Flory-Huggins relation

And, finally, we need an expression for the free enthalpy of dilution, AG. It is common usage to apply the Flory-Huggins relation ... 

If the Flory-Huggins relation is used, the energy part of Q is given by... 

It is important first to determine the chemical potentials associated with the Flory-Huggins relation. By standard methods it is may be shown that... 

Progressing to the polymer-solvent system (Figure 1.29), the ideal entropy term above must be replaced by a relationship that recognizes the features of interconnection of segments in the polymer chain. This is the Flory-Huggins relation ... 

In the Wilson equation, the effects of difference both in molecular size and intermolecular forces are incorporated by an extension of the Flory-Huggins relation (5-8). Overall solution volume fractions ( i = XiViJvi) are replaced by local volume fractions, d> which are related to local molecule segregations caused by differing energies of interaction between pairs of molecules. The concept of local compositions that differ from overall compositions is shown schematically for an overall equimolar binary solution in Fig. 5.6, which is taken... 

The Flory-Huggins relation as given in Equation (3) is used to describe thermodynamicahy polymer-polymer miscibility (Huggins, 1942 Flory, 1942 Utracki, 1962 Koningsveld, 1967 McMaster, 1973) ... 

Polymer-solvent mixtures are highly non-ideal. Because of the very long polymer molecules, the polymer exerts an influence far in excess of its molar concentration. This behavior is often described by the Flory-Huggins relations [22, 23] ... 

The conventional melting point-composition relation, Eq. (3.9), cannot be used for the higher dialkyl substituted poly(siloxanes) because the equilibrium is between a crystalline phase and an anisotropic melt. Thus, the Flory-Huggins relation is not applicable. 

There is increasing evidence that the activity of the solvent such as plasticisers in highly concentrated systems is not adequately represented by existing formulations, such as the Flory-Huggins relations and their various higher approximations (13). 

In this section and the last, we have examined the lattice model of the Flory-Huggins theory for general expressions relating AHj and ASj to the composition of the mixture. The separate components can therefore be put together to give an expression for AGj as a function of temperature and composition ... 

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. 

In the Flory-Huggins picture, the interchain interaction parameter should be related to the intersegment interaction parameter by... 

There Is a large body of experimental literature relating to polymer fractionation In liquid-liquid equilibria. In addition, numerous authors have analyzed polymer fractionation using Flory-Huggins theory. We have considered use of the corresponding states theory to model polymer fractionation for the ethylene/ polyethylene system at reactor conditions (18). Results of the... 

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... 

One of the most common techniques for determining x parameters for polymer-solvent systems is the vapor pressure method.(10) In this approach, the uncrosslinked polymer is exposed to solvent vapor of known pressure, p. The polymer absorbs solvent until equilibrium is established, x is related to p and V2, the volume fraction of polymer at equilibrium, by the Flory-Huggins equation (ll)... 

What is the physical significance of the x parameter in the Flory-Huggins theory How is it related to solute/solute and solute-solvent interactions ... 

Recently, a series of hexafluoro-isopropylidene-containing polyimides have become available, providing an opportunity to investigate the miscibility of pairs of closely related polyimides. The miscibility criteria of these fluoro-polyimides with one another and the use of the Flory-Huggins theory to predict the miscibility in these systems will be summarized. 

Flory-Huggins /u. The Flory-Huggins n value measures the interaction between polymer and solvent (plasticizer). It derives from the so-called lattice theory, which represents a statistical approach to the behavior of polymer molecules in solution (10, 14, 75, 16, 22). The n value may be experimentally determined for any polvmer-plasticizer system (where the plasticizer can dissolve the polymer) by osmotic pressure measurements according to the relation ... 

As pointed out in Chapter III, Section 1 some specific diluent effects, or even remnants of the excluded volume effect on chain dimensions, may be present in swollen networks. Flory and Hoeve (88, 89) have stated never to have found such effects, but especially Rijke s experiments on highly swollen poly(methyl methacrylates) do point in this direction. Fig. 15 shows the relation between q0 in a series of diluents (Rijke assumed A = 1) and the second virial coefficient of the uncrosslinked polymer in those solvents. Apparently a relation, which could be interpreted as pointing to an excluded volume effect in q0, exists. A criticism which could be raised against Rijke s work lies in the fact that he determined % in a separate osmotic experiment on the polymer solutions. This introduces an uncertainty because % in the network may be different. More fundamentally incorrect is the use of the Flory-Huggins free enthalpy expression because it implies constant segment density in the swollen network. We have seen that this means that the reference dimensions excluded volume effect. 

Taking into account the modes in which the water can be sorbed in the resin, different models should be considered to describe the overall process. First, the ordinary dissolution of a substance in the polymer may be described by the Flory-Huggins theory which treats the random mixing of an unoriented polymer and a solvent by using the liquid lattice approach. If as is the penetrant external activity, vp the polymer volume fraction and the solvent-polymer interaction parameter, the relationship relating these variables in the case of polymer of infinite molecular weight is as follows ... 

A modified Cahn-Hilliard (CH) model [114] is used for the theoretical analysis of the impact of thermal diffusion on phase separation by taking into account an inhomogeneous temperature distribution, which couples to a concentration variation via the Soret effect. The Flory-Huggins model is used for the free energy of binary polymer-mixtures. The composition is naturally measured in terms of volume fraction 0 of a component A, which can be related to the weight fraction c by... 

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