Radiofrequency interaction with conductive colloids: Permittivity and electrical conductivity of single‐wall carbon nanotubes in saline

Abstract

Conductive nanoparticles may enhance tissue heating during radiofrequency (RF) irradiation. Specific absorption rate (SAR) is known to rise with the electrical conductivity of tissue. However, no studies to date have measured the relationship between complex permittivity and nanoparticle concentration in tissue-like samples. The complex permittivities of colloids containing single-wall carbon nanotubes (SWCNTs) in normal (0.9%) saline were measured from 20 MHz to 1 GHz. Carbon concentrations ranged from 0 to 93 mM (0.06% volume), based on SWCNT weight per volume. Measurements were made with 0.02% Pluronic F108 surfactant added to the colloids to prevent SWCNT flocculation. The data were fit to the Cole-Cole relaxation model with an added constant phase angle element to correct for electrode polarization effects at low RF frequencies. Electrode polarization effects increased with carbon concentration. The real parts of the permittivities of the colloids increased with carbon concentration. The static conductivity rose linearly with carbon concentration, doubling from 0 to 93 mM. The SAR of the colloids is expected to increase with RF frequency, based on the properties of the imaginary part of the permittivity.

Comparison of complex permittivities of isotonic colloids containing single‐wall carbon nanotubes of varying chirality

“…The results tend to support our second hypothesis that the composition of the isotonic electrolyte has a significant effect on the colloid permittivity. The mixed SWCNTs used in this study had fewer impurities than the purified HiPCO SWCNTs ($7% Fe) used in our previous study [Gach and Nair, 2010]. Nevertheless, the static conductivities of the colloids were similar.…”

“…SWCNTs flocculate in PBS due to their hydrophobic nature. Therefore, nonionic surfactant Pluronic F108 (0.02% weight/volume) was added to the PBS colloids prior to the complex permittivity measurements to ensure adequate suspension of the SWCNTs during the measurements and minimize the effects of the surfactant on the complex permittivities [Gach and Nair, 2010]. Bovine serum albumin (0.5% weight/volume) was added to the DMEM samples after their characterization by the dielectric probe, and the resulting colloids were remeasured.…”

“…Electrode polarization effects that arise during the characterization of conductive colloids can be modeled using a constant phase angle element that is added to the complex permittivity [Bordi et al, 2006;Gach and Nair, 2010]:…”

“…The plasmon resonances and permittivities of isolated carbon nanotubes are conducive for optical and RF hyperthermia, respectively. The complex permittivities of saline-based colloids containing purified single-wall carbon nanotubes (SWCNTs) of mixed chiralities were recently reported, demonstrating that both the real and imaginary parts of the permittivities of the bulk colloid rose with SWCNT concentration [Gach and Nair, 2010]. The SAR was found to rise linearly with the colloid's electrical conductivity under RF irradiation.…”

“…However, in theory, RF fields will cause higher heat loss in conductive nanoparticles than magnetic nanoparticles assuming equivalent field conditions and achievable nanoparticle conductivities and permeabilities [Hanson, 1991;Schaefer, 2001;Pankhurst et al, 2003;Hergt et al, 2004;Ma et al, 2004;Chen et al, 2008;Gach and Nair, 2010;Poo et al, 2010]. Optical hyperthermia based on nanoparticle plasmon resonances can achieve heat losses approximately one billion times higher than E-or H-field heating, but optical techniques are generally not feasible in vivo because the light source must be placed at the treatment site [Zharov and Lapotko, 2005;Jain et al, 2006].…”