Calculation of microwave peak absorbing frequency of polar liquids including dielectric friction

Reorientation time is the basis of the calculation of microwave peak absorbing frequency (MPAF) of liquids. In the Stokes–Einstein–Debye theory, the reorientation time of polar molecules is considered mainly due to mechanical friction, and an obvious deviation exists between the predictions of this theory and the experimental observations. In this paper, with the theory of Onsager’s effective field, the phase relation between reaction field and rotating polar molecule is derived, and this reaction field hinders the rotation of molecules due to the hysteretic phase. Hence, the reorientation time is extended to the sum of mechanical reorientation time and dielectric reorientation time. With the relation of reorientation time of molecule and Debye relaxation time of dielectric, Debye relaxation time of dielectric is modified, and then an improved formula of MPAF is derived. The MPAFs of coumarin C522B, C307, C138 in alcohol solvents are calculated with this formula, and the changes in MPAFs of water, methanol and ethanol with temperature are also numerically studied. These calculated results are consistent with the experimental data. Graphical abstract