Flory-Huggins theory mixing enthalpy

Numerical parameter employed in the Flory-Huggins theory, to account for the contribution of the noncombinatorial entropy of mixing and the enthalpy of mixing to the Gibbs energy of mixing. 

Outline how the Flory-Huggins theory accounts for enthalpy of mixing. 

To calculate AWm (the enthalpy of mixing) the polymer solution is approximated by a mixture of solvent molecules and polymer segments, and AW is estimated from the number of 1,2 contacts, as in Section 12.2.1. The terminology is somewhat different in the Flory-Huggins theory, however. A site in the liquid lattice is assumed to have z nearest neighbors and a line of reasoning similar to that developed above for the solubility parameter model leads to the expression... 

The effect of solvency for the polymer chain has been considered in the thermodynamic treatment of Flory and Huggins [6], usually referred to as the Flory- Huggins theory. This theory considers the free energy of mixing of a pure polymer with a pure solvent, in terms of two contributions, namely the enthalpy of... 

Mathematically, the sorption data for the amorphous acrylic pol)nners which will be considered here cannot be correlated by a single parameter sorption Isotherm. In the Flory-Huggins theory, the parameter is the Interaction parameter, which for the simplest possible case characterizes the enthalpy of mixing which results from the Intermolecular bonding mismatch between polymer and water. A two parameter sorption Isotherm provides an excellent vehicle for data treatment. The two parameters can be identified as the interaction parameter and a clustering parameter. 

The enthalpy of mixing is introduced into the Flory-Huggins theory in the spirit of the classical van Laar approach. The mixing can be considered as a quasichemical reaction between solvent contacts and segment contacts l-l+2-2-2(l-2)... 

The subscript 1, referring to the solvent, is used here because )j,A ris just the difference in energy of a solvent molecule immersed in pure polymer compared with that in pure solvent. Note that Xi is pivotal parameter in Flory-Huggins theory. With these relationships, the enthalpy of mixing can be expressed as... 

The simple Flory-Huggins theory discussed above is based on a series of questionable assumptions lattice sites of equal size for solvent segments and polymer monomeric units, uniform distribution of the monomeric units in the lattice, random distribution of the molecules, and the use of volume fractions instead of surface-area fractions in deriving the enthalpy of mixing. Proposed improvements, however, have led to more complicated equations or to worse agreement between theory and experiment. Obviously, various simplifications in the Flory-Huggins theory are self-compensating in character. 

Flory-Huggins theory This theory calculates the free energy of mixing of pure amorphous polymers with pure solvent. The entropy and the enthalpy of mixing can be calculated separately, and the following relationship applies ... 

The Flory-Huggins theory considers the free energy of mixing of pure polymer with pure solvent, AG ix, in terms of two contributions the enthalpy of mixing, AH,, and the entropy of mixing AS a ... 

The Flory — Huggins theory considers that the two components, i.e. solute and solvent, have identical local structures thus it does not take account of the influence of structural characteristics of components on the thermodynamic properties of the mixture. Therefore (a) the volume change at mixing, is zero and (b) the enthalpy of mixing may be assigned only to the differences in contact energies. 

The same positive AH, which arises from interactions between different species, usually prevails in polymer mixtures and most polymer pairs are mutually immiscible. The strengths of the interactions between components is usually expressed in terms of an interaction parameter Xab (Eq- 3), which originates from Flory-Huggins theory of polymer solutions. The enthalpy of mixing, or interaction energy term, arises in a van Laar type expression of heats of mixing and is of the form... 

In real systems, nonrandom mixing effects, potentially caused by local polymer architecture and interchain forces, can have profound consequences on how intermolecular attractive potentials influence miscibility. Such nonideal effects can lead to large corrections, of both excess entropic and enthalpic origin, to the mean-field Flory-Huggins theory. As discussed in Section IV, for flexible chain blends of prime experimental interest the excess entropic contribution seems very small. Thus, attractive interactions, or enthalpy of mixing effects, are expected to often play a dominant role in determining blend miscibility. In this section we examine these enthalpic effects within the context of thermodynamic pertubation theory for atomistic, semiflexible, and Gaussian thread models. In addition, the validity of a Hildebrand-like molecular solubility parameter approach based on pure component properties is examined. 

The entropy and enthalpy change on mixing are, according to the modified Flory-Huggins theory, given by ... 

The most relevant theory for modeling the free energy of binary polymer mixtures is the Flory-Huggins theory, initially employed for solvent-solvent and polymer-solvent mixtures. This theory was independently derived by Flory [4, 5] and Huggins [6, 7]. The key equation (combined from discussions earlier in this chapter on entropy and enthalpy of mixing) is ... 

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