Concentrated polymer systems

Doi, M. and Edwards, S.F., 1978. Dynamics of concentrated polymer systems 1. Brownian motion in equilibrium state, 2. Molecular motion under flow, 3. Constitutive equation and 4. Rheological properties. J. Cheni. Soc., Faraday Trans. 2 74, 1789, 1802, 1818-18.32. 

Portions of the literature on viscoelasticity in concentrated polymer systems of narrow distribution have been reviewed recently (15, 16, 152, 153). The following discussion concerns three principal characteristics, the viscosity-molecular weight relation, the plateau modulus, and the steady-state compliance. 

Chikahisa (216) and Williams (217-219) have examined flow behavior in concentrated polymer systems without detailed consideration of the mechanism of intermolecular interaction. Williams explicitly limits his discussion to unentangled systems Chikahisa uses an entanglement terminology, although not in a specific way. Both approaches grow out of the formalism which was developed to deal with transport properties in small-molecule liquids. 

M. Doi and S. F. Edwards, Dynamics of concentrated polymer systems. Part I. Brownian motion in the equilibrium state, J. Chem. Soc. Faraday Trans. II, 74, 1789 (1978) M. Doi and S. F. Edwards, Dynamics of concentrated polymer systems. Part 2. Molecular motion under flow, J. Chem. Soc. Faraday Trans.II, 74, 1802 (1978) M. Doi and S. F. Edwards, Dynamics of concentrated polymer systems. Part 3. The constitutive equation, J. Chem. Soc. Faraday Trans. II, 74,1818 (1978) M. Doi and S. F. Edwards, Dynamics of concentrated polymer systems. Part 4. Rheological properties, J. Chem. Soc. Faraday Trans. II, 75,38 (1979). 

Initially, the elasticity of concentrated polymer systems was ascribed to the existence of a network in the system formed by long macromolecules with junction sites (Ferry 1980). The sites were assumed to exist for an appreciable time, so that, for observable times which are less than the lifetime of the site, the entangled system appears to be elastic. Equation (1.44) was used to estimate the number density of sites in the system. The number of entanglements for a single macromolecule Z = M/Me can be calculated according to the modified formula... 

For the weakly entangled system, the steady-state modulus depends on the molecular weight of polymer as M 1, while for strongly entangled system, the steady-state modulus does not depend on the molecular weight of polymer, which is consistent with typical experimental data for concentrated polymer systems (Graessley 1974). The expression for the modulus is exactly the same as for the plateau value of the dynamic modulus (equations (6.52) and (6.58)) Expressions (9.42) lead to the following relation for the ratio of the normal stresses differences... 

The nature of the static and dynamic properties of concentrated polymer systems is the focus of our work. We have already examined some static properties and are presently starting our study of the system dynamics. 

M.Doi, S.F.Edwards, Dynamics of concentrated polymer systems- Part 2 Molecular motion under flow, J. Chem. Soc, Faraday Trans II 24 (1978), 1802-1817. 

The usefulness of inverse gas chromatography for determining polymer-small molecule interactions is well established (1,2). This method provides a fast and convenient way of obtaining thermodynamic data for concentrated polymer systems. However, this technique can also be used to measure polymer-polymer interaction parameters via a ternary solution approach Q). Measurements of specific retention volumes of two binary (volatile probe-polymer) and one ternary (volatile probe-polymer blend) system are sufficient to calculate xp3 > the Flory-Huggins interaction parameter, which is a measure of the thermodynamic... 

This difference in behaviour necessitated the development of polymer-dynamics theories for concentrated polymer systems or melts. 

Altogether, polymer solutions show essential differences with normal solutions as well as with colloidal dispersions and need a special treatment. Highly concentrated polymer systems behave differently, again, and tend to form amorphous solids. Typical concentrated synthetic polymers are plastics and rubbers. 

FIGURE 13.8 Schematic representation of dilute, semidilute, and concentrated polymer systems. 

Concentrated polymer systems containing plasticizer show the existence of slow and fast relaxations which are temperatnre dependent Slow motions are characteristic of a polymer. Fast reorientations are characteristic of relatively small molecnles of a plasticizer. The dynamics of molecules and their rates of motion can be estimated based on... 

At increasing polymer concentration, the scission process becomes less effective and eventually stops. This is a drawback for the development of a scission process based on ultrasound, because concentrated polymer systems are favored in industry. The addition of an anti-solvent for the polymer can prevent the increase in viscosity at higher polymer concentrations. To determine the influence of CO2 as an anti-solvent on the ultrasound-induced scission rate,... 

The elastic and the FENE dumbbell models lack interactions between different parts of the chain, and between different chains (such as cross-linking or entanglements in a concentrated polymer system). There are two more sophisticated theories network and reptation theories. The Phan-Thien-Tanner (PTT) model (Phan-Thien and Tanner 1977) was derived based on network theory (Lodge 1964). This approach is concerned with a balance between the creation and destruction of strands in the network of long chain polymer molecules. The result for the one-relaxation-tome form is... 

M. Doi and S. F. Edwards, Dynamics of Concentrated Polymer Systems. Part I Brownian Motion in the Equilibrium State , J. Chem. Soa, Faraday Trans. 2 74,1789-1801 (1978). 

Concentrated polymer systems have fascinating motions. They show a unique combination of viscous and elastic behavior, which has been studied in careful experiments and is analyzed in a classical book by J. Ferry. Theoretically, the situation is less brilliant the dynamics of entangled chains (which can slip onto each other but cannot cross each other) is still poorly understood. The main ideas are described in a review by W. Graessley. In this chapter, we first summarize the concepts extracted from the mechanical data on melts. Then we proceed to the simpler problem of one chain which is moving inside a crosslinked network. Here a relatively plausible picture of the motions can be constructed and is known as the reptation model. Finally we return to the melts and discuss some generalizations of reptation for these systems. This third area, however, is largely conjectural. 

The models described so far are applicable to concentrated polymer systems, providing the chains are not too long. A dramatic failure of these models is observed for all polymer melts and concentrated solutions if molecular weight exceeds a critical value which depends on the chain structure and concentration in the case of solutions. Since concentrated solutions behave similarly to polymer melts with renormalized parameters, we shall focus on polymer melts in this chapter. The main signatures of entangled melts that unentangled models fail to describe are the following ... 

Similarly, molecular theory successfully describes one aspect of polymeric systems, namely their dilute solution behavior, but on occasion does not even predict qualitatively the phase equilibria of concentrated polymer systems, and rarely does so quantitatively. The high viscosity of such systems often prevents or certainly slows the approach to equilibrium, so that the measurement problem can be substantial. 

In 1971 DeGennes proposed a new model for molecular motion in concentrated polymer systems, one that now dominates all theoretical considerations (Lodge et al., 1990). His model is known as reptation because it describes macromolecular motion much like that of a snake moving in a contorted tunnel formed by the surrounding polymer molecules (Figure 11.5.7). The basic idea is... 

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