Properties of polymer solutions

Dilute solutions of completely soluble polymers exhibit the usual col-ligative properties of solutions. These properties have frequently been used to determine polymeric molecular weights e.g., viscosity and lightscattering measurements are frequently made on polymer solutions for molecular weight determinations. 

One of the methods used to study the behavior of polymer molecules is an investigation of their properties in solution. Of particular importance is the study of dilute polymer solutions, in which the molecules are separated from each other so as to eliminate possible interference. This technique has 5delded much fundamental information. For instance, the molecular weight of polymer molecules and the variation (distribution function) of the molecular species in one polymeric sample can be determined by measurements of certain physical characteristics of a very dilute polymer solu- 

It has to be emphasized that these parameters require a study of molecules separated from each other by means of high dilution of the solution. There are, however, other characteristics of polymer molecules which must be studied in concentrated solution or in the solid state. 

The basic equation relating molecular weight to osmotic pressure was derived by Van t Hoff and is 

The molecular weight is determined by a series of. osmotic-pressure measurements on solutions of varying concentration. A plot of t/c versus c is roughly linear, and the intercept on the ordinate yields tt/c at infinite dilution. (See Fig. 15-10.) Substi-. tuting this value in Eq. (1) the number-average molecular weight M can be calculated. 

The quantity A2 in Eq. (2) is an important measure of polymer-solvent interaction. Its thermodynamic significance is somewhat complicated, the magnitude of the effect being determined by both the heat and entropy of solution. For any given polymer, A 2 is highest in the best solvent and lowest in the worst. If A2-becomes appreciably negative, the solvent becomes too weak to keep the polymer in solution and precipitation takes place. 

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Hydrogen bonding stabilizes some protein molecules in helical forms, and disulfide cross-links stabilize some protein molecules in globular forms. We shall consider helical structures in Sec. 1.11 and shall learn more about ellipsoidal globular proteins in the chapters concerned with the solution properties of polymers, especially Chap. 9. Both secondary and tertiary levels of structure are also influenced by the distribution of polar and nonpolar amino acid molecules relative to the aqueous environment of the protein molecules. Nonpolar amino acids are designated in Table 1.3. 

The solution properties of polymers have been subjected to intensive study, in particular to highly complex mathematical treatment This section will, however, confine discussion to a qualitative and practical level . ... 

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 dilute solution properties of polymers discussed so far had to do with randomly coiled macromolecules. In some cases, however, dissolved polymer molecules tend to assume a completely stretched rod-like shape. 

Theoretical treatments on the viscosity of solutions of polymer chains are too numerous to give even a brief summary. Originally their principal objective was to explain the intrinsic viscosity-molecular weight relationship as described in Eq. (5). Now the major interest goes far beyond that and toward a better understanding of the solution properties of polymers. Our brief discussion will be confined only to general terms. The approach... 

Table 2. The Effect of Polymer Functional Croup on the Thermal and Solution Properties of Polymers 3 and 4...

The first section of this chapter describes the solution properties of polymers, and this is followed by a general classification of polymeric surfactants. Examples are provided of polymeric surfactants and polyelectrolytes that are used as dispersants and emulsifiers. 

As mentioned in Section 1.C.2 and listed among the references for Chapter 1, many articles applying the formalism of graph theory to the properties of polymer chains that can be studied in solutions, including viscoelastic behavior and chain configurations, have been published. This work, however, has almost exclusively been of academic interest. It has focused mainly on developing elaborate and rigorous mathematical formalisms, and has not provided simple predictive techniques and correlations that could be used on a routine basis in industrial research and development. In this chapter, we will develop simple correlations based on variations of the formalism of connectivity indices, for selected dilute solution properties of polymers. 

As may be expected, polymers behave differently toward solvents than do low-molecular-weight compounds. Studies of the solution properties of polymers provide useful information about the size and shape of polymer molecules. In this section we discuss how some of the molecular parameters discussed in the previous sections are related to and can be calculated from thermodynamic quantities. We start with a discussion of the simplest case of an ideal solution. This is followed by a treatment of deviations from ideal behavior. 

The solution properties of polymers in general are of interest for two reasons. First they influence the choice of processing method and of polymer for a specific application whilst secondly being very different to those of simple molecules they arouse academic curiosity. In the particular case of rubbers the swelling behaviour of networks is of interest in characterizing network structure. 

As mentioned earlier, a considerable number of reviews exists in the field of solution properties of polymer-surfactant complexes. Therefore, only the main points are recapped in this section. 

Solution Properties of Polymers Recent Advances in Free Radical Polymerization Microstructure of Proteins Novel Polymerization Problems in Polymerization Absorption of Macromolecules... 

Since Professor Gardner soon went to Washington, D,C. on official mission and no young organic chemist was immediately available we started to concentrate on the mechanism of polymerization processes, on molecular weight and molecular weight distribution and on the solution properties of polymers. Much work had been... 

These concepts which form the basis for the solution properties of polymers, are extended to macromolecular reactivity in the work of Morawetz and collaborators. For example Goodman and Morawetz [30] investigated the influence of chain flexibility vdien catalytic and substrate-groups are contained in the same macromolecule, and the reaction is studied in very dilute solution. In particular, they considered the solvolysis of p-nitrophenylester groups catalyzed by pyridine residues in terpolymers of acrylamide containing a small proportion of p-nitrophenyl ester and catalytic pyridinei residues (XXII). 

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