Flory-Huggins, multicomponent

Equivalent expressions for equations (3) and (6) exist for the polymer (7). The Flory-Huggins expressions can also be extended to multicomponent systems (2) ... 

The first mean-field theories, the lattice models, are typified by the Flory-Huggins model. Numerous reviews (see, e.g., de Gennes, 1979 Billmeyer, 1982 Forsman, 1986) describe the assumptions and predictions of the theory extensions to polydisperse and multicomponent systems are summarized in Kurata s monograph (1982). The key results are reiterated here. 

The Flory-Huggins theory, originally developed for polymer/solvent systems, was extended to polymer blends and other multicomponent mixtures by R. L. Scott, J. Polym. Sci. 9,423 (1952). 

The lattice theories are the oldest and most frequently used to interpret and to predict the thermodynamic properties of multicomponent systems containing polymers. The Flory-Huggins theory is the best known. To use the theory, one must know the temperature, pressure, and concentration dependence of the enthalpic and entropic contributions to the binary interaction parameter, Xi2 = Xh P,[Pg.239]

Similar expressions hold for the volatile monomers, which at high dilutions can be treated independently. At low conversions, the infinite dilution is not applicable and the multicomponent Flory-Huggins equation [Eq. (26)], for example, should be used instead. Here the y, are the volume (or segment) fractions of the various components, i = 1 up to Ny being the volatile components and the polymer being component Ny - -1 the yy, are their mole fractions, Vy the molar volumes, and the Xij the binary interaction parameters. 

The justification for using the original Flory-Huggins theory, in some cases with small modifications lies in the fact that we are often dealing with multicomponent systems which would be difficult to treat with Flory snew theory. Moreover it turns out that the lattice theory suffices to give a good qualitative and in most cases also a semi quantitative acceptable picture of the often large effects of the different parameters which are involved in the description of the systems. 

A number of analytical off-lattice approaches are based on the extension of various simple one-component analytical models (such as Flory-Huggins theory, Flory s equation of state model, or Guggenheim theory) to multicomponent systems by the use of some ad hoc combining rules [5-8,15,16]. These approaches likewise neglect the influence of chain connectivity and monomer... 

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