ROUGH DRAFT authorea.com/115594

# Radiative properties of ordered and disordered porous ceria particle clouds under solar irradiation

Abstract

We study the radiative behavior of particle clouds consisting of two types of highly porous spherical ceria particles under direct solar irradiation—one with a templated three-dimensionally ordered macroporous (3DOM) structure and the other with pores randomly located within the structure. Individual radiative properties—the scattering efficiency factor, absorption efficiency factor, and the scattering phase function—of the randomly porous particles are numerically predicted in this work for comparison against existing 3DOM data. Clouds of monodisperse particles with a spatially uniform particle density are studied for each case. Solutions are compared to results based on individual particle scattering properties obtained from an effective medium theory combined with Mie theory results. It is found that the high degree of order in 3DOM particles does not significantly change the radiative properties of the cloud. However *something interesting*.

## introduction

The emerging field of high-temperature solar thermochemistry holds tremendous promise to disrupt the conventional paths of producing fuels, energy-intensive commodity materials and generating dispatchable power. Direct solar irradiation is concentrated by mirrors, captured by a receiver, converted into high-temperature process heat, often exceeding $$\mathrm{1000K}$$, and used to drive highly-endothermic processes for production of chemical fuels and materials including synthesis gas, carbon black, ammonia, lime, and metals (Bader in print)(Fletcher 2001)(Steinfeld 2003)(Kodama 2003). Production of the components of synthesis gas, $$\mathrm{H_{2}}$$ and $$\mathrm{CO}$$, can be achieved in a single thermal dissociation step (thermolysis) followed by a high-temperature gas separation. However, the excessively high temperatures required for such chemistry pose serious limitations for practical implementation. For example, the thermolysis of $$\mathrm{H_{2}O}$$ and $$\mathrm{CO_{2}}$$ require temperatures exceeding $$\mathrm{2500K}$$ in order to obtain significant $$\mathrm{H_{2}}$$ and $$\mathrm{CO}$$ concentrations, respectively (Bader in print). Alternatively, thermochemical redox cycles can be employed, in which active materials undergo cyclic reduction and oxidation (redox) reactions, with the net effect of splitting $$\mathrm{H_{2}O}$$ and $$\mathrm{CO_{2}}$$. In addition to lowering process temperatures, the added process steps can be leveraged to eliminate energetically expensive gas-phase separation requirements. High-temperature solar thermochemical reactors are designed for maximum solar-to-chemical energy conversion efficiency, to minimise the required size of the optical concentrators, and thus to improve the economic viability of the process (Palumbo 2004). The rapid and efficient transfer of energy from a concentrated solar source to the redox material—i.e. the transfer of energy from photons to chemical bonds—is therefore a critical research aspect for efficient reactor design. To this end, we study here the performance of a class of porous particles of cerium dioxide redox materials under highly-concentrated, direct solar irradiation. We believe these materials to hold promise for efficient energy transfer for a number of reasons we outline here. More specifically, we will answer the questions: ”Why particles?”, ”Why ceria?”, and ”Why porous?” while outlining the relevant literature in the process.

Unlike bulk materials, particles can have an absorption efficiency (potentially much) greater than unity. Note that this may seem impossible given the fact that absorption efficiency must be equal to emissivity by Kirchoff’s law and that a blackbody—the perfect emitter—cannot have an emissivity greater than one. However, the idea of a perfect blackbody is restricted to surfaces with low curvature. Both Planck and Kirchoff were clear on this when deriving their famous laws (Bohren 1998). Thus, for a material to absorb very well relative to its size—the trait needed to achieve high energy densities within a particle with relatively little input—we look at materials with features on the scale of the wavelength of light. Perhaps the simplest conceivable geometry is the sphere as we consider here.

Ceria has received significant attention as a redox material because of its relatively fast reaction rates and ability to remain in a solid state throughout the redox process which relieves previous problems associated with ferrite-based oxides and volatile metal oxides such as $$\mathrm{ZnO}$$ and $$\mathrm{SnO_{2}}$$ (Chueh 2010) (Chueh 2010a). The demonstrated ability of ceria to be used as a redox active material and the availability of relevant data make it a very strong candidate to be optimized for high-efficiency thermochemical cycling. The spectral optical properties of ceria are well-known (Patsalas 2002) at room temperature in its stoichiometric form and the thermodynamic properties of non-stoichometric ceria are available allowing detailed modeling in pursuit of this goal. Indeed, researchers have already begun to explore the potential for ceria-particle-based solar thermochemical reactor designs using numerical modeling (Scheffe 2014) (Oles 2015) (Bader 2014a).

The work we present here is divided in two parts. First we study the effect of pore and particle size on scattering properties of highly porous ($$\approx 85\%$$) ceria particles with a random pore structure in the spectral range $$\mathrm{0.29-10\mu m}$$ using electromagnetic theory. These results are then used to study the behavior of clouds of such particles under the single scattering approximation in the geometrical optics limit. Radiative properties of the cloud is compared against clouds of previously characterized ceria particles with the same porosity but a highly ordered pore structure. An effective medium theory along with Lorenz–Mie theory is used as an inexpensive alternative to the full electromagnetic characterization. Particle densities considered correspond to estimates of the densities achievable in the pneumatic transport regime of fluidization according to a well-known correlation.