Thermodynamic behavior of polymer solutions

Whatever the detailed interpretation of the thermodynamic behavior of polymer solutions, the term... 

Knowledge of solvent activities in polymer solutions is a necessity for a large number of industrial and laboratory processes. Such data are an essential tool for tmderstanding the thermodynamic behavior of polymer solutions, for studying their intermolecular interactions and for getting insights into their molecular nature. Besides, they are the necessary basis for any development of theoretical thermodynamic models. Scientists and engineers in academic and industrial research need such data. 

While the measurement of osmotic pressure n and the calculation of the second virial coefficient A2 are relatively simple, their theoretical interpretations are rather comphcated. Throughout the past half century, many investigators have tried to set up a model and derive equations for n and A2. Because of the unsymmetrical nature with respect to the sizes of solute (macromolecule) and solvent (small molecule), polymer solutions involve unusually large intermolecular interactions. Furthermore, since n is directly related to pj, any theoretical knowledge learned from the osmotic pressure and the second virial coefficient contributes to the knowledge of the general thermodynamic behavior of polymer solutions. For this reason. Chapter 4 and 9 are closely related in macromolecular chemistry. 

Maron,S.H., Nakajima,N. A theory of the thermodynamic behavior of nonelectrolyte solutions. III. The osmotic pressure of polymer solutions. J. Polymer Sci. 42, 327-340 (1966). 

Summary The classical treatment of the physicochemical behavior of polymers is presented in such a way that the chapter will meet the requirements of a beginner in the study of polymeric systems in solution. This chapter is an introduction to the classical conformational and thermodynamic analysis of polymeric solutions where the different theories that describe these behaviors of polymers are analyzed. Owing to the importance of the basic knowledge of the solution properties of polymers, the description of the conformational and thermodynamic behavior of polymers is presented in a classical way. The basic concepts like theta condition, excluded volume, good and poor solvents, critical phenomena, concentration regime, cosolvent effect of polymers in binary solvents, preferential adsorption are analyzed in an intelligible way. The thermodynamic theory of association equilibria which is capable to describe quantitatively the preferential adsorption of polymers by polar binary solvents is also analyzed. 

The important structural details of macromolecules, such as molecular weight, chain length, branching, and chain stiffness, are best studied when the individual molecules are separated from each other. Such studies are therefore made with dilute solutions of polymers. However, the dissolution of a polymer also brings with it a host of new problems. For a correct interpretation of the behavior of polymer solutions it is essential to understand the thermodynamics of polymer-solvent interaction. We will therefore explore some of the basic underlying thermodynamic principles of polymer solutions in this chapter. 

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. 

The thermodynamic interactions and the size of polymer coil enter dependencies that describe the transport behavior of polymer solutions, viz. viscosity, diffusion, sedimentation, etc. To complete this short summary, the intrinsic viscosity should be mentioned. 

Phase separation is frequently observed in polymer solutions and it is mainly due to their low entropy of mixing. At a state of equilibrium each species of the mixture is partitioned between two phases, namely, the supernatant (extremely dilute) and precipitated (moderately dilute) phases [78]. Theoretical models and experimental techniques have been developed to predict the solubility behavior of polymer solutions, polymer blends, and other related systems [79, 80]. Simple theories only permit a rather qualitative description of this phenomenon [78]. Refined and improved theoretical and semiempirical models allow a more accurate prediction of the demixing phenomena and related thermodynamic properties [57, 81]. 

Since then. Dr. Woldfarth s main researeh has been related to polymer systems. Currently, his research topics are molecular thermodynamics, continuous thermodynamics, phase equilibria in polymer mixtures and solutions, polymers in supercritical fluids, PVT behavior and equations of state, and sorption properties of polymers, about which he has published approximately 100 original papers. He has written the following books Vapor-Liquid Equilibria of Binary Polymer Solutions, CRC Handbook of Thermodynamic Data of Copolymer Solutions, CRC Handbook of Thermodynamic Data of Aqueous Polymer Solutions, CRC Handbook of Thermodynamic Data of Polymer Solutions at Elevated Pressures, CRC Handbook of Enthalpy Data of Polymer-Solvent Systems, and CRC Handbook of Liquid-Liquid Equilibrium Data of Polymer Solutions. 

Many attempts have been made to find theoretical explanations for the non-ideal behavior of polymer solutions. There exist books and reviews on this topic, e.g., Refs. " " Therefore, only a short summary of some of the most important thermodynamic approaches and models will be given here. The following explanations are restricted to concentrated polymer solutions only because one has to describe mainly concentrated polymer solutions when solvent activities have to be calculated. For dilute polymer solutions, with the second virial coefficient region, Yamakawa s book provides a good survey. 

The thermodynamic interactions and the size of polymer coil also enter dependencies that describe the transport behavior of polymer solutions, viz., viscosity, diffusion, sedimentation, etc. To complete this short summary, the viscosity relations should be mentioned. Defining rj as the solution viscosity and as the solvent viscosity, the following, relative (rjf), specific (rj f), and intrinsic ([77]) viscosities, are typically expressed as... 

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 ). 

We begin our study of macromolecular thermodynamics by discussing these three basic quantities AS, AH, and AG. Our interpretation of the change in a polymeric system is based on the change in the values of AS, AH, and AG. A change in the properties of the polymer always occurs whenever there is a change in the surroundings (environment). In later sections we discuss two more thermodynamic quantities v, the partial specific volume, and p, the chemical potential. Both are related to the behavior of polymer solutions. 

Abstract This introductory chapter provides a brief (textbook-like) survey of important facts concerning the conformational and dynamic behavior of polymer chains in dilute solutions. The effect of polymer-solvent interactions on the behavior of polymer solutions is reviewed. The physical meanings of the terms good, 9-, and poor thermodynamic quality of the solvent are discussed in detail. Basic assumptions of the Kuhn model, which describes the conformational behavior of ideal flexible chains, are outlined first. Then, the correction terms due to finite bond angles and excluded volume of structural units are introduced, and their role is discussed. Special attention is paid to the conformational behavior of polyelectrolytes. The pearl necklace model, which predicts the cascade of conformational transitions of quenched polymer chains (i.e., of those with fixed position of charges on the chain) in solvents with deteriorating solvent quality, is described and discussed in detail. The incomplete (up-to-date) knowledge of the behavior of annealed (i.e., weak) polyelectrolytes and some characteristics of semiflexible chains are addressed at the end of the chapter. 

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