Abstract
In the course-grained approximation, polymer solutions and melts can be considered as a suspension of interacting Brownian particles, which allow us to determine a general expression for the stress tensor, following a method developed in the theory of liquids (Rice and Gray in Statistical mechanics of simple liquids (Wiley, New York), 1965; Gray in Physics of simple liquids, ed by H.N.V Temperley (North Holland, Amsterdam, pp. 507–562), 1968). The general theory is specified to calculate dynamic modulus both for dilute and concentrated polymer systems. The approach allows one correctly to describe the linear viscoelastic behaviour of dilute polymer solutions over a wide range of frequencies, if the effects of excluded volume, hydrodynamic interaction, and internal viscosity are taken into account. As far as the very concentrated solutions and melts of polymers – entangled polymers – are concerned, the results for the linear approximation of macromolecular dynamics are only available now. As one can anticipate, it is not sufficient for complete description of relaxation processes in strongly entangled systems, though some relations for terminal characteristics are obtained for these systems. Remarkably, the mesoscopic theory appears to be self-consistent for entangled systems: the relaxation time of the environment is equal to the relaxation time of the entire system, which is calculated in this chapter. The intermediate scale introduced in Chapter 5 appears here once more as connected with the well-known length of a macromolecule between adjacent entanglements \(M_{\rm e}.\) It casts a new light on the old terms and old theories. The pictures given earlier by different theories appear to be consistent.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Keywords
- Dynamic Modulus
- Brownian Particle
- Hydrodynamic Interaction
- Linear Viscoelasticity
- Characteristic Quantity
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Gray P (1968) The kinetic theory of transport phenomena in simple liquids. In: Temperley HNV, Rowlinson JS, Rushbrook GS (eds) Physics of simple liquids. North-Holland, Amsterdam, pp 507–562
Rice SA, Gray P (1965) Statistical mechanics of simple liquids. Wiley, New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Pokrovskii, V.N. (2010). Linear Viscoelasticity. In: The Mesoscopic Theory of Polymer Dynamics. Springer Series in Chemical Physics, vol 95. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2231-8_6
Download citation
DOI: https://doi.org/10.1007/978-90-481-2231-8_6
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-2230-1
Online ISBN: 978-90-481-2231-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)