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Entanglement and excluded volume effects in rubber elasticity
Author(s) -
Gaylord Richard J.
Publication year - 1979
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.760190407
Subject(s) - rubber elasticity , quantum entanglement , chain (unit) , materials science , elasticity (physics) , excluded volume , deformation (meteorology) , cylinder , volume (thermodynamics) , natural rubber , physics , mechanics , composite material , polymer , geometry , thermodynamics , mathematics , quantum mechanics , quantum
The role of interchain excluded volume and entanglement in the elastic behavior of polymeric networks is theoretically examined. A three‐chain network model is used, with each chain confined within an infinite, rectangular cylinder. The cylinders and the network crosslinks, are assumed to deform affinely. When the cross sections of the cylinders are small, the network elastic free energy equation has the form\documentclass{article}\pagestyle{empty}\begin{document}$$ \Delta F_e = A[\lambda _x^2 + \lambda _y^2 + \lambda _z^2 - 3] + B[\lambda _x^{ - 2} + \lambda _y^{ - 2} + \lambda _z^{ - 2} - 3] + C{\rm }\ln [\lambda _x \lambda _y \lambda _z] $$\end{document} The λs represent the macroscopic deformation ratios. The constants A , B and C are functions of the number of each type of network chain (i.e., A contains the number of tie chains; C contains the number of loops and tie chains; B contains the number of dangling chain ends, unattached chains, loops and tie chains), their unperturbed dimensions and the sizes of the cylinders which confine them.