Flory-Huggins theory thermodynamics

POLYMER BLEND THERMODYNAMICS FLORY HUGGINS THEORY AND ITS APPLICATION TO EXCIMER FLUORESCENCE STUDIES... 

We shall devote a considerable portion of this chapter to discussing the thermodynamics of mixing according to the Flory-Huggins theory. Other important concepts we discuss in less detail include the cohesive energy density, the Flory-Krigbaum theory, and a brief look at charged polymers. 

The wolume fraction emerges from the Einstein derivation at the natural concentration unit to describe viscosity. This parallels the way volume fraction arises as a natural thermodynamic concentration unit in the Flory-Huggins theory as seen in Sec. 8.3. 

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. 

The corresponding-states theory of polymer solution thermodynamics, developed principally by Prigogine and Flory, has provided a reliable predictive tool requiring only minimal information. We have seen here several examples of the use of the corresponding-states theory. We have also seen that the corresponding-states theory is a considerable improvement over the older Flory-Huggins theory. 

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 ... 

It should also be mentioned that polymer-solvent interactions can be characterized by the second virial coefficients that appear in equations (8) and (13) and by the free energy of interaction parameter Z1 that appears in the Flory-Huggins theory of polymer solution thermodynamics.1,61... 

The Flory-Huggins theory is generally applied to define the thermodynamic properties of a polymer solution (I). It gives an expression for experimentally obtainable quantities such as the partial molar free energy of mixing. 

The thermodynamic definition of the spinodal, binodal and critical point were given earlier by Eqs. (9), (7) and (8) respectively. The variation of AG with temperature and composition and the resulting phase diagram for a UCST behaviour were illustrated in Fig. 1. It is well known that the classical Flory-Huggins theory is incapable of predicting an LCST phase boundary. If has, however, been used by several authors to deal with ternary phase diagrams Other workers have extensively used a modified version of the classical model to explain binary UCST or ternary phase boundaries The more advanced equation-of-state theories, such as the theory... 

The solubility of hydrocarbons in rubbery polymers can be described in more detail by several theories of solutions using various criteria of thermodynamic affinity [7,25-28], of which the Flory-Huggins theory is the most popular one. It takes into account the volume content of the penetrant dissolved in the polymer and the change in the length of the polymer s thermodynamic segment as a result of dissolution [7]. However, it should be pointed out that to describe dissolution, a rehned dual-mode sorption model can be used, e.g., the model by Pace and Datyner [7,29,30]. 

Additionally, the parameters A and B are often found to depend weakly on chain lengths and composition. Shortcomings of the Flory-Huggins theory are usually lumped into the interaction parameter x- The Flory-Huggins equation (with all the corrections combined in x) contains all of the thermodynamic information needed to decide the equilibrium... 

Since the mean-field Flory-Huggins theory puts everything that is not understood about thermodynamics into the x parameter, this parameter is experimentally found to vary with composition and temperature. For solutions of linear polystyrene in cyclohexane, the interaction parameter... 

The effect of solvency for the polymer chain has been considered in the thermodynamic treatment of Flory and Huggins [6], usually referred to as the Flory- Huggins theory. This theory considers the free energy of mixing of a pure polymer with a pure solvent, in terms of two contributions, namely the enthalpy of... 

Most theoretical procedures for deriving expressions for AG iix start with the construction of a model of the mixture. The model is then analyzed by the techniques of statistical thermodynamics. The nature and sophistication of different models vary depending on the level of the statistical mechanical approach and the seriousness of the mathematical approximations that are invariably introduced into the calculation. The immensely popular Flory-Huggins theory, which was developed in the early 1940s, is based on the pseudolattice model and a rather low-level statistical treatment with many approximations. The theory is remarkably simple, explains correctly (at least qualitatively) a large number of experimental observations, and serves as a starting point for many more sophisticated theories. 

Using Flory-Huggins theory it is possible to account for the equilibrium thermodynamic properties of polymer solutions, particularly the fact that polymer solutions show major deviations from ideal solution behavior, as for example, the vapor pressure of solvent above a polymer solution invariably is very much lower than predicted from Raoult s law. The theory also accounts for the phase separation and fractionation behavior of polymer solutions, melting point depressions in crystalline polymers, and swelling of polymer networks. However, the theory is only able to predict general trends and fails to achieve precise agreement with experimental data. 

Equation 5.7 [10], where do, d[, 62 and d3 are fitting parameters, and d>B is the volume fraction of Component B, can produce all of the binary phase diagram types shown in Figure 5.1, when used either to lit experimental data in the context of the Flory-Huggins theory of thermodynamics or to express interaction energies calculated by atomistic simulations in a convenient manner as a function of the temperature and the component volume fractions. 

The pertinence of the Flory-Huggins theory (18) has been discussed in detail elsewhere (2), It continues to be used and is valuable in the study of thermodynamics of dilute solutions. It is of relatively little help in solving engineering and formulation problems. 

Thus it is clear that the term "clustering" can be used in a variety of situations, and is not precisely defined. In the present case, it will be used in the context of the statistical thermodynamic treatment of binary solutions developed by Zlmm ( ) and Zimm and Lundberg ( ), which provides a calculation of a cluster integral, and which can be extended to specify a cluster size for each component. In describing the role of the "clustering" theory in relationship to previously developed solution theories, such as the widely used Flory-Huggins theory ( ), Zimm and Lundberg point out that "Our considerations are not intended as a replacement for the previous theories, but as... 

In polymer solutions or blends, one of the most important thermodynamic parameters that can be calculated from the (neutron) scattering data is the enthalpic interaction parameter x between the components. Based on the Flory-Huggins theory [41. 42], the scattering intensity from a polymer in a solution can be expressed as... 

Any discussion of the role played by polymers, whether free or attached, in stabilizing colloidal dispersions must inevitably be couched in terms of polymer solution thermodynamics. The earliest, and still the best known, theory of polymer solution thermodynamics was that set forth by Flory (1941 1942) and Huggins (1941 1942a,b). Despite its serious inadequacies, which will be detailed later, the Flory-Huggins theory has had such a profound impact on polymer science that Manfred Gordon has properly referred to it as a paradigm of polymer science . It embodies concepts that remain central to the theory of polymer solution thermodynamics whilst ignoring certain features that are vital to the explanation of the entire spectrum of observed phenomena. 

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