rotational correlation time, \(\tau_{\text{c}}\), \(\theta\)

https://doi.org/10.1351/goldbook.RT07474
Parameter describing the time dependence of the tumbling of a molecular entity in a medium of @[email protected] \(\eta\). The rotational correlation time can be obtained from the decay of the @[email protected] or @[email protected] @[email protected] and is related to the average molecular @[email protected], \(D_{\text{r}}\), in turn related to the hydrodynamic molecular volume of the @[email protected], \(V\), and to \(\eta\) (see Note 3).
Notes:
  1. Mathematical definition: \(r(t) = r_{\text{0}}\, \text{exp}\! \left ( -\frac{t}{\tau_{\text{c}}} \right )\) with \(r(t)\) the @[email protected] at time \(t\) and \(r_{\text{0}}\) the fundamental @[email protected]
  2. In the case of a spherical emitting species reorienting itself in a homogeneous fluid, \(\tau_{\text{c}} = \frac{1}{6D_{\text{r}}}\).
  3. Often, the @[email protected]–@[email protected] relationship is used for the calculation of \(D_{\text{r}}\), i.e., \(D_{\text{r}} = R\, T/6\, V\eta\) with \(R\) the @[email protected], \(T\) the absolute temperature and \(V\) the hydrodynamic molecular volume. However, the use of this relationship at a molecular level is questionable, and \(D_{\text{r}}\) should be independently determined by time-resolved @[email protected] @[email protected] methods. Compare with @[email protected]
Source:
PAC, 2007, 79, 293. (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 416 [Terms] [Paper]