Supercritical diffusion

Hydrothermal crystallisation processes occur widely in nature and are responsible for the formation of many crystalline minerals. The most widely used commercial appHcation of hydrothermal crystallization is for the production of synthetic quartz (see Silica, synthetic quartz crystals). Piezoelectric quartz crystals weighing up to several pounds can be produced for use in electronic equipment. Hydrothermal crystallization takes place in near- or supercritical water solutions (see Supercritical fluids). Near and above the critical point of water, the viscosity (300-1400 mPa s(=cP) at 374°C) decreases significantly, allowing for relatively rapid diffusion and growth processes to occur. 

A paiticularly attiactive and useful feature of supeicritical fluids is that these materials can have properties somewhere between those of a gas and a hquid (Table 2). A supercritical fluid has more hquid-hke densities, and subsequent solvation strengths, while possessiag transport properties, ie, viscosities and diffusivities, that are more like gases. Thus, an SCF may diffuse iato a matrix more quickly than a Hquid solvent, yet still possess a Hquid-like solvent strength for extracting a component from the matrix. 

Reactions. Supercritical fluids are attractive as media for chemical reactions. Solvent properties such as solvent strength, viscosity, diffusivity, and dielectric constant may be adjusted over the continuum of gas-like to Hquid-like densities by varying pressure and temperature. Subsequently, these changes can be used to affect reaction conditions. A review encompassing the majority of studies and apphcations of reactions in supercritical fluids is available (96). 

Supercritical Mixtures Dehenedetti-Reid showed that conven-tionaf correlations based on the Stokes-Einstein relation (for hquid phase) tend to overpredict diffusivities in the supercritical state. Nevertheless, they observed that the Stokes-Einstein group D g l/T was constant. Thus, although no general correlation ap es, only one data point is necessaiy to examine variations of fluid viscosity and/or temperature effects. They explored certain combinations of aromatic solids in SFg and COg. 

Sun-Chen examined tracer diffusion data of aromatic solutes in alcohols up to the supercritical range and found their data correlated with average deviations of 5 percent and a maximum deviation of 17 percent for their rather hmited set of data. 

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,... 

These values are as much as one hundred times larger than those typically observed in conventional liquids. The improved transport rates in SCFs versus liquid solvents are important in practical appheations including supercritical extraction. Furthermore, carbon dioxide diffuses through condensed-hquid phases (e.g., adsorbents and polymers) faster than do typical solvents which have larger molecular sizes. 

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. 

The use of both sub- and supercritical fluids as eluents yields mobile phases with increased diffusivity and decreased viscosity relative to liquid eluents [23]. These properties enhance chromatographic efficiency and improve resolution. Higher efficiency in SFC shifts the optimum flowrate to higher values so that analysis time can be reduced without compromising resolution [12]. The low viscosity of the eluent also reduces the pressure-drop across the chromatographic column and facilitates the... 

The high diffusivity and low viscosity of sub- and supercritical fluids make them particularly attractive eluents for enantiomeric separations. Mourier et al. first exploited sub- and supercritical eluents for the separation of phosphine oxides on a brush-type chiral stationary phase [28]. They compared analysis time and resolution per unit time for separations performed by LC and SFC. Although selectivity (a) was comparable in LC and SFC for the compounds studied, resolution was consistently... 

Supercritical fluids (SCFs) are compounds that exist at a temperature and pressure that are above their corresponding critical values [70,71]. They exhibit the properties of both gases and Hquids. With gases, they share the properties of low surface tension, low viscosity, and high diffusivity. Their main Hquid-like feature is the density, which results in enhanced solubility of solutes compared with the solubility of gases. Furthermore, the solubility of solutes can be manipulated by changes in pressure and temperature near the critical point [72]. 

Although critical pressures are many times greater than atmospheric pressure, supercritical fluids have important commercial applications. The most important of these is the use of supercritical carbon dioxide as a solvent. Supercritical CO2 diffuses through a solid matrix rapidly, and it transports materials well because it has a lower... 

The development of CO2 fixation reactions in supercritical CO2 attracts increasing attention due to its gas-like low viscosities and high diffusivities and its liquid-like solubilizing power. Matsuda et al. attempted to carry out the con-... 

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...

Principles and Characteristics Supercritical fluid extraction uses the principles of traditional LSE. Recently SFE has become a much studied means of analytical sample preparation, particularly for the removal of analytes of interest from solid matrices prior to chromatography. SFE has also been evaluated for its potential for extraction of in-polymer additives. In SFE three interrelated factors, solubility, diffusion and matrix, influence recovery. For successful extraction, the solute must be sufficiently soluble in the SCF. The timescale for diffusion/transport depends on the shape and dimensions of the matrix particles. Mass transfer from the polymer surface to the SCF extractant is very fast because of the high diffusivity in SCFs and the layer of stagnant SCF around the solid particles is very thin. Therefore, the rate-limiting step in SFE is either... 

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