Supercritical fluid thermodynamic critical point

In general, any substance that is above the temperature and pressure of its thermodynamic critical point is called a supercritical fluid. A critical point represents a limit of both equilibrium and stability conditions, and is formally delincd as a point where the first, second, and third derivatives of the energy basis function for a system equal zero (or, more precisely, where 9P/9V r = d P/dV T = 0 for a pure compound). In practical terms, a critical point is identifled as a point where two or more coexisting fluid phases become indistinguishable. For a pure compound, the critical point occurs at the limit of vapor-Uquid equilibrium where the densities of the two phases approach each other (Figures la and lb). Above this critical point, no phase transformation is possible and the substance is considered neither a Uquid nor a gas, but a homogeneous, supercritical fluid. The particular conditions (such as pressure and temperature) at which the critical point of a substance is achieved are unique for every substance and are referred to as its critical constants (Table 1). 

A supercritical fluid (SCF) is any substance at a temperature and pressure above its thermodynamic critical point. Such a fluid can diffuse through soHds such as a gas and dissolve materials such as a liquid. Carbon dioxide and water are the most commonly used SCFs. 

SFC is the application of a supercritical fluid, any substance at a temperature and pressure above its thermodynamic critical point (Figure 9.2) with both gas- and liquid-like abilities to diffuse through solids, and dissolve materials, respectively, as the mobile phase in the chromatographic process. The most widely used mobile phase for SFC is carbon dioxide because of its low critical pressure (73 atm), low critical temperature (31°C), inertness, low toxicity, and high purity at low cost [12,13], Historically there were two approaches in developing modern SFC the use of either the packed and microbore columns designed for HPLC application or the open-tubular capillary GC type columns [13,14], The conventional packed HPLC... 

A supercritical fluid is defined as one that is above its thermodynamic critical point, as identified by the critical pressure (p ) and critical temperature (Tc). Supercritical fluid behavior can be peculiar because of the variation of theimophysical properties such as density and specific heat near and at the critical point. Supercritical fluids have some properties similar to liquids (e.g., density), and some properties that are comparable to those of gases (e.g., viscosity). Thus, they cannot be considered either a liquid or a gas. 

Supercritical fluid, especially supercritical water (SCW), that is above the thermodynamic critical point of water (374"C, 22.1 MPa), has attracted increasing attention in various applications, such as in supercritical water oxidation (SC WO), in supercritical water gasification (SCWG), and for the continuous synthesis of nanoparticles. The environment of reactors presents a big challenge for structural materials used in the components. Many kinds of materials including stainless steel, alloys, and ceramics have been studied for using in SCW atmosphere. However, the details of the corrosion mechanism of each ceramic in an SCW environment were not fully clarified. 

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). 

A gaseous pure component can be defined as supercritical when its state is determined by values of temperature T and pressure P that are above its critical parameters (Tc and Pc). In the proximity of its critical point, a pure supercritical fluid (or a dense gas as it is alternatively known) has a very high isothermal compressibility, and this makes possible to change significantly the density of the fluid with relatively limited modifications of T and P. On the other hand, it has been shown that the thermodynamic and transport properties of supercritical fluids can be tuned simply by changing the density of the medium. This is particularly interesting for... 

The operating pressure is obtained from the vapor pressure and the partial pressure of the gaseous educts and products. In this process, the temperatures applied are between 150 and 500 °C. In recent times, supercritical fluids have attracted a great deal of attention as potential extraction agents and reaction media in chemical reactions. This has resulted from an unusual combination of thermodynamic properties and transport properties. As a rule supercritical reactions like hydrolysis or oxidation are carried out in water. Above the critical point of water, its properties are very different to those of normal liquid water or atmospheric steam. 

For a pure supercritical fluid, the relationships between pressure, temperature and density are easily estimated (except very near the critical point) with reasonable precision from equations of state and conform quite closely to that given in Figure 1. The phase behavior of binary fluid systems is highly varied and much more complex than in single-component systems and has been well-described for selected binary systems (see, for example, reference 13 and references therein). A detailed discussion of the different types of binary fluid mixtures and the phase behavior of these systems can be found elsewhere (X2). Cubic ecjuations of state have been used successfully to describe the properties and phase behavior of multicomponent systems, particularly fot hydrocarbon mixtures (14.) The use of conventional ecjuations of state to describe properties of surfactant-supercritical fluid mixtures is not appropriate since they do not account for the formation of aggregates (the micellar pseudophase) or their solubilization in a supercritical fluid phase. A complete thermodynamic description of micelle and microemulsion formation in liquids remains a challenging problem, and no attempts have been made to extend these models to supercritical fluid phases. 

Gas flow processes through microporous materials are important to many industrial applications involving membrane gas separations. Permeability measurements through mesoporous media have been published exhibiting a maximum at some relative pressure, a fact that has been attributed to the occurrence of capillary condensation and the menisci formed at the gas-liquid interface [1,2]. Although, similar results, implying a transition in the adsorbed phase, have been reported for microporous media [3] and several theoretical studies [4-6] have been carried out, a comprehensive explanation of the static and dynamic behavior of fluids in micropores is yet to be given, especially when supercritical conditions are considered. Supercritical fluids attract, nowadays, both industrial and scientific interest, due to their unique thermodynamic properties at the vicinity of the critical point. For example supercritical CO2 is widely used in industry as an extraction solvent as well as for chemical... 

