Spectral Radiative Properties of Three-dimensionally Ordered Macroporous Ceria Particles

Radiative properties of spherical heterogeneous particles consisting of threedimensionally ordered macroporous (3DOM) cerium dioxide (ceria) are numerically predicted in the spectral range 0.3–10μm. The particles are 1μm in diameter, with interconnected pores of diameter 330 nm and a face-centered cubic lattice arrangement. Predictions are obtained by solving macroscopic Maxwell’s equations using the discrete dipole approximation and the finite element method as a complementary means of numerical prediction. The scattering and absorption efficiency factors as well as the asymmetry factor are determined as a function of the particle orientation relative to the direction of the incident plane wave. The scattering and absorption efficiency factors show significant dependence on the particle orientation in the spectral range equal to particle diameter to 560 nm. Compared to homogeneous ceria particles, 3DOM particles of identical size tend to cancel the wave extinction for wavelength greater than 560 nm. Approximating the 3DOM particles as a homogeneous sphere with properties calculated from an effective medium theory is also considered. This approach is shown to be valid only for wavelengths much greater than the pore size, demonstrating that a detailed geometrical representation of the internal particle structure is essential to obtain accurate radiative characteristics of nano-structured particles. NOMENCLATURE ap lattice parameter, m A dipole moment coefficient matrix d dipole lattice parameter, m Dp pore diameter, m ~ E electric field, N C−1 g asymmetry factor ~ H magnetic field, A m−1 k complex component of refractive index m complex refractive index n real component of refractive index Q efficiency factor p porosity ~ P dipole moment vector, A m−1 rp particle radius, m ~r location in space, m ~S time-averaged Poynting vector, W m−2 V integration volume, m3 Greek symbols α polarizability Γ integration surface, m2 permitivity, F m−1 η wavenumber, m−1 θ particle orientation angle λ wavelength, m σ electrical conductivity, S m−1 φ particle orientation angle ω angular frequency Ω solid angle, sr Subscripts and superscripts abs absorption eff effective ext extinction inc incident rel relative sca scattering tot total 0 vaccuum 1Corresponding author. Tel.: +1 612 626 0875; fax: +1 612 626 1854. E-mail address: [email protected] (W. Lipiński)