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Computational Analysis of Laser Induced, Plasmonic Nanobubble Generation

by Ioannis H. Karampelas, Qian Xie and Edward P. Furlani

In recent years, the study of metallic nanoparticles is becoming an ever growing research field. The fact that nanoparticles can be excited by NIR wavelengths makes them perfect for bio-applications. Many research groups around the world have shown that nanoparticles can be used for therapeutic applications such as localized cell damage and drug dispersal through laser induced nanobubble generation. However, experimentalists in this field do not have any guidelines on the details governing nanobubble generation, such as plasmonic wavelength and required laser intensity, often exagerating the amount of power required and eventually destroying the nanoparticles by reaching the evaporation temperature of the metal. With this work we aim to give experimentalists a basic guide on appropriate wavelength, laser intensity and required amount of power to create and sustain nanobubbles, for different particle geometries. More specifically:

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Pulsed Illumination of Gold Nanosphere in Fluid

In this study, we present an analysis of photothermal effects associated with nanosecond-pulsed, laser-illuminated gold nanoparticles immersed in aqueous solutions. We used combined computational electromagnetic and fluid analysis to model the fundamental aspects of this process. We studied energy conversion within the nanoparticles at plasmon resonance, heat transfer to the fluid, homogenous bubble nucleation and the dynamic behavior of the bubble and surrounding fluid. In addition, we demonstrated the theory via application to various nanoparticle geometries such as spheres, rods and tori. We show that process parameters such as laser intensity, pulse duration, wavelength, polarization and particle geometry can be tuned to control the size and behavior of nucleated bubbles. Moreover, we present results on multi-particle systems and demonstrate that cooperative heating allows for the generation of larger bubbles using significantly less energy as compared to single-particle systems. We discuss details of the modelling approach and specific applications including recent advances in photothermal tissue therapy at the cellular level.

Sphere

The first type of geometry we studied is a gold nanosphere, 30 nm in radius, immersed in water. Both photonic and fluidics analyses were performed. The plasmon resonance wavelength was found to be 532nm. The power required to reach nucleation is 152E-6 W with a pulse duration of 5ns. The nanoparticle reaches a maximum temperature of ~1100K which is below the melting point of gold. The results are presented in the following pictures/video:

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Nanosphere Photonic Analysis: Absorbed Power vs. Wavelength

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Fluidic Analysis: Photothermal heat cycle of gold nanosphere (a) initial heating, (b) primary bubble, (c) primary bubble collapse, (d) secondary bubble, (e) secondary bubble collapse with cooling

Fluidic Analysis: Video of cross-sectional view of gold nanosphere showing stages (a) to (e) as described above

Nanorod

The second geometry we studied is a gold nanorod, 8.5 nm in radius and 60 nm in length. Nanorods have properties that are significantly different than nanospheres. Most notably, they have two distinct plasmon resonant frequencies (high and low) and different heat transfer coefficients along their surface (main body and spherical tips). Based on our analysis, it was concluded that the plasmon resonance wavelength is 770 nm. The amount of power necessary to reach nucleation is 76.8E-6 W with a pulse duration of 1.9 ns. The nanoparticle reaches a maximum instantaneous temperature of ~915K. The results are presented in the following pictures/video:

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Nanorod Photonic Analysis: Absorbed Power vs. Wavelength

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Fluidic Analysis: Photothermal heat cycle of gold nanorod (a) initial heating, (b) bubble formation, (c) bubble (maximum size), (d) bubble collapse, (e) cooling

Fluidic Analysis: Video of cross-sectional view of gold nanorod showing stages (a) to (e) as described above

Torus

The last geometry we studied is the torus. We consider a specific torus with major radius R = 30 nm and minor radius r = 10 nm. Nanotori, similarly to nanorods, are characterized by a long wavelength resonance and a short wavelength resonance. We are most interested in the long wavelength resonance because it can be tuned by varying major and minor radii during synthesis. Our analysis shows that the plasmon resonance wavelength is 828 nm. The amount of power necessary to reach nucleation is 172.8E-6 W with a pulse duration of 4.1 ns. The nanotorus reaches a maximum temperature of approximately 1000K. The results are presented in the following pictures/video:

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Nanotorus Photonic Analysis: Absorbed Power vs. Wavelength

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Fluidic Analysis: Photothermal heat cycle of gold nanotorus (a) initial heating, (b) bubble formation, (c) bubble (maximum size), (d) bubble collapse, (e) cooling

Fluidic Analysis: Video of cross-sectional view of gold nanotorus showing stages (a) to (e) as described above. It is instructive to note that the capillary force that acts to collapse the bubble is relatively weak because of the relatively large radius of curvature that defines the fluid - vapour interface as it gets closer to the torus. Thus, the nanobubble requires a substantial amount of time to completely collapse, compared to other geometries.

Multiple Tori

In addition, a system comprised of two tori was studied. Both tori have identical dimensions, similar to the single torus described above. It is shown that the two tori system has significant advantages over the single torus system. Most importantly, it is characterized by strong cooperative heating that causes the formation of larger nanobubbles while consuming less energy. We performed a parametric analysis for a torus-to-torus spacing of 10 to 100 nm that showed a significant energy reduction as the distance between the tori decreases. Moreover, we studied bubble nucleation for a 2 tori system with a distance of 60 nm between the centres of the tori. It was concluded that the 2 coaxial tori system was able to generate a bubble of approximately 3.6 times larger size than the single torus while requiring ~84% of the energy consumed by the single torus system. The results of the study are presented below:

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Parametric Analysis: Percentage of single nanotorus energy required to achieve 2 tori nucleation vs. nanotorus separation. Separation distance between edges is represrented in increments of minor radii (10 nm)

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Fluidic Analysis: Photothermal heat cycle of a 2 coaxial nanotori system (a) initial heating, (b) bubble formation, (c) bubble (maximum size), (d) bubble collapse, (e) further bubble collapse and cooling

Fluidic Analysis: Video of cross-sectional view of 2 coaxial tori system showing stages (a) to (e) as described above. Similarly to the single torus, the nanobubble requires a substantial amount of time to completely collapse for the reasons described above.

Conclusions

With this work we have for the first time used combined continuum level computational electromagnetic and fluid dynamic analysis to study nanosecond-pulsed laser heating and bubble generation due to subwavelength gold nanospheres, nanorods and nanotori. We have used the modelling to determine power levels and pulse durations that are sufficient to generate a desired bubble size and dynamics, while avoiding damage to the particle through excessive heating. We have also used modelling to quantify the effects cooperative heating in multiparticle systems. We have demonstrated for the first time that more robust bubble generation can be achieved with lower laser energy when particles are within a few radii of one another as compared to corresponding single particle systems. The modelling approach presented here enables fundamental understanding of plasmonassisted photothermal heating including fluidic phase change leading bubble nucleation. It should prove useful for the rational design of novel nanoparticle-based photothermal systems.

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