Viscoelastic Effects on Molecular Dynamics of Dielectric Probes in Polymer Matrices

Viscoelastic effects of the matrix polymer on molecular dynamics of dielectric probes were examined using the generalized Langevin equation, which was derived to include the retardation effect of viscous force. By solving the equation, we successfully obtained the universal relationship between the complex relaxation modulus and the dielectric spectrum of the probe. When the viscoelastic properties of the matrix are assumed to be viscous, the obtained dielectric relaxation spectrum is described with the Debye function. On the other hand, if they are supposed to be a power-law type relaxation spectrum, the dielectric relaxation spectrum is found to be the Cole-Cole function. The proposed method was applied to a previous study on a low-mass probe in a polystyrene matrix. The estimated effective modulus of the polystyrene was found to be close to a power-law-type relaxation. The present study provides a new microrheological method to estimate the viscoelastic properties in nanometer size.