Flory-Huggins interaction theory

Han Y, Booth J, Meehan E, Jones DS, Li S, Andrews GP (2013) Construction of dmg-polymer thermodynamic phase diagrams using flory-huggins interaction theory identifying the relevance of temperature and drug weight fraction to phase separation within solid dispersions. Mol Pharm 10(l) 236-248... 

More fundamental treatments of polymer solubihty go back to the lattice theory developed independentiy and almost simultaneously by Flory (13) and Huggins (14) in 1942. By imagining the solvent molecules and polymer chain segments to be distributed on a lattice, they statistically evaluated the entropy of solution. The enthalpy of solution was characterized by the Flory-Huggins interaction parameter, which is related to solubihty parameters by equation 5. For high molecular weight polymers in monomeric solvents, the Flory-Huggins solubihty criterion is X A 0.5. 

The Flory-Huggins interaction parameter, x Is the sum of enthalpic (xH) and entropic (x ) contributions to the polymer-solute interactions (28). xs is an emPitical constant related to the coordination of the polymer subunits (29). Chiou et al. (20) have selected a value of 0.25 for xs of humlc matter. From regular solution theory, xq is given by... 

Fint is the free energy of non-Coulomb interactions of monomer units. Finl can be expressed, for example, in terms of the Flory-Huggins lattice theory [21]. In the general case, when network is immersed in solvent which includes 1 different components some of which can be polymeric with the degree of polymerization Pi(Pi 1, i = L 2,... k), Fim in the Flory-Huggins theory has the following form [21-22] ... 

In 2006, McKenna and co-workers reviewed recent work on the use of TPM to study polymer heterogeneity [35]. In this work, uncrosslinked and crosslinked polysisoprene was studied with benzene and hexadecane as swelling solvents. The authors were able to distinguish contributions coming from the confinement as described by the Gibbs-Thomson equation and contributions from polymer-solvent interactions described by the Flory-Huggins (FH) theory [36, 37]. For the first time, it was shown that for an uncrosslinked sample an excess shift AT is... 

Bednorz-Muller theory Beer-Lambert law Bose-Einstein statistics Debye-Huckel theory Diels-Alder reaction Fermi-Dirac statistics Fischer-Tropsch effect Fisher-lohns hypothesis Flory-Huggins interaction Franck-Condon factor Friedel-Crafts reaction Geiger-Miiller effect... 

It should be pointed out that since I.G.C. measures the total free energy of the interaction, any value of the Flory-Huggins interaction parameter which is derived will be a total value including combinatorial and residual interaction parameters as well as any residual entropy contributions. Similarly when using Equation-of-state theory one will obtain Xj2 rather than Xj. The interactions are measured at high polymer concentration and are therefore of more direct relevance to interactions in the bulk state but this does not remove problems associated with the disruption of intereactions in a blend by a third component. 

The theory of the scattering of radiation by large molecules has been reviewed in several recent publications Thermodynamic data can be obtained using scattering techniques via the Flory-Huggins interaction parameter, Xi2> or the second osmotic... 

Our discussion here explores active connections between the potential distribution theorem (PDT) and the theory of polymer solutions. In Chapter 4 we have already derived the Flory-Huggins model in broad form, and discussed its basis in a van der Waals model of solution thermodynamics. That derivation highlighted the origins of composition, temperature, and pressure effects on the Flory-Huggins interaction parameter. We recall that this theory is based upon a van der Waals treatment of solutions with the additional assumptions of zero volume of mixing and more technical approximations such as Eq. (4.45), p. 81. Considering a system of a polymer (p) of polymerization index M dissolved in a solvent (s), the Rory-Huggins model is... 

If strong specific interactions (such as hydrogen bonds) are present between structural units on polymers A and B, more elaborate versions of the Flory-Huggins solution theory, which attempt to account for these interactions, can be used [8],... 

Predicting blend miscibility correctly is, however, often considerably more challenging than one might guess by looking at the equations given above or even their somewhat more refined versions. Flory-Huggins interaction parameters, their more elaborate versions, and alternative methods such as the equation-of-state theories [9] discussed in Section 3.E, all provide correct predictions in many cases, but unfortunately provide incorrect predictions in many other cases. 

First we introduce the isotropic interaction which results from the mixing of rods and solvents. The previous theory, without the mixing contribution to entropy, is only applicable to an athermal system. If there is a mixing entropy contribution, the free energy in Equation 2.39 is implemented by a term x4>ns, where x is the Flory-Huggins interaction parameter. Flory called the mixing term the isotropic soft interaction to distinguish it from the steric interaction of rods. 

Bednorz—Muller theory Beer—Lambert law Bose—Einstein statistics Debye-Hiickel theory Diels—Alder reaction Fermi—Dirac statistics Fischer—Tropsch effect Fisher—Johns hypothesis Flory—Huggins interaction Franck—Condon factor Friedel—Crafts reaction Geiger-Miiller effect... 

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