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Plasmonic Nanoframes for Photothermal Energy Conversion Ioannis H Karampelas, Kai Liu, Fatema Alali, and Edward P. Furlani J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b12743 • Publication Date (Web): 23 Feb 2016 Downloaded from http://pubs.acs.org on February 24, 2016

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The Journal of Physical Chemistry

Plasmonic Nanoframes for Photothermal Energy Conversion Ioannis H. Karampelas1, Kai Liu2, Fatema Alali3 and Edward P. Furlani1,2,* 1

Dept. of Chemical and Biological Engineering, University at Buffalo SUNY, NY 14260

2

Dept. of Electrical Engineering, University at Buffalo SUNY, NY 14260

3

College of Technological Studies, Public Authority of Applied Education and Training, Kuwait City

ABSTRACT:

We study the photothermal behavior of laser-pulsed colloidal metallic nanoframe

structures using three-dimensional (3D) photonic and thermofluidic computational models. The models predict the optical response of the nanoframe, photothermal transduction at plasmon resonance, heat transfer to the surrounding fluid and the dynamics of nanobubble generation under conditions of superheating. We quantify for the first time the photothermal transduction of Au nanoframes as a function of their orientation with respect to the polarization of the incident field and also, cooperative heating effects as a function of nanoframe spacing. We further demonstrate that laser illumination parameters and nanoframe properties can be tuned to control spatio-temporal heating and nanobubble dynamics.

KEYWORDS: Localized surface plasmon resonance (LSPR), nanoframes, plasmonic nanoframes photothermal energy conversion, plasmonic-enhanced photothermal energy transfer, LSPR-induced optical absorption, pulsed-laser photothermal heating, photothermal therapy, plasmonic nanobubble cancer treatment

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1. INTRODUCTION The ability to generate and control thermal energy with nanoscale spatio-temporal resolution is finding increasing use in a diverse range of applications including nanoparticle synthesis, nanofabrication, bio-imaging and medical therapy.1-2 Nanoscale heating can be achieved using a variety of methods including ultrasonics,3 chemical processes,4 nanoelectronics,5 6 nanomagnetics and various photothermal phenomena.7 One of the most promising approaches in this field involves the use of plasmonics, wherein a laser is used to heat metallic nanostructures at their localized surface plasmon resonance (LSPR) wavelength. At LSPR there is a uniform and coherent oscillation of the electrons within the nanostructures that gives rise to intense absorption of incident light and highly localized field enhancement. The absorbed photon energy is converted to heat, which is ultimately transferred to the surrounding medium. Moreover, the LSPR wavelength λLSPR can be tuned from the ultraviolet (UV) through the nearinfrared (NIR) spectrum by controlling the size and especially the shape of the particle during synthesis.8-9 The ability to tune λLSPR and the associated plasmonic effects in this fashion has proven useful for a range of applications in the fields of biosensing, optical coherence tomography,10 photoacoustic imaging11 and twophoton luminescence imaging.12 Laser-induced photothermal therapy has drawn particular interest for minimally-invasive cancer treatment. In this approach, plasmonic nanoparticles that are functionalized to selectively bind to target malignant cells are introduced into the vasculature where they circulate and preferentially bind to cancerous tissue. The nanoparticles can be heated using a pulsed laser with sufficient intensity to selectively destroy the targeted malignant cells, with limited collateral damage to nearby healthy tissue. This highly localized therapy avoids the harmful systemic side effects of chemotherapy. Generally, NIR

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light is preferred for such therapy since it more effectively penetrates soft tissues compared to other wavelengths.13 During the last several years, various transducers have been studied for photothermal therapy including organic dyes (e.g. indocyanine green14), metallic (e.g. Au) nanostructures15 and carbon-based nanomaterials (e.g. carbon 16 nanotubes ). Among these, there has been an emphasis on applications of Au nanoparticles. Such particles are well-suited for bioapplications because they can be synthesized in various sizes and shapes and can be readily coated with a variety of enabling agents using thiolate monolayer chemistry. These agents include polyethylene glycol (PEG), which enhances biocompatibility and circulation time,17 cancer specific antibodies (e.g. HER2-antibody18) to enable selective cancer cell targeting, smart polymers such as poly(N-isopropylacrylamide) (pNIPAAm)19 for photothermally controlled drug delivery or combinations thereof. Various Au nanoparticle geometries have been studied including nanoshells,20 nanorods,7 nanotori,21-22 and, more recently, nanocages23 and nanoframes.24 A review of the research on various plasmonic heating applications of different nanoparticle geometries can be found in the litterature25 Nanoframes are hollow nanostructures with porous walls that are defined by a metallic frame. In an idealized nanoframe, the frame can be thought of as consisting of twelve identical

