Corresponding states principle shape factors

CORRESPONDING STATES PRINCIPLE USING SHAPE FACTORS. 

Leach, J. W., Chappelear, P. S. Leland, T. W. (1968). Use of molecular shape factors in vapour-liquid equilibrium calculations with the corresponding states principle. AIChE J., 14, 568-576. 

Fisher, G. D. Leland, T. W. (1970). Corresponding states principle using shape factors. 

Once this function is determined, it could be applied to any substance, provided its critical constants Pc, T, and V are known. One way of applying this principle is to choose a reference substance for which accurate PVT data are available. The properties of other substances are then related to it, based on the assumption of comparable reduced properties. This straightforward application of the principle is valid for components having similar chemical structure. In order to broaden its applicability to disparate substances, additional characterizing parameters have been introduced, such as shape factors, the acentric factor, and the critical compressibility factor. Another difficulty that must be overcome before the principle of corresponding states can successfully be applied to real fluids is the handling of mixtures. The problem concerns the definitions of Pq P(> and Vc for a mixture. It is evident that mixing rules of some sort need to be formulated. One method that is commonly used follows the Kay s rules (Kay, 1936), which define mixture pseudocritical constants in terms of constituent component critical constants ... 

The complete current-potential relation under illumination has already been derived in Section 7.3.3 (Eq. 7.68). In this case it was assumed that the cathodic dark current is only due to the injection of holes into the valence band of an n-type electrode. It was further shown that the current-potential relation could be simplified if the recombination is the rate-determining step (Eq. 7.73). The pre-exponential factor in Eq. (7.73), y o, mainly depends on material parameters such as diffusion constant and length of minority carriers as given by Eq. (7.65). For instance, the recombination is fast if the diffusion length is short, which leads to high /o values and thereby to large cathodic dark currents (Eq. 7.73). As already mentioned, there arc many cases where the photocurrent is due to a hole transfer to occupied states of the redox system but the dark current corresponds to an electron transfer from the conduction band to the empty states of the redox system. In this case the current-potential dependence for an n-type electrode has in principle the same shape... 

The molecular theory predicts strong temperature dependenee of the relaxation ehar-acteristics of polymeric systems that is described by the time-temperature superposition (TTS) principle. This principle is based on numerous experimental data and states that with the change in temperature flie relaxation spectrum as a whole shifts in a self-similar manner along t axis. Therefore, dynamie functions corresponding to different temperatures are similar to each otiier in shape but are shifted along the frequency axis by the value a flie latter is named the temperature-shift factor. With war for an argument it becomes possible to plot temperature-invariant curves Re G (War) and lm G, (war). The temperature dependence of a is defined by the formula... 

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