Binary interaction density parameter

By considering both temperature and density effects on the binary interaction parameter, its standard form can be modified as ... 

Beyond applications reported in the literature, process simulation is ubiquitous throughout the chemical industry and academia. Every time users select the Soave, or SRK, thermodynamics model, they apply the Soave equation. One motivation for this selection is the long experience with the model and the compilation of correction factors, when the basic model is deficient. For example, binary interaction parameters (ky s) have been compiled for a large number of binary mixtures to improve VLE correlation. It is also possible to compensate for inaccuracies in density through volume translations. ... 

Using the proposed procedure in conjunction with literature values for the density (11) and vapor pressure (12) of solid carbon dioxide, the solid-formation conditions have been determined for a number of mixtures containing carbon dioxide as the solid-forming component. The binary interaction parameters used in Equation 14 were the same as those used previously for two-phase vapor-liquid equilibrium systems (6). The value for methane-carbon dioxide was 0.110 and that for ethane-carbon dioxide was 0.130. Excellent agreement has been obtained between the calculated results and the experimental data found in the literature. As shown in Figure 2, the predicted SLV locus for the methane-carbon... 

In Eq 2.86 k and b are ratios of, respectively, ACp s and densities of polymers 1 and 2, and is the thermodynamic binary interaction parameter. Thus, the relation makes it possible to compute the interaction parameter of miscible blends from T vs. composition dependence. 

The domain size and shape, as well as the interfacial thickness, depend on the following factors (i) magnitude of the repulsive interactions between the A and B blocks, x b (ii) conformation entropy loss necessary to maintain constant segment density (iii) the localization entropy loss that causes the chemical links to be present at the interface and (iv) the composition. These mutually compensating factors (i vs. ii H-iii) depend on molecular weight of each block and the binary interaction parameter [Helfand, 1975 Helfand and Wasserman, 1976,1978,1980 Hashimoto et al, 1980 Inoue et al, 1969 JCrause, 1980 Meir, 1969, 1987 Hashimoto et al, 1993],... 

Helfand and Tagami [1971, 1972] model is based on self-consistent field that determines the configurational statistics of the macromolecules in the interfacial region. The interactions between the statistic segments of polymers A and B are determined by the thermodynamic binary interaction parameter, The isothermal segmental density profile shown in Figure 9.12, Pj (i = A or B), was calculated for infinitely long macromolecules, M — oo. The interfacial thickness, A1, and the interfacial tension coefficient, v, were expressed as ... 

Solution. We use our program (Dimian and Groenendijk, 1994). Bubble point pressures, equilibrium X-factors and densities are presented in Table 6.2. Values calculated using interaction coefficients are marked by star. The differences between properties with and without binary interaction parameters are considerable. 

As expected, PC-SAFT performs better than PR EoS for both systems. A comparison between the predictions by PC-SAFT and PR and experimental data measured by Creton et al. [6] is seen in Figure 1. Furthermore, Table 3 shows the average absolute deviation for PR and PC-SAFT predictions for all three systems. The molecular simulation data for the C02-N2-Ar-02-S02 mixture lie far from the critical point so the density is more accurately predicted by both PC-SAFT and PR EoS resulting in a lower %AAD. These results show that PC-SAFT follows the trend of experimental data more closely and with higher accuracy than PR. The use of the optimized binary interaction parameters further improves the prediction of density by both PR and PC-SAFT. 

Finally, the pure-component parameters in the Sanchez-Lacombe equation of state can be evaluated to reproduce puredensity versus temperature data), whereas the mixture parameters are evaluated through selected mixing rales. These in turn involve one or two binary interaction parameters per component pair, which are usually obtained by fitting binary data (for example sorption data for the pair C02-polymer). 

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-... 

In order to model this phase behavior using PC-SAFT, the pure-component parameters of the two solvents and the polymer and three binary interaction parameters must be known. The pure-component parameters of the solvents (CO2 and pentane) can be fitted to the vapor pressure and the saturated liquid density. The identification of the pure-component parameters for the polymer is challenging and it is afflicted with a higher degree of uncertainty compared to the one for the volatile components, because no vapor pressure data, no liquid densities, and no heats of vaporization are available for polymers. 

Diamond (2003) use this as a starting point to develop an equation of state for nonelectrolytes, many of which are gaseous under normal conditions. This is of course derived from the virial equation, and has the usual limitation of being valid only at low to moderate densities. Akinfiev and Diamond propose an equation to describe the binary interaction parameter By as a function of P and T. Because By in the virial equation is a function only of T and is independent of P, the development in Akinfiev and Diamond departs from virial theory, using it only as a starting point. For two components, the B terms in (13.47) become AB, called AB, to which they ascribe the temperature dependence... 

By using experimental values of the binary interaction parameters it is possible to calculate miscibility maps and therefore predict the phase behavior of poly-mer/copolymer, copolymer/copolymer, and more complex blends. A list of segment-segment interaction parameters and corresponding interaction energy densities,... 

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