + C\rho_{{\text{r}}} } \right)T_{{\text{r}}} + \left( {D + E\rho_{{\text{r}}} } \right)\rho_{{\text{r}}} T_{{\text{r}}}^{2} + F\rho_{{\text{r}}}^{2 } T_{{\text{r}}}^{3}\). The performance ability of the new model is compared with number of existing literature solubility models in terms of various statistical parameters of (AARD, R2, Adj. R2, SSE, and RMSE) as well as Akaike’s Information Criterion (AIC). Moreover, thermodynamic parameters such as sublimation pressure (\(P_{{{\text{sub}}}}\)), sublimation enthalpy (\(\Delta H_{{{\text{sub}}}}\)) and enthalpy of solvation (\(\Delta H_{{{\text{sol}}}}\)) were estimated for anthraquinone and azobenzene derivatives. It was found the proposed model is correlating better than existing models.
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Abbreviations
- A − F :
-
Constants of the proposed model
- a 0 − s 9 :
-
Correlation parameters of semiempirical models
- AARD:
-
The overall average absolute relative deviation
- Adj. R 2 :
-
Adjusted R2
- AIC:
-
Akaike’s Information Criterion
- \(b_{ij}\) :
-
The mixing rules of binary interaction parameters
- E :
-
Enhancement factor
- \(H_{{{\text{sol}}}}\) :
-
Solvation heat
- \(H_{{{\text{sub}}}}\) :
-
Vaporization heat
- \(H_{{{\text{tot}}}}\) :
-
Total reaction heat
- K :
-
Number of parameters
- \(k_{ij}\) :
-
The mixing rules of binary interaction parameters
- M w :
-
The molecular weight
- \(N\) :
-
The number of experimental data
- P :
-
The system pressure
- \(P_{i}^{{\text{s}}}\) :
-
Sublimation of the pure solid
- \(P_{{{\text{ref}}}}\) :
-
The reference pressure (0.1 MPa)
- PR:
-
Peng –Robinson
- \(P_{{{\text{sub}}}}\) :
-
Sublimation pressures
- \(P_{{\text{r}}}\) :
-
Reduced pressure
- \(P_{{\text{c}}}\) :
-
The critical pressure
- Q :
-
Objective function
- R :
-
Universal gas constant
- EOS:
-
Equation of state
- \(R^{2}\) :
-
Correlation coefficient
- \({\text{RMSE}}\) :
-
Root-mean-square deviation
- \({\text{SSE}}\) :
-
Sum of squares error
- S :
-
The solute solubility in kg/m3
- T :
-
Temperature
- \(T_{{\text{c}}}\) :
-
The critical temperature
- \(T_{{\text{r}}}\) :
-
Reduced temperature
- VDW2:
-
Two adjustable parameters of van der Waals mixing rule
- \(y_{2}\) :
-
Mole fraction
- \(\Delta\) :
-
Difference
- \(\phi_{i}^{{\text{s}}}\) :
-
Fugacity coefficient of the pure substance at saturation
- \(\phi_{i}^{{{\text{scCO}}_{2} }}\) :
-
Solute fugacity in supercritical carbon dioxide (scCO2)
- \(\omega\) :
-
Acentric factor
- \( \alpha ,\beta ,\gamma \) :
-
Vapor pressure expression constants
- \(\rho\) :
-
Density
- \(\rho_{{{\text{ref}}}}\) :
-
Reference density
- \(\rho_{{{\text{ScCO}}_{2} }}\) :
-
Density of ScCO2
- exp:
-
Experimental
- cal:
-
Calculated
- 2:
-
Solute
- 1:
-
ScCO2
- i , j :
-
Component
- sub:
-
Sublimation
- c:
-
Critical
- s:
-
Solute
- r:
-
Reduced
- w:
-
Weights graph
References
Adachi Y, Sugie H (1986) A new mixing rule-modified conventional mixing rule. Fluid Phase Equilib 28:103–118. https://doi.org/10.1016/0378-3812(86)85072-5
Akaike H (1981) Likelihood of a model and information criteria. J Econom 16:3–14. https://doi.org/10.1016/0304-4076(81)90071-3
Akaike H (1974) A New Look at the Statistical Model Identification. IEEE Trans Automat Contr 19:716–723. https://doi.org/10.1109/TAC.1974.1100705
Alwi RS, Garlapati C (2021) A new semi empirical model for the solubility of dyestuffs in supercritical carbon dioxide. Chem Pap. https://doi.org/10.1007/s11696-020-01482-x
Alwi RS, Garlapati C, Tamura K (2021) Solubility of anthraquinone derivatives in supercritical carbon dioxide: new correlations. Molecules 26:460. https://doi.org/10.3390/molecules26020460
