1. Lecture 14: RF Optics of Nanoparticles
Content:
Introduction
Method
One-Temperature Model
Absorption Efficiency of Nanoparticles in the RF Range of the Spectrum
RF Absorption Efficiency of Metal Nanoparticles
RF Absorption Efficiency of Dielectric Nanoparticles
Conclusions

2. Introduction
In Section 4.2 we discussed x-rays as a universal tool for nanoparticle activation.
X- rays have the ability to penetrate into the human body and have high photon energies, giving a great opportunity to activate/heat nanoparticles inside the body for diagnostic and treatment purposes.
However, the x-ray itself is toxic to the body and can cause a secondary cancer at the therapeutic doses.
Another candidate for an ideal radiation for nanoparticles activation is radiofrequency (RF) waves.
RF waves have an excellent ability to penetrate into the human body, giving a great opportunity to activate/heat nanoparticles delivered inside the body as a contrast agent for diagnosis and treatment purposes.

3. Introduction (continued)
However, the heating of NPs in the RF spectral range is controversial in the research community because of the low power load of RF waves and low absorption efficiency of nanoparticles in the RF range.
For example, a theoretical paper by Hanson et al. analyzed several absorption mechanisms, including both classical and quantum effects, by which nonmagnetic spherical nanoparticles can absorb RF and far-infrared radiation, which can be subsequently released to their host medium as heat.
They concluded that none of these absorption mechanisms can increase temperatures by tens of degrees as reported in many RF-GHz experiments.

4. Introduction (continued)
On the other hand, there is recent experimental evidence of using metal NPs to deposit heat in a local confined space for RF ablation of cancer.
For example, Raoof et al. reported the death of liver cancer cells after targeting those cells with Au nanoparticles and exposing them to an RF field.
Moran et al. examined the capacitive RF heating properties of Au nanoparticles with respect to their volume fraction and diameter.
In these experiments it has been shown that using RF fields along with conjugated gold nanoparticles significantly decreases the volumes of pancreatic tumor cells.
99% tumor death in human gastrointestinal cancer cells has been demonstrated using a MHz RF field and 1-5 min exposures for a concentration of 67 μM/L Au nanoparticles.

5. Introduction (continued)
Overall, all of the experiments listed in the table below have reached significant temperature changes that confirm the possibility of cell ablation.
In this lecture, we use a phenomenological approach to find the absorption efficiency for different types of nanoparticles.

6. Method
We use a reverse phenomenological approach to estimate the absorption efficiency for different types of nanoparticles in the radiofrequency range of the spectrum.
The reverse method consists of three steps:
(1) plugging the available RF experimental data into a well-proven thermal model for heating the nanoparticles, known as the one-temperature model (OTM) developed by Letfullin et al.;
(2) solving the OTM numerically to compute temperature curves based on the nanoparticle’s shape, its composition material, the type and intensity of radiation it is exposed to, and its surrounding medium; and
(3) determining the absorption efficiency of NPs in the RF spectral range by adjusting the OTM results until the theoretical temperature change meets that observed experimentally under the same heating conditions.

7. One-Temperature Model
The one-temperature model is derived in Chapter 6 with provided computer code for simulation of heating of nanoparticles by radiation.
Here, the OTM is briefly demonstrated below, with a table that explains each variable:
Table. OTM variables and their units.
Qabs
Absorption efficiency of NP
I0 [W/cm2]
Intensity of RF radiation
f(t)
Pulse shape r0
Radius of NP
C(T)
Specific heat of NP 0
Density of NP µ0
Heat conductivity of surrounding medium T
Final temperature of NP s
Exponential power T0
Initial temperature of NP L
Latent heat dt
Time step

8. One-Temperature Model (continued)
The first term on the right side of the equation expresses the amount of energy absorbed by the spherical nanoparticle. It depends on the size, material properties of the nanoparticle, absorption efficiency, and the intensity of the radio wave.
The second term describes nanoparticle’s energy loss due to thermal diffusion into the surrounding medium. This term is governed by the size and material properties of the nanoparticle, as well as the thermal properties of the medium.
The final term deals with evaporation of the nanoparticle, if the phase transition temperature is reached.

9. RF Absorption Efficiency of Metal Nanoparticles
Gold is nontoxic to living tissue, and Au nanoparticles have been well studied.
In experiments by Moran et al., a colloidal solution of gold nanoparticles with radius 5 nm in deionized water was exposed to a radiofrequency field.
The achieved temperature change in this experiment is ΔT = 45 K above ambience.
This temperature change is attained then in the OTM by varying the absorption efficiency value until the maximum temperature matches the maximum temperature change achieved in the experimental study.
The simulations show that the absorption efficiency of Au nanoparticles in the RF range corresponding to this experimental change in temperature is 1.2 × 10−9.

