In this paper we provide a mathematical framework for localized plasmon resonance of nanoparticles. Using layer potential techniques associated with the full Maxwell equations, we derive small-volume expansions for the electromagnetic fields, which are uniformly valid with respect to the nanoparticle's bulk electron relaxation rate. Then, we discuss the scattering and absorption enhancements by plasmon resonant nanoparticles. We study both the cases of a single and multiple nanoparticles. We present numerical simulations of the localized surface plasmonic resonances associated to multiple particles in terms of their separation distance.

Caustic nuclear wastes have leaked from tanks at the US Department of Energy’s Hanford site in Washington State (USA) causing hundreds of thousands of gallons of waste fluids to migrate into the underlying sediments. In this study, four simulant tank waste (STW) solutions, which are high in NaOH (1.4 and 2.8 mol/kg), NaNO3 (3.7 mol/kg) and NaAlO2 (0.125 and 0.25 mol/kg), were prepared and reacted with reference kaolinite KGa-1 and KGa-2 at 50 and 80°C for up to 2 months. The structure and morphology of the resulting products were characterized using X-ray diffraction, scanning electron microscopy, and Fourier transform infrared spectroscopy. The products were also examined for cation exchange and Cs+ sorption as a function of ionic strength and types of cations in the background solutions. Cancrinite and sodalite were the only new minerals observed in all of the conditions tested in this experiment. Two major chemical processes were involved in the reactions: dissolution of kaolinite and precipitation of cancrinite and sodalite. Increasing NaOH concentration and temperature, and decreasing NaAlO2 concentration increased the transformation rate. Both cancrinite and sodalite appeared stable thermodynamically under the experimental conditions. The newly formed feldspathoids were vulnerable to acid attack and pronounced dissolution occurred at pH below 5.5. Cancrinite and sodalite can incorporate NaNO3 ion pairs in their cages or channels. Sodium in cancrinite and sodalite was readily exchangeable by K+, but less easily by Cs+ or Ca2+. The feldspathoid products sorb nearly an order of magnitude more Cs+ than the unaltered kaolinite. The Cs adsorption is reduced by competing cations in the background solutions. At low ionic strength (0.01 M NaNO3 or 0.005 M Ca(NO3)2), Ca2+ was more competitive than Na+. When the concentration of the background solution was increased 10 times, Na+ was more competitive than Ca2+.

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[1] Capillary forces acting at the air-water interface play an important role in colloid fate and transport in subsurface porous media. We quantified capillary forces between different particles (sphere, cylinder, cube, disk, sheet, and natural mineral particles) and a moving air-water interface. The particles had different sizes and contact angles (ranging from 14°to 121°). Theoretical calculations using the Young-Laplace equation were used to support and generalize the experimental data. When the air-water interface moved over the particles, there were strong capillary forces acting on the particles in the direction of the moving interface. The measured maximum capillary forces were similar to those calculated by the Young-Laplace equation. The larger the contact angles and the larger the particle size, the stronger were the capillary forces. Particles with irregular shape and sharp edges experienced greater forces than smooth particles. Generalization of the results indicates that capillary forces exerted by a moving air-water interface can readily exceed attractive Derjaguin-Landau-Verwey-Overbeek (DLVO) and gravity forces for typical subsurface particles, and a moving air-water interface is therefore an effective mechanism for mobilization of particles in porous media. Particles in the colloidal size range are particularly susceptible for mobilization by a moving air-water interface.Citation: Shang, J., M. Flury, and Y. Deng (2009), Force measurements between particles and the air-water interface: Implications for particle mobilization in unsaturated porous media, Water Resour. Res., 45, W06420,

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We consider plasmon resonances and cloaking for the elastostatic system in R 3 via the spectral theory of Neumann-Poincaré operator. We first derive the full spectral properties of the Neumann-Poincaré operator for the 3D elastostatic system in the spherical geometry. The spectral result is of significant interest for its own sake, and serves as a highly nontrivial extension of the corresponding 2D study in [8]. The derivation of the spectral result in 3D involves much more complicated and subtle calculations and arguments than that for the 2D case. Then we consider a 3D plasmonic structure in elastostatics which takes a general core-shell-matrix form with the metamaterial located in the shell. Using the obtained spectral result, we provide an accurate characterisation of the anomalous localised resonance and cloaking associated to such a plasmonic structure.

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