Figure 1. Nanoframe structure and characteristic dimensions (Edge length L and edge thickness W).


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rectangular nanowires with length L and width W as shown in Fig. 1. Some of the pioneering work in the field of nanoframe fabrication was performed by Y. Xia and his group who introduced a simplified method of fabricating nanoframes through the galvanic replacement reaction between silver (Ag) nanocubes and chloroauric acid (HAuCl4). The geometrical characteristics of the ensuing structures can be easily controlled by carefully selecting the concentration of chloroauric acid in the solution. The resulting nanoparticles were found to have absorption peaks ranging from 400nm to 900nm.26-27 The optical properties of nanoframes were further investigated by M.A. Mahmoud and M.A. El-Sayed. In a combination of theoretical and experimental studies, they were able to determine that nanoframes exhibit strong field enhancement at their surface and throughout their hollow interior. Moreover the authors demonstrated that gold nanoframes have significantly higher sensitivity factors (an indication of the strength of a nanoparticle’s plasmonic surface field), compared to other similar size solid nanoparticles. As such, gold nanoframes represent promising candidates for nanosensors in the NIR.24, 28 Despite the plethora of research on their optical characteristics, compared to other metallic nanoparticles, relatively few theoretical studies have been reported to quantify the photothermal and thermofluidic behavior of colloidal Au nanoframes under pulsed-laser illumination.25 This is the focus of the present work. In this article, we study the photothermal behavior of Au nanoframe structures using rigorous 3D photonic and thermofluidic computational models. Thus far, we have applied such models to elucidate the fundamental physics of photothermal transduction for various metallic nanoparticles that exhibit some form of axial symmetry, including Au nanorods, nanotori and Nanorings.21-22 It suffices to use 2D analysis for these structures because of their axial symmetry. However, the analysis of nanoframe structures is significantly more challenging since a full 3D

computation is required for both the photonic and thermofluidic studies. To our best knowledge, for the first time, we use 3D photonic analysis to quantify the photothermal transduction of Au nanoframes as a function of their geometry and orientation with respect to the polarization of the incident field. The analysis shows that nanoframes exhibit a high photothermal energy conversion efficiency that is essentially independent of their orientation. This is an attractive feature for photothermal applications involving colloids where the particles are randomly oriented within a carrier fluid. For the thermofluidic analysis, we consider nanosecondpulsed laser illumination of the nanoparticles in fluid wherein the laser operates at the LSPR wavelength and the pulse duration exceeds the characteristic time constants for transient nonequilibrium photothermal effects. We study, for the first time, superheating of the particles that leads to homogeneous bubble nucleation and track the full physics of the process including the generation, expansion and subsequent collapse of the nanobubble. This analysis demonstrates how the laser illumination parameters and nanoframe properties can be tuned to control spatio-temporal heating at the nanoscale as well as nanobubble dynamics. The 3D modelling approach presented herein can advance fundamental understanding of plasmon-enhanced photothermal physics and is broadly applicable to arbitrary particle geometries and material properties. The modelling approach can enable the rational design of novel photothermal applications. 2. PHOTONIC ANALYSIS In this section we explore the optical properties of nanoframes with different dimensions and orientations. For this analysis, we use the finite element (FE)-based Radio Frequency (RF) solver in the COMSOL multiphysics program (www.comsol.com). The computational domain for this analysis is shown in Fig. 2a. A single Au nanoframe is centered at the origin of the domain. The geometry of the nanoframe is defined by its length L that defines the size of the cube (i.e. the