Alwi RS, Tamura K (2015) Measurement and correlation of derivatized anthraquinone solubility in supercritical carbon dioxide. J Chem Eng Data 60:3046–3052. https://doi.org/10.1021/acs.jced.5b00480
Alwi RS, Tanaka T, Tamura K (2014) Measurement and correlation of solubility of anthraquinone dyestuffs in supercritical carbon dioxide. J Chem Thermodyn. https://doi.org/10.1016/j.jct.2014.01.015
Andonova V, Garlapati C (2016) A new empirical model to correlate the solubility of penicillin G and penicillin V in supercritical carbon dioxide. J Appl Sci Eng Methodol 2:220–223
Baek JK, Kim S, Lee GS, Shim JJ (2004) Density correlation of solubility of C. I. disperse orange 30 dye in supercritical carbon dioxide. Korean j Chem Eng 21:230–235. https://doi.org/10.1007/bf02705403
Bartle KD, Clifford AA, Jafar SA, Shilstone GF (1991) Solubilities of solids and liquids of low volatility in supercritical carbon dioxide. J Phys Chem Ref Data 20:713–756. https://doi.org/10.1063/1.555893
Bian X-Q, Zhang Q, Du Z-M, Chen J, Jaubert J-N (2016) A five-parameter empirical model for correlating the solubility of solid compounds in supercritical carbon dioxide. Fluid Phase Equilib 411:74–80. https://doi.org/10.1016/j.fluid.2015.12.017
Bradley RS, Bird CL, Jones F (1960) The vapour pressures and heats of sublimation of some disperse dyes. Trans Faraday Soc 56:23. https://doi.org/10.1039/tf9605600023
Brown M, Conn AD (1990) Enthalpies of combustion of γ-butyrolactone, γ-valerolactone, and δ-valerolactone. J Chem Thermodyn 22(9):885–891
Chinh VD, Bavasso I, Di Palma L, Felici AC, Scarsella M, Vilardi G, Bracciale MP, Van NT (2021) Enhancing the photocatalytic activity of TiO2 and TiO2–SiO2 by coupling with graphene–gold nanocomposites. J Mater Sci Mater Electron 32:5082–5093. https://doi.org/10.1007/s10854-021-05242-9
Chinh VD, Broggi A, Di Palma L, Scarsella M, Speranza G, Vilardi G, Thang PN (2018) XPS spectra analysis of Ti2+, Ti3+ ions and dye photodegradation evaluation of titania-silica mixed oxide nanoparticles. J Electron Mater 47:2215–2224. https://doi.org/10.1007/s11664-017-6036-1
Chinh VD, Hung LX, Di Palma L, Hanh VTH, Vilardi G (2019) Effect of carbon nanotubes and carbon nanotubes/gold nanoparticles composite on the photocatalytic activity of TiO2 and TiO2–SiO2. Chem Eng Technol 42:308–315. https://doi.org/10.1002/ceat.201800265
Chrastil J (1982) Solubility of solids and liquids in supercritical gases. J Phys Chem 86:3016–3021. https://doi.org/10.1021/j100212a041
Coelho JP, Stateva RP (2011) Solubility of red 153 and blue 1 in supercritical carbon dioxide. J Chem Eng Data 56:4686–4690. https://doi.org/10.1021/je200652j
Del Valle JM, Aguilera JM (1988) An improved equation for predicting the solubility of vegetable oils in supercritical carbon dioxide. Ind Eng Chem Res 27:1551–1553. https://doi.org/10.1021/ie00080a036
Dong P, Xu M, Lu X, Lin C (2010) Measurement and correlation of solubilities of C.I. Disperse Red 73, C.I. Disperse Yellow 119 and their mixture in supercritical carbon dioxide. Fluid Phase Equilib 297:46–51. https://doi.org/10.1016/j.fluid.2010.05.026
Draper S, Montero G, Smith B, Beck K (2000) Solubility relationships for disperse dyes in supercritical carbon dioxide. Dye Pigment 45:177–183. https://doi.org/10.1016/S0143-7208(00)00008-5
Fat’shi MR, Yamini Y, Sharghi H, Shamsipur M (1998) Solubilities of some 1,4-dihydroxy-9,10-anthraquinone derivatives in supercritical carbon dioxide. J Chem Eng Data 43:400–402. https://doi.org/10.1021/je970266u
Fedors RF (1974) A method for estimating both the solubility parameters and molar volumes of liquids. Polym Eng Sci 14:147–154. https://doi.org/10.1002/pen.760140211
