SAFT model

Xiong, Y, and Kiran, E., 1995. Comparison of Sanchez-Lacombe and SAFT model in predicting solubility of polyethylene in high-pressure fluids. J. Appl. Polym. Set, 55 1805-1818. 

Several reviews and comparisons of varions models have been published. " hi their recent and more indnstrially oriented review, Bokis et al. mention the UNIFAC, UNIFAC-FV, FH, and SAFT models as the ones currently available in the ASPEN polymer software. Of these, the first... 

The SAFT model may prove to be a very successful tool in the future for polymer systems. The low-pressure and especially the high-pressure results for systems including solvents and nonpolar polymers (with emphasis on those of interest to the polyolefin industry) are very satisfactory. However, its failure to extend to polar systems represents so far a significant limitation of the model. 

Chen, S.-J., Economou, I.G., and Radosz, M., Density-tuned polyolefin phase equihbria. 1. Multi-component solutions of alternating poly(ethylene-propylene) in subcritical and supercritical olefins. Experimental and SAFT model, Macrontolecules, 25, 4987 995, 1992. 

Kinzl, M. et al., SAFT modeling of inert-gas effects on the cloud-point pressures in ethylene copolymerization systems poly(ethylene-co-vinyl acetate)- -vinyl acetate-i-ethylene and poly(ethylene-co-hexene-l)-thexene-l-tethylene with carbon dioxide, nitrogen or -butane, Ind. Eng. Ghent. Res., 39, 541-546, 2000. 

The two models (SAFT and PHSC) differ substantially in the way they represent the different contributions to the expression of the residual Helmholtz free energy of a system. In the SAFT model, is the sum of different contributions due to hard spheres, dispersion, chain, and association, respectively ... 

BEC Becker, F., Buback, M., Latz, H., Sadowski, G., and Tumakaka, F., Cloud-point curves of ethylene-(meth)acrylate copolymers in fluid ethene up to high pressures and temperatures Experimental study and PC-SAFT modeling. Fluid Phase Equil, 215, 263, 2004. 

NDI Ndiaye, P.M., Dariva, C., Ofiveira, J.V., and Tavares, F.W., Phase behavior of isotactic polypropylene/C4-solvents at high pressure. Experimental data and SAFT modeling, J. 

The polymer solutions warrant use of a special class of lattice models such as Florry-Huggins. For correlation purposes Sanchez-Lacombe " method is sufficient but one may also use Statistical Association Fluid Theoiy (SAFT) models to obtain a better representation. 

Lines are modeling results using the PC-SAFT model [27]. 

The best-known model of this kind is the Statistical Associated Fluid Theory (SAFT) model [58-61]. Here, a non-spherical molecule (solvent or polymer) is assumed to be a chain of identical spherical segments. Starting from a reference system of m hard spheres (A ), this model considers three perturbation contributions, which are assumed to effect independently attractive interactions of the (non-bonded) segments (A ), hard-sphere chain formation (A ), and association (A ° ) ... 

The recently proposed Perturbed-Chain SAFT (PC-SAFT) model [75, 76] adopts the opposite idea here, a perturbation theory of second order is applied to the reference system of hard chains instead of hard spheres to develop a dispersion term for chain-Hke molecules ... 

The PC-SAFT model was successfully applied to describe a whole variety of polymer solubilities in liquids as well as in supercritical solvents [18, 27, 76-78,... 

Fig. 2.10 Solubility of poly(vinyl acetate) (PVA Mv,= 125 kg/mol) and poly(methyl acrylate) (PMA M =31 kg/mol) in supercritical carbon dioxide. Symbols are experimental data (Rindfleisch et at 1996). Lines are modeling results using the PC-SAFT model [79].

