Improvement of Flory-Huggins lattice theory

Despite the drawbacks, Flory-Huggins lattice theory was a major step forward towards understanding the thermodynamics of polymer solutions and is the basis of many other theories. Since it was first proposed, other workers have elaborated on it to improve on the assumptions involved. Some of these more refined theories will be given brief consideration, but in general are beyond the scope of the book. 

Several other studies have also been made in an attempt to account theoretically for the phase transition in terms different from those of the Flory-Huggins theory. Otake et al. [55] thus proposed a theoretical model that takes hydrophobic interaction into account in explaining the thermally induced discontinuous volume collapse of hydrogels. In addition, Prausnitz et al. [56] proposed a lattice model, an improvement of which was made to explain the swelling curves of gels consisting of /V,/V -methylenebis(acrylamide) (MBA)-crosslinked copolymers of AAm with [(methacrylamide)propyl]trimethyl-ammonium chloride (MAPTAC) [57],... 

The simple Flory-Huggins theory discussed above is based on a series of questionable assumptions lattice sites of equal size for solvent segments and polymer monomeric units, uniform distribution of the monomeric units in the lattice, random distribution of the molecules, and the use of volume fractions instead of surface-area fractions in deriving the enthalpy of mixing. Proposed improvements, however, have led to more complicated equations or to worse agreement between theory and experiment. Obviously, various simplifications in the Flory-Huggins theory are self-compensating in character. 

Recently, phase behaviour of mixtures consisting of a polydisperse polymer (polystyrene) and nematic liquid crystals (p-ethoxy-benzylidene-p-n-butylani-line) was calculated and determined experimentally. The former used a semi-empirical model based on the extended Flory-Huggins model in the framework of continuous thermodynamics and predicted the nematic-isotropic transition. The model was improved with a modified double-lattice model including Maier-Saupe theory for anisotropic ordering and able to describe isotropic mixing. ... 

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