Molecular Theories for the Viscoelasticity of Flexible Homogeneous Polymeric Liquids

The fact that a polymer consists of a number of chains of different lengths, each in turn consisting of a series of monomer units, means that the motion of one part of the polymer chain will profoundly affect the motion of other parts. Hence, for a given polymer, a description of microscopic processes occurring under a given flow field depends on hypotheses regarding the molecular stmcture and mechanisms of flow in the polymer. 

The critical molecular weight is believed to correspond to a value beyond which molecular entanglements (i.e., temporary couplings between neighboring chains) begin to dominate the resistance to flow. Such characteristics, and other characteristics that will be discussed later in this chapter, are attributed to entanglement effects because they appear to derive essentially from topological restrictions on the chain motions. 

In this chapter, we present currently held molecular theories for the viscoelasticity of linear, flexible macromolecular chains. We begin with a presentation of the static properties of macromolecules and the stochastic processes in the motion of macromolecular chains, as much as they will be necessary to present the molecular aspects of viscoelasticity in this and later chapters. We first present the molecular theories of Rouse (1953) and Zimm (1956), which are basically applicable to dilute polymer solutions and unentangled polymer melts, and then present the molecular theory of Doi and Edwards (1978a, 1978b, 1978c, 1979), which is applicable to concentrated polymer solutions and entangled polymer melts. 

Static Properties of Macromolecules and Stochastic Processes in the Motion of Macromolecular Chains 

In this section, we first introduce the most frequently used definitions of static properties, which will be used throughout this chapter and in some later chapters, and then discuss stochastic processes in the motion of macromolecular chains that is. Brownian motion that leads to the well-known Fokker-Planck equation, which further reduces to the Smoluchowski equation and Langevin equation. These two equations play a very important role in describing the motion of macromolecular chains. Owing to the limited space available here, we do not present rigorous derivations of various expressions. 

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Molecular Theories for the Viscoelasticity of Flexible Homogeneous Polymeric Liquids... 

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