Precipitation from supercritical fluids is of interest not only in relation to the production of uniform particles. The thermodynamics of dilute mixtures in the vicinity of the solvent s critical point (more specifically, the phenomenon known as retrograde solubility, whereby solubility decreases with temperature near the solvent s critical point) has been cleverly exploited by Chlmowitz and coworkers (12-13) and later by Johnston et al. (14). These researchers implemented an elegant process based on retrograde solubility for the separation of physical solid mixtures which gives rise to high purity materials. 

A number of researchers have developed techniques to determine partial molar volume. Eckert and coworkers (Eckert et al., 1986) provide a very good description of the method for obtaining partial molar volumes. They facilitated this difficult measurement by using a vibrating-tube densitometer (Mettler-Paar DMA 512). The major uncertainties with this technique are associated with the temperature control, which becomes crucial if experiments are performed at infinite dilution near the solvent s critical point. Shim and Johnston (1991) also note that it is possible to determine partial molar volume information using supercritical fluid chromatography if the mobile and stationary phases can be thermodynamically characterized. 

As a result of the significant variation in thermodynamic properties near and at the critical point, it is difficult to use Computational Fluid Dynamics (CFD) when modeling supercritical flows. Also, since small changes in temperature and pressure can have large effects on the structure of a fluid near the critical point, local property values are very important. 

In thermally non-homogeneous supercritical fluids, very intense convective motion can occur [Ij. Moreovei thermal transport measurements report a very fast heat transport although the heat diffusivity is extremely small. In 1985, experiments were performed in a sounding rocket in which the bulk temperature followed the wall temperature with a very short time delay [11]. This implies that instead of a critical slowing down of heat transport, an adiabatic critical speeding up was observed, although this was not interpreted as such at that time. In 1990 the thermo-compressive nature of this phenomenon was explained in a pure thermodynamic approach in which the phenomenon has been called adiabatic effect [12]. Based on a semi-hydrodynamic method [13] and numerically solved Navier-Stokes equations for a Van der Waals fluid [14], the speeding effect is called the piston effecf. The piston effect can be observed in the very close vicinity of the critical point and has some remarkable properties [1, 15] ... 

In this Chapter we have made an attempt to describe mixing and heat and mass transfer in supercritical fluids. Using Laser Doppler Anemometry, Computational Fluid Dynamics and High-Pressure Calorimetry, some basic guidelines have been derived. When compared to the behavior of ordinary liquids, the behavior of SCCO2 is quite different, especially near the critical point. However, when the thermodynamic behavior of CO2 is taken into account (in terms of constant-pressure heat capacity, viscosity, and thermal conductivity), its behavior is consistent with that of other liquids. 

Because of the rapidly growing number of reactions which can be carried out in supercritical fluids, there is an increasing demand for in situ techniques to monitor the course of chemical syntheses in these reaction media. There is a growing need to have efficient analytical techniques in order to determine chemical properties (like concentration and chemical species), physicochemical parameters (Uke heat capacities, conductivity, density, refractive index, and solu-bihty), thermodynamical information (like phase behavior and boundaries, partitioning, and critical points) and/or engineering information (like transfer phenomena, mixing, and scale-up). 

Levelt Sengers, J. M. H. (1991a) Thermodynamics of Solutions Near the Solvent s Critical Point. In Supercritical Fluid Technology, T. J. Bruno and J. F. Ely, Ed. CRC Press Boca Raton, pp 1-56. 

Chialvo, A. A. Kalyuzhnyi, Y. V. Cummings, P. T. (1996) Solvation Thermodynamics of Gas Solubility at Sub- and Near Critical Conditions, AICHE J. 42, 571-584 Harvey, A. H. Crovetto, R. Levelt Sengers, J. M. H. (1990) Limiting vs. Apparent Critical Behavior of Henry s Constant and K Factors, AICHE Journal 36, 1901-1904 Levelt Sengers, J. M. H. (1991) Solubility Near the Solvent s Critical Point, Journal of Supercritical Fluids 4, 215-222... 

The first chapter by Levelt Sengers and the second chapter by Schneider and his coworkers introduce the basic concepts on supercritical fluids, fluid mixtures, and provide an overview of applications. Thermodynamics and phase equilibria in binary and ternary mixtures are treated in Chapter 3 by Gauter and Peters. Chapter 4 by Anisimov and Sengers describes the recent developments on crossover phenomena that attempt to bridge the gap between the behavior of fluids asymptotically close to the critical point with behavior away from criticality. 

Above its critical point, carbon dioxide forms a supercritical fluid (SCF), which is widely used in the food industry because of its nontoxic nature, for example in ultra-clean processes employed to decaffeinate coffee and to extract cholesterol and triglycerides from eggs. Similarly, SCFs promise to be an environmentally responsible replacement for the organic solvents cvurently used in polymerizations and many other industrial applications. SANS has been used [24] to elucidate the thermodynamics of COi-soluble polymers (e.g. fluoropolymers and siloxanes) and the technique is particularly suited to studying the structure of matter under pressure, due to the well-known high neutron transmission of many of the materials used in the construction of pressure vessels. 

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