rotational correlation time, τ c or θ

Parameter describing the time dependence of the tumbling of a molecular entity in a medium of viscosityη. The rotational correlation time can be obtained from the decay of the fluorescence or phosphorescenceanisotropy and is related to the average molecular rotational diffusion coefficient, D r, in turn related to the hydrodynamic molecular volume of the fluorophore, V, and to η (see Note 3).
Notes:
  1. Mathematical definition: r t = r 0 exp ( − t τ c ) with r t the emission anisotropy at time t and r 0 the fundamental emission anisotropy.
  2. In the case of a spherical emitting species reorienting itself in a homogeneous fluid, τ c = 1 6 D r.
  3. Often, the Stokes–Einstein relationship is used for the calculation of D r, i.e., D r = R T / 6 V η with R the gas constant, T the absolute temperature and V the hydrodynamic molecular volume. However, the use of this relationship at a molecular level is questionable, and D r should be independently determined by time-resolved fluorescencepolarization methods. Compare with rotational relaxation time.
Source:
PAC, 2007, 79, 293 (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 416