Property generalized correlations

Table 8.1a Effect of molecular weight or MWD on polymer properties (general correlations) ...

Fig. 23. Correlation between properties (general characteristics), melt flow index (MFI), and mol wt for standard BPA polycarbonate and CD-modified...

The volumetric properties of fluids are represented not only by equations of state but also by generalized correlations. The most popular generalized correlations are based on a three-parameter theorem of corresponding states which asserts that the compressibiHty factor is a universal function of reduced temperature, reduced pressure, and a parameter CO, called the acentric factor ... 

According to equation 184, all fluids having the same value of CO have identical values of Z when compared at the same T and P. This principle of corresponding states is presumed vaHd for all T and P and therefore provides generalized correlations for properties derived from Z, ie, for residual properties and fugacity coefficients, which depend on T and P through Z and its derivatives. 

Generalized Correlations. Generalized correlations are often the only recourse when a property value cannot be determined from empirical correlations or by other means. Several powerful correlating techniques fall under this category, including the principle of corresponding states (3,17), reduced property models (1), and the Polanyi-type characteristic curve for microporous adsorbents (14). 

Miscellaneous Generalized Correlations. Generalized charts and corresponding states equations have been pubhshed for many other properties in addition to those presented. Most produce accurate results over a wide range of conditions. Some of these properties include (/) transport properties (64,91) (2) second virial coefficients (80,92) (J) third virial coefficients (72) (4) Hquid mixture activity coefficients (93) (5) Henry s constant (94) and 6) diffusivity (95). 

Values of all of these parameters must be available or estimated if we are to determine the global reaction rate. Some of these quantities can be evaluated from standard handbooks of physical property data, or generalized correlations such as those compiled by Reid and Sherwood (87). Others can be determined only by experimental measurements on the specific reactant/catalyst system under consideration. 

Considerable evidence suggests that the major site of calcium sequestration and the source of intracellular calcium for signaling is the ER. In addition to the points already made, subcellular fractionation studies have demonstrated positive correlations of ATP-dependent Ca2+ accumulation and of IP3-mediated Ca2+ release with classical enzymatic markers for ER. Calcium uptake into the IP3-sensitive store is augmented by oxalate this augmentation is a property generally associated with the ER. 

The basis for the foam properties is given by interfacial parameters. Although correlations have been shown between a single parameter and foam properties, there is still a lack in a general correlation between interfacial properties and the foam behavior of complex systems in detergency. The simplest approach to correlate interfacial parameters to foam properties is the comparison of the surface activity measured by the surface tension of a surfactant system and foam stability. 

The general correlations of structure and properties of homopolymers are summarized in Table 2.13. Some experiments which demonstrate the influence of the molecular weight or the structure on selected properties of polymers are described in Examples 3-6 (degree of polymerization of polystyrene and solution viscosity), 3-15, 3-21, 3-31 (stereoregularity of polyisoprene resp. polystyrene), 4-7 and 5-11 (influence of crosslinking) or Sects. 4.1.1 and 4.1.2 (stiffness of the main chain of aliphatic and aromatic polyesters and polyamides). 

A variety of methods has been presented in the literature, for correlation of pressure-drops, or of in situ volume fractions for specified conditions of system geometry, operating conditions, or phase properties but no completely generalized correlation yet exists. Only those methods which have been most widely used are discussed in the following section. For more complete listings, reference to recent reviews should be made (B9, G7). 

However, the correlation of the electrical properties of the bulk phase with the catalytic properties of the essentially heterogeneous catalyst surface is a classical difficulty. This may be one of the reasons why no general correlation between these properties is found when a variety of different metal oxide catalysts is compared. A close relationship is often shown, on the other hand, when a particular catalyst is modified or doped with minor amounts of an additional metal oxide. It is very likely that the correlation is successful in this case, because the nature of surface sites is not essentially changed. 

Disperse Dyes. There is a general correlation between heat fastness, the propensity to desorb under conditions of dry heat onto a white piece of polyester, and the dyeing properties of disperse dyes. Low energy dyes are not usually used in thermofixation. as their low heat fastness at the thermofixation temperatures used (200-210 C) results in the subliming of them from the hot fabric. 

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