We employ the coupled dipole method to calculate the polarizability tensor of various anisotropic dielectric clusters of polarizable atoms, such as cuboid-, bowl-, and dumbbell-shaped nanoparticles. Starting from a Hamiltonian of a many-atom system, we investigate how this tensor depends on the size and shape of the cluster. We use the polarizability tensor to calculate the energy difference associated with turning a nanocluster from its least to its most favorable orientation in a homogeneous static electric field, and we determine the cluster dimension for which this energy difference exceeds the thermal energy such that particle alignment by the field is possible. Finally, we study in detail the (local) polarizability of a cubic-shaped cluster and present results indicating that, when retardation is ignored, a bulk polarizability cannot be reached by scaling up the system.
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This proof relies on the fact that , which, in turn, can be proven by using induction in combination with the general expression for the inverse of a matrix built up of submatrices: where
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From Eq. (18), we could also have derived an explicit expression for the orientational energy of the cluster shapes discussed in this article: where in the first line we used αxx = αyy and in the second line, we introduced the angle θ between and the z axis. From the resulting expression, it is clear that the extrema of the orientational energy are located at θ = 0 and θ = π/2 and that the difference in orientational energy between the two extrema is indeed given by Eq. (19).
51.
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2011
American Institute of Physics
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