concentration regime and can be used to fit data for even more complicated blends with higher concentrations. The theory qualitatively predicts phase separation, the tendency for high molecular weight species to be immiscible, the interaction-temperature dependence and other features commonly observed in polymer mixtures. However, unmodified Flory-Huggins theory fails to predict the lower critical solution temperature observed in some polymer blends and the lack of dependence of the critical temperature on chain length . Additionally, it can be shown that for a binary blend of polymer species with equal chain lengths the critical concentration should be ; however, polymers blends have been observed where this parameter is highly asymmetric. In certain blends, mixing entropy can dominate over monomer interaction. By adopting the mean-field approximation, parameter complex dependence on temperature, blend composition, and chain length was discarded. Specifically, interactions beyond the nearest neighbor may be highly relevant to the behavior of the blend and the distribution of polymer segments is not necessarily uniform, so certain lattice sites may experience interaction energies disparate from that approximated by the mean-field theory. One well-studied effect on interaction energies neglected by unmodified Flory Huggins theory is chain correlation. In dilute polymer mixtures, where chains are well separated, intramolecular forces between monomers of the polymer chain dominate and drive demixing leading to regions where polymer concentration is high. As the polymer concentration increases, chains tend to overlap and the effect becomes less important. In fact, the demarcation between dilute and semi-dilute solutions is commonly defined by the concentration where polymers begin to overlap which can be estimated as Here, m is the mass of a single polymer chain, and is the chain's radius of gyration. References External links "Conformations, Solutions and Molecular Weight" (book chapter), Chapter 3 of Book Title: Polymer Science and Technology; by Joel R. Fried; 2nd Edition, 2003 Footnotes "Thermodynamics of High Polymer Solutions," Paul J. Flory Journal of Chemical Physics, August 1941, Volume 9, Issue 8, p. 660 Abstract. Flory suggested that Huggins' name ought to be first since he had published several months earlier: Flory, P.J., "Thermodynamics of high polymer solutions," J. Chem. Phys. 10:51-61 (1942) Citation Classic No. 18, May 6, 1985 "Solutions of Long Chain Compounds," Maurice L. Huggins Journal of Chemical Physics, May 1941 Volume 9, Issue 5, p. 440 Abstract We are ignoring the free volume due to molecular disorder in liquids and amorphous solids as compared