Flory—Huggins theory polymer phase behaviour

From the theoretical viewpoint, much of the phase behaviour of blends containing block copolymers has been anticipated or accounted for. The primary approaches consist of theories based on polymer brushes (in this case block copolymer chains segregated to an interface), Flory-Huggins or random phase approximation mean field theories and the self-consistent mean field theory. The latter has an unsurpassed predictive capability but requires intensive numerical computations, and does not lead itself to intuitive relationships such as scaling laws. 

In conclusion, it can be said that the partitioning behaviour of monomers between the different phases present during an emulsion polymerisation can be described and predicted using a simple thermodynamic model derived from the classical Flory-Huggins theory for polymer solutions. In general, therefore, the monomer concentrations at the locus of polymerisation are relatively easily accessible. However, this is not the case for more water-soluble monomers (acrylic acid etc). For these monomers suitable models are not readily available and one has to rely on the experimental data. 

Most theoretical approaches to polymer blends are extensions of models for polymer solutions and thus focus on the liquid state. They aim to describe experimental phase behaviour and most authors claim to be able to predict trends in phase behaviour outside the range of measurements. Current theories are combinations of Flory-Huggins, Guggenheim, and Equations of State approaches. All of these theories make use of empirical parameters and are based on assumptions about the underlying molecular model. 

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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