Thickness Effects on Light Absorption and Scattering for Nanoparticles in the Shape of Hollow Spheres

We reveal the thickness effects on optical properties for nanoparticles in the shape of hollow spheres theoretically and experimentally. Within and beyond the electrically small limit, hollow spheres are shown to have almost the same light absorption power as that of solid ones, when the ratio of inner core to whole particle radii is smaller than 0.4. It means that one can maintain the level of light absorption even with a large empty core. In the electrically small limit, we expand the exact solution of Mie theory in power of the thickness parameter and show that the thickness ratio has less influence on light absorption. Moreover, we synthesize highly uniform hollow spheres of TiO2 anatase through a self-sacrificing template method. A variety of particle radii from 94 to 500 nm, with 50 nm in the shell thickness, are performed experimentally in photocatalytic activity. With experimental demonstrations and theoretical simulations, our results provide a guideline in the design on the thickness for hollow-sphere nanoparticles with an optimized absorption power in light harvesting. ■ INTRODUCTION Photocatalyst has acted as one of solutions to utilize solar light into available energy, with environmental friendly and highly efficient materials synthesized for water splitting, CO2 reduction, and green energy applications. In particular, TiO2 is the major photocatalyst to decompose water into hydrogen and oxygen and used as a clean and recyclable energy source for hydrogen fuel. It is known that TiO2 has the energy gap about 3.2 eV, and when excited by a UV−visible light source, a pair of electron and hole is generated. Consequently, this excited electron−hole pair migrates to the surface to serve as electron donor and acceptor, resulting in the photocatalytic reaction. Based on this series of electrochemical reactions, several methods are demonstrated to enhance the photocatalytic activity with TiO2. For example, to reduce the recombination of separated electron−hole pairs, one can blend various TiO2 phases, deposit metal materials on the surface, or introduce trapping sites to inhibit the recombination. As the aim to extend absorption regime in TiO2 to visible wavelength, doping specific metal or nonmetal elements are demonstrated for light harvesting. Instead of chemical or material approaches mentioned above, intricate structure and morphology can exhibit fascinating properties to improve photocatalytic activity. Inspired by materials in nature, like seashells and plant seeds, an alternative way to enhance photocatalytic performance is utilizing nanosized TiO2 particles. 15 As a rule of thumb, the exposure surface area grows when the size of particles decreases. For light absorption and scattering, it is known that resonance effect emerges as the size of the nanoparticle approaches the wavelength of incident light, known as Mie’s scattering effect. Recently, size-dependent Mie’s scattering effect with TiO2 nanoparticles is reported for a superior photoactivity of H2 evolution. In addition to synthesizing different geometrical sizes, nanoparticles can also be formed in the shape of hollow spheres, which have been widely used as adsorbents, delivery carriers, catalysts, and biomedical detectors. Even though enhancement in photocatalytic function by a variety of geometrical structures has been demonstrated, a systematic investigation to understand the thickness effect on light absorption for nanoparticles in the shape of hollow spheres is still needed to provide a guideline to design optimized core− shell structures for light harvesting. By taking the complicated photoelectrochemical reaction as a pure optical problem, in this work, we study optical response of incoherent hollow spheres with different geometrical and material parameters based on the exact solutions of Mie’s scattering theory. Analytically, we derive the formula for light absorption and scattering coefficients by expanding the thickness parameter. Our theoretical results not only give good agreement to the numerical solutions conducted from Mie theory, but also reveal a counterintuitive scattering property of hollow spheres. We find that as long as the thickness ratio, that is, the ratio of inner core radius to whole particle radius is smaller than a critical value, about 0.4, an individual hollow sphere is shown to have almost the same light Received: August 30, 2015 Revised: October 16, 2015 Published: October 23, 2015 Article