Volume polymer thermodynamics

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... 

Long chain branched polyethylene, commonly termed low density polyethylene typifies this class of polymers. Thermodynamic measurements, such as heat capacity (148,149) and specific volume,(150,151) indicate that long chain branched... 

The aforementioned list shows some of the many applications where polymer thermodynamics plays a key role. Polymer solutions and blends are complex systems frequent existence of liquid-liquid equilibria (LLE) (UCST, LCST, closed loop, etc.), the significant effect of temperature and polymer molecular weight including polydispersity in phase equilibria, free-volume (FV) effects, and other factors may cause difficulties. For this reason, many different models have been developed for polymer systems and often the situation may seem rather confusing to the practicing engineer. 

The importance of excluded volume in thermodynamics of polymer solutions is discussed later in terms of virial coefficients. 

This work offers a contribution to the understanding of some fundamental aspects of sorption and diffusion in glassy polymers. The research focuses on an extensive experimental study of sorption and mass transport in a specific polymeric matrix. A high free volume polymer, (poly l-trimethylsilyl-l-propyne) [PTMSP], has been used here in order to emphasise aspects of sorption and transport which are peculiar to polymer/penetrant mixtures below the glass transition temperature. The discussion of the experimental data presented in this work permits a clarification of concepts which are of general validity for the interpretation of thermodynamic and mass transport properties in glassy systems. 

The title of this chapter is somewhat misleading. In one sense it is too broad, in another sense too restrictive. We shall really discuss in detail only the phase separation and osmostic pressure of polymer solutions a variety of other thermodynamic phenomena are ignored. In this regard the chapter title would better read Some aspects of. . . . Throughout this volume only a small part of what might be said about any topic is actually presented, so this modifying phrase is taken to be understood and is omitted. 

It is conventional to use molality—moles of solute per kilogram of solvent (symbol m)—as the concentration unit in electrolyte thermodynamics. Accordingly, we shall represent the concentrations of both the indifferent electrolyte and the polymer in these units in this section m3 and m2, respectively. In the same dilute (with respect to polymer) approximation that we have used elsewhere in this chapter, m2 is related to the mass volume system of units C2 by... 

The parameters which characterize the thermodynamic equilibrium of the gel, viz. the swelling degree, swelling pressure, as well as other characteristics of the gel like the elastic modulus, can be substantially changed due to changes in external conditions, i.e., temperature, composition of the solution, pressure and some other factors. The changes in the state of the gel which are visually observed as volume changes can be both continuous and discontinuous [96], In principle, the latter is a transition between the phases of different concentration of the network polymer one of which corresponds to the swollen gel and the other to the collapsed one. 

Pn gogine s work led to a complete representation of polymer solution thermodynamics. Because of the form of Prigogine s expressions, they are often referred to as free-volume expressions. 

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