### Abstract

Stress-optical measurements are used to quantitatively determine the third-normal stress difference (N_{3} = N_{1} + N_{2}) in three entangled polymer melts during small amplitude (<15%) oscillatory shear over a wide dynamic range. The results are presented in terms of the three material functions that describe N_{3} in oscillatory shear: the real and imaginary parts of its complex amplitude ψ_{3}^{*}= ψ_{3}^{′}- iψ_{3}^{″}, and its displacement ψ_{3}^{d}. The results confirm that these functions are related to the dynamic modulus by ω^{2}ψ_{3}^{*}(ω)=(1-β)[G^{*}(ω))- {Mathematical expression}G^{*}(2ω)] and ω^{2}ψ_{3}^{d}(ω)=(1- β)G′(ω) as predicted by many constitutive equations, where β = -N_{2}/N_{1}. The value of (1-β) is found to be 0.69±0.07 for poly(ethylene-propylene) and 0.76±0.07 for polyisoprene. This corresponds to -N_{2}/N_{1} = 0.31 and 0.24±0.07, close to the prediction of the reptation model when the independent alignment approximation is used, i.e., -N_{2}/N_{1} = 2/7 - 0.28.

Original language | English (US) |
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Pages (from-to) | 535-544 |

Number of pages | 10 |

Journal | Rheologica Acta |

Volume | 31 |

Issue number | 6 |

DOIs | |

State | Published - Nov 1 1992 |

Externally published | Yes |

### Keywords

- entangled melts
- flow birefringence
- oscillatory shear
- poly(ethylene-propylene)
- polyisoprene
- third normal stress difference

### ASJC Scopus subject areas

- Materials Science(all)
- Condensed Matter Physics

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## Cite this

*Rheologica Acta*,

*31*(6), 535-544. https://doi.org/10.1007/BF00367008