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the width of the computational domain in the x and y directions, respectively. The lattice spacing is chosen to be large enough so that the resulting predictions will reflect the response of a single isolated particle, i.e. with negligible coupling with neighboring particles. The time-harmonic E field within the domain satisfies the equation:

 σ  ∇ × ( µ r−1∇ × E ) − k02  ε r − j  E = 0, ωε 0  

Figure 2. Photonic analysis of an Au nanoframe (L=28nm and R=4) with parallel alignment to the incident polarization: (a) computational domain, (b) in plane spatial plot of electric field intensity enhancement (|E|2/|E0|2) (plane shown in inset).

length of the rectangular nanowire frame element), and the width W that defines the crosssectional area of the nanowire as shown in Fig. 1. The aspect ratio, R=L/W is also used in our analysis. The particle is illuminated with a uniform downward-directed plane wave with the E field parallel to the x-axis. Perfectly matched layers (PMLs) are applied at the top and bottom of the domain to reduce backscatter from these boundaries. Perfect electric conductor (PEC) conditions are applied at the boundaries perpendicular to E, and perfect magnetic conductor (PMC) conditions are applied at the boundaries perpendicular to H. These symmetry boundary conditions mimic the response of a 2D array of identical nanoframe structures with center-to-center x and y lattice spacing equal to

(1)

where µr and εr are the relative permeability and permittivity of the media, respectively. For gold nanoparticles at optical frequencies, µr=1 and εr is modeled using an analytical expression that is based on the experiment-fitted critical points model of gold.29-31 The fluid surrounding the nanoparticle is assumed to be non-absorbing water with an index of refraction of nf=1.3. The incident field is generated by a time-harmonic surface current positioned in the x-y plane directly below the upper PML.32-35 We compute the (wavelength dependent) power absorbed by the particle Qabs (watts), which is converted to heat. Thus, this analysis predicts photothermal energy conversion within the particle. In Fig. 2b we plot the spatial profile of electric field intensity enhancement (|E|2/|E0|2) in the x-y plane, shown in the inset. The size of the nanoframe is L=28nm with R=4 and the LSPR occurs when λLSPR=830nm. The mode profile demonstrates a high degree of field localization and enhancement due to the coupled surface plasmons of the neighboring nanowire frame elements. This property can be leveraged for theranostic biomedical applications. For example, the surface of gold nanoframes can be functionalized to achieve cancer cell specificity. Specifically, by manipulating thiolate-Au monolayer chemistry, excellent compatibility between Au surfaces and various molecules and ligands can be achieved.36-37 Through the functionalization process, fluorescent labels can be attached to the Au surface to enable spatial tracking and imaging.18 The LSPR of Au


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Figure 3. Nanoframe absorption spectra as a function of geometric parameters: (a) absorption spectra vs. L (W=7nm) (b) absorption spectra vs. R=L/W (L=28nm).

nanoparticles can be used to enhance fluorescent signal intensity for a variety of biophotonic applications. Such enhanced fluorescence is directly related to the localized field enhancement at LSPR.38 Figure 2b shows that strong E field enhancement (∼500 fold) occurs around the nanowires. This could dramatically increase the signal from surface-bound fluorescent molecules. Highly localized regions that exhibit even higher enhancement (∼3000) can also be observed. If the frame elements of a nanoframe are sufficiently close to one another, their LSPR modes are coupled, which can produce a significant field enhancement throughout the interior of the nanoframe. We have predicted enhancement factors of ~300 for this region. This could prove to be especially useful for biomedical applications wherein photoactivated theranostic agents are transported to target tissue in the porous interior of a nanoframe. These include therapeutic drugs and fluorescent probes39-40 that can enable high-resolution in vivo imaging and tracking. For in vivo biomedical applications, the LSPR of the nanoparticles should be tuned to the spectral range of 700-900nm. This is often referred to as the “optical or therapeutic window” because light penetrates deeper into tissues at these wavelengths, i.e. with less absorption and