Ferri, a., Banchero, M., Manna, L., Sicardi, S., (2004) A new correlation of solubilities of azoic compounds and anthraquinone derivatives in supercritical carbon dioxide. J Supercrit Fluids 32:27–35. https://doi.org/10.1016/j.supflu.2003.12.013
Garlapati C, Madras G (2010) New empirical expressions to correlate solubilities of solids in supercritical carbon dioxide. Thermochim Acta 500:123–127. https://doi.org/10.1016/j.tca.2009.12.004
Gordillo M, Blanco M, Molero A, Martinez de la Ossa E (1999) Solubility of the antibiotic Penicillin G in supercritical carbon dioxide. J Supercrit Fluids 15:183–190. https://doi.org/10.1016/S0896-8446(99)00008-X
Gordon PF, Gregory P (1987) Anthraquinone dyes. In: Organic chemistry in colour. Springer, Berlin, pp 163–199. https://doi.org/10.1007/978-3-642-82959-8_4
Haghbakhsh R, Hayer H, Saidi M, Keshtkari S, Esmaeilzadeh F (2013) Density estimation of pure carbon dioxide at supercritical region and estimation solubility of solid compounds in supercritical carbon dioxide: Correlation approach based on sensitivity analysis. Fluid Phase Equilib 342:31–41. https://doi.org/10.1016/j.fluid.2012.12.029
Hunger K (2007) Industrial dyes: chemistry, properties, applications. Wiley, New York
Jafari Nejad S, Abolghasemi H, Moosavian MA, Maragheh MG (2010) Prediction of solute solubility in supercritical carbon dioxide: a novel semi-empirical model. Chem Eng Res Des 88:893–898. https://doi.org/10.1016/j.cherd.2009.12.006
Keshmiri K, Vatanara A, Yamini Y (2014) Development and evaluation of a new semi-empirical model for correlation of drug solubility in supercritical CO2. Fluid Phase Equilib 363:18–26. https://doi.org/10.1016/j.fluid.2013.11.013
Kumar SK, Johnston KP (1988) Modelling the solubility of solids in supercritical fluids with density as the independent variable. J Supercrit Fluids 1:15–22. https://doi.org/10.1016/0896-8446(88)90005-8
Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the Nelder–Mead simplex method in low dimensions. Siam J Optim 9:112–147. https://doi.org/10.1137/S1052623496303470
Lee BI, Kesler MG (1975) A generalized thermodynamic correlation based on three-parameter corresponding states. AIChE J 21:510–527. https://doi.org/10.1002/aic.690210313
Lin H, Ho C-C, Lee M-J (2004) Solubilities of disperse dyes of blue 79:1, red 82 and modified yellow 119 in supercritical carbon dioxide and nitrous oxide. J Supercrit Fluids 32:105–114. https://doi.org/10.1016/j.supflu.2004.03.001
Lin H, Liu C, Cheng C, Chen Y, Lee M (2001) Solubilities of disperse dyes of blue 79, red 153, and yellow 119 in supercritical carbon dioxide. J Supercrit 21:1–9
Lucien FP, Foster NR (2000) Solubilities of solid mixtures in supercritical carbon dioxide: a review. J Supercrit Fluids 17:111–134. https://doi.org/10.1016/S0896-8446(99)00048-0
Méndez-Santiago J, Teja AS (1999) The solubility of solids in supercritical fluids. Fluid Phase Equilib 158–160:501–510. https://doi.org/10.1016/S0378-3812(99)00154-5
Mitra S, Wilson NK (1991) An empirical method to predict solubility in supercritical fluids. J Chromatogr Sci 29:305–309. https://doi.org/10.1093/chromsci/29.7.305
Motulsky H, Christopoulos A (2002) Comparing models and curves. In: Fitting models to biological data using linear and nonlinear regression. A practical guide to curve fitting. GraphPad Software, pp 3–49
Özcan AS, Clifford AA, Bartle KD, Lewis DM (1997) Solubility of disperse dyes in supercritical carbon dioxide. J Chem Eng Data 42:590–592. https://doi.org/10.1021/je960337+
Prausnitz JM, Lichtenthaler RN, de Azvedo EG (1999) Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd edn. Prentice-Hall, Upper Saddle River, NJ
