Multiphase multicomponent equilibria for mixtures containing polymers by the perturbation theory
Introduction
As an answer to the cost reduction and the increasing efficiency of the polymer industry it is necessary to have a thermodynamic model able to describe the behavior of the mixtures in the widest range of operating conditions. This model, essentially used for describing phase equilibrium, is the most important tool of any process simulator, which in turn is a key tool in the modern chemical engineering profession. Examples of relevant industrial applications in this respect are the devolatilization of a solvent from a polymer solution, processes involving polymer blends and the new separation processes of a polymer–solvent mixture using supercritical solvents and antisolvents (SAS).
The SAS process is particularly interesting both from a practical and theoretical point of view (Bungert, Sadowski & Arlt, 1997). In practice, this separation technique may be successfully applied when thermal degradation of the polymer may occur if a traditional process is used. Basically, it uses the phase separation of a liquid polymer solution into a polymer-rich phase and a solvent-rich phase, which is almost polymer free. This phenomenon, which appears at elevated pressures by increasing temperature, according to the lower critical solution temperature behavior, can be obtained to lower temperatures by the addition of a compressed gas to a polymer–solvent system. This is so because the increased free volume of the solvent due to the supercritical additive is equivalent to the temperature effect in causing the high-temperature phase separation (Seckner, McClellan & McHugh, 1988). Solvent recovery processes from a polymer solution can then be carried out under less severe conditions, in terms of thermal stability of the polymer, and with less energetic demand.
To be useful for such complex industrial applications, the thermodynamic model that we need must be able to describe mixtures containing components with large differences in size and molecular interactions, in the simultaneous presence of two liquid and one vapor phases. It must be also able to reproduce all the different types of phase equilibria experimentally observed in these systems, i.e. both the lower critical solution temperature (LCST) and the upper critical solution temperature (UCST) behavior.
Cubic equations of state are not useful to this aim, as was already shown by Fermeglia, Bertucco and Patrizio (1997). Also among the molecular-based thermodynamic models, the most commonly used Flory–Huggins theory (Flory, 1953) is not suitable to explain the complex liquid behavior displayed by polymer mixtures. One attempt of describing compressibility effects has been done by introducing the free volume concept in the Compressible-Lattice models (Sanchez & Lacombe, 1976, Sanchez & Lacombe, 1978). Other variations of the Lattice-Fluid model have been developed (High & Danner, 1989, High & Danner, 1990; Panayioutou & Vera, 1982) but all these theories ignore the continuos nature of the real polymer configurations. Recently, a number of statistical–mechanical equations of state, based on a more physically reasonable Continuous-Space theories of polymer mixtures have been developed (Chapman, Jackson & Gubbins, 1988; Chiew, 1990; Dickman & Hall, 1986; Honnel & Hall, 1989). In these relatively simple models, a molecule is represented by a series of freely jointed tangent hard spheres, the hard-sphere chain, which is able to take into account the complex phase behavior of real polymer systems including excluded volume effects and segment connectivity.
Among them is the perturbed hard-sphere chain (PHSC) equation of state, which is based on a modified Chiew equation of state for athermal hard-sphere chains. This model is applicable to fluids containing small or large molecules, because the effective hard-sphere diameter and attractive energy parameters are theoretically based functions of temperature (Song & Mason, 1991). Moreover, previous works (Song, Lambert & Prausnitz, 1994; Song, Hino, Lambert & Prausnitz, 1996) have demonstrated that the PHSC equation of state successfully reproduces all types of phase equilibria experimentally observed in binary mixtures containing polymers, including the lower critical solution temperature (LCST), the upper critical solution temperature (UCST), or both. Calculated liquid–liquid coexistence curves were found to be in good agreement with experiments for several binary mixtures containing polymers.
The primary purpose of this paper is to extend the use of the PHSC EOS to multicomponent mixtures containing molecules with large differences in size and interactions, and to describe with the same set of parameters a wide range of process conditions. In particular, this paper focuses on ternary systems containing polymer, solvent and antisolvent, because of the complexity of the phase behavior of these three-phase systems of recent industrial interest.
Although a systematic investigation of the influence of a supercritical fluid on the phase behavior of polymer systems has already been made (Irani & Cozewith, 1986; Seckner et al., 1988; Kennis, De Loos & De Swann Arons, 1990; Bungert et al., 1997) and the physical basis of observed experimental phenomena is well understood, experimental investigation in an extended range of temperature and composition have been carried out only recently. Furthermore, few systems have been experimentally considered and a complete characterization in terms of multicomponent systems is available only for the system polystyrene–cyclohexane–carbon dioxide system (Behme, Bungert, Sadowski & Arlt, 1998). As a consequence, we have considered this case as the reference system for showing how a new generation equation of state can help in solving the problem of phase equilibria calculations under wide process conditions in the presence of a complex phase behavior.
Section snippets
Pure components
The equation of state considered in this paper is the simplified PHSC EOS (Song et al., 1996). It takes the hard sphere chains as its reference system, in the form of the Chiew equation of state (Chiew, 1990), derived from the Percus–Yevick integral-theory coupled with chain connectivity (and modified by the introduction of the Carnahan–Starling radial distribution function of hard spheres at contact), and a van der Waals attractive term as the perturbation. The EOS in terms of pressure is the
Pure components
A set of three molecular parameters has been obtained by fitting experimental data for each pure component considered in this work. For pure volatile fluids the three molecular parameters and have been fitted to vapor pressure and saturated liquid density data as functions of temperature. For pure polymer liquids parameters and have been regressed from pressure–volume–temperature (PVT) data.
Details on the fitting procedure are given elsewhere (Fermeglia et al., 1998): the
Pure components
Table 1 summarizes the 21 pure polymers investigated, along with the temperature and pressure range of the PVT data considered. The database used in this work is exactly the same as that of a previous paper (Song et al., 1994), where a previous version of the PHSC model was considered. Table 1 also reports the numerical values of parameters obtained by fitting the experimental data for pure polymers. The root-mean-square relative deviation (RMSD%) reported in Table 1 between calculated and
Conclusions
The simplified PHSCT model has been applied to pure polymers and to mixtures of polymers, solvents and supercritical fluids with the aim of investigating its correlating and predictive capabilities in the description of the complex phase behavior of such systems.
The results obtained show clearly that the model is able to describe such systems in a qualitative and semi-quantitative way.
Specifically, for pure polymers good calculations can be made, which lie within the experimental uncertainty of
Acknowledgements
The authors wish to thank J.M. Prausnitz for his helpful suggestions and the Ministero dell'Università e della Ricerca Scientifica (MURST — Roma) for the financial support.
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