scattering than at other wavelengths.41-42 Subwavelength Au nanospheres typically have LSPR peaks in the visible region ∼532nm43 and are therefore not optimum for in vivo photothermal applications. However, various particle geometries including spherical dielectricmetallic core-shell particles, non-spherical (e.g. ellipsoidal rod-shaped) particles, and hollow Au nanoparticles can be designed to have LSPR peaks in the NIR region.44 This is also true of Au nanoframes, which makes them of interest for theranostic applications.45 However, despite the plethora of experiments that demonstrate the potential use of Au nanoframes for such applications, many fundamental aspects of their photothermal behavior remain unknown. 3. PHOTONIC SIMULATIONS In this section we investigate the absorption cross-section spectra σabs (m2) (absorbed power Qabs (W) divided by the incident irradiance Ilaser (W/m2)) and especially the LSPR peak wavelength of a nanoframe as a function of its geometric parameters, i.e. L and W and orientation with respect to the polarization of the incident field. While many groups have studied the optical response of nanoframe structures as a function their geometry, to our best knowledge this is the first such study with respect to



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Figure 4. Pulsed laser heating of colloidal Au nanoparticles. Nanoparticle orientation is defined by angles θ and φ. Inset plot illustrates a laser pulse profile, irradiance I vs. t.

Figure 5. Optical absorption cross section σabs vs. orientation. Plot of the dependence of σabs on the orientation of Au nanoframe. The p-polarized light is employed to illuminate the nanoparticle at different orientations.

orientation, which is important for understanding colloidal applications where the particles are randomly oriented. As a first step in the analysis, we compute σabs as a function of L in the range of 22-37nm with W fixed at 7nm. As shown in Fig. 3a, as L increases, the LSPR absorption peak redshifts from 690nm to 1060nm, demonstrating a strong L-dependent LSPR sensitivity, similar to that observed in nanorods.21 Our analysis also indicates that the optical absorption of a nanoframe at LSPR increases with the amount of gold it contains (Fig. 3a). Next, we study the optical response of the nanoframe as a function of the aspect ratio R=L/W where R ranges from 3 to 5.5 and L=28nm is kept constant. The absorption cross section σabs is calculated as a function of wavelength and plotted in Fig. 3b. Note that the LSPR peak wavelength red-shifts from 680nm to 1090nm as R increases. We found that the absorption cross-section of the nanoframe monotonically decreases with W. Moreover, as previously noted nanoframes with strong absorption in the NIR hold promise for theranostic applications. Lastly, we investigate LSPR absorption of a nanoframe as a function of its orientation with respect to the polarization of the incident light. This is important for applications involving

colloids where nanoframes have random orientations within a carrier fluid as illustrated in Fig. 4. Since nanoframes have a relatively high degree of geometric symmetry we expect that their LSPR absorption will be somewhat insensitive to their orientation. Here, we quantify the orientation dependence for the first time. The orientation of the nanoframe can be specified using angles φ and θ that define the rotation of the particle relative to the x- and zaxis, respectively. Throughout this paper the incident field is assumed to be linearly polarized along the x-axis and propagating downward, i.e. with k in the -z-direction as shown in Fig. 2a. Figure 4 illustrates a colloid of nanoframe structures being illuminated with a pulsed laser. A reference frame is shown along with angles φ and θ that define the orientation of the nanoframe. The inset plot in Fig. 4 depicts the laser pulse profile (irradiance Ilaser (W/m2) vs. t). In this figure, n is a unit vector that describes the orientation of the nanoframe. Specifically, n is normal to the top area, as shown. The angle φ lies in the x-y plane and is measured from the x-axis to the projection of n onto x-y plane, whereas θ is the angle between n and the z-axis. We perform parametric calculations of σabs for the nanoframe as a function of its orientation with