Reddy TA, Garlapati C (2019) Dimensionless empirical model to correlate pharmaceutical compound solubility in supercritical carbon dioxide. Chem Eng Technol 42:2621–2630. https://doi.org/10.1002/ceat.201900283
Reddy TA, Srividya R, Garlapati C (2018) A new empirical model to correlate solubility of pharmaceutical compounds in supercritical carbon dioxide. J Appl Sci Eng Methodol 4:575–590
Reid RC, Prausnitz JM, Poling BE (1987) The properties of gases and liquids. McGraw Hill Book Co., New York
Roux MV, Temprado M, Chickos JS, Nagano Y (2008) Critically evaluated thermochemical properties of polycyclic aromatic hydrocarbons. J Phys Chem Ref Data 37:1855–1996. https://doi.org/10.1063/1.2955570
Shamsipur M, Karami AR, Yamini Y, Sharghi H (2004) Solubilities of some 1-hydroxy-9,10-anthraquinone derivatives in supercritical carbon dioxide. J Supercrit Fluids 32:47–53. https://doi.org/10.1016/j.supflu.2004.01.006
Shamsipur M, Karami AR, Yamini Y, Sharghi H (2003) Solubilities of some aminoanthraquinone derivatives in supercritical carbon dioxide. J Chem Eng Data 48:71–74. https://doi.org/10.1021/je020088r
Sodeifian G, Alwi RS, Razmimanesh F, Tamura K (2021a) Solubility of Quetiapine hemifumarate (antipsychotic drug) in supercritical carbon dioxide: Experimental, modeling and Hansen solubility parameter application. Fluid Phase Equilib. https://doi.org/10.1016/j.fluid.2021.113003
Sodeifian G, Garlapati C, Razmimanesh F, Sodeifian F (2021) Solubility of amlodipine besylate (calcium channel blocker drug) in supercritical carbon dioxide: measurement and correlations. J Chem Eng Data. https://doi.org/10.1021/acs.jced.0c00913
Sparks DL, Hernandez R, Estévez LA (2008) Evaluation of density-based models for the solubility of solids in supercritical carbon dioxide and formulation of a new model. Chem Eng Sci 63:4292–4301. https://doi.org/10.1016/j.ces.2008.05.031
Sung H-D, Shim J-J (1999) Solubility of C. I. disperse red 60 and C. I. disperse blue 60 in supercritical carbon dioxide. J Chem Eng Data 44:985–989. https://doi.org/10.1021/je990018t
Tamura K, Alwi RS (2015) Solubility of anthraquinone derivatives in supercritical carbon dioxide. Dye Pigment. https://doi.org/10.1016/j.dyepig.2014.09.003
Tamura K, Alwi RS, Tanaka T, Shimizu K (2017) Solubility of 1-aminoanthraquinone and 1-nitroanthraquinone in supercritical carbon dioxide. J Chem Thermodyn. https://doi.org/10.1016/j.jct.2016.09.032
Valderrama JO, Alvarez VH (2008) Correct way of reporting results when modelling supercritical phase equilibria using equations of state. Can J Chem Eng 83:578–581. https://doi.org/10.1002/cjce.5450830323
Yamini Y, Moradi M, Hojjati M, Nourmohammadian F, Saleh A (2010) Solubilities of some disperse yellow dyes in supercritical CO2. J Chem Eng Data 55:3896–3900. https://doi.org/10.1021/je901049r
Yu Z-R, Singh B, Rizvi SSH, Zollweg JA (1994) Solubilities of fatty acids, fatty acid esters, triglycerides, and fats and oils in supercritical carbon dioxide. J Supercrit Fluids 7:51–59. https://doi.org/10.1016/0896-8446(94)90006-X
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This work was supported by Directorate of Research and Community Services, Directorate General of Strengthening Research and Development, Ministry of Research Technology and Higher Education, Republic Indonesia.
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Alwi, R.S., Garlapati, C. A new model and estimation of thermodynamic parameters for the solubility of azobenzene and anthraquinone derivatives in supercritical carbon dioxide. Chem. Pap. 75, 4589–4610 (2021). https://doi.org/10.1007/s11696-021-01688-7
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DOI: https://doi.org/10.1007/s11696-021-01688-7