Thermodynamics Flory-Huggins model

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... 

If we turn from phenomenological thermodynamics to statistical thermodynamics, then we can interpret the second virial coefficient in terms of molecular parameters via a model. We pursue this approach for two different models, namely, the excluded-volume model for solute molecules with rigid structures and the Flory-Huggins model for polymer chains, in Section 3.4. 

Our discussion here explores active connections between the potential distribution theorem (PDT) and the theory of polymer solutions. In Chapter 4 we have already derived the Flory-Huggins model in broad form, and discussed its basis in a van der Waals model of solution thermodynamics. That derivation highlighted the origins of composition, temperature, and pressure effects on the Flory-Huggins interaction parameter. We recall that this theory is based upon a van der Waals treatment of solutions with the additional assumptions of zero volume of mixing and more technical approximations such as Eq. (4.45), p. 81. Considering a system of a polymer (p) of polymerization index M dissolved in a solvent (s), the Rory-Huggins model is... 

Section 16.3 reviews the basics of polymer thermodynamics, discusses the differences compared to thermodynamics of systems having only low-molecular-weight compounds, and finally gives an overview of the Flory-Huggins model, which has been considered one of the cornerstones of polymer thermodynamics. 

The solubility parameter is a very important property in science and has found widespread use in many fields and not just in the smdy of polymer-solvent thermodynamics. It is connected to the Flory-Huggins model as well, as explained in Section 16.3.3.2, but can also be used independent of it, as discussed in Sections 16.3.3.1 and 16.3.3.3. Several handbooks and reference books provide extensive lists of solubility parameters of numerous chemicals.The solubility parameter is defined as... 

The solid curves in Fig. 5 are the results of a thermodynamic analysis based on a Flory-Huggins model for the interaction between the monomer and polymer and a phenomenological curvature energy model to describe the chemical potential of the monomer in the micelle [30]. 

DE2 DeSousa, H.C. and Rebelo, L.P.N., A continuous polydisperse thermodynamic algorithm for a modified Flory-Huggins model The (polystyrene + nitroethane) example, J. Polym. Sci. PartB Polym. Phys., 38, 632, 2000. 

Recently, phase behaviour of mixtures consisting of a polydisperse polymer (polystyrene) and nematic liquid crystals (p-ethoxy-benzylidene-p-n-butylani-line) was calculated and determined experimentally. The former used a semi-empirical model based on the extended Flory-Huggins model in the framework of continuous thermodynamics and predicted the nematic-isotropic transition. The model was improved with a modified double-lattice model including Maier-Saupe theory for anisotropic ordering and able to describe isotropic mixing. ... 

In the preceding chapter we have, based on the Flory-Huggins theory, discussed the basis for the phase behavior of polymer blends. Miscible polymer blends and polymer solutions have, even in the mixed one-phase system, spatial variations in the polymer concentration. These concentration fluctuations reflect the thermodynamic parameters of the free energy, as described in the Flory-Huggins model. 

The thermodynamic properties of an A + B polymer mixture in the fluid state are usually described by the Flory-Huggins model the chains are inscribed on a lattice, all sites being filled either by a monomer A (probability (j) ) or by a monomer B (probability 1 - ( )). The free energy... 

The formation mechanism of structure of the crosslinked copolymer in the presence of solvents described on the basis of the Flory-Huggins theory of polymer solutions has been considered by Dusek [1,2]. In accordance with the proposed thermodynamic model [3], the main factors affecting phase separation in the course of heterophase crosslinking polymerization are the thermodynamic quality of the solvent determined by Huggins constant x for the polymer-solvent system and the quantity of the crosslinking agent introduced (polyvinyl comonomers). The theory makes it possible to determine the critical degree of copolymerization at which phase separation takes place. The study of this phenomenon is complex also because the comonomers act as diluents. 

From a thermodynamic point of view, the heteropolymer globule in hand represents a subsystem which is composed of a macromolecule involving lu l2 units Mi, M2 and molecules of monomers Mi, M2 whose numbers are Mi,M2. Among these variables and volume fractions a in the framework of the simplest Flory-Huggins lattice model there are obvious stoichiometric relationships... 

Futerko and Hsing presented a thermodynamic model for water vapor uptake in perfluorosulfonic acid membranes.The following expression was used for the membrane—internal water activity, a, which was borrowed from the standard Flory—Huggins theory of concentrated polymer solutions ... 

The authors discuss Schroeder s paradox, referred to elsewhere in this review, and the fact that liquid water uptake increases but saturated water uptake decreases with temperature. And, at low temperature, the water uptake by membranes in contact with saturated vapor is greater than that by membranes in contact with liquid water, which suggests a fundamental difference in membrane microstructure for the two situations. An energy level diagram of thermodynamic states versus temperature was proposed, based on this Flory—Huggins-based model. 

Another important application of experimentally determined values of the osmotic second virial coefficient is in the estimation of the corresponding values of the Flory-Huggins interaction parameters x 12, X14 and X24. In practice, these parameters are commonly used within the framework of the Flory-Huggins lattice model approach to the thermodynamic description of solutions of polymer + solvent or polymer] + polymer2 + solvent (Flory, 1942 Huggins, 1942 Tanford, 1961 Zeman and Patterson, 1972 Hsu and Prausnitz, 1974 Johansson et al., 2000) ... 

Current thermodynamic theories for polymer systems are combinations of the Flory -Huggins, Guggenheim, and Equations-of-State approaches. All of these theories make use of empirical parameters and are based on assumptions about the underlying molecular model. 

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)... 

For a higher accuracy of the isotherm, the activities in the liquid phase instead of the concentrations can be used. If a thermodynamic model for the computation of the solid-phase activities exists, the equilibrium concentration q and qi can also be calculated from the condition of equal activity, as was done for example for the esterification of acetic acid on Amberlyst 15 using the Flory-Huggins activity model for the solid phase and a UNI FAC model for the liquid phase [17]. 

---