  When a hydrophilic solute in water is suddenly turned into a hydrophobic
species, for instance, by photoionization, a layer of hydrated water molecules
forms around the solute on a time scale of a few picoseconds. We study the
dynamic build-up of the hydration shell around a hydrophobic solute on the
basis of a time-dependent dielectric continuum model. Information about the
solvent is spectroscopically extracted from the relaxation dynamics of a test
dipole inside a static Onsager sphere in the nonequilibrium solvent. The growth
process is described phenomenologically within two approaches. First, we
consider a time-dependent thickness of the hydration layer which grows from
zero to a finite value over a finite time. Second, we assume a time-dependent
complex permittivity within a finite layer region around the Onsager sphere.
The layer is modeled as a continuous dielectric with a much slower fluctuation
dynamics. We find a time-dependent frequency shift down to the blue of the
resonant absorption of the dipole, together with a dynamically decreasing line
width, as compared to bulk water. The blue shift reflects the work performed
against the hydrogen bonded network of the bulk solvent and is a directly
measurable quantity. Our results are in agreement with an experiment on the
hydrophobic solvation of iodine in water.
