Computational analysis of pulsed-laser plasmon-enhanced photothermal energy conversion and nanobubble generation in the nanoscale
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The ability to generate and control thermal energy with nanoscale resolution is finding increasing use in a variety of applications spanning the fields of nanoparticle synthesis, nanofabrication, bio-imaging and medical therapy. One of the most promising approaches to achieving this involves the use of plasmonics, wherein a laser is used to heat metallic nanostructures at their localized surface plasmon resonance (LSPR) wavelength. At plasmon resonance there is a collective and coherent oscillation of electrons within the nanostructures that gives rise to peak absorption of the incident photons and highly localized (sub-wavelength) heating and field enhancement. Laser-based plasmon-enhanced photothermal energy conversion in the nanoscale has drawn increased interest in recent years for applications such as photothermal therapy and nanoscale imaging since it can provide efficient heating with unprecedented (subwavelength) spatial resolution. In the current work, we study pulsed-laser plasmon-assisted nanoscale bubble nucleation around various nanoparticle geometries using combined computational electromagnetic and CFD-based fluidic analysis. This combined modeling approach will aid in the development of a rational guide to experimentalists in this field since it enables fundamental understanding and, hence, rational design of plasmon-based photothermal processes; eventually leading to the development of novel photothermal applications. Our primary goal is to develop computational electromagnetic and CFD-based models for some of the most commonly used nanoparticle geometries. Such modeled geometries include nanospheres, nanorods, nanoframes, nanotori and nanorings. Two types of computational models will be developed: a) Computational Electromagnetics models for the photonic analysis, used to calculate photothermal energy conversion within the nanoparticles, i.e. the time-averaged power absorbed by a particle as a function of the wavelength, intensity and polarization of the incident light and b) Computational Fluid Dynamic (CFD)-based models that predict thermal, pressure and flow effects including the temperature rise in the particle, heat transfer from the particle to the fluid, phase change within the fluid leading to homogeneous bubble nucleation, the dynamic behavior of the bubble as it expands and collapses, and the temperature, pressure and flow throughout the fluid during the entire process. In order to achieve that goal, we use state-of-the-art software packages including but not limited to: FLOW 3D versions 10.1 and 11.1 from Flow Science Corp. (www.flow3d.com) and COMSOL Multiphysics Software versions 4.4 and 5.2 with full CFD-FSI, nanofluidics and RF analysis capability, respectively. The initial modeling effort is mainly focused on modeling nanoparticles exhibiting some kind of axial symmetry, such as nanospheres and nanorods, with constant fluid and particle properties. It will be used to determine heretofore unknown properties such as the plasmon resonance wavelength, the amount of power required to generate and sustain nanobubbles without melting the nanoparticles and the size and duration of occurring nanobubbles for each nanoparticle geometry. In the next phase of the study, we proceed with the development of enhanced computational models to account for colloidal effects. Although initial models are able to predict the details of the generation of a nanobubble around a single nanoparticle illuminated in parallel orientation relative to the polarization of the incident field, most in-vivo applications involve a colloidal solution of particles: a collection of particles at random orientations. Therefore, a series of models to account for colloidal effects for certain nanoparticle geometries will be developed. Such models include a) cooperative colloidal nanoparticle heating models that predict the average temperature rise of a colloidal solution of identical nanoparticles under fixed illumination as a function of nanoparticle concentration, b) cooperative nanobubble nucleation models that are able to calculate the effects of cooperative nucleation including the generation of nanobubbles around multiple identical nanoparticles and merging of nanobubbles and c) photonic models for colloidal nanoparticles at varying orientations that can determine the fall off in the peak absorption under fixed illumination as the nanoparticles take on different orientations. This study directly addresses the knowledge gap concerning the colloidal behavior of plasmonic nanoparticles. Finally, we will be suggesting new potential paths of research such as a non-continuum, high accuracy approach. Although, the models developed in this study represent the most accurate nanobubble modeling attempt thus far, the assumptions of continuum theory and of constant nanoparticle properties might lead to potential discrepancies between modeling and experimental results. Hence, in the interest of increased accuracy, we will suggest the use of the Two-temperature Model (TTM) to describe non-equilibrium femto-second electron relaxation in the nanoparticles. Such models may enable the proposed theory to be extended to femto- and pico-second pulsing. A further refinement of the models developed initially can be potentially realized with the inclusion of temperature dependent properties for the fluid and the nanoparticle. The combination of non-equilibrium effects and temperature pertinent properties will provide most sophistication to an already complex modeling effort. In addition to the enhanced models, initial computational models could also be extended to include the fall off on the peak absorption when a nanobubble is being formed around a nanoparticle while it is still being illuminated. Overall, the modeling approach described herein will a) directly address the knowledge gap of photothermal therapy nanobubble specifics for each geometry such as required wavelength for plasmon resonance, required energy and pulse duration to achieve nucleation without melting or even evaporating the nanoparticles, b) explain the temperature related behavior of colloidal plasmonic nanoparticles for photothermal drug delivery and c) provide experimentalists in the field with a most accurate rational guide for the development of novel photothermal applications.