The concept of two stochastic processes in liquid water and analytical theory of the complex permittivity in the wavenumber range 0–1000 cm–1

Abstract

The linear dielectric response of liquid H2O is investigated in terms of two stochastic processes, which govern the wideband spectrum of water. These processes differ in the molecular motion and involve different dipole moments. One process concerns a single-molecule reorientation of a dipole with a moment μor in an intermolecular potential well, of which the lifetime τor≈0.3 ps. The second process is a damped bending vibration of a dipole with a small (μvib/μor≈0.15) moment μvib about the direction of the H-bond. This process is characterised by shorter (τvib≈0.1 ps) lifetime and is accompanied by a stretching vibration of the H-bonded molecules. The key aspect of the presented work is that we show that such vibration is partially responsible: (i) for the narrow translational absorption band arising in the water near the frequency νtr∽200 cm−1, and (ii) for the dielectric relaxation in the submillimetre wavelength range, which is characterised by a fast relaxation time τ2≈0.3 ps. The first process (reorientation) is mostly responsible for the main (librational) band arising in water around frequency νlib = 600 cm−1 and for the main Debye relaxation in the microwave region. The spectra are described in the analytical form for the composite hybrid-cosine squared (HYB-CS) model. In the hybrid model the dielectric behaviour of a polar molecule reorienting in a rectangular well is considered. In the cosine squared model such behaviour is found for a dipole oscillating about the H-bond direction. The calculated spectra of the complex permittivity and absorption coefficient agree satisfactorily with the measured water spectrum for a temperature of 300 K. The typical spatial and time scales of the molecular events are estimated.