A study of the interaction between nanoparticles and light: an experimental proof and visualisation of Mie theory in polymer composites

E. G. Wrigglesworth, J.H. Johnston
Victoria University of Wellington,
New Zealand

Keywords: gold nanoparticles, Mie theory, polymer composites, localised surface plasmon resonance, absorption, scattering


Gold nanoparticles have long been utilised for their attractive colours. A well-known example is the Lycurgus cup, dated at the 4th century, which appears red when viewed in transmitted light and green in reflected light due to the presence of gold/silver/copper nanoparticles in the glass. About 1500 years later in the 1850s, the science behind gold nanoparticle colour was first explored with Michael Faraday’s studies on the optical properties of gold colloids. However the theory behind the observed colours was not truly understood until Gustav Mie published a mathematical description of the absorption and scattering of electromagnetic radiation by a spherical nanoparticle in 1908. This became known as Mie theory. The interaction between nanoparticles and light remains of significant interest to the nanotechnology community, as understanding this interaction allows us to predict the nanoparticle size, shape and material that is most suitable for various applications. Metallic nanoparticles undergo localised surface plasmon resonance (LSPR) effects; the oscillation of nanoparticle conduction electrons upon resonance interaction with incoming electromagnetic radiation. LSPR greatly enhances the absorption and scattering of light by nanoparticles described by Mie theory. The size, shape and composition of the particles determine the frequency at which the electron oscillation and incoming light are resonant, and hence the wavelength of the LSPR absorption/scattering and the colour that is displayed. For example, spherical gold nanoparticles with diameters of 20 nm undergo LSPR resonance at approximately 520 nm which gives a red coloured colloid. Increasing the size of the particles results in a red-shift in the LSPR absorption and a change in colour from red to purple to grey. It is also known that nanoparticle size and shape determine the ratio of LSPR scattering to absorption. First shown computationally by Jain and co-workers for spherical gold nanoparticles, increasing nanoparticle size results in an increase in scattering and a proportional decrease in absorption. The high scattering property of large metallic nanoparticles is exploited in biomedical imaging and other applications. We present an experimental proof of Mie theory first demonstrated computationally by Jain and co-workers. Utilising the CloudSpec spectrophotometer developed by MaramaLabs, we have experimentally determined the relationship between gold nanoparticle size and the ratio of scattering to absorption. The resulting relationship compares well to Mie theory analysis, acting as an experimental proof of the theory developed over 100 years ago. We have further incorporated these particles into polymers to create solid-state composites that provide a visualisation of Mie theory. A colour change from purple to grey as well as an increase in the scattered colour is observed with an increase in nanoparticle size. Such materials have a range of applications in the areas of security and design. Additionally they could be used as a teaching tool to aid in understanding of gold nanoparticle physics and Mie theory.