The Flory-Huggins theory although chronologically speaking it should be known as the Huggins-Flory theory  for solutions of polymers was developed by Maurice L. Huggins  and Paul J. Flory   , following the work by Kurt H. Meyer .
The description can be easily generalized to the case of polymer mixtures. The Flory-Huggins theory defines the volume of a polymer system as a lattice which is divided into microscopic subspaces called sites of the same volume.
In the case of polymer solutions, the solvent molecules are assumed to occupy single sites, while a polymer chain of a given type, , occupies sites. The repulsive forces in the system are modelled by requiring each lattice site to be occupied by only a single segment. Attractive interactions between non-bonded sites are included at the lattice neighbour level.
Assuming random and ideal mixing, i. Applying the concept of regular solutions and assuming all pair interactions in the framework of a mean-field theory yields for the enthalpy of mixing Eq. According to the preceding equations, the Flory-Huggins equation can be expressed in terms of the Gibbs energy function of mixing for a binary system  :.
Although the theory considers as a fixed parameter, experimental data reveal that actually depends on such quantities as temperature, concentration, pressure , molar mass, molar mass distribution. From a theoretical point of view it may also depend on model parameters as the coordination number of the lattice and segment length.
For polymers of high molecular weight i. In this case, miscibility can only be achieved when is negative.
Assuming a temperature-dependent parameter, T vs. For long polymers, miscibility can only be achieved when. The parameter at the critical point can be obtained from the definition of the critical point and the Flory-Huggins expression for the free-energy of mixing. The result is. The parameter is somewhat similar to a second virial coefficient expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of.
A usual interpretation is that represents an enthalpic quantity and an entropic contribution, although both and are actually empirical parameters. According to this description, the systems should show an upper critical temperature.
Many polymer mixtures and solutions, however, show an increase of for increasing temperatures negative entropic contribution what implies the existence of a lower critical temperature.
From SklogWiki. Jump to: navigation , search. According to the preceding equations, the Flory-Huggins equation can be expressed in terms of the Gibbs energy function of mixing for a binary system  : where is the dimensionless Flory-Huggins binary interaction parameter similar to the van Laar heat of mixing  , which can be expressed as Eq.
The result is Therefore: Positive values of necessarily lead to immiscibility for polymer mixtures of high molecular weight. Polymer mixing always take place if the parameter is negative.
Flory–Huggins solution theory
Miscible polymer mixtures with negative exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.
Ep12 Flory Huggins Entropy and Enthalpy - UC San Diego - NANO 134 Darren Lipomi
Good solvent systems show significantly smaller positive values of , e. For polymer mixtures, should be referred to the arbitrarily chosen microscopic volume defined as a site, e.
Flory in Citation Classic 18 p. Balsara "Thermodynamics of Polymer Blends", in J.