The measured pressure-time curves have been combined with the conversion-pressure curves calculated by either the SAFT-LKP or the SAFT-PR model as described in Section 8.4.2.2 to yield the conversion as a function of time (see, e.g., Fig. 8.10 b) [9]. The shape of the conversion-versus-time curves of all polymerizations is similar. At the start of the polymerization, high conversion rates were observed which gradually decrease. The reaction rate does not become zero, which indicates that the catalyst is still active at the end of the experiment. As the volume of the polymer phase is approximately 4—8 vol% according to the SAFT model, the choice for the LKP or PR eos model to describe the supercritical phase largely determines the outcome of the calculations. 

The application of SolventPro with NRTL-SAC and the PC-SAFT models for solubility predictions, multi-level property estimation and solution of some common solvent-based calculations needed in pharmaceutical industry have been demonstrated using selected case studies. The NRTL-SAC model in combination with the UNISAC model and a GC version of the PC-SAFT have shown great potential in the calculation of solid solubility data. A comprehensive database of pure component data (or their reliable predicted values), however, is necessary for predictions of solid solubility for a wide range of chemical systems needed by the pharmaceutical industry. The option available in SolventPro is a very good start. 

The PC-SAFT model (Eq. (10.33)) is a theory-based EOS. In contrast to many other models, PC-SAFT explicitly accounts for the nonspherical shape of a polymer. Therefore, the model reveals predictive capabilities and allows reliable correlations as well as extrapolations for polymer systems. 

Figure 10.12 Comparison between experimental data ((a) density of the mixture [35] and (b) gas solubility [34]) and PC-SAFT modeling [32] for the system CO2 + polystyrene (PS) with a molar mass of 158 kg/mol.

The phase behavior of polymer/SCF mixtures can be described using versions of the lattice fluid (LF) model such as that developed by Sanchez and Lacombe [17]. The LF equation of state is relatively simple, and has been successfully used to describe either polymers dissolved in SCFs, or SCFs dissolved in polymers [18,19], including phenomena such as retrograde vitrification. The statistical associating fluid theory (SAFT) [20] can also describe the phase behavior of polymers dissolved in SCFs. The SAFT model, while somewhat more cumbersome to implement than the LF model, is especially well-suited for polymers with varying backbone architecture, such as branched polymers or copolymers. Both the Sanchez-Lacombe and SAFT models have been incorporated into commercially available modeling software [21]. 

Chen, S.J., LG. Economou, and M. Radosz, Density-tuned polyolefin phase-equilibria. 2. multicomponent solutions of alternating poly (ethylene propylene) in subcritical and supercritical olefins - experiment and saft model. Macromolecules, 1992.25(19) p. 4987-4995. 

Chem S., Economou I.G., Radosz M., (1992), Density-Tuned Polyolefin Equilibria. 2. Multicomponent Solutions of Alternating Poly(ethylene-propylene) in Subcritical and Supercritical Olefins. Experiment and SAFT Model, Macromoleculs 25., 4987. 

Fig. 2 Solution densities, vapour pressures, salt activity coefficients, and solubility behaviour of KBr/water solutions. Symbols represent experimental data, lines are ePC-SAFT modelling...

In the SAFT model, a molecule is considered to consist of a collection of segments, and the Helmholtz function is written as ... 

Gross and Vrabrec developed the polar terms used for systems consisting of one multipolar molecule with either a dipole or a quadrupole and one nonpolar molecule. Perhaps not surprisingly, therefore the theory was found to fail for systems in which one molecule has a significant dipole and the other a significant quadrupole. Lucas and co-workers use multiple moments determined from quantum mechanical calculations and so the experimental dipole and quadrupole moments are not needed (see Section 8.5.2). In a subsequent paper they compared their PCP-SAFT equation with a new approach in which the PC-SAFT equation is combined with polar terms derived from perturbation theory with a spherical reference (based on a Pade approximation for multipolar species with constants from one-centre LJ MC simulations) and an equation that combines the PC-SAFT equation with the GV term for the dipolar interactions and spherical-reference perturbation theory for all other multipolar terms (dipole-quadrupole and quadrupole-quadrupole). The equation based on the latter approach was found to out-perform both their original PCP-SAFT model and the new polar contribution. 

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