Dynamics of Confined Water

Abstract

Do the dynamics of confined water differ from that of bulk water? A rather simple and direct method is to investigate the water dipole relaxation depending on its environmental conditions by microwave spectroscopy. The main relaxation or Debye frequency of liquid water is in the microwave range. For instance the Debye frequency jumps at 0°C from 16kHz in the ice to 9GHz in the liquid state. The Debye relaxation frequency ${f_D}$ is given by the relation

$$ {f_D}\,\, = \,\,{f_0}{e^{ - \Delta G/kT}}, $$

(1)

where the change in the chemical potential ΔG = 574 meV describes ice and ΔG = 213 meV is valid for the liquid state. The hydrogen bond energy is about ΔH = ΔG + TΔS = 130 meV. The viscosity η is related to the Debye frequency as

$$ \eta \, = \,\frac{{{\tau _D}kT}}{{4\pi {a^3}}}, $$

(2)

where ${\tau _D}\,\, = \,\,{\left( {2\pi {f_D}} \right)^{ - 1}}$ and a is the radius of a water molecule. Water belongs to the highly polar molecules. Negative charge is shifted from the hydrogen atoms to the oxygen atom generating a permanent dipole moment of 1.9D or about 6×10⁻³⁰ Asm. The above given relaxation frequency in the microwave range does not correspond to a two-fold bound molecule, where only one hydrogen bond has to be overcome. This frequency is observed in the infrared of the spectrum. The Debye frequency in the microwave regime, however, corresponds to the rate at which three- and four-fold bound molecules become two-fold bounded. Their rotation now is much faster than forming back molecules with three or four hydrogen bonds. This model was suggested by Haggis et al. already in 1952.⁴

Lecture notes prepared by Harald Spieker and Susanne Stölzle.