  This paper presents a study on the physical limitations for radio frequency
absorption in gold nanoparticle suspensions. A canonical spherical geometry is
considered consisting of a spherical suspension of colloidal gold nanoparticles
characterized as an arbitrary passive dielectric material which is immersed in
an arbitrary lossy medium. A relative heating coefficient and a corresponding
optimal near field excitation are defined taking the skin effect of the
surrounding medium into account. For small particle suspensions the optimal
excitation is an electric dipole field for which explicit asymptotic
expressions are readily obtained. It is then proven that the optimal
permittivity function yielding a maximal absorption inside the spherical
suspension is a conjugate match with respect to the surrounding lossy material.
For a surrounding medium consisting of a weak electrolyte solution the optimal
conjugate match can then readily be realized at a single frequency, e.g., by
tuning the parameters of a Drude model corresponding to the electrophoretic
particle acceleration mechanism. As such, the conjugate match can also be
regarded to yield an optimal plasmonic resonance. Finally, a convex
optimization approach is used to investigate the realizability of a passive
material to approximate the desired conjugate match over a finite bandwidth.
The relation of the proposed approach to general Mie theory as well as to the
approximation of metamaterials are discussed. Numerical examples are included
to illustrate the ultimate potential of heating in a realistic scenario in the
microwave regime.