10. RF Absorption Efficiency of Metal Nanoparticles (continued)
Here we present the results of the simulations for heating a 5-nm radius gold nanoparticle by a single RF pulse performed under the same experimental conditions.

11. RF Absorption Efficiency of Metal Nanoparticles (continued)
Similar experiments were conducted by Gannon et al., who measured the heat generation in a 2.5-nm Au nanoparticle colloidal solution by RF waves (13.56 MHz, 600 & 800 W).
Applying the technique described above, we find that the average absorption efficiency for 2.5-nm gold nanoparticles with concentration 11.1 μM/L is 0.8 × 10−9 for MHz radiation and W power range.
In the experiments by Raoof et al. and Moran et al., the highest temperature reached was 348 K.
The absorption efficiencies that we calculated using experimental data from Moran et al. and Raoof et al. were averaged to give 1.15 × 10−9 for identical conditions used in the experiments: both used 5-nm radius Au nanoparticles, 600 W of power, MHz, and 120 s heating time.

12. RF Absorption Efficiency of Dielectric Nanoparticles
Lots of research has been done with carbon nanotubes in recent years.
For example, Gannon et al. achieved a rise in temperature of 25-45°C above ambience using single-wall carbon nanotubes that range from 300 nm to 1 μm in length at a concentration of 50 mg/L exposed to an RF field with a peak field strength of approximately 15 kV/m.
The OTM simulations were performed using the same conditions as Gannon’s experiment to compute the absorption efficiency for a wide range of carbon nanoparticles sizes of 5 nm-500 nm.
All of the obtained absorption efficiencies for carbon nanoparticles are in the range of 1.01 × 10−8 to 8.70 × 10−6.
The reason for a large range of absorption efficiencies is because of various possibilities between dimensions of length.

13. RF Absorption Efficiency of Dielectric Nanoparticles (continued)
By extrapolating absorption efficiencies from the simulation results, the curve shown in the figure below is plotted, which can be used to predict the absorption efficiency for carbon nanoparticles of various sizes.

14. RF Absorption Efficiency of Nanoparticles
The results for the absorption efficiency in the RF spectral range along with the highest temperature achieved for metal and dielectric nanoparticles studied are summarized in Table below.
Material
Absorption efficiency
Maximum temperature (K)
Metal (aluminum oxide, gold, magnesium oxide, nickel oxide, silver) sphere, 2.5-nm radius
0.8×10-9
366.5
Metal sphere, 5-nm radius
1.15×10-9
349.1
Metal sphere, 20-nm radius
6.10×10-9
360.1
Metal sphere, 50-nm radius
2.73×10-8
360.2
Metal sphere, 100-nm radius
1.47×10-7
360.5
Dielectric (carbon, fullerene, glass, polystyrene) sphere, 5-nm radius
1.21×10-11
300.6
Dielectric sphere, 50-nm radius
1.01×10-8
326.0
Dielectric sphere, 100-nm radius
7.62×10-8
339.0
Dielectric sphere, 150-nm radius
26×10-8
344.6
Dielectric sphere, 250-nm radius
112×10-8
344.8
Dielectric sphere, 500-nm radius
870×10-8
345.2

15. RF Absorption Efficiency of Nanoparticles (continued)
The curves achieved through the OTM simulations can be viewed in the figure below.
The simulations show that all of the metals have the same heating kinetics and almost identical time-temperature profiles for the same conditions of RF heating.
The heating of different dielectric nanoparticles, like in the metal case, has similar curves as well for the same conditions of RF heating.

16. Conclusions
We have applied a reverse phenomenological approach to determine the absorption efficiency for different types of nanoparticles in the RF range of the spectrum by matching the theoretically achieved maximum temperature of the nanoparticles to the experimentally observed temperature change at the same heating conditions.
This method based on the study of heating kinetics gives the following estimations for the absorption efficiency of nanoparticles in the RF range of the spectrum:
The absorption efficiency of the researched metal nanoparticles with radius 5 nm is ~ 1.15×10-9.
The absorption efficiencies of carbon spherical nanoparticles with radii of 5 nm and 500 nm are 1.21×10-11and 8.70×10-6, respectively.
The absorption efficiency of dielectric nanoparticles such as glass, polystyrene and fullerene with radius of 5 nm is estimated to be 1.21×10-11.