A comparative study of classical approaches to surface plasmon resonance of colloidal gold nanorods

We report the errors in the evaluation of the surface plasmon resonance of gold nanorods by three classical approaches: the Gans model, the Discrete Dipole Approximation and the Surface Integral method. Using these methods, which are based on the propagation of an electromagnetic wave through a composite medium with different refractive indices, might result in an inaccurate prediction of absorption maxima. For test samples of nanorods prepared by a seed-mediated method, whose homogeneity and quality were also fully demonstrated in this study, the mismatches in the wavelengths of absorption maxima $ \left| {\varDelta {\lambda_{\max }}} \right| $ between experimental and theoretical data were observed to be greater than 50 nm. In general, the observed surface plasmon resonances exhibit two distinctive bands corresponding to the transverse and longitudinal modes. The weak transverse mode was located in the region from 510 to 518 nm and varied slightly with the aspect ratio of the rods. In contrast, the longitudinal mode showed a strong dependence on aspect ratio and ranged from 658 to 768 nm. We demonstrated that the mismatches may be sufficiently reduced if the interdependence between these two modes is taken into account.