Flory-Huggins lattice theory

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] ... 

A wide variety of theories have been developed for polymer solutions over the later half of the last century. Among them, lattice model is still a convenient starting point. The most widely used and best known is the Flory-Huggins lattice theory (Flory, 1941 Huggins, 1941) based on a mean-field approach. However, it is known that a mean-field approximation cannot correctly describe the coexistence curves near the critical point (Fisher, 1967 Heller, 1967 Sengers and Sengers, 1978). The lattice cluster theory (LCT) developed by Freed and coworkers (Freed, 1985 Pesci and Freed, 1989 Madden et al., 1990 Dudowicz and Freed, 1990 Dudowicz et al., 1990 Dudowicz and Freed, 1992) in 1990s was a landmark. 

A thermodynamic approach was put forward by one of us (10), based on the Flory-Huggins lattice theory of a polymer solution the chemical potentials of each monomer must be equal in each phase copolymerization increment causes a little change in the chemical potential in the particles diffusion of monomers from the water phase will reequilibrate the system and in turn diffusion from droplets to water phase takes place. For instance, expression from monomer 1 in the particles is ... 

On the other hand, the Flory-Huggins lattice theory (Flory, 1953) predicts for polymer solutions ... 

Despite the drawbacks, Flory-Huggins lattice theory was a major step forward towards understanding the thermodynamics of polymer solutions and is the basis of many other theories. Since it was first proposed, other workers have elaborated on it to improve on the assumptions involved. Some of these more refined theories will be given brief consideration, but in general are beyond the scope of the book. 

Flory-Huggins Lattice Theory and Related Theories... 

Flory-Huggins Lattice Theory of Polymer Solutions... 

Basic Assumptions of Flory-Huggins Lattice Theory... 

The infortnation provided in this chapter can be divided into four parts 1. introduction, 2. thermodynamic theories of polymer blends, 3. characteristic thermodynamic parameters for polymer blends, and 4. experimental methods. The introduction presents the basic principles of the classical equilibrium thermodynamics, describes behavior of the single-component materials, and then focuses on the two-component systems solutions and polymer blends. The main focus of the second part is on the theories (and experimental parameters related to them) for the thermodynamic behavior of polymer blends. Several theoretical approaches are presented, starting with the classical Flory-Huggins lattice theory and, those evolving from it, solubility parameter and analog calorimetry approaches. Also, equation of state (EoS) types of theories were summarized. Finally, descriptions based on the atomistic considerations, in particular the polymer reference interaction site model (PRISM), were briefly outlined. 

The Flory-Huggins lattice theory is originally developed to describe the solubility of a crystalline material in a solvent and can be derived to describe the relationship between drug and polymer, in which the polymer is the substitute of the solvent and the relationship is illustrated by Eqs. 16.5 and 16.6 ... 

Y vj.i. aiiu wiui 0,5, the curves for the swelling capacity calculated applying an ideal entropy coincide with those obtained using the combinatorial entropy of Flory-Huggins lattice theory. 

It has been widely confirmed with numerous experiments that polymer solutions reveal remarkable deviation from the behaviour expected for an ideal solution [5]. According to the Flory-Huggins lattice theory of polymer solutions [6,7], Apo is given by ... 

Another approach has been used by Tanaka and Ushiki. These authors used a simple Flory argument for the self-crosslinked molecule in solution. To account for the elastic and solution properties a combination of the Flory-Huggins lattice theory and phantom rubber model has been applied to the microgel. 

Phase Equilibrium (PE) Binary mixtures of a polymer in a single solvent phase-separate at various temperatures, Tsep, depending on the volmne fi-action (/12 of the polymer. The maximmn of the 7 sep=/(< 2) fiuiction is called the critical solution temperature Test-The experiment is repeated for a series of dilute solutions of polymers of the same constitution and configmation but of different molar mass. The relation between the eritieal solution temperature and the molar mass of the polymer is based on the Flory-Huggins lattice theory which predicts that... 

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