R. T. Deam and S. F. Edwards

in Stealing the Gold

Published in print December 2004 | ISBN: 9780198528531
Published online September 2007 | e-ISBN: 9780191713415 | DOI:

Series: International Series of Monographs on Physics


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This chapter reprints a paper which attempts to improve upon several weaknesses in the classical theories of rubber elasticity. It develops a formulation of the statistical thermodynamics of amorphous materials analogous to the Gibbs formalism for conventional statistical mechanics. This then permits the replacement of ‘phantom chains’, i.e., long polymer molecules with the fictitious property that they experience no forces except at cross link points and are transparent to one another, by realistic molecules which do experience forces and which can become entangled. The chapter is divided into four sections. The first section demonstrates that just as Gibbs's famous formula provides an abstract formula for the statistical mechanics of systems in which all states are accessible, the new formula extends to systems with frozen-in degrees of freedom. The second section shows how the formalism fits the problem of rubber elasticity. In the third section, the effect of excluded volume, i.e., of short-range forces, is included in the calculation of the free energy of a rubber, while in fourth section, the effects of entanglements are included to complete the kinds of force normally encountered.

Keywords: phantom chain models; polymer networks; free energy; Gibbs formula; rubber elasticity; entanglement

Chapter.  26757 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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