Supercritical diffusion coefficients

Transport Properties Although the densities of supercritical fluids approach those of conventional hquids, their transport properties are closer to those of gases, as shown for a typical SCF such as CO9 in Table 22-12. For example, the viscosity is several orders of magnitude lower than at liquidlike conditions. The self-diffusion coefficient ranges between 10" and 10" em /s, and binaiy-diffusiou coefficients are similar [Liong, Wells, and Foster, J. Supercritical Fluids 4, 91 (1991) Catchpole and King, Ind. Eng. Chem. Research, 33,... 

Supercritical fluid chromatography (SFC) refers to the use of mobile phases at temperatures and pressures above the critical point (supercritical) or just below (sub-critical). SFC shows several features that can be advantageous for its application to large-scale separations [132-135]. One of the most interesting properties of this technique is the low viscosity of the solvents used that, combined with high diffusion coefficients for solutes, leads to a higher efficiency and a shorter analysis time than in HPLC. 

A supercritical fluid exhibits physical-chemical properties intermediate between those of liquids and gases. Mass transfer is rapid with supercritical fluids. Their dynamic viscosities are nearer to those in normal gaseous states. In the vicinity of the critical point the diffusion coefficient is more than 10 times that of a liquid. Carbon dioxide can be compressed readily to form a liquid. Under typical borehole conditions, carbon dioxide is a supercritical fluid. 

Supercritical fluid extraction (SFE) is a technique in which a supercritical fluid [formed when the critical temperature Tf) and critical pressure Pf) for the fluid are exceeded simultaneously] is used as an extraction solvent instead of an organic solvent. By far the most common choice of a supercritical fluid is carbon dioxide (CO2) because CO2 has a low critical temperature (re = 31.1 °C), is inexpensive, and is safe." SFE has the advantage of lower viscosity and improved diffusion coefficients relative to traditional organic solvents. Also, if supercritical CO2 is used as the extraction solvent, the solvent (CO2) can easily be removed by bringing the extract to atmospheric pressure. Supercritical CO2 itself is a very nonpolar solvent that may not have broad applicability as an extraction solvent. To overcome this problem, modifiers such as methanol can be used to increase the polarity of the SFE extraction solvent. Another problem associated with SFE using CO2 is the co-extraction of lipids and other nonpolar interferents. To overcome this problem, a combination of SFE with SPE can be used. Stolker et al." provided a review of several SFE/SPE methods described in the literature. 

Table 3.12 Density, viscosity, and diffusion coefficient of gas, liquid and supercritical fluids...

Sassiat, P.R., Mourier, P., Caude, M.H. and Rosset, R.H. (1987) Measurement of diffusion coefficients in supercritical carbon dioxide and correlation with the equation of Wilke and Chang. Analytical Chemistry, 59 (8), 1164-1170. 

The first use of supercritical fluid extraction (SFE) as an extraction technique was reported by Zosel [379]. Since then there have been many reports on the use of SFE to extract PCBs, phenols, PAHs, and other organic compounds from particulate matter, soils and sediments [362, 363, 380-389]. The attraction of SFE as an extraction technique is directly related to the unique properties of the supercritical fluid [390]. Supercritical fluids, which have been used, have low viscosities, high diffusion coefficients, and low flammabilities, which are all clearly superior to the organic solvents normally used. Carbon dioxide (C02, [362,363]) is the most common supercritical fluid used for SFE, since it is inexpensive and has a low critical temperature (31.3 °C) and pressure (72.2 bar). Other less commonly used fluids include nitrous oxide (N20), ammonia, fluoro-form, methane, pentane, methanol, ethanol, sulfur hexafluoride (SF6), and dichlorofluoromethane [362, 363, 391]. Most of these fluids are clearly less attractive as solvents in terms of toxicity or as environmentally benign chemicals. Commercial SFE systems are available, but some workers have also made inexpensive modular systems [390]. 

Supercritical fluids possess favorable physical properties that result in good behavior for mass transfer of solutes in a column. Some important physical properties of liquids, gases, and supercritical fluids are compared in Table 4.1 [49]. It can be seen that solute diffusion coefficients are greater in a supercritical fluid than in a liquid phase. When compared to HPLC, higher analyte diffusivity leads to lower mass transfer resistance, which results in sharper peaks. Higher diffusivity also results in higher optimum linear velocities, since the optimum linear velocity for a packed column is proportional to the diffusion coefficient of the mobile phase for liquid-like fluids [50, 51]. 

The diffusion coefficients of small molecular weight solutes in supercritical fluids and liquids are typically in the range of 1 x 10 " and 10 cm /s [18,19], respectively, while those of EFLs are typically intermediate [4] between these two values (10 cm /s). 

Supercritical fluid chromatography provides increased speed and resolution, relative to liquid chromatography, because of increased diffusion coefficients of solutes in supercritical fluids. (However, speed and resolution are slower than those of gas chromatography.) Unlike gases, supercritical fluids can dissolve nonvolatile solutes. When the pressure on the supercritical solution is released, the solvent turns to gas. leaving the solute in the gas phase for easy detection. Carbon dioxide is the supercritical fluid of choice for chromatography because it is compatible with flame ionization and ultraviolet detectors, it has a low critical temperature. and it is nontoxic. 