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respect to the incident polarization. In our analysis, the nanoframe is illuminated by an xpolarized light at the LSPR peak wavelength. We analyze an Au nanoframe with L=28nm and W=7nm, which has an LSPR peak wavelength of 830nm. The absorption cross section σabs of the nanoframe is plotted in Fig. 5. Note that there is very little variation in σabs throughout the entire range of orientations. This is desired for applications such as photothermal cancer treatment as it implies a higher heating efficiency for a given laser irradiance. 4. THERMOFLUIDIC ANALYSIS We use 3D CFD analysis to study the thermofluidic behavior of a nanoframe in a fluid under pulsed laser illumination. This is a complex process in which non-equilibrium thermal effects occur at femto- to pico-second time scales.46-47 A more thorough discussion of our computational approach and its validity for this nanoscale study can be found in our previously published work.2122 We briefly summarize this approach in the following to make the presentation somewhat self-contained. The thermofluidic analysis was preformed using the FLOW-3D program (www.flow3d.com). This multiphysics CFD program is based on the volume of fluid (VOF) method, which is implemented using a finitedifference numerical scheme.48 In our computational model the nanoframes are immersed in an incompressible Newtonian fluid with viscosity µ, density ρ, specific heat at constant pressure cp and thermal conductivity k. The equations governing heat and mass transfer are as follows: Navier-Stokes:

 ∂ν  + ν ∇ν  = − ∇p + µ∇ 2ν , (2)  ∂t 

ρ

Incompressibility:

∇ v = 0.

(3)

Heat transfer: Fluid:

 ∂T  + ν ∇T  = k∇2T ,  ∂t 

ρ cp 

(4)

Nanoparticle:

ρ np cnp

∂Tnp ∂t

= Qabs (t ) + k np ∇ 2Tnp ,

(5)

where ν, p are the velocity and pressure in the fluid and ρnp, cnp and knp are the density, specific heat at constant pressure and thermal conductivity of the nanoparticle, respectively. Qabs is the power generated uniformly within by the nanoparticle due to absorption of incident laser light, T and Tnp are the corresponding temperatures in the fluid and the nanoparticle. If the fluid in the vicinity of the nanostructure reaches a sufficiently high “superheat” temperature then it undergoes a phase change (vaporization) that initiates bubble nucleation. This is taken to be 580K for H2O. Before nucleation, the temperature in the particle and surrounding fluid is calculated using Eqs. (4) and (5). Once a bubble is nucleated, its interface is tracked using the VOF method. The pressure in the bubble is initially set to the saturation pressure at the superheat temperature (approximately 100 Atm), which is computed using the Clausius-Clayperon equation:  ∆H vap psat (T ) = p1 exp   R

 1 1   −   T1 T  

(6)

where p1 and T1 are the pressure and temperature at a point on the saturation curve ∆Hvap is the molar enthalpy of vaporization and R is the universal gas constant. This pressure exerts an outward force at the liquid-bubble interface that causes it to expand outward from the particle. As the bubble grows, the pressure pvap, temperature Tvap and density ρvap of the vapor within it are computed using the equation-of-state of an ideal gas



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Figure 6. Photothermal heat cycle of a nanoframe (L=50nm, W=5nm) (cutaway perspective of heated nanocage): plot of nanoframe temperature vs. time, pulse duration indicated by red arrow and dashed line and inset plots showing various phases of the thermal cycle; (a) nanobubble formation, (b) nanobubble (maximum size), (c) nanobubble collapse, (d) cooling.

pvap = ( γ −1) ρvapCvap,vTvap

(7)

where cvap is the specific heat of the vapor at constant volume and γ = cvap,p/cvap,v is the ratio of specific heats. The pressure, temperature and density are assumed to be spatially uniform (i.e., homogeneous) within the bubble at every time step. The mass flux m& at the fluid-bubble interface is proportional to the deviation of the fluid from its saturation conditions, i.e. p plsat MW   m& = cevap − ccond vap 2π R  Tl Tvap 

