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 μ_or in an intermolecular potential well, of which the lifetime τ_or≈0.3 ps. The second process is a damped bending vibration of a dipole with a small (μ_vib/μ_or≈0.15) moment μ_vib about the direction of the H-bond. This process is characterised by shorter (τ_vib≈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 ν_tr∽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 ν_lib = 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.