Structure and properties of polymers in dilute solution

The detailed structure of an isolated polymer molecule in a solution depends on the solvent and the temperature as well as the intramolecular energies discussed in Chapter 2. This chapter presents the principles necessary to understand the solvent and temperature dependence of the global structure. The classical name for this issue is the excluded voliune problem.  

The thermod5mamic properties of a dilute polymer solution depend on the interaction of polymer molecules with the solvent and with each other. Thermod5mamic fimctions can be expressed in terms of virial expansions in the polymer concentration. The osmotic pressure will be explained in terms of the potential of mean force between pairs of polymer molecules. A detailed discussion of the osmotic second virial coefficient, A2, will be presented. 

One of the most useful techniques for the study of the structure and thermodynamics of dilute polymer solutions is light scattering. The principles of light scattering from an ensemble of solute molecules will be presented and illustrated. The analysis of a Zimm plot will also be explained and discussed. 

Polymer molecules are in constant motion in solution. The long-time trajectory of the center of mass is governed by the self-diffusion coefficient, Dj. The molecular theory of the self-diffusion coefficient of a polymer molecule will be presented. The concept of the molecular friction coefficient will be developed. The process of mutual diffusion will then be presented, and an expression for the mutual-diffusion coefficient, D , will be derived. 

Dynamic light scattering allows the determination of the self-diffusion coefficient and the mutual-diffusion coefficient. In addition, internal conformational fluctuations can be observed for large-chain molecules. 

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Chapter five Structure and properties of polymers in dilute solution 45... 

Dilute Solution Properties. The rheology of dilute polymer solutions has been used extensively to gain insight into the structure and conformation of polymers in solution (11). The intrinsic viscosity provides a measure of the molecular weight of a polymer through a relationship such as the Mark-Houwink-Sakurada equation. Earlier studies of polyacrylamide (PAM) systems and details of the complexity of the characterization of high-molecular-weight water-soluble systems can be found in references 9, 13, and 14. 

The existence of the rubbery state of polymers was introduced in Chapter 1. The present chapter provides a more formal development of the properties of rubber and explains the observed phenomena in terms of the structural properties of macromolecules developed in Chapter 2. A thorough understanding of the behavior of rubber is essential to explain the properties of macromolecules in dilute solution, which is the subject of Chapter 5. 

The accurate prediction of material properties of specific polymers is only one kind of the many tasks that one may wish to solve by MC simulation another task is to elucidate some universal predictions of general features of polymers that should hold irrespective of their chemical structure. For example, for polymers in dilute solution under good solvent conditions, nontrivial universal exponents V and y describe the scaling of the gyration radius, Rg, and the configural free energy, Fconf, with the degree of polymerization, n. ... 

Relationships between the synthesis and molecular properties of polymers (Chapter 2), and between their molecular and bulk properties (Chapters 4 and 5), provide the foundations of Polymer Science. In order to establish these relationships, and to test theories, it is essential to accurately and thoroughly characterize the polymers under investigation. Furthermore, use of these relationships to predict and understand the in-use performance of a particular polymer depends upon the availability of good characterization data for that polymer. Thus polymer characterization is of great importance, both academically and commercially. The current chapter is concerned with molecular characterization of polymer samples, by which is meant the determination of their average molar masses, molar mass distributions, molecular dimensions, overall compositions, basic chemical structures and detailed molecular microstructures. Since most methods of molecular characterization involve analysis of polymers in dilute solution (<20gdm ), the relevant theories for polymers in solution will be introduced before considering the individual methods. 

An overview of the synthesis and characterization of a unique class of polymers with a phosphorus-nitrogen backbone Is presented, with a focus on poly(dichloro-phosphazene) as a common Intermediate for a wide variety of poly(organophosphazenes). Melt and solution polymerization techniques are Illustrated, Including the role of catalysts. The elucidation of chain structure and molecular weight by various dilute solution techniques Is considered. Factors which determine the properties of polymers derived from poly(dichlorophos-phazene) are discussed, with an emphasis on the role that the organic substituent can play In determining the final properties. 

Abstract Macromolecular coils are deformed in flow, while optically anisotropic parts (and segments) of the macromolecules are oriented by flow, so that polymers and their solutions become optically anisotropic. This is true for a macromolecule whether it is in a viscous liquid or is surrounded by other chains. The optical anisotropy of a system appears to be directly connected with the mean orientation of segments and, thus, it provides the most direct observation of the relaxation of the segments, both in dilute and in concentrated solutions of polymers. The results of the theory for dilute solutions provide an instrument for the investigation of the structure and properties of a macromolecule. In application to very concentrated solutions, the optical anisotropy provides the important means for the investigation of slow relaxation processes. The evidence can be decisive for understanding the mechanism of the relaxation. 

The nature of hydrophobic interactions and their effects on the structure and properties of water have been extensively studied, particularly for small molecules (i 3). In contrast, the introduction of hydrophobic associations into synthetic water-soluble polymers to control solution rheology has received rather limited and recent study (4-7). To better understand the relationships between polymer structure and solution properties, we have synthesized and characterized a series of copolymers of acrylamide and N-substituted alkylacrylamides and terpolymers containing anionically charged carboxyl groups. Solution properties of these systems have been obtained in both the dilute and semidilute concentration regime, to probe the influence of intra- and intermolecular interactions. In addition, the influence of the shear field and solvent quality on the associations was studied. 

The systems consisting of a macromolecular component and others composed by low molecular weight molecules are of peculiar theoretical and practical importance. The diluted solutions are especially investigated, since the description of different properties of macromolecules could be performed only on this type of models. In diluted solutions the interactions between the macromolecules are practically cancelled. In this way, the determination of the structural particularities of polymer chains (shape, dimensions, and molecular weight) as well as of thermodynamic characteristics of polymer solutions became possible. 

Study of the structure and physicochemical properties of comb-shaped polymers in dilute solutions, gels, and the solid phase genoalized in [8] permitted describing the structural features of this special class of branched polym systems in detail within the framework of the so-called rotational-crystalline state, a variety of the LC state. 

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