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%\subsection{Radius measurement from anisotropy}
It is also possible to measure the hydrodynamic radius of a molecule by time-resolved Time-resolved fluorescence anisotropy
measurements, which measurements can
help determine
the molecule's rotational mobility which depends on the molecular
volume, mobility, rigidity, shape, volume and the
molecule's viscosity of the environment surrounding
environment.\cite{Lakowicz2006} the molecule.\cite{Lakowicz2006} The sample solution is excited with a pulse of polarised light, and the fluorescence is collected in parallel and perpendicular polarisation directions as a function of time. The anisotropy $r(t)$ of a molecule undergoing rotational diffusion in the solution can be obtained from the measured intensities $I_\parallel$ and $I_\perp$ by
\begin{equation}
r(t)= \frac{I(t)_\parallel-GI(t)_\perp}{I(t)_\parallel+2GI(t)_\perp} \label{eq:anisotropy}
\end{equation}
where $G$ is a correction factor that compensates for different transmission and detection efficiencies in the parallel and the perpendicular
directions. directions.\cite{Suhling2014} If the sample solution contains spherical molecules of homogeneous size, the anisotropy decay follows a single-exponential function
\begin{equation}
r(t) = r_0\cdot e^{-\frac{t}{\phi}} \label{eq:1expfit}
\end{equation}
where $r_0$ is the initial anisotropy at $t=0$ and $\phi$ is the rotational correlation time. If the rotating unit is not spherical, a more complex
multi-exponential model is
required. required.\cite{Phillips1984}
$\phi$ can thus be obtained by fitting eq~\ref{eq:1expfit} (or the more complex model) to the experimental anisotropy decay. $\phi$ is related to the volume $V$, and thus the effective radius, of the rotating molecule by the Stokes-Einstein-Debye equation \cite{VanHolde1998}
\begin{equation}