Flory-Huggins interaction parameter blended polymer thermodynamics

IGC was used to determine the thermodynamic miscibility behavior of several polymer blends polystyrene-poly(n-butyl methacrylate), poly(vinylidene fluoride)-poly(methyl methacrylate), and polystyrene-poly(2,6-dimethyl-1,4-phenylene oxide) blends. Specific retention volumes were measured for a variety of probes in pure and mixed stationary phases of the molten polymers, and Flory-Huggins interaction parameters were calculated. A generally consistent and realistic measure of the polymer-polymer interaction can be obtained with this technique. 

The usefulness of inverse gas chromatography for determining polymer-small molecule interactions is well established (1,2). This method provides a fast and convenient way of obtaining thermodynamic data for concentrated polymer systems. However, this technique can also be used to measure polymer-polymer interaction parameters via a ternary solution approach Q). Measurements of specific retention volumes of two binary (volatile probe-polymer) and one ternary (volatile probe-polymer blend) system are sufficient to calculate xp3 > the Flory-Huggins interaction parameter, which is a measure of the thermodynamic... 

Flory-Huggins Approach. One explanation of blend behavior lies in the thermodynamics of the preceding section, where instead of a polymer-solvent mixture, we now have a polymer-polymer mixture. In these instances, the heat of mixing for polymer pairs (labeled 1 and 2) tends to be endothermic and can be approximated using the solubility parameter. The interaction parameter for a polymer-polymer mixture, Xi2, can be approximated by... 

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... 

The values of the 5 -components can be calculated for any chemical substance from the tabulated group and bond contributions. Once 8j is known for both polymers in the blend, the Huggins-Flory binary thermodynamic interaction parameter, can be calculated from ... 

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 binary interactirMi generally refers to the interactions between polymer-polymer and polymer-solvent The nature of solvent-polymer interaction plays an important role in the miscibility of blends. Many thermodynamic properties of polymer solutions such as solubility, swelling behavior, etc., depend on the polymer-solvent interaction parameter (y). The quantity was introduced by Flory and Huggins. Discussions of polymer miscibility usually start with Flory-Huggins equation for free energy of mixing of a blend (refer to Chap. 2, Thermodynamics of Polymer Blends ). 

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 real systems, nonrandom mixing effects, potentially caused by local polymer architecture and interchain forces, can have profound consequences on how intermolecular attractive potentials influence miscibility. Such nonideal effects can lead to large corrections, of both excess entropic and enthalpic origin, to the mean-field Flory-Huggins theory. As discussed in Section IV, for flexible chain blends of prime experimental interest the excess entropic contribution seems very small. Thus, attractive interactions, or enthalpy of mixing effects, are expected to often play a dominant role in determining blend miscibility. In this section we examine these enthalpic effects within the context of thermodynamic pertubation theory for atomistic, semiflexible, and Gaussian thread models. In addition, the validity of a Hildebrand-like molecular solubility parameter approach based on pure component properties is examined. 

Biros, et al. [47] compared the predictions of both the equation of state and modified solubility parameter approaches for the dependence of the binary interaction parameter on temperature, pressure, solvent chain length, and polymer flexibility. Both treatments gave qualitatively similar predictions with values of x based on solubility parameters always lower than the equatiiS of state predictions. Quantitative agreement between the two approaches could be achieved if an entropic correction term, represented by a in Eq. (31), were employed. Thus, this modified Flory-Huggins approach should provide a good representation of the equilibrium thermodynamic state of the blends. 

Due to their technological importance, polymer blends have attracted considerable attention during the past decade. For thermodynamic reasons, most polymer pairs are immiscible and their degree of compatibility is of underlying importance to the microphase structure and consequently, to the mechanical properties of the blend. The Flory-Huggins x interaction parameter for the polymer pair plays a dominant role in explaining critical phase behavior of a compatible pair and in estimating interfacial tension and interfacial thickness for semicompatible or incompatible pairs. Direct measurement of this parameter is not always possible, thus the obtained information, in conjunction with suitable theoretical models of polymer solutions may lead to an assessment of the interaction parameters for the actual polymeric case. 

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