PvT Behavior of Pure Components

Adidharma and Radosz provides an engineering form for such a copolymer SAFT approach. SAFT has successfully applied to correlate thermodynamic properties and phase behavior of pure liquid polymers and polymer solutions, including gas solubility and supercritical solutions by Radosz and coworkers Sadowski et al. applied SAFT to calculate solvent activities of polycarbonate solutions in various solvents and found that it may be necessary to refit the pure-component characteristic data of the polymer to some VLE-data of one binary polymer solution to calculate correct solvent activities, because otherwise demixing was calculated. GroB and Sadowski developed a Perturbed-Chain SAFT equation of state to improve for the chain behavior within the reference term to get better calculation results for the PVT - and VLE-behavior of polymer systems. McHugh and coworkers applied SAFT extensively to calculate the phase behavior of polymers in supercritical fluids, a comprehensive summary is given in the review by Kirby and McHugh. They also state that characteristic SAFT parameters for polymers from PVT-data lead to... 

The aim of activities in this field is the numerical determination of phase equilibrium data of mixtures including critical phenomena from properties of the pure components. Here, the use of equations of state (EOS) is at present the most promising approach. The EOS chosen must describe the pVT behavior of the pure components and the mixtures sufficiently well in a quantitative manner (if possible in both coexisting phases), contain only few parameters easily obtainable from experiments, and allow the calculation of both phase equilibria and critical phenomena at elevated pressures at least semi-quantitatively. 

We will now discuss the problem of determining effective or optimal diameters for use with the HSE theory for real fluids when both the form of the intermolecular potential and its parameters are unknown but accurate equations of state which represent the PVT behavior over an extensive range are available for the pure components. 

Evaluation of Fugacities Using an Equation of State. The fugaci-ties of the components in the fluid phases are related to the volumetric and phase behavior of the mixture while the fugacity of the solid component depends only on the PVT relationship of the pure component. Theoretically it is possible to evaluate the fugacities using experimental volumetric and/or phase equilibrium data in conjunction with Equations 3 and 6. However, these data are normally either unavailable or insufficient and an equation-of-state model has to be used to compute the fugacities. 

Basic to the thermodynamic description is the heat capacity which is defined as the partial differential Cp = (dH/dT)n,p, where H is the enthalpy and T the temperature. The partial differential is taken at constant pressure and composition, as indicated by the subscripts p and n, respectively A close link between microscopic and macroscopic description is possible for this fundamental property. The integral thermodynamic functions include enthalpy H entropy S, and free enthalpy G (Gibbs function). In addition, information on pressure p, volume V, and temperature T is of importance (PVT properties). The transition parameters of pure, one-component systems are seen as first-order and glass transitions. Mesophase transitions, in general, were reviewed (12) and the effect of specific interest to polymers, the conformational disorder, was described in more detail (13). The broad field of multicomponent systems is particularly troubled by nonequilibrium behavior. Polymerization thermodynamics relies on the properties of the monomers and does not have as many problems with nonequilibrium. 

We begin by looking at the phase diagram for a pure component. Pure fluids may be present in any one of three phases sohd, hquid, or gas. The phase boundaries occur along well-defined equilibrium curves, which determine where two phases can exist simultaneously. Figure 7.7 is a typical phase diagram (PVT diagram), which describes the phase behavior of some arbitrary fluid. 

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