Statistical Association Fluid Theory

Various equations of state have been developed to treat association ia supercritical fluids. Two of the most often used are the statistical association fluid theory (SAET) (60,61) and the lattice fluid hydrogen bonding model (LEHB) (62). These models iaclude parameters that describe the enthalpy and entropy of association. The most detailed description of association ia supercritical water has been obtained usiag molecular dynamics and Monte Carlo computer simulations (63), but this requires much larger amounts of computer time (64—66). 

The non-cubic equations of state are characterized by the use of a repulsive term that is based on the Camahan-Starling or on the HCB expressions already reported in Table 3. The attractive part is generally based on that derived from the perturbed hard chain theory (PHCT) [49], or from the statistical associating fluid theory SAFT [50, 51]. These approaches were the precursors of many theoretical attractive terms and consequently of different equations of... 

The contribution "Application of Meso-Scale Field-based Models to Predict Stability of Particle Dispersions in Polymer Melts" by Prasanna Jog, Valeriy Ginzburg, Rakesh Srivastava, Jeffrey Weinhold, Shekhar Jain, and Walter Chapman examines and compares Self Consistent Field Theory and interfacial Statistical Associating Fluid Theory for use in predicting the thermodynamic phase behavior of dispersions in polymer melts. Such dispersions are of quite some technological importance in the... 

Gordon, P.A. (2001a) Statistical associating fluid theory. 1. Application toward describing isoparafflns. Ind. Eng. Chem. Res., 40, 2947-2955. 

The Statistical Associating Fluid Theory (SAFT) (Section 16.6)... 

Equations of state offer a number of advantages over activity coefficient models for example, they can be applied to both low and high pressures, for properties other than phase equilibria, and the density is not required as an input parameter. However, often they are more difficult to develop for complex fluids and mixtures than are activity coefficient models. Very many equations of state have been proposed for polymers Section 16.7 discusses the reason. Recent reviews have been presented. " " We will not attempt to cover all the various approaches, but essentially discuss in detail only two of them, which seem promising for polymer solutions and blends the cubic equations of state and the SAFT (Statistical Associating Fluid Theory) method. 

Very many noncubic equations of state have been proposed for polymers. Most of them are rather complicated and a few of them, such as several of the models discussed previously, are based on the GC concept, like the GC-Flory and the GCLF equation of state. Several of these equations of state are reviewed elsewhere, and we will restrict here our presentation to one equation of state that is very promising for polymer systems and has already found widespread acceptance. This is the Statistical Associating Fluid Theory (SAFT). 

Economou, I.G., Statistical Associating Fluid Theory a successful model for the calculation of thermodynamic and phase equilibrium properties of complex fluid mixtures, Ind. Eng. Ghent. Res., 41(5), 953-962, 2002. 

The statistical-associated fluid theory (SAFT) of Chapman et al. [25, 26] is based on the perturbation theory of Wertheim [27]. The model molecule is a chain of hard spheres that is perturbed with a dispersion attractive potential and association potential. The residual Helmholtz energy of the fluid is given by the sum of the Helmholtz energies of the initially free hard spheres bonding the hard spheres to form a chain the dispersion attractive potential and the association potential,... 

A variety of equations-of-state have been applied to supercritical fluids, ranging from simple cubic equations like the Peng-Robinson equation-of-state to the Statistical Associating Fluid Theory. All are able to model nonpolar systems fairly successfully, but most are increasingly challenged as the polarity of the components increases. The key is to calculate the solute-fluid molecular interaction parameter from the pure-component properties. Often the standard approach (i.e. corresponding states based on critical properties) is of limited accuracy due to the vastly different critical temperatures of the solutes (if known) and the solvents other properties of the solute... 

For the calculations, different EoS have been used the lattice fluid (LF) model developed by Sanchez and Lacombet , as well as two recently developed equations of state - the statistical-associating-fluid theory (SAFT)f l and the perturbed-hard-spheres-chain (PHSC) theoryt ° . Such models have been considered due to their solid physical background and to their ability to represent the equilibrium properties of pure substances and fluid mixfures. As will be shown, fhey are also able to describe, if not to predict completely, the solubility isotherms of gases and vapors in polymeric phases, by using their original equilibrium version for rubbery mixtures, and their respective extensions to non-equilibrium phases (NELF, NE-SAFT, NE-PHSC) for glassy polymers. 

The statistical associating fluid theory (SAFT) is the first and the most popular approach that uses real hard-chain reference fluids, ineluding chain-bonding contributions. Its basic ideas have been developed by Chapman et Without going into details, the fi-... 

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 ° ) ... 

For the application of supercritical carbon dioxide as a medium for the production of polyolefins, it is important to have rehable thermodynamic data for the systems involved. Knowledge of the phase behavior of the reaction mixture is crucial to properly choose process variables such as temperature and pressure in order to achieve maximum process efficiency. For this reason, the ethylene-poly (ethylene-co-propylene) (PEP)-C02 system has been taken as a representative model system [3]. The effect of molecular weight as well as the influence of CO2 on the phase behavior has been studied experimentally by cloud-point measurements. In addition, the Statistical Associating Fluid Theory (SAFT) has been applied to predict the experimental results. 

The model assumes that the reaction mixture consists of a polymer phase swollen with ethylene and CO2, and an ethylene-C02 phase. The assumption that no polymer dissolves in the ethylene-C02 phase within the experimental conditions has previously been confirmed experimentally for a similar polymer [3]. The swollen polymer phase, i.e. the polymer-ethylene-C02 system, is modeled using the Statistical Associating Fluid Theory (SAFT) eos [6, 7], see Section 8.2.2. The supercritical phase, i.e. the ethylene-C02 system, is either modeled with the Lee-Kessler-Plocker (LKP) eos [30] or with the Peng-Robinson (PR) eos [31], because the use of the SAFT eos for the simulation of both phases results in physically inconsistent behavior [9]. The temperatures used in this work are just above the critical tern-... 

This work is far from complete because only a few of the systems in the database were tested and no contemporary EOS models, such as Statistical Associating Fluids Theory (SAFT) (Muller and Gubbins 2001 Economou 2002), Perturbed... 

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