Estimation of cluster sizes in associated liquids based on characteristic time scales of orientation polarization

A simplified derivation for the ratio of macroscopic to microscopic relaxation times of polar liquids is based on the Mori-Zwanzig projection-operator technique, with added statistical assumptions. We obtain several useful forms for the lifetime ratio, which we apply to the dynamics of liquid water. Our theoretical single-molecule relaxation times agree with the second Debye relaxation times as measured by frequency-domain dielectric spectroscopy of water and alcohols. From the theory, fast relaxation modes couple to the Debye relaxation time, $\tau\mathrm{D}$. Slower modes are localized to smaller water clusters. This is exemplified by the lifetime ratios measured by time-domain dielectric spectroscopy and optical Kerr effect spectroscopy, respectively.