Flory-Huggins formula

To compare the vapour pressure of solutions of rubber in benzene with the Flory-Huggins formula. 

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. 

Fiber-reinforced polymer systems, 38 Fickian diffusion, 665 Fick s law, 663,684 Field flow fractionation, 20 Filled polymers, 38 First normal stress coefficient, 545 difference, 640 First-order transition, 27,152 Flame-retardant additives, 861 Flammability, 847 Flashing, 804 Flash line region, 807 Flexibility of a chain molecule, 246 Flexible polymer molecules, 706 Flexural deformation under constant load, 825 Flexural formulas, 826 Flexural rigidity, 877 Floor temperature, 751 Flory-Huggins... 

For polymers, x is usually defined on a per monomer basis or on the basis of a reference volume of order one monomer in size. However, x is usually not computed from formulas for van der Waals interactions, but is adjusted to obtain the best agreement between the Flory-Huggins theory and experimental data on the scattering or phase behavior of mixtures (Balsara 1996). In this fitting process, inaccuracies and ambiguities in the lattice model, as well as in the mean-field approximations used to obtain Eq. (2-28), are papered over, and contributions to the free energy from sources other than simple van der Waals interactions get lumped into the x parameter. The temperature dependences of x for polymeric mixtures are often fit to... 

It is remarkable that no empirical mixture parameters and no experimental data are required to use the equation. The only parameters in the Flory-Huggins equation are the hard core volumes V, which are a pme-component property, and the atomic or group contribution values are found in standard compilations. Since the v/s are significant in the FH equation only in terms of their ratios, pure-liquid molar volumes are often used for V in place of hard core volumes. For solutions of polymers of the same chemical formula, molecular masses are legitimate substitutes for V , for the same reason. Thus the volume fractions ( ) can be substituted by mass fractions W . Either volume fraction or mass fraction is directly related to laboratory data. To avoid mole fractions, the activity tti from Equations (4.368) and (4.369) can be used to calculate by / = aj. ... 

In a poor solvent, one parameter is no longer sufficient and now the three-body terms must be taken into account, not only implicitly but also explicitly. The second basic parameter required to study chains in the vicinity of TF is the repulsive three-body interaction c. The comparison made in Chapter 14 between the Flory-Huggins theory and the continuous model suggests calculating c by the formula... 

The Flory-Huggins theory and the simple-tree approximation in the standard continuous model lead to formulae that are in both cases similar to (16.2.7), Let us consider the parameter ( — / ) of the Flory-Huggins theory (see Chapter 14, Section 5.3). The correspondence with the continuous model is given by (14.5.13)... 

Although the mixing interaction parameter exhibits the same formulas with the Flory-Huggins parameter, it contains contributions from both the mixing energy and the parallel packing energy. 

Following Huggins, Flory and others, we shall denote this expression as Van Laar heat of dilution. An equation of this type has been used by a number of workers. In those cases where A o is positive and not too lai e, it represents a useful overall formula which accounts fairly well for the dependence on concentration. 

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