Integral and differential constitutive equations for entangled polymers with simple versions of CCR and force balance on entanglements |
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Authors: | Guiseppe Marrucci Francesco Greco Giovanni Ianniruberto |
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Institution: | (1) Dipartimento di Ingegneria Chimica Università di Napoli Federico II, and ITMC, CNR, Piazzale Tecchio 80 80125 Napoli, Italy e-mail: marrucci@unina.it, IT |
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Abstract: | The theory of Doi and Edwards for entangled polymers has been recently modified for the case of fast flows to account for
convective contributions to molecular dynamics. The flow-induced relative motion between neighboring chains removes constraints
and speeds up relaxation. Convective constraint release (CCR) may thus explain why the shear stress is seen to approach a
plateau at high shear rates instead of decreasing as predicted by the basic theory. In slow flows, as well as in step strain,
another discrepancy between theory and observations can be found in the normal stress ratio in shear Ψ=−N2/N1. The theoretical value for Ψ at low deformations is 1/7 whereas measured values for well-entangled systems are systematically
larger. We have recently considered the possibility that this discrepancy arises because force balance requirements at the
entanglement nodes are ignored in the classical theory. Accordingly, we have proposed a change in the orientational tensor
Q. Here, we sum up on these recent findings by proposing single-relaxation-time constitutive equations of the integral or rate
type incorporating those concepts in a simple way. Such equations should be suitable for numerical simulation of complex flows.
Received: 1 January 2000 Accepted: 8 August 2000 |
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Keywords: | Entangled polymers Convective constraint release Force balance on entanglements Constitutive equations |
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