On the physical limitations for radio frequency absorption in gold nanoparticle suspensions

Abstract

Abstract. 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.

Parameter studies on optimal absorption and electrophoretic resonances in lossy media

“…A relative heating coefficient is defined as F = P loc (r 1 )/P b (r) where P loc (r 1 ) is the mean local heating (in W/m 3 ) generated inside the sphere of radius r 1 , and P b (r) the mean background heating (in W/m 3 ) at some observation radius r > r 1 . In a close vicinity to a small sphere (both r and r 1 are small), an asymptotic analysis, similar as presented in [4], reveals that the optimal excitation that maximizes F is an electric dipole field yielding the relative heating coefficient…”

“…and where k 0 is the wave number of vacuum, see [4,5]. It has recently been shown in [4] that (2), and hence also (1) are locally concave functions in the complex parameter ε 1 and which are maximized by the conjugate match…”

“…In particular, gold nanoparticles (GNPs) can be coated with ligands that target specific cancer cells as well as providing a net electronic charge of the GNPs. One hypothesis is then that the charged GNPs will facilitate an electrophoretic current that can destroy the cancer under electromagnetic radiation [1,4,5]. However, it is also important to observe the complexity of the clinical application with many possible physical and biophysical phenomena to consider, as well as the fact that several authors have questioned whether metal nanoparticles can be heated in radio frequency at all, see e.g., [1,3].…”

“…However, it is also important to observe the complexity of the clinical application with many possible physical and biophysical phenomena to consider, as well as the fact that several authors have questioned whether metal nanoparticles can be heated in radio frequency at all, see e.g., [1,3]. We have recently performed a study on the physical limitations for radio frequency absorption in a spherical suspension where the main theoretical result is the derivation of an optimal conjugate match with respect to the surrounding medium [4]. It is demonstrated in [4] that for a surrounding medium consisting of a weak electrolyte solution, a significant RF-heating can be achieved inside a small GNP suspension, provided that an electrophoretic particle acceleration (Drude) mechanism is valid and can be tuned into resonance at the desired frequency.…”

“…We have recently performed a study on the physical limitations for radio frequency absorption in a spherical suspension where the main theoretical result is the derivation of an optimal conjugate match with respect to the surrounding medium [4]. It is demonstrated in [4] that for a surrounding medium consisting of a weak electrolyte solution, a significant RF-heating can be achieved inside a small GNP suspension, provided that an electrophoretic particle acceleration (Drude) mechanism is valid and can be tuned into resonance at the desired frequency. In this paper, we summarize briefly the new theory, we expand the asymptotic analysis and we demonstrate some new parameter studies related to this application.…”