Supercritical fluids models

Figure 21.8 Supercritical fluid extraction. Comparison of the solvation strength of the COj with respect to the usual solvents (HUdehrand scale) as a function of the temperature and pressure. The polarity of carhon dioxide in the supercritical state is comparable with that of hexane (for 100 atm and 35 °C). SPE is a method for which automation becomes a justified investment when the sample throughput is large. Above, sample extractor by supercritical fluids (Model SFE-703 reproduced courtesy of Dionex).

Figure A2.5.28. The coexistence curve and the heat capacity of the binary mixture 3-methylpentane + nitroethane. The circles are the experimental points, and the lines are calculated from the two-tenn crossover model. Reproduced from [28], 2000 Supercritical Fluids—Fundamentals and Applications ed E Kiran, P G Debenedetti and C J Peters (Dordrecht Kluwer) Anisimov M A and Sengers J V Critical and crossover phenomena in fluids and fluid mixtures, p 16, figure 3, by kind pemiission from Kluwer Academic Publishers.

As it has appeared in recent years that many hmdamental aspects of elementary chemical reactions in solution can be understood on the basis of the dependence of reaction rate coefficients on solvent density [2, 3, 4 and 5], increasing attention is paid to reaction kinetics in the gas-to-liquid transition range and supercritical fluids under varying pressure. In this way, the essential differences between the regime of binary collisions in the low-pressure gas phase and tliat of a dense enviromnent with typical many-body interactions become apparent. An extremely useful approach in this respect is the investigation of rate coefficients, reaction yields and concentration-time profiles of some typical model reactions over as wide a pressure range as possible, which pemiits the continuous and well controlled variation of the physical properties of the solvent. Among these the most important are density, polarity and viscosity in a contimiiim description or collision frequency. 

Although modeling of supercritical phase behavior can sometimes be done using relatively simple thermodynamics, this is not the norm. Especially in the region of the critical point, extreme nonideahties occur and high compressibilities must be addressed. Several review papers and books discuss modeling of systems comprised of supercritical fluids and soHd orHquid solutes (rl,i4—r7,r9,i49,r50). 

Various equations of state have been developed to treat association ia supercritical fluids. Two of the most often used are the statistical association fluid theory (SAET) (60,61) and the lattice fluid hydrogen bonding model (LEHB) (62). These models iaclude parameters that describe the enthalpy and entropy of association. The most detailed description of association ia supercritical water has been obtained usiag molecular dynamics and Monte Carlo computer simulations (63), but this requires much larger amounts of computer time (64—66). 

A number of theoretical models have been proposed to describe the phase behavior of polymer—supercritical fluid systems, eg, the SAET and LEHB equations of state, and mean-field lattice gas models (67—69). Many examples of polymer—supercritical fluid systems are discussed ia the Hterature (1,3). 

Phase Equihbria Models Two approaches are available for modeling the fugacity of a solute,, in a supercritical fluid solution. The compressed gas approach is the most common where ... 

A variety of equations-of-state have been applied to supercritical fluids, ranging from simple cubic equations like the Peng-Robinson equation-of-state to the Statistical Associating Fluid Theoiy. All are able to model nonpolar systems fairly successfully, but most are increasingly chaUenged as the polarity of the components increases. The key is to calculate the solute-fluid molecular interaction parameter from the pure-component properties. Often the standard approach (i.e. corresponding states based on critical properties) is of limited accuracy due to the vastly different critical temperatures of the solutes (if known) and the solvents other properties of the solute... 

R. M. Smith and M. D. Buifoi d, Optimization of supercritical fluid extraaion of volatile constituents from a model plant matrix , 7. Chromatogr. 600 175-181 (1992). 

The coupling of supercritical fluid extraction (SEE) with gas chromatography (SEE-GC) provides an excellent example of the application of multidimensional chromatography principles to a sample preparation method. In SEE, the analytical matrix is packed into an extraction vessel and a supercritical fluid, usually carbon dioxide, is passed through it. The analyte matrix may be viewed as the stationary phase, while the supercritical fluid can be viewed as the mobile phase. In order to obtain an effective extraction, the solubility of the analyte in the supercritical fluid mobile phase must be considered, along with its affinity to the matrix stationary phase. The effluent from the extraction is then collected and transferred to a gas chromatograph. In his comprehensive text, Taylor provides an excellent description of the principles and applications of SEE (44), while Pawliszyn presents a description of the supercritical fluid as the mobile phase in his development of a kinetic model for the extraction process (45). 

