## 3 Monodispersed Nanorods: Bimodal Distributions due to Translation and Rotation
### DLS Measurement of Rotational and Translational Contributions in Particle Motions: Nanorods  
For non-spherical particles translational and rotational motion takes place, both affect the observed decay of the autocorrelation function. For monodispersed nanorods, the autocorrelation function is thus governed by two exponential decay parameters, one is proportional to the translational diffusion coefficient \(\mathrm{D_{t}}\), the other one to the rotational diffusion coefficient \(\mathrm{D_{r}}\). One distinguishes in this case a hydrodynamic radius related to translational motion, \(\mathrm{R_{Ht}}\), which is calculated according to Equation (1), and a hydrodynamic radius related to rotational motion, \(\mathrm{D_{Hr}}\), which is expressed by Equation (3) [17]:  
\[\mathrm{D_{r}}=\mathrm{kT}/8\pi\eta(\mathrm{R_{Hr}})^{3}, \tag{3}\]  
### DLS Measurement of Rotational and Translational Contributions in Particle Motions: Nanorods  
The analysis of nanorods in DLS leads to two relaxation modes in the intensity correlation function, as observed and discussed by [PERSON] et al. [18]. From angular dependent DLS experiments on gold nanorods, recorded in different polarization geometries (vertical-vertical vs vertical-horizontal), they have shown that it is possible to determine translational and rotational diffusion coefficients of nanorods from the decay of the intensity correlation function, and attributed this to anisotropy of the polarizability caused by the shape of the particles [18]. Methods for the analysis of non-spherical nanoparticles based electrical birefringence methods are discussed in [19]. Using 3D-ccDLS measurements and the CONTIN and CORENN methods, has allowed us, to determine the rotational and translational diffusion coefficients for gold nanoparticles (spheres and rods, aspect ratios varying from 1 to 5.6), and to calculate the corresponding hydrodynamic radii [10]. A comparison of Cumulants, which are stable in the range of investigated concentrations from 5 to 16 \(\mathrm{\mu}\)g/mL [9], with the CORENN analysis has recently been performed by analyzing the modes of the CORENN size distributions. The values obtained from Cumulants and CORENN analysis were compared by an extrapolation to zero concentration limit by linear regression. We could show that the CORENN method provides precise values of the hydrodynamic radius for rotational and translational motion of the nanorods [9]. The obtained values for the rotational motion (as listed in Table 2) are smaller than the ones earlier obtained using the CONTIN analysis which led to \(\mathrm{R_{H}}\) values around 2-nm for the rotational motion and around 19 nm for the translational motion [10]. For example, for the gold nanospheres a hydrodynamic radius of (\(24.2\pm 0.7\)) nm was found from the analysis of the mode by the CORENN method, compared to an average of 27.6 nm by the CONTIN algorithm [10] and (\(28.50\pm 0.16\)) from Cumulants [9]. The fact that the hydrodynamic radius obtained for nanospheres in DLS experiments exceeds the nominal particle radius of 20 nm (40 nm diameter) as indicated by the supplier based on TEM analysis, is observed in all three cases and could potentially be explained by interaction of the particle with molecules from the liquid [20]. We note, that the above listed values correspond to the hydrodynamic radii as obtained from the analysis of intensity size-distributions. For the nanospheres, by analyzing the number-size distributions, we obtain values around 19 nm, which is in good agreement with the nominal particle radius. An example of an intensity correlation function as measured for the Au NPs at a concentration of 0.0016 mg/mL, as well as the intensity and number distributions obtained from CORENN analysis are shown in Figure 1.