Pure Polymer PVT Data

The typical form in which dilatometry data are reported is in terms of a volume difference and a relative volume as a function of temperature and pressure. 

V0 = the specific volume at zero pressure (often taken as atmospheric pressure) and the temperature of the system, cubic meters per kilogram. 

We can solve for V in Equation (4C-1) and substitute into Equation (4C-2). Rearranging we obtain 

From this value of V0, the quantity of interest, V, can be calculated. 

In most cases a slightly different value of V0 is obtained for each pair of Vre, and AV because of rounding errors. Therefore the average value of all the V0 s calculated for each temperature, VQ/ is used. 

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PURE.DAT This file contains PVT data for each pure polymer. Each block is constructed as follows ... 

There are some exceptions from this type of presentation within the tables for 2 data, the UCST and LCST data, or the PVT data of pure polymers. These tables are prepared in the forms as chosen in 2001WOH. ... 

The ratio Uo/k or u/k is analogous to the characteristic parameter T in the equations above. There are two additional volume and energy parameters if association is taken into account. In its essence, the SAFT equation of state needs three pure component parameters which have to be fitted to equilibrium data V , Uj/k and r. Fitting of the segment number looks somewhat curious to a polymer scientist, but it is simply a model parameter, like the c-parameter in the equations above, which is also proportional to r. One may note additionally that fitting to specific volume PVT-data leads to a characteristic ratio r/M (which is a specific r-value), as in the equations above, with a specific c-parameter. Several modifications and approximations within the SAFT-framework have been developed in the literature. Banaszak et or Shukla and Chapman extended the concept to copolymers. 

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 procedure to obtain the pure component parameters and binary interaction parameters for the ethylene-PEP-C02 system has been described in detail previously [3]. The pure-component parameters for the small molecules (carbon dioxide and ethylene) have been obtained by fitting to experimental vapor pressure data and saturated liquid densities. The procedure to obtain parameters for large molecules such as polymers is less evident. For PEP, the set of pure component parameters has been obtained by fitting the parameters to PEP PVT data [8] by minimization of the residual squares of calculated and measured densi-... 

The application of an EOS is much more convenient. For the thermodynamics of low-molar-mass components, usually experimental vapor pressures as a function of temperature and experimental PvT data, especially saturated liquid densities, of the pure components are used to estimate the model parameters of this component. However, the vapor pressure of polymers is practically zero. The measurement of the liquid density is often also not possible, because the polymer might degrade before it melts. For these reasons, the estimation of the pure polymer parameters used in EOS is a challenging issue. Recently, methods have been developed where the parameter fitting procedure is based on PvT data of the considered polymer and extrapolating equations that relate the polymer parameters to those of the corresponding monomer. 

In Figure 2.15 [66] experimental isothermal cloud-point curves of the linear low density polyethylene + hexane system are compared with the results of a fit of these data using the Sanchez-Lacombe equation of state. The pure component parameters of hexane were calculated from the critical point of hexane and its acentric factor [67]. The pure component parameters of the polymer were obtained from a simultaneous fit of PVT data and the data presented in Figure 2.15. The equations solved were those described by Koak and Heidemann [68]. The binary interaction parameter was linearly dependent on temperature. The polymer was... 

Both SAFT and PC-SAFT contain pure component parameters the energy parameter or u, the hard-sphere diameter a, or the hard-sphere volume and the number of segments m per molecule. For small (solvent) molecules these parameters are obtained from a fit of vapor pressure data and saturated liquid volume data. Since they do not have a vapor pressure, this fit is not possible for polymers, and the pure component polymer parameters are obtained from a fit to PVT data of the molten polymer or from a fit to PVT data and binary phase equilibrium data. For the description of a mixture one needs one binary interaction parameter ky per binary, which has to be fitted to phase equilibrium data. If necessary, ky can be made temperature-dependent. In general, phase equilibria are very sensitive to the kij value. 

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