Determination of SWCNT diameters from the Raman response of the radial breathing mode

We report on the evaluation of the distribution of diameters for nanotube s amples with a wide variation of mean diameters. Such results were obtained from a detailed analysis of the radial breathing mode Raman response and co mpared to results obtained from an evaluation of optical spectra and X-ray diffraction pattern. The evaluation of the Raman data needs a well refined analysis as the experimental analysis exhibits a rather complicated and osc illating relation between response and exciting laser. Both, an exact calcu lation where the density of states was considered explicitly and an approxi mate calculation were applied. Both models used for the analysis are able t o explain several unexpected results from the experiment such as the oscill ating behavior of the spectral moments, unusual discontintuities in the. fi rst moments of the Raman response for excitation in the IR, a fine structur e for the response in optics and Raman, and an up shift of the RBM frequenc y as compared to qualified ab initio calculations. In detail the first mome nt and the variance of the spectra were used for the evaluation of the diam eter distribution. To obtain good results between experimental and theoreti cal oscillation pattern the transition energy between the first two van Hov e singularities had to be scaled up which is considered as a result from co ulomb interaction of the electrons in the tubular material. On the other ha nd the analysis does not only allow to determine the mean value and the wid th of the diameter distribution but yields also a value for the average bun dle diameters or, alternatively, the strength of the tube-tube interaction. The model used for the analysis of the Raman data is also appropriate to a nalyze the optical response, at least for the spectral range from 0.5 eV to 3.5 eV. The fine structure in the response for the transitions between the three lowest van Hove singularities is well reproduced and the mean tube d iameters and their distribution is obtained in very good agreement with the results from the Raman analysis. From the X-ray analysis the same mean val ues and comparable distributions for the tube diameters were received where as the bundle diameters could not be retained with high precision in this c ase.