Homopolymer Flory-Huggins theory

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. 

We now illustrate how the moment method is applied and demonstrate its usefulness for several examples. The first two (Flory-Huggins theory for length-polydisperse homopolymers and dense chemically polydisperse copolymers, respectively) contain only a single moment density in the excess free energy and are therefore particularly simple to analyze and visualize. In the third example (chemically polydisperse copolymers in a polymeric solvent), the excess free energy depends on two moment densities, and this will give us the opportunity to discuss the appearance of more complex phenomena such as tricritical points. 

The tendency of differing blocks to microseparate from each other is quantified by Flory s chi parameter /, introduced in Chapter 2. An increasing, positive value of x implies an increasing tendency for the two chemically dissimilar species to segregate from each other. As discussed in Section 2.3.1.2, for a blend of two different homopolymers (A and B) of equal degree of polymerization Na — Ag at a 50/50 composition, the Flory-Huggins theory predicts that phase separation should occur at a critical value of Xc = For block... 

FIGURE 6.17 Solubility of a homopolymer according to the Flory-Huggins theory. Variables are the excluded volume parameter ft (or the polymer-solvent interaction parameter y), the net volume fraction of polymer q>, and the polymer-to-solvent molecular volume ratio q. Solid lines denote binodal, the broken line spinodal decomposition. Critical points for decomposition (phase separation) are denoted by . See text. 

The concepts derived from polymer solutions have been extended to considerations of polymer/polymer miscibility Scott [18] discussed the case of two homopolymers dissolved in a common solvent forming an equilibrium mixture and derived expressions for the free energy of mixing, using the Flory-Huggins theory... 

The Flory-Huggins theory provides an expression for the free energy density of mixing of two homopolymers labeled A andB [5-7]. 

In the case of copolymer solutions, the melting temperature also depends on interactions between the different monomeric imits and the solvent. Considering the case in which the crystalline phase is pure (i.e., only monomeric units of a single type crystallize and no solvent is present in the lattice), the decrease in the melting temperature can be derived in a similar manner as for the homopolymer solution case using the Flory-Huggins theory with an appropriate modification [15]. To take into accoimt the interactions between both comonomers and solvent, the net interaction parameter for binary copolymers should be calculated as follows ... 

A miscibility window was identified in the temperature-composition plane. The miscibility windows of polyphenylene oxide/orthochlorostyrene/parachlrostyrene (PPO/ oClS-pClS) and polyphenylene oxide/orthoflurostyrene-parafluorostyrene (PPO/oFS-pFS) were compared with each other. The maxima in the miscibility window of PPO/ oClS-pClS were found at the center of the composition axis, and the maxima in the PPO/oFS-pFS system were found skewed to the o-FS-rich side. The miscibility window was not observed for the PPO/o-bromostyrene and / -bromostyrene copolymer blend system. Kambour et al. [1] formulated a Flory-Huggins type theory for mixtures of homopolymers and random copolymers. They argued that such a system can be miscible for a suitable choice of the copolymer composition, without the presence of any specific interaction, because of a so-called repulsion between the two different monomers comprising the copolymer. 

Flory-Huggins mean-field theory. A similar mean-field theory successfully describes thermodynamics of polymer blends and, with some modifications, diblock copolymers and their blends with homopolymers. 

Experimentally, there are many miscible polymer pairs in which at least one of the components is a random copolymer but specific interactions are not present [40]. This phenomenon is attributed to the so-called intramolecular repulsion effect. Within the familiar Flory-Huggins description, and in the case of a random copolymer A Bi blended with a homopolymer C, three interaction parameters, Xab,Xac and Xbc are required to describe the enthalpy of mixing. Using a mean field theory, the mixture can be described in terms of one parameter XeS given by ... 

The solution properties of blocks and grafts are complicated since the copolymer components A and B behave differently in different solvents. In order to simplify the analysis, one usually starts with a solvent in which both A and B are soluble. In this case, the solution properties approach those of a homopolymer, for which accurate theories exist, e.g. in the thermodynamic treatment of Flory and Huggins (1, 2). The latter considers the free energy of mixing of pure polymer with pure solvent, AGmix in terms of two contributions, i.e. the enthalpy of mixing, A//mix, and the entropy of mixing, A mix, as follows ... 

---