Polymer thermodynamic

The close molecular packing makes diffusion more difficult than with amorphous polymers compared in similar circumstances, i.e. both below Tg or both above (but below of the crystalline polymer). Thermodynamic considerations lead to considerable restriction in the range of solvents available for such polymers. 

Polymer thermodynamics is a supporting science that has proved to be very successful owing to its intensive interactions with neighbouring disciplines. The future of polymer thermodynamics will thus strongly depend on developments made in these neighbouring research areas [59]. 

Over the past decade, SCFT was often applied to analyze the problem of particle dispersion in polymers (thermodynamics of nanocomposites). Vaia and Giannelis (1997a, 1997b) formulated a simple version of SCFT... 

Chapter 2 is an in depth discussion of the various theories important to phase equilibria in general and polymer thermodynamics specifically. First a review of phase equilibria is provided followed by more specific discussions of the thermodynamic models that are important to polymer solution thermodynamics. The chapter concludes with an analysis of the behavior of liquid-liquid systems and how their phase equilibrium can be correlated. 

McMaster, L. P., "Aspects of Polymer-Polymer Thermodynamics," Macromolecules, 6, 760 (1973). 

Polymer thermodynamics plays an important role in a large number of processes and the design of many different products that are are based on polymers. In these applications, knowledge of phase equilibria is crucial for systems involving polymer solutions and polymer blends. We mention here a few examples of such applications ... 

This chapter presents the basics of polymer thermodynamics and some important thermodynamic models, which can be useful for the design/understanding of the processes and the products discussed above and many others. 

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. 

BASIC CONCEPTS AND MODELS IN POLYMER THERMODYNAMICS 16.3.1 Phase Equilibria Principles Applied to Polymers... 

The molar activity coefficient y, shown in Equations 16.20 and 16.21, is not always a suitable quantity in polymer thermodynamics. Molar activity coefficients can reach very low values, especially at very high polymer molecular weights. More convenient is the weight fraction activity coefficient (Qj), which is the ratio of the activity to the weight fraction ... 

Since 1980 polymer thermodynamics has been developed considerably and, to date, models are available that are suitable for at least satisfactory calculations of VLE and, qualitatively, also for LLE. Some of these methods are models for the activity coefficient, which are modifications of the FH equation. These modifications use a similar to FH but better combinatorial/free-volume expression and a local-composition-type energetic term such as those found in the UNIQUAC and UNIFAC models. Models like the UNIFAC-FV and the Entropic-FV are discussed in Section 16.4. 

The free-volume (FV) concept has a special importance in polymer thermodynamics. FV is the volume allocated to the molecules for movement when their own volume is substracted. Patterson,in his excellent review on FV, offers a qualitative description of the relationship between FV and polymer solubility. Elbro demonstrated, using a simple defiiution for the FV (Equation 16.46), that the FV percentages of solvents and polymers are different. It is exactly these differences in FV (or expansivities), which were ignored in early theories like the famous FH equation, hi the typical case, the FV percentage of solvents is greater (40 to 50%) than that of polymers (30 to 40%). There are two exceptions to this rule water and Water has lower FV than other solvents and closer to that of most... 

Attempting to summarize in few words the current status in polymer thermodynamics, we could state the following ... 

Most theoretical/modeUng studies in polymer thermodynamics are limited to ... 

Some of the future challenges in the area of polymer thermodynamics will involve the following ... 

Closer collaboration with indnstry, e.g., for testing existing theories for polymers with novel strnctnres, for commercial polymers for which so far the structure is not revealed to academic researchers, and for many other applications of practical interest. Many indnstrial systems are much more complex than the systems studied in academia. Closer collaboration in the future between academia and the polymer and paint/adhesives indns-tries may farther help the advancements in the area of polymer thermodynamics in the coming years. 

Fried, J.R., Jiang, J.S., andYeh, E., Group-contribution methods in polymer thermodynamics, Comput. Polym. ScL, 2, 95, 1992. 

This remarkably simple expression is the famous Floiy-Hug ns equation for the Gibbs free energy of mixing, which has been the cornerstone of polymer thermodynamics for more than five decades. 

Over the years, many versions of the EoS theories have been proposed. Several comprehensive reviews of the EoS s used in the polymer thermodynamics have been published. For example, Curro [1974] discussed applications of EoS within a full range of materials and variables, viz. to crystals, glasses, molten polymers and monoatomic liquids. The review discusses fundamentals of the theories as well as it provides a list of available experimental data. The comparison between different EoS was made on two levels, first by comparing the derived expressions for physical quantities (e.g., the characteristic reducing parameters, cohesive energy density, or internal pressure), then comparing how well the EoS describes the observed PVT dependencies for polymers. 

Since this chapter is not intended to be a review of polymer thermodynamics, but to provide information on diverse thermodynamic aspects pertinent to polymer blends, only EoS derived by Simha and Somcynsky [1969], will be discussed in some detail. 

VIL Vilcu, R. and Leca, M., Polymer Thermodynamics by Gas Chromatography, Elsevier, Amsterdam, 1989. 

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