### Abstract

A new model is presented for entangled polymer solutions which accounts for the observed molecular weight and concentration dependences of the zero-shear viscosity ή_{0}and the terminal relaxation time λ_{d}. Our development, based upon the coupling model of relaxation, quantitatively describes how relaxation of a primitive mode is modified by coupling through entanglements to its environment. The primitive mode is represented by a Rouse chain of Gaussian submolecules, each of root mean square length σ equal to the entanglement distance and each characterized by an entanglement friction coefficient f_{0}. By extending the analyses developed previously for polymer melts, the model predicts thatή_{0}αM^{2/(1-n)}φ^{γ}[φ(^{α(1-v)}]^{2}/(1-n) where φ is the polymer volume fraction. Here n is the coupling parameter describing the terminal relaxation and γ, α, and v are given by G_{N}° φ ^{γ}, M_{e} α φ^{-α}, and σ φ^{-vα}. Numerical examples are shown to agree with experiment; e.g., for n = 0.41, γ = 2, α = 1, v = 0.6, ή_{0} α f⋆M^{3.4}φ^{3.4}. Comparison of the present results is also made to the reptation and scaling theory predictions.

Original language | English |
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Pages (from-to) | 2250-2256 |

Number of pages | 7 |

Journal | Macromolecules |

Volume | 20 |

Issue number | 9 |

DOIs | |

State | Published - Sep 1 1987 |

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## Cite this

*Macromolecules*,

*20*(9), 2250-2256. https://doi.org/10.1021/ma00175a033