Flory-Huggins description, thermodynamics

In the Flory-Huggins description of polymer melt thermodynamics, the interactions between segments, depending only on the local concentration of the different types of chemical functions, constitute the enthalpy contribution, whereas the entropy is a non-local contribution, depending on the number of allowed conformation of the entire copolymer chains [27, 28]. Entropy is related to elasticity and will be optimized when all tensions are released within the chains. 

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) ... 

SCFT today is one of the most commonly used tools in polymer science. SCFT is based on de Gennes-Edwards description of a polymer molecule as a flexible Gaussian chain combined with the Flory-Huggins "local" treatment of intermolecular interactions. Applications of SCFT include thermodynamics of block copolymers (Bates and Fredrickson, 1999 Matsen and Bates, 1996), adsorption of polymer chains on solid surfaces (Scheutjens and Fleer, 1979,1980), and calculation of interfacial tension in binary polymer blends compatibilized by block copolymers (Lyatskaya et al., 1996), among others. 

The simplest description of swelling is based on equilibrium thermodynamics (Equation 25.21), and considers as the driving force the affinity of the monomer to the polymer via the Flory-Huggins theory of polymer solutions and as counteracting contribution the increase in the interfacial free energy due to the growth of swelling particles. Equation 25.21 was derived by Morton-Kaizerman-Altier (MKA equation) over 50 years ago [22, 23] ... 

Thus we have strong experimental evidence that Flory-Huggins theory is inadequate as a quantitative description of mixing thermodynamics in polymer mixtures. From a theoretical point of view we can see four potential sources of error. 

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. 

Although Flory-Huggins theory does not give an accurate description of polymer blends, it identifies the origins of polymer-polymer immiscibility and usually forms the basis of discussions interaction parameters are usually calculated assuming its applicability. For a more accurate description of the thermodynamics of mixing it is necessary to use a more complete equation-of-state theory [37,38]. 

In this section the basic principles of membrane formation by phase inversion will be described in greater detail. All phase inversion processes are based on the same thermodynamic principles, since the starting point in all cases is a thermodynamically stable solution which is subjected to demixing. Special attention will be paid to the immersion precipitation process with the basic charaaeristic that at least three components are used a polymer, a solvent and a nonsolvent where the solvent and nonsolvent must be miscible with each other. In fact, most of the commercial phase inversion membranes are prepared from multi-component mixtures, but in order to understand the basic principles only three component systems will be considered. An introduction to the thermodynamics of. polymer solutions is first given, a qualitatively useful approach for describing polymer solubility or polymer-penetrant interaction is the solubility parameter theory. A more quantitative description is provided by the Flory-Huggins theory. Other more sophisticated theories have been developed but they will not be considered here. 

A convenient method of describing the solubility of organic vapours and liquids in polymers is via Flory-Huggins thermodynamics (11], a detailed description having already... 

Polymer blends. Although it is well known that the mean-field Flory-Huggins theory of the thermodynamics of polymer systems is not a rigorously accurate description, especially for polymer blends, it is sufficiently valid that its use does not incur serious errors. Furthermore, de Gennes [16] used the mean-field random-phase approximation to obtain the scattering law for a binary polymer blend as ... 

Wolf BA (2003) Chain connectivity and conformational variability of polymers clues to an adequate thermodynamic description of their solutions II Composition dependence of Flory-Huggins interaction parameters. Macromol Chem Phys 204 1381... 

The classical thermodynamics of binary polymer-solvent systems was developed independently by P. J. Flory (1-3) and M. L. Huggins (4-6). It is based on the well-known lattice model qualitatively formulated by K. H. Meyer (7), who pointed out the effect of the differences in molecular size of polymer and solvent molecules on the entropy of mixing. The quantitative calculation of the entropy of mixing led to the introduction of a dimensionless quantity, the so-called Flory-Huggins interaction parameter for the thermodynamic description of polymer solutions. 

Thermodynamic descriptions of polymer systems are usually based on a rigid-lattice model published in 1941 independently by Staverman and Van Santen, Huggins and Flory where the symbol x(T) is used to express the binary interaction function [16]. Once the interaction parameter is known we can calculate the liquid liquid phase behaviour. 

Only a short description of the basic theory is given here, so that experimental results can be interpreted qualitatively. A more detailed mathematical treatment can be found elsewhere (Flory, 1953). The basic theory for interpreting the thermodynamic properties of polymer solutions is that due to Flory and Huggins (Flory, 1953). According to this theory the chemical potential is given by ... 

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