Modeling the viscoelastic behavior in the frequency domain of crosslinked polystyrene with different degrees of crosslinking from the perspective of relaxation

The viscoelastic behavior in the frequency domain of crosslinked polystyrene (CPS) with two different degrees of crosslinking is characterized and modeled. A viscoelastic model from a relaxation perspective (VR model) was established considering different relaxation spectra. The relaxation spectrum is described by the distribution function of relaxation times in the VR model. The fitting quality of the VR model based on the distribution function corresponding to the Kohlrausch–Williams–Watts function is much higher than that of the conventional Zener model, but slightly lower than that of the fractional-derivative Kelvin–Voigt (FKV) model. The fitting quality of the VR model based on the distribution function corresponding to the Cole–Cole (CC) function is much better than that of the VR model with other distribution functions. This shows that the CC distribution function can better describe the relaxation spectrum of the CPS. Although the modulus expression of the Cole–Cole relaxation function is mathematically consistent with FKV, the VR model with the CC distribution function shows its superiority in having a definite physical meaning. The effect of the degree of crosslinking on the model parameters is analyzed. A higher equilibrium modulus, longer relaxation time, and narrower distribution of relaxation times are observed for CPS2.5 with a higher degree of crosslinking. The result shows that the viscoelastic behavior in the frequency domain of the crosslinked polymer can be well described through the VR model, which is applied by the distribution function of relaxation times.