# Chaotic Signatures Exhibited by Plasmonic Effects in Au Nanoparticles with Cells

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## Abstract

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_{2}thin solid film. The inclusion of the nanoparticles in an inhomogeneous biological sample integrated by human cells deposited in an ITO glass substrate was evaluated with a high level of sensitivity using an opto-electronic chaotic circuit. The optical response of the nanoparticles was determined using nanosecond laser pulses in order to guarantee the sensing performance of the system. It was shown that high-intensity irradiances at a wavelength of 532 nm could promote a change in the absorption band of the localized surface plasmon resonance associated with an increase in the nanoparticle density of the film. Moreover, it was revealed that interferometrically-controlled energy transfer mechanisms can be useful for thermo-plasmonic functions and sharp selective optical damage induced by the vectorial nature of light. Immediate applications of two-wave mixing techniques, together with chaotic effects, can be contemplated in the development of nanostructured sensors and laser-induced controlled explosions, with potential applications for biomedical photo-thermal processes.

## 1. Introduction

_{2}-supported Au NPs were studied. An electronic modulator governed by Rössler equations was implemented to identify the electronic effects in the sample irradiated by light. The inclusion of NPs into human cells deposited onto a highly conductive ITO matrix was explored using our chaotic technique. We believe that these findings may be a basis for designing plasmonic and opto-electronic devices which will be improved by chaos theory.

_{2}thin film. Finally, vectorial two-wave mixing experiments were carried out to analyze the evolution of the ablation threshold of biological samples. Potential applications for the instrumentation of multi-scale signals are proposed.

## 2. Materials and Methods

#### 2.1. Synthesis of the Au NPs in a TiO_{2} Film

_{2}solution was prepared using 0.03 mol of precursor. The precursor solution was firstly dissolved in 200 mL of absolute ethanol, and then mixed with a 30% v/v of water-ethanol. Once the mixture was prepared, it was necessary to adjust its pH to 1.25 using hydrochloric acid. The resulting mixture was incorporated into a standard solution of an Au precursor with a volume of 0.7 mL using a metal concentration of 1000 mg/L. An ultraviolet lamp source was used to promote the formation of NPs in the solution. Film samples with an average thickness of 200 nm were prepared by a spin coating technique. Spectrophotometric measurements were undertaken with a Perkin Elmer UV/VIS XLS system. High-Resolution Transmission Electron Microscopy (HRTEM) analysis was carried out with a JEM—ARM200CF&Gatan Ultrascan 1000XP system. The electrical impedance of the samples was measured by an Autolab PGSTAT302N station; this device is a high power potentionstat/galvanostat. The impedance spectra were measured with a 10 mV signal on a 5 mm

^{2}surface of the studied samples and with an integration time of 1 s.

#### 2.2. Preparation of the Biological Sample

^{®}CRL-1427™) derived from osteosarcoma was obtained from the American Type Culture Collection (ATCC, Rockville, Maryland, USA). To evidence the actin cytoskeleton of the osteoblasts, monolayers were prepared on a glass coverslip. Osteoblasts monolayers were fixed with 4% paraformaldehyde for 1 h at room temperature. Then, cells were washed twice with Hank’s balanced saline solution (HBSS) and covered with 80 ng of a rhodamine-phalloidin (Sigma-Aldrich, St. Louis, MO, USA). Excess phalloidin was removed by washing 3 times with HBSS. Finally, the labeled cells were mounted on a glass slide with Vectashield-DAPI (4’, 6-diamidino- 2-phenylindole) (Vector Laboratories, Inc., Burlingame, CA, USA) and observed with a confocal system coupled to an inverted microscope (LSM5 PASCAL Zeiss, Jena, Germany).

#### 2.3. Modeling of Chaotic Electronic Rössler System

#### 2.4. Modification of the LSPR of the Sample by Nanosecond Pulses

#### 2.5. Biosensing Assisted by Au NPs and Steady-State Rössler Attractors

#### 2.6. Laser Ablation Threshold in the Biomarkers under a Vectorial Two-Wave Mixing Irradiation

_{0}, ς

_{0}) is the mathematical description of the amplitude distribution located at the ζ = 0 position S, with a normal direction $\overrightarrow{n}$, r and r’ are the vector located between point ζ = 0 and a normalized point in the plane ζ, and κ = 2π/λ is the wavevector employed in the numerical simulations.

