Composition Dependence and

The application of cubic equations of state to mixtures requires expression of the equation-of-state parameters as func tions of composition. No exact theory like that for the virial coefficients prescribes this composition dependence, and empirical mixing rules provide approximate relationships. The mixing rules that have found general favor for the Redhch/Kwong equation are ... 

The isoteric heat of adsorption qf is composition-dependent, and the sum of integrals Eq. (16-60) is difficult to evaluate for multicomponent adsorption if the isosteric heats indeed depend on loading. Because each isosteric heat depends on the loadings of all components, the sum must be evaluated for a path beginning with clean adsorbent and ending with the proper loadings of all components, if the isosteric heat of adsorption is constant, as is commonly assumed, then the energy balance (Eq. 16-55) becomes... 

Solubility diagrams were prepared for the phases that separated in the lemon oil extractions performed in this study with carbon dioxide. Such diagrams can serve only as-guides, since solubility is composition-dependent and is a function of the amount extracted. The data are shown in Figures 4, 5, and 6 at 303, 308, and 313 K, respect vely. 

Mixed monolayers of OA and DPPC do appear to exhibit squeeze-out at surface pressures above that of the collapse pressure of oleic acid (about 32 mN m ), implying the coexistence of two separate phases at these higher pressures (Street et al., unpublished data). The surface pressures at which squeeze-out begins are composition dependent and always greater than the collapse pressure of a pure OA monolayer. The pressure of onset increases as the DPPC/OA ratio increases, possibly implying some increase in the... 

An empirical approach to overcome the shortcomings of the van der Waals one-fluid model for a cubic EOS has simply been to add an additional composition dependence and parameters to the combining rule for the a parameter, generally leaving the b parameter rule unchanged. Some examples are the combining rules of Panagiotopoulos and Reid (1986)... 

In specific cases the gas mixture is almost isotherm and the chemical process are not altering the mixture molecular mass very much, thus the system and transport properties may be considered constant. Otherwise, the system and transport properties have to be considered temperature and composition dependent and calculated from approximate parameterizations or kinetic theory relations. 

Another point that should be observed in extraction calculations is the non-ideal nature of the system, which is responsible for the occurrence of two liquid phases in equilibrium. The liquid-liquid equilibrium distribution coefficients, or A -values, are highly composition-dependent and must be calculated by appropriate methods, namely those based on liquid activity coefficients. The NRTL and UNIQUAC liquid activity equations (Chapter 1) are among the more accurate ones for predicting liquid-liquid equilibria. The A -Value is defined as the ratio of the mole fraction of a component in one liquid phase to its mole fraction in the other, and is calculated as... 

The eos parameters a and b for the mixture, so far unspecified by any mixing rules, make then-appearance in Equation (4.433). By setting the equal to the of a solution model, one could solve for a to make part of a, thus specifying its composition dependence and making up a mixing rule. By using the a thus obtained in the eos, the solution model becomes incorporated in the eos. To proceed to solve for a, the v s in Equation (4.433) that are so far undetermined must be specified. 

A more extreme situation occurs when solvent diffuses into a glassy polymer. Here the tracer diffusion coefficient of the polymer is negligible compared with the tracer diffusion coefficient of the solvent. In addition the rate of non-diffusive relaxation of the polymer is also slow compared with the solvent diffusion, as well as being highly composition dependent, and it is this relaxation that is the rate-limiting step. The diffusion equation must now be modified by a term that expresses the mechanical response of the glassy polymer to the build-up of osmotic pressure caused by the ingress of the solvent (Thomas and Windle 1982). 

Mar] Marinelli, R, Guillermet, A.F., Sade, M., The Enthalpy Change of the hep —> fee Martensitic Transformation in Fe-Mn-Co Alloys Composition Dependence and Thermal Cycling Effects , Mater. Sci. Eng. A, 373(1-2), 1-9 (2004) (Experimental, Phase Relations, Phys. Prop., Thermodyn., 30)... 

The separation factors for the Cg aromatics are composition dependent and may be profoundly altered by the addition of other components to the system. It is therefore essential to consider the performance of adsorbent-desorbent combinations rather than the performance of individual adsorbents and desorbents. What is required is a suitable combination of adsorbent and desorbent which, within the appropriate concentration range, gives an adequate separation factor between the components which are to be separated and for which the ancillary separations of extract and raffinate products from the desorbent are easily accomplished. The total number of theoretical plates required for the separation process is minimized when the desorbent is... 

In order to allow a simple treatment, the decomposition problem will be discussed for a binary, one-dimensional system. A one-dimensional decomposition process in reality always occurs if the lattice parameter is strongly composition dependent and if the crystal exhibits elastical anisotropy. In this case, the strain energy during decomposition is strongly dependent upon the crystallographic direction in the crystal. The extension of the one-dimensional treatment to a three-dimensional case, however, offers no difficulties in principle. 

Zhang and Prud homme estimated values of the binary interaction parameters for PCL with vinylidene chloride copolymers known as Saran, that is with copolymers of vinylidene chloride with, separately, vinyl chloride, acrylonitrile or vinyl acetate [74]. Interaction parameters were estimated from melting point depressions. Values obtained were found to be composition-dependent and are... 

The partial molar quantity AGh is composition dependent and can be obtained from infra-red measurements. The parameter x can be estimated from group contributions to the solubility parameters. Better agreement between theory and experiment is found for specific hydrogen bonding systems by use of Eq. (4.11), although the observed melting temperatures involved are small.(54)... 

The dynamic mechanical results in Figure 5 demonstrate the effect of hard segment content for a fixed molecular weight of the polyether soft segment. A rubbery plateau, from the E curves, is observed to be composition-dependent and extends to 200 C for 23.3 hard segment content material and near 300 C for the sample with hard segment... 

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