Experimental approach to the fundamental limit of the extinction coefficients of ultra-smooth and highly spherical gold nanoparticles

The theoretical extinction coefficients of gold nanoparticles (AuNPs) have been mainly verified by the analytical solving of the Maxwell equation for an ideal sphere, which was firstly founded by Mie (generally referred to as Mie theory). However, in principle, it has not been directly feasible with experimental verification especially for relatively large AuNPs (i.e., >40 nm), as conventionally proposed synthetic methods have inevitably resulted in a polygonal shaped, non-ideal Au nanosphere. Here, mono-crystalline, ultra-smooth, and highly spherical AuNPs of 40-100 nm were prepared by the procedure reported in our recent work (ACS Nano, 2013, 7, 11064). The extinction coefficients of the ideally spherical AuNPs of 40-100 nm were empirically extracted using the Beer-Lambert law, and were then compared with the theoretical limits obtained by the analytical and numerical methods. The obtained extinction coefficients of the ideally spherical AuNPs herein agree much more closely with the theoretical limits, compared with those of the faceted or polygonal shaped AuNPs. In addition, in order to further elucidate the importance of being spherical, we systematically compared our ideally spherical AuNPs with the polygonal counterparts; effectively addressing the role of the surface morphology on the spectral responses in both theoretical and experimental manners.