## 3. Results

_{0}= 2.1 GW/cm

^{2}. Figure 4 reveals a gradual irreversible increase in the LSPR absorbance as a function of the optical irradiation.

^{−1}·K

^{−1}, the density ρ = 1 × 10

^{−3}kg/cm

^{3}and the heat capacity C = 1 × 10

^{3}J·Kg

^{−}1·K

^{−1}. Furthermore, the time irradiation exposure for the sample was defined as t = 5 s, whereas the linear absorption coefficient calculated by considering the LSPR spectra was α = 3 × 10

^{6}m

^{−1}. Figure 5 shows a numerical simulation related to the heat transference in our sample irradiated by nanosecond pulses, as described by Equation (8). According to the numerical results, the temperature increases at the region where the Au NPs were located, evidencing laser absorption; this confirms the increase in temperature in this process featuring about 220 K.

_{0}/100 in the TiO

_{2}film without NPs. The conditions for the stability of the system are calibrated according to a reference that may represent the electrical and optical characteristics of a particular region of the sample. The instability of the system is also depicted in Figure 7a; this corresponds to the sample measured in darkness. The incorporation of Au NPs into the TiO

_{2}film generates a well-defined orbit that describes stability, as shown in Figure 7b. Moreover, photoconductivity was confirmed by the steady-state of the chaotic attractor controlled by the increase of the irradiance in the Au NPs doping the TiO

_{2}sample.

^{2}), as illustrated in Figure 10b.

^{2}.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Representative HRTEM micrograph of a region of the studied thin solid film sample showing the Au NPs in dark color.

**Figure 4.**UV-vis absorbance spectra of the studied sample before and after nanosecond pulsed irradiation at 532 nm.

**Figure 5.**Numerical curve for temperature changes exhibited by Au NPs under optical irradiation vs. time.

**Figure 6.**Impedance spectra of the studied sample before and after nanosecond pulsed irradiation at 532 nm.

**Figure 7.**Experimental and numerical data obtained by chaotic modulation in conductivity measurements. (

**a**) Comparison of one experimental measurement on the edge stability of the system, and another with unstable behavior; the first one under irradiation and the second one in darkness; (

**b**) Steady-state Rössler attractors obtained in the studied sample.

**Figure 8.**Representative images of the studied human osteoblasts. (

**a**) Confocal micrograph. Actin cytoskeleton was labeled with rhodamine-phalloidin (green) and cells nuclei were stained with DAPI (blue); (

**b**) Microscopic image of the studied human osteoblasts deposited in the substrate.

**Figure 9.**(

**a**) Evolution of the steady-state Rössler attractors obtained in the Au NPs incorporated into cells; (

**b**) Measurement obtained in dead cells.

**Figure 10.**(

**a**) Fourier spectrum of the steady-state Rössler attractor signal; (

**b**) Calibration curve for the sensitivity calculation.

**Figure 11.**(

**a**) Laser ablation threshold as a function on the angle between the planes of polarization of the incident beams in the cells with incorporated Au NPs; (

**b**) Electric potential distribution field in a pair of Au NPs.

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**MDPI and ACS Style**

Martines-Arano, H.; García-Pérez, B.E.; Vidales-Hurtado, M.A.; Trejo-Valdez, M.; Hernández-Gómez, L.H.; Torres-Torres, C.
Chaotic Signatures Exhibited by Plasmonic Effects in Au Nanoparticles with Cells. *Sensors* **2019**, *19*, 4728.
https://doi.org/10.3390/s19214728

**AMA Style**

Martines-Arano H, García-Pérez BE, Vidales-Hurtado MA, Trejo-Valdez M, Hernández-Gómez LH, Torres-Torres C.
Chaotic Signatures Exhibited by Plasmonic Effects in Au Nanoparticles with Cells. *Sensors*. 2019; 19(21):4728.
https://doi.org/10.3390/s19214728

**Chicago/Turabian Style**

Martines-Arano, Hilario, Blanca Estela García-Pérez, Mónica Araceli Vidales-Hurtado, Martín Trejo-Valdez, Luis Héctor Hernández-Gómez, and Carlos Torres-Torres.
2019. "Chaotic Signatures Exhibited by Plasmonic Effects in Au Nanoparticles with Cells" *Sensors* 19, no. 21: 4728.
https://doi.org/10.3390/s19214728