 ,  

(8)

where MW is the molecular weight of the vapor, R is the vapor gas constant, T is temperature (K), and the subscripts l and vap refer to liquid and vapor phases, respectively. The term pl is the saturation pressure corresponding to the liquid temperature Tl, and cevap and ccond are accommodation coefficients for evaporation and condensation. More information on the values of the parameters listed above can be found in our previously published work.21-22 After the bubble has nucleated, the nanoparticle

is surrounded by vapor and the heat transfer at the particle-vapor interface is greatly diminished. Thus, if the laser pulse continues beyond nucleation, the temperature of the essentially insulated nanoparticle rises rapidly and can reach its melting or even vaporization temperature within a nanosecond or less. For bulk gold, these values are Tm=1336K and Tvap=2933K, respectively. However, experiments have shown that Au nanoparticles have a lower melting point that can differ by as much as 200K from the bulk value.49-50 In order to avoid high temperature damage to the particle, the laser power level and pulse duration must be carefully controlled. We use modelling to determine values of these parameters that keep the nanoparticle below a maximum temperature of 1100K. The thermofluidic analysis is based on the following assumptions: For simplicity and better result reproducibility, we consider all fluid and solid properties as constant throughout the photothermal cycle. As a result, we also consider the nanoparticle size variations (maximum of ~1.5% increase) caused by density changes due to heating as negligible.51 The shape of the nanoparticle is assumed to remain unaltered for


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Figure 7. Photothermal heat cycle of a nanoframe (L=50nm, W=10nm) (cutaway perspective of heated nanocage): plot of nanoframe temperature vs. time, pulse duration indicated by red arrow and dashed line and inset plots showing various phases of the thermal cycle; (a) nanobubble formation, (b) nanobubble (maximum size), (c) nanobubble collapse, (d) cooling.

all simulations and any mechanical damage to the nanoparticle from the pressure generated by the nanobubble is considered trivial because of the inherent structural rigidity of the rectangular frame structure and the symmetry of the nucleated nanobubble. Finally, we assume that no heat transfer occurs from the nanoparticle to the surrounding gas post-nucleation since energy losses to the rarefied gas are significantly lower compared to the effects of laser heating. 5. THERMOFLUIDIC SIMULATIONS A 3D CFD analysis was performed to determine the incident optical irradiance and pulse duration Nanoframe Dimensions (nm)

Power (µW)

L=50, W=5

180

Pulse Duration (ns) 3.18

L=50, W=10

200

3.2

L=70, W=5

288

3.42

Laser Irradiance (mW/µ µm ) 2

(λ λ nm) 209 (1500) 4.96 (1015) 633 (1500)

needed to superheat the nanoframe to nucleate an explosive homogeneous nanobubble without destroying the nanoframe, i.e. without melting or vaporizing the metal. Owing to its symmetrical nature, it was only necessary to model a 3D octant of the nanoframe. The CFD computational domain spanned a length scale that ranged from 2.8 to 8 times the edge length L of the nanoframe depending on the size of the bubble that was generated. A computational mesh of cubical cells was used for the analysis. The cell size was fixed at 1 cubic nanometer for x, y, z ≤ 150nm, gradually increasing in size to a maximum of 2 cubic nanometers for the rest of the domain. The

Absorption CrossSection (m2) 8.59×10-16 4.03×10

Maximum Nanoparticle Temperature (K)

Maximum Bubble Radius (nm)

Nucleation Time (ns)

977

120

2.8

754

185

3.0

1068

95

3.2

-14

4.55×10-16

Table 1. Summary of nanoframe geometries with heating and nanobubble parameters.



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Figure 8 Photothermal heat cycle of a nanoframe (L=70nm, W=5nm) (cutaway perspective of heated nanocage): plot of nanoframe temperature vs. time, pulse duration indicated by red arrow and dashed line and inset plots showing various phases of the thermal cycle; (a) nanobubble formation, (b) nanobubble (maximum size), (c) nanobubble collapse, (d) cooling.

cell size was chosen to optimize the accuracy of the simulation (better surface tracking during the onset of bubble nucleation) while maintaining computational efficiency (lower total runtime). Symmetry boundary conditions were imposed along the x-, y- and z-axes in order to account for the remaining octants of the nanoframe. A stagnation pressure condition was imposed at the outer boundaries along with a thermal Dirichlet condition (T=300K) to account for the ambient temperature of the surrounding fluid. The pressure and temperature throughout the computational domain were initialized to 1Atm and 300K, respectively. These initial values and boundary conditions were used for all cases studied in our thermofluidic analysis. We chose water as the working fluid but the analysis can be applied to any Newtonian fluid. Various gold