Flory-Huggins free energy

Considering an (incompressible) polymer mixture with volume fraction (j)A = (j) of A-monomers and volume fraction (j)B = 1 - (j) of B monomers, the mean-field expression for the excess-free energy of mixing is given by the well-known Flory-Huggins expression " ... 

The symbol Xs stands for the interaction energy per solvent molecule divided by kT. Combining equations (5.7) and (5.8) gives the Flory-Huggins equation for the free energy of mixing of a polymer solution ... 

Flory-Huggins model for polymer solutions, based on statistical thermodynamics, is often used for illustrating the behavior of polymer blends [6,7]. The expression for the free energy change... 

To calculate the liquid-liquid coexistence curves, we cast Eq. 5 in the standard Flory-Huggins form where all terms linear in 0 are subtracted. The free-energy expression then becomes... 

The experimental thickness measurements may also be compared with theoretical results based on profiles generated by the S.F., Scheutjens Fleer, theory (11). For this calculation we use a value for xs °f 1 (net adsorption free energy), for x of 0.45 (experimental value of the Flory-Huggins parameter) and a polymer solution concentration of 200 ppm. Although the value for xs seems rather arbitrary it has been shown (10) that 6jj is insensitive to this parameter. 

However, let note, that the assumption about independence of the osmotic pressure of semi-diluted solutions on the length of a chain is not physically definitely well-founded per se it is equivalent to position that the system of strongly intertwined chains is thermodynamically equivalent to the system of gaped monomeric links of the same concentration. Therefore, both Flory-Huggins method and Scaling method do not take into account the conformation constituent of free energy of polymeric chains. 

Any parameter that influences either the enthalpy or the entropy of the system might change the free energy in such a manner that phase separation occurs. For a system like those studied here, being composed of a polymer and a solvent, the entropy of mixing, AS, has been calculated independently by Flory [53,55,56] and Huggins [57,58] based on the lattice model. It is assumed that each solvent molecule occupies one cell of the lattice. The volume of the smallest unit serves as reference volume. It is stated that the macromolecule can be composed of ad-... 

There have been many attempts to describe the process of mixing and solubility of polymer molecules in thermodynamic terms. By assuming that the sizes of polymer segments are similar to those of solvent molecules, Flory and Huggins derived an expression for the partial molar Gibbs free energy of dilution that included the dimensionless Flory Higgins interaction parameter X = ZAH/RT, where Z is the lattice coordination number. It is now... 

Fint is the free energy of non-Coulomb interactions of monomer units. Finl can be expressed, for example, in terms of the Flory-Huggins lattice theory [21]. In the general case, when network is immersed in solvent which includes 1 different components some of which can be polymeric with the degree of polymerization Pi(Pi 1, i = L 2,... k), Fim in the Flory-Huggins theory has the following form [21-22] ... 

Accepting the conventional Flory-Huggins treatment, one deduces then the free energy of polymerization, A G1(S, of a liquid monomer into solid monomer to be... 

Recently Leonard and Ivin (28) have pointed out that the application of equation (1) is valid only if the mixture of monomer and polymer behaves ideally over the range of compositions covered by the experiment. They reexamined some of the early data, making allowance for non-ideal mixing by use of the Flory-Huggins expression. They derived a equation for the free energy of polymerization in terms of the volume fractions of the polymer and monomer, tp2 and polymer-monomer interaction parameter ... 

Micelle formation in solutions of an AB diblock in low-molecular-weight A homopolymer has been considered by Leibler et al. (1983), using Flory-Huggins theory to determine the free energy of mixing of micelles. This model is discussed in detail in Section 3.4.2. 

Of course, it is uncommon for the free energy/ to obey (1). In particular, the entropy of an ideal mixture (or, for polymers, the Flory-Huggins entropy term) is definitely not of this form. On the other hand, in very many thermodynamic (especially mean field) models the excess (i.e., nonideal) part of the free energy does have the simple form (1). In other words, if we decompose the free energy as (setting kn = 1)... 

---