The supercritical fluid extraction of analytes from solid sorbents is controlled by a variety of factors including the affinity of the analytes for the sorbent, the tortuosity of the sorbent bed, the vapor pressure of the analytes, and the solubility and the diffusion coefficient of the analytes in the supercritical fluid. Additionally, SFE efficiencies are affected by a complex relationship between many experimental variables, several of which are listed in Table I. Although it is well established that, to a first approximation, the solvent power of a supercritical fluid is related to its density, little is known about the relative effects of many of the other controllable variables for analytical-scale SFE. A better understanding of the relative effects of controllable SFE variables will more readily allow SFE extractions to be optimized for maximum selectivity as well as maximum overall recoveries. 

A number of other methods, not falling within any of the earlier-mentioned categories, may prove useful for process intensification. Some of them, such as supercritical fluids, are already known and have been applied in other industries (104,105). Because of their unique properties, especially the high diffusion coefficient, supercritical fluids are attractive media for mass transfer operations,... 

Supercritical fluid extraction (SFE) procedures have been developed for extractions of species of elements from samples. Viscosities and diffusion coefficients... 

Table 3.3 presents the approximate physical properties of gases, supercritical fluids, and liquids. It shows that the densities of supercritical fluids are close to that of a liquid, whereas their viscosities are gaslike. The diffusion coefficients are in between. Due to these unique properties, supercritical fluids have good solvating power (like liquid), high diffusivity (better than liquid), low viscosity, and minimal surface tension (like gas). With rapid mass transfer in the supercritical phase and with better ability to penetrate the pores in a matrix, extraction is fast in SFE, along with high extraction efficiency. 

Accelerated solvent extraction (ASE) is also known as pressurized fluid extraction (PFE) or pressurized liquid extraction (PLE). It uses conventional solvents at elevated temperatures (100 to 180°C) and pressures (1500 to 2000 psi) to enhance the extraction of organic analytes from solids. ASE was introduced by Dionex Corp. (Sunnyvale, CA) in 1995. It evolved as a consequence of many years of research on SFE [45], SFE is matrix dependent and often requires the addition of organic modifiers. ASE was developed to overcome these limitations. It was expected that conventional solvents would be less efficient than supercritical fluids, which have higher diffusion coefficients and lower viscosity. However, the results turned out to be quite the opposite. In many cases, extraction was faster and more complete with organic solvents at elevated temperature and pressure than with SFE. Extensive research has been done on the extraction of a variety of samples with ASE. ASE was approved by EPA as a standard method in 1996. 

After substituting the background and the critical terms from equations 3 and 4 into equation 2, the diffusion coefficient in the supercritical region is given by... 

In this study, we employed PCS to measure the decay rate of the order-parameter fluctuations in dilute supercritical solutions of heptane, benzene, and decane in CC - The refractive index increment with concentration is much larger than the refractive index increment with temperature in these systems. Therefore the order-parameter fluctuations detected by light scattering are mainly concentration fluctuations and their decay rate T is proportional to the binary diffusion coefficient, D = V/q. The... 

The self-diffusion coefficients in supercritical ethylene were measured using the pulsed NMR spectrometer described elsewhere (9,10), automated for the measurement of diffusion coefficients by the Hahn spin echo method (11). The measurements were made at the proton resonance frequency of 60 MHz using a 1 1.2 kG electromagnet. 

Some measurements have been made of self diffusion in pure ethylene and in ethylene-sulfur hexafluoride mixtures (22), but these measurements were made very close to the critical temperature and up to pressures of only about 100 bar. Proton spin-lattice relaxation times (T.) of ethylene have been measured at temperatures from 0°C to 50°C and pressures up to about 2300 bar (13). The relaxation time values were -M0—50 sec for much of the region studied. Several relaxation mechanisms contribute to this long relaxation time and make both the measurement and analysis of the relaxation times very difficult. For these reasons, we decided to limit our study to the measurement of the self-diffusion coefficient in supercritical ethylene (60. 

Figure 2. Density and temperature dependence of the experimental self-diffusion coefficients of compressed supercritical ethylene.

The hard sphere diameters were then used to calculate the theoretical Enskog coefficients at each density and temperature. The results are shown in Figure 3 as plots of the ratio of the experimental to calculated coefficients vs. the packing fraction, along with the molecular dynamics results (24) for comparison. The agreement between the calculated ratios and the molecular dynamics results is excellent at the intermediate densities, especially for those ratios calculated with diameters determined from PVT data. Discrepancies at the intermediate densities can be easily accounted for by errors in measured diffusion coefficients and calculated diameters. The corrected Enskog theory of hard spheres gives an accurate description of the self-diffusion in dense supercritical ethylene. 

The experimental temperature dependence is much more closely reproduced by the empirical correlations of Dawson et al. (43) and of Mathur and Thodos (44). The exact experimental values are not reproduced by any of the methods. However, considering the difference in molecular weight between toluene and tolu-ene-d0,the approximations involved,and the error in the experimental values (which gets higher as the density decreases), the correlation of Mathur and Thodos gives a very good estimation of the self diffusion coefficient in supercritical toluene. 

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