Flory-Huggins’ model/equation

Roult s law is known to fail for vapour-liquid equilibrium calculations in polymeric systems. The Flory-Huggins relationship is generally used for this purpose (for details, see mass-transfer models in Section 3.2.1). The polymer-solvent interaction parameter, xo of the Flory-Huggins equation is not known accurately for PET. Cheong and Choi used a value of 1.3 for the system PET/EG for modelling a rotating-disc reactor [113], For other polymer solvent systems, yj was found to be in the range between 0.3 and 0.5 [96],... 

Linking this molecular model to observed bulk fluid PVT-composition behavior requires a calculation of the number of possible configurations (microstructures) of a mixture. There is no exact method available to solve this combinatorial problem (28). ASOG assumes the athermal (no heat of mixing) Flory-Huggins equation for this purpose (118,170,171). UNIQUAC claims to have a formula that avoids this assumption, although some aspects of athermal mixing are still present in the model. 

Although the Wilson activity coefficient model has proven to be useful for solutions of small molecules, it has seen very limited use for polymer solutions most likely because of its increased complexity relative to the Flory-Huggins equation. 

Traditionally, the thermodynamics of polymer mixtures was developed in terms of a lattice model, with each monomer unit of the polymer chains occupying a single lattice site. The free energy of mixing of polymers in solution can be described by the Flory-Huggins equation ... 

Fig. IS. Cloud-point conversion as a function of the volume fraction of CO in a DGEBA-EDA system for two different reaction temperatures. Full lines are theoretical predictions from the Flory Huggins equation using x(T) from Eq. (35) (Reprinted from Polymer International, 30, R.A. Ruseckaite, R.JJ. Williams, Castor-oil-modified epoxy resins as model systems of rubber-modified thermosets. 1 Thermodynamic analysis of the phase separation, 11-16, Copyright (1993), with kind permission from the Society of Chemical Industry, London, UK)...

The VSM-W isotherm equation is a four parameters model, A i, K and C s). The pairwise interaction constants Aj and A j have been found to be highly correlated. To avoid this problem, Cochran et al. (1985) used the Flory-Huggin equation for the activity coefficient instead of the Wilson equation ... 

The two VSM isotherm equations are given in eqs. (2.7-5) and (2.7-7) depending on whether the Wilson equation or the Flory-Huggin equation is used to calculate the activity coefficient. Observing the form of these equations, the vacancy solution model equation can be written in general form as follows ... 

The Flory-Huggins equation is one of the simpler models in polymer systems to accurately predict the phase behavior of a real system. In its original version with constant interaction parameters, it cannot even predict the LCST, a common phenomenon in polymer systems. However, its simple form and requirement for less number of parameters make it very suitable for more complex systems. Furthermore, parameters in the Flory-Huggins equation can be made a function of composition or even molecular weight to account for the deviation from experimental data. Thus, the Flory-Huggins model is still very useftil and one of the most frequently used methods for polymer systems. 

Statistical thermodynamic theories provide a powerful tool to bridge between the microscopic chemical structures and the macroscopic properties. Lattice models have been widely used to describe the solution systems (Prigogine 1957). Chang (1939) and Meyer (1939) reported the earliest work related with the lattice model of polymer solution. The lattice model was then successfully established by Flory (1941, 1942) and Huggins (1942) to deal with the solutions of flexible polymers by using a mean-field approximation, and to derive the well-known Flory-Huggins equation. 

The local free energy was presented with variety of mathematical models in different studies, such as the double-well model. A well Flory-Huggjns equation can be adapted for a polymer blend the ternary Flory-Huggins equation is as follows [33] ... 

Haeany Solution Model The initial model (37) considered the adsorbed phase to be a mixture of adsorbed molecules and vacancies (a vacancy solution) and assumed that nonideaUties of the solution can be described by the two-parameter Wilson activity coefficient equation. Subsequendy, it was found that the use of the three-parameter Flory-Huggins activity coefficient equation provided improved prediction of binary isotherms (38). 

Current thermodynamic theories for polymer systems are combinations of the 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. 

Flory-Huggins Theory. The simplest quantitative model for AGmx that includes the most essential elements needed for polymer blends is the Flory-Huggins theory, originally developed for polymer solutions (3,4). It assumes the only contribution to the entropy of mixing is combinatorial in origin and is given by equation 3, for a unit volume of a mixture of polymers A. and B. Here, pt and... 

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