Title: rotational correlation time
Long Title: IUPAC Gold Book - rotational correlation time
DOI: 10.1351/goldbook.RT07474
Status: current
Index: quantity

Definition
Parameter describing the time dependence of the tumbling of a molecular entity in a medium of viscosity \(\eta\). The rotational correlation time can be obtained from the decay of the fluorescence or phosphorescence anisotropy and is related to the average molecular rotational diffusion coefficient, \(D_{\rm{r}}\), in turn related to the hydrodynamic molecular volume of the fluorophore, \(V\), and to \(\eta\) (see Note 3).

Notes
1) Mathematical definition: \(r(t) = r_{\rm{0}}\, \rm{exp}\! \left ( -\frac{t}{\tau_{\rm{c}}} \right )\) with \(r(t)\) the emission anisotropy at time \(t\) and \(r_{\rm{0}}\) the fundamental emission anisotropy.
2) In the case of a spherical emitting species reorienting itself in a homogeneous fluid, \(\tau_{\rm{c}} = \frac{1}{6D_{\rm{r}}}\).
3) Often, the Stokes–Einstein relationship is used for the calculation of \(D_{\rm{r}}\), i.e., \(D_{\rm{r}} = R\, T/6\, V\eta\) 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 \(D_{\rm{r}}\) should be independently determined by time-resolved fluorescence polarization methods. Compare with rotational relaxation time.

Related Terms
- Einstein: https://dev.goldbook.iupac.org/terms/view/E01914
- Stokes: https://dev.goldbook.iupac.org/terms/view/S06027
- anisotropy: https://dev.goldbook.iupac.org/terms/view/AT06776
- emission anisotropy: https://dev.goldbook.iupac.org/terms/view/ET07370
- fluorescence: https://dev.goldbook.iupac.org/terms/view/F02453
- fluorophore: https://dev.goldbook.iupac.org/terms/view/FT07380
- gas constant: https://dev.goldbook.iupac.org/terms/view/G02579
- phosphorescence: https://dev.goldbook.iupac.org/terms/view/P04569
- polarization: https://dev.goldbook.iupac.org/terms/view/P04712
- rotational diffusion coefficient: https://dev.goldbook.iupac.org/terms/view/R05411
- rotational relaxation time: https://dev.goldbook.iupac.org/terms/view/RT07475
- viscosity: https://dev.goldbook.iupac.org/terms/view/V06627

Source
- PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 416 (https://doi.org/10.1351/pac200779030293)

Other Outputs
- html: https://dev.goldbook.iupac.org/terms/view/RT07474/html
- json: https://dev.goldbook.iupac.org/terms/view/RT07474/json
- xml: https://dev.goldbook.iupac.org/terms/view/RT07474/xml

Citation: Citation: 'rotational correlation time' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.RT07474
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Accessed: 2026-06-13T01:53:44+00:00