Pressurized fluid extraction theory

To understand the theory relating to pressurized fluid extraction (PFE). 

To understand any extraction technique it is first necessary to discuss some underlying principles that govern all extraction procedures. The chemical properties of the analyte are important to an extraction, as are the properties of the liquid medium in which it is dissolved and the gaseous, liquid, supercritical fluid, or solid extractant used to effect a separation. Of all the relevant solute properties, five chemical properties are fundamental to understanding extraction theory vapor pressure, solubility, molecular weight, hydrophobicity, and acid dissociation. These essential properties determine the transport of chemicals in the human body, the transport of chemicals in the air water-soil environmental compartments, and the transport between immiscible phases during analytical extraction. 

A novel approach is reported for the accurate evaluation of pore size distributions for mesoporous and microporous silicas from nitrogen adsorption data. The model used is a hybrid combination of statistical mechanical calculations and experimental observations for macroporous silicas and for MCM-41 ordered mesoporous silicas, which are regarded as the best model mesoporous solids currently available. Thus, an accurate reference isotherm has been developed from extensive experimental observations and surface heterogeneity analysis by density functional theory the critical pore filling pressures have been determined as a function of the pore size from adsorption isotherms on MCM-41 materials well characterized by independent X-ray techniques and finally, the important variation of the pore fluid density with pressure and pore size has been accounted for by density functional theory calculations. The pore size distribution for an unknown sample is extracted from its experimental nitrogen isotherm by inversion of the integral equation of adsorption using the hybrid models as the kernel matrix. The approach reported in the current study opens new opportunities in characterization of mesoporous and microporous-mesoporous materials. 

The free-volume concept dates back to the Clausius [1880] equation of state. The need for postulating the presence of occupied and free space in a material has been imposed by the fluid behavior. Only recently has positron annihilation lifetime spectroscopy (PALS see Chapters 10 to 12) provided direct evidence of free-volume presence. Chapter 6 traces the evolution of equations of state up to derivation of the configurational hole-cell theory [Simha and Somcynsky, 1969 Somcynsky and Simha, 1971], in which the lattice hole fraction, h, a measure of the free-volume content, is given explicitly. Extracted from the pressure-volume-temperature PVT) data, the dependence, h = h T, P), has been used successfully for the interpretation of a plethora of physical phenomena under thermodynamic equilibria as well as in nonequilibrium dynamic systems. 

Stability of phase boundaries depends on the surface tension. Surface tension in a supercritical fluid system is of major importance for drying, surfactant eflicacy, and extraction. The surface tension of a gas increases with pressure and approaches zero at the critical point while the surface tension of liquid decreases with pressure resulting in dissolution of supercritical components in the liquid phase. The mefliods useful in correlating surface tension include Macleod-Sugden correlation and corresponding states theory. ... 

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