Flory-Huggins free-energy function

The de Gennes-Flory-Huggins-Free Energy-Functional.197... 

The first theories for this phenomenon used the simple forms for the Flory-Huggins free energy functional discussed in Sect. 2.3, and augmented them by a local boundary condition at the surface [124,125], Denoting A as the surface area of the wall, the free energy functional per unit area then is, cf. Eq. (47)... 

The crystalUzation step in Crystaf and Tref, however, occms in dilute solution. Theoretically, this situation is more compUcated because polymer segments are nonuniformly distributed through the solution. Strictly speaking, for dilute solutions the Flory-Huggins free-energy function shown in... 

When the extrapolation q - 0 is carried out in (6.47), noting that D(0) = 1, we obtain an expression that is identical to (6.23) derived in Section 6.1.1.3 on the basis of the Flory-Huggins free energy of mixing. This shows that the assumptions embodied in (6.47) are essentially equivalent to those in the Flory-Huggins theory. Using the approximation for the Debye function given by (5.33), Equation (6.47) can be written as... 

This chapter presents a general theoretical framework for the stndy of polymer solutions in which polymers are associated with each other by strongly attractive forces, such as hydrogen bonding and hydrophobic interaction. The Flory-Huggins free energy is combined with the free energy of association (reversible reaction) to study the mutual interference between phase separation and molecular association. The effective interaction parameters renormalized by the specific interactions are derived as functions of the polymer concentration. 

An immiscible polymer pair is implemented in this numerical modeling. The degree of polymerization was chosen as 100, according to experimental data. The interaction parameter, Xij> in the Flory-Huggins free energy for polymers can be evaluated as a function of temperature in a binary case. In a ternary phase separation, the critical value of the interaction parameter for spinodal decomposition to occur between two polymers can be estimated as ... 

The interpretation of the Flory-Huggins interaction parameter as a residual free energy function [14] rather than the original enthalpy parameter allows separation into enthalpic and entropic contributions... 

A Cahn-Hilliard description of the interface and surface behavior can be adopted. For a symmetric, incompressible, binary blend in the bulk the excess free energy functional takes the simple Flory-Huggins-de Germes form ... 

Whitmore and Noolandi [101] derived the structural parameters of monodis-persed AB diblock copolymer micelles within an A homopolymer by minimizing a simple free energy functional. The CMC was calculated and shown to be dominated by an exponential dependence on (x is the Flory-Huggins interaction parameter and Nb the degree of polymerization of the B block of the copolymer). The importance of diblock copolymer composition was emphasized as well. The CMC was calculated as ... 

The free energy of the two surface system is calculated from the partition function expressed in terms of Flory-Huggins solution theory. The Helmholtz free energy per site, relative to pure solvent, and at constant [Pg.175]

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