J. Pawliszyn, Kinetic model for supercritical fluid extraction , J. Chromatogr. Sci. 31 31-37(1992). 

Garimella et investigated the effect on trifluralin recovery of different extraction methods. A supercritical fluid extraction (SEE) procedure for the isolation of the analytes from the matrices with a commercial SEE system (Dionex Model 703)... 

Figure 3.8 Ln(m/m0) vs. scaled time tt(= 7t2Dt/r2) for the hot-ball model, including the effect of particle shape. After Bartle et al. [286]. Reproduced from Journal of Supercritical Fluids, 3, K.D. Bartle et al., 143-149, Copyright (1990), with...

Esquivel MM, Bemardo-Gil MG and King MB. 1999. Mathematical models for supercritical extraction of olive husk oil. J Supercrit Fluids 16(1) 43—58. 

Subra P, Castellani S, Jestin P and Aoufi A. 1998. Extraction of (5-carotene with supercritical fluids experiments and modeling. J Supercrit Fluids 12 261-269. 

The several theoretical and/or simulation methods developed for modelling the solvation phenomena can be applied to the treatment of solvent effects on chemical reactivity. A variety of systems - ranging from small molecules to very large ones, such as biomolecules [236-238], biological membranes [239] and polymers [240] -and problems - mechanism of organic reactions [25, 79, 223, 241-247], chemical reactions in supercritical fluids [216, 248-250], ultrafast spectroscopy [251-255], electrochemical processes [256, 257], proton transfer [74, 75, 231], electron transfer [76, 77, 104, 258-261], charge transfer reactions and complexes [262-264], molecular and ionic spectra and excited states [24, 265-268], solvent-induced polarizability [221, 269], reaction dynamics [28, 78, 270-276], isomerization [110, 277-279], tautomeric equilibrium [280-282], conformational changes [283], dissociation reactions [199, 200, 227], stability [284] - have been treated by these techniques. Some of these... 

Figure 6. A simple model for the aggregation of supercritical fluid molecules around a polar solute molecule.

Kado, N. Y., J. M. Wing, P. A. Kuzmicky, J. E. Woodrow, H. Ning, J. N. Seiber, and D. P. H. Hsieh, Quantitative Integration of the Salmonella Microsuspension Assay with Supercritical Fluid Extraction of Model Airborne Vapor-Phase Mutagens, Mutat. Res., 271, 253-260 (1992). 

Shariati, A. and Peters, C. J., High-pressure phase behavior of systems with ionic liquids Measurements and modeling of the binary system fluoroform + l-ethyl-3-methylimidazolium hexafluorophosphate, /. Supercrit. Fluids, 25, 109, 2003. 

Current work with supercritical fluids can also illustrate the importance of cosolvents. Cosolvent effects in supercritical fluids can be considerable for systems where the cosolvent interacts strongly with the solute. A correlation suggests that both physical and chemical forces are important in the solvation process in polar cosolvent supercritical CO2 mixtures. The model coupled with the correlation represents a step toward predicting solubilities in cosolvent-modified supercritical fluids using nonthermody-namic data. This method of modeling cosolvent effects allows a more intuitive interpretation of the data than either a purely physical equation of state or ideal chemical theory can provide (Ting et al., 1993). 

Optimizing solvents and solvent mixtures can be done empirically or through modeling. An example of the latter involves a single Sanchez-Lacombe lattice fluid equation of state, used to model both phases for a polymer-supercritical fluid-cosolvent system. This method works well over a wide pressure range both volumetric and phase equilibrium properties for a cross-linked poly(dimethyl siloxane) phase in contact with CO2 modified by a number of cosolvents (West et al., 1998). 

A linear solvation energy relationship (LSER) has been developed to predict the water-supercritical CO2 partition coefficients for a published collection of data. The independent variables in the model are empirically determined descriptors of the solute and solvent molecules. The LSER approach provides an average absolute relative deviation of 22% in the prediction of the water-supercritical CO2 partition coefficients for the six solutes considered. Results suggest that other types of equilibrium processes in supercritical fluids may be modeled using a LSER approach (Lagalante and Bruno, 1998). 

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