### Abstract

Thermal-induced gelation for waterborne polyurethane dispersion has been studied rheologically under isothermal condition over a wide range of frequencies at different constant temperatures (55, 60, 65, and 70 °C). The elastic storage modulus, G′, at a constant temperature in the vicinity of the gel point increases abruptly, and the magnitude of the elevation in G′ was found to be temperature dependent. Similar behavior has been observed for both the viscous loss modulus, G″, and the complex dynamic viscosity, η*. The gel point, t _{gel}, was determined from the point of intersection in tan δ vs gelation time for different constant shear frequencies, where tan δ is frequency independent and all curves cross over, indicating the validity of the Winter-Chambon criterion. The value of t _{gel} obtained from the coincidence of G′ and G″ was in excellent agreement with that obtained from tan δ vs t. At the gel point, G′ and G″ showed a power law with shear frequency, i.e., G′ ∼ G″ ∼ ω ^{n} with critical exponents n′ and n″ for G′and G″, respectively. The values of n′ and n″ are identical at t _{gel} (n′ and n″ ∼ 0.58), and both decreased exponentially with gelation time at 70 °C. The exponent values n′ and n″ are in good agreement with that predicted from the percolation theory (i.e., n = 2/3). In addition, the temperature dependence of n′ and n″ was investigated in the vicinity of the gel point. Both n′ and n″ decreased with temperature and intersected at the gel temperature, i.e., n′ = n″ at T _{gel} = 67 °C. The value of T _{gel} = 67 °C was in good agreement with that obtained previously from the temperature at which tan δ is frequency independent and also from the temperature at which G′ and G″ coincided. The zero shear viscosity, η _{0}, and the equilibrium shear modulus, G _{eq}, conformed well with power law scaling functions of the relative distance from the gel point, ε, i.e., η _{0} ∼ ε ^{-k} and G _{eq} ∼ ε ^{z} (where k and z are scaling parameters).

Original language | English (US) |
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Pages (from-to) | 10178-10184 |

Number of pages | 7 |

Journal | Macromolecules |

Volume | 38 |

Issue number | 24 |

DOIs | |

Publication status | Published - Nov 29 2005 |

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### All Science Journal Classification (ASJC) codes

- Organic Chemistry
- Polymers and Plastics
- Inorganic Chemistry
- Materials Chemistry

### Cite this

*Macromolecules*,

*38*(24), 10178-10184. https://doi.org/10.1021/ma0511088