Analysis of Linear Viscoelasticity of a Crosslinking Polymer at the Gel Point

Abstract

We suggest a very simple memory integral constitutive equation for the stress in crosslinking polymers at their transition from liquid to solid state (gel point). The equation allows for only a single (!) material parameter, the strength S[Pas1/2], and it is able to describe every known viscoelastic phenomenon at the gel point. Measurements were performed on polydimethylsiloxane model networks with balanced stoichiometry for which the crosslinking reaction has been stopped at different degrees of conversion. At the gel point, the loss and storage moduli were found to be congruent and proportional to ω1/2 over a wide range of temperature (−50°C to +180°C) and five decades of frequency ω. The hypothesis is made that this behavior is valid in the entire range 0<ω<∞. This congruence hypothesis is consistent with the Kramers‐Kronig relation and leads to a constitutive equation which shows that, for our polymer, congruent functions G′(ω)=G″(ω) are as much a rheological property at the gel point as are infinite ...