Critical properties, values

Critical point, 54-57, 81-82, 184-185, 364-368 Critical properties, values of, 571-572 Critical-solution temperature, 455-456 Cubic equation of state, 80-84, 475-493 parameters for, 83-84, 476, 488-489, 491, 493 vapor pressure from, 480-482... 

Among the fluids mentioned (Table 1), CO2 has been the most widely used due to its peculiarities, its low critical property values, and its advantages over the other solvents. It is considered ideal for use in food products since this process does not contain organic solvent residues, elements that are considered contaminants and promoters of major changes in food composition (Brunner, 2005 . Sajfrotova et al., 2005). 

Limited data - basically critical properties and some vapor pressures -are available, however, for a rather large number of compounds. The most comprehensive compilations of such data are given by Reid et al (1987) and by Daubert and Danner (1985,1986). Critical property values for some selected compounds are presented in Appendix C. 

In the typical case, therefore, the volumetric behavior of a fluid is estimated using the available critical property values. This task is accomplished through two approaches ... 

Critical properties Critical stress values Critical value... 

Molecular Weight. The values of the mechanical properties of polymers increase as the molecular weight increases. However, beyond some critical molecular weight, often about 100,000 to 200,000 for amorphous polymers, the increase in property values is slight and levels off asymptotically. As an example, the glass-transition temperature of a polymer usually follows the relationship... 

Values for many properties can be determined using reference substances, including density, surface tension, viscosity, partition coefficient, solubihty, diffusion coefficient, vapor pressure, latent heat, critical properties, entropies of vaporization, heats of solution, coUigative properties, and activity coefficients. Table 1 Hsts the equations needed for determining these properties. 

Critical Compressibility Factor The critical compressibility factor of a compound is calculated from the experimental or predicted values of the critical properties by the definition, Eq. (2-21). 

The constants Cj and C9 are both obtained from Fig. 2-40 Ci, usually from the saturated liquid line and C2, at the higher pressure. Errors should be less than 1 percent for pure hydrocarbons except at reduced temperatures above 0.95 where errors of up to 10 percent may occur. The method can be used for defined mixtures substituting pseiidocritical properties for critical properties. For mixtures, the Technical Data Book—Fehvleum Refining gives a more complex and accurate mixing rule than merely using the pseiidocritical properties. The saturated low pressure value should be obtained from experiment or from prediction procedures discussed in this section for both pure and mixed liquids. 

To be effective, the antiozonants should have two important functions decrease the rate of crack growth in the rubber, and increase the critical stress value (i.e. the stress at which crack growth occurs). Therefore, the following properties of an antiozonant are desirable. 

Understand the critical properties of the mixed compound that affect processability. It should be understood that the properties and acceptable operating values of those properties, which control the compound processability, are dependent on the processes under consideration, e.g., hot or cold feed extrusion, compression or injection molding. 

In addition to the properties noted above, the formulation parameter in iPP-E-plastomer blends have a profound influence on the dynamic loading (e.g., vibration) performance. The load limits of the blend for applications in which dynamic stresses are predominant were studied by using the hysteresis measurement method. However, their technical application requires knowledge of critical load values. 

Also useful, and convenient to use, are prediction methods based on the use of reduced properties (corresponding states) providing that values for the critical properties are available, or can be estimated with sufficient accuracy see Sterbacek et al. (1979). 

Thermal property is another critical property for furnace slag. Because of their more porous structure, blast furnace slag aggregates have lower thermal conductivities than conventional aggregates. Their insulating value is of particular advantage in applications such as frost tapers (transition treatments in pavement subgrades between frost-susceptible and nonfrost-susceptible soils) or pavement base courses over frost-susceptible soils. 

Extensive PVT data as well as precise values for critical property IE s are available for 3He/4He, CH4/CD4, H2/D2 and H20/D20 and these isotopomer pairs comprise an excellent reference in formulating EOS analysis of PVT IE s. Critical properties and critical property IE s for these and a few other selected isotopomer... 

The method described above can be applied to isotopomer pairs for which critical property IE data exists or can be estimated. Calculated values of ln(p7p) are insensitive to IE s on the acentric factor, Aoo/oo (equivalently Aa/a). The VPIE, on the other hand, is strongly dependent on Aoo/oo. For 3He/4He and H2/D2 critical property IE data are complete and MpIE and VPIE are available across the entire liquid range, are one to two orders of magnitude larger, and known to better precision than for other pairs (save perhaps H2O/D2O). For heavier pairs critical property IE data are usually incomplete or uncertain, and often data on MpIE and VPIE exist only over a limited temperature range. 

To model the solubility of a solute in an SCF using an EOS, it is necessary to have critical properties and acentric factors of all components as well as molar volumes and sublimation pressures in the case of solid components. When some of these values are not available, as is often the case, estimation techniques must be employed. When neither critical properties nor acentric factors are available, it is desirable to have the normal boiling point of the compound, since some estimation techniques only require the boiling point together with the molecular structure. A customary approach to describing high-pressure phenomena like the solubility in SCFs is based on the Peng-Robinson EOS [48,49], but there are also several other EOS s [50]. 

In 1954, Mullins, in a modification to the Overton hypothesis, proposed that besides the membrane concentration of the anesthetic, its volume, expressed as its volume fraction (mole fraction X partial molal volume), is important. This reasoning implied that the anesthetic, due to its solubility properties, expands the cell membrane, and that anesthesia occurs when a critical expansion value is reached, at about 0.3-0.5% of the original volume. 

Erpenbeck Miller (Addnl Ref I) stated that the Dieterici equation better represents the fluid properties near the liquid region and it gives a value RTc/pcvc =3.69, nearly the average for all common gases. Subscript c means critical. Same value is given by Joffe (Ref 2b, p 1216) for eqs (1)... 

Most industrial polymers have average chain lengths above critical threshold value. In general, the physical properties improve rapidly as the threshold value is approached and then tend to level off above this value. 

Critical Properties. The critical temperature, pressure and volume for methylamine, nitrous oxide and their binary mixtures were experimentally determined and have been previously reported (34). The critical temperatures of the mixtures are intermediate between those of the pure components (Tc methylamine = 156.9°C Tc nitrous oxide = 36.5°C). The critical pressure goes through a maximum between the pure component values (Pc methylamine = 7.43 bar Pc nitrous oxide = 72.4 bar). The maximum (92.5 bar) is observed at about 46 wt.% methylamine content. The extraction conditions reported in the present study are all above the critical T and P of the fluids used. 

The critical properties, that are essential basic data if a cubic equation of state is used, can be evaluated using group contribution methods but the numerical values obtained depend on the method used. In particular, this fact represents a problem for multifunctional components that are generally involved in processing natural products and/or pharmaceuticals. As an example, depending on the prediction method used, a critical temperature ranging from 817.8 to 1254.0 K can be obtained for cholesterol [60]. 

Values of a-pj and bj for each component of the mixture are obtained with Equations 15-9 through 15-12 from a knowledge of the critical properties and acentric factors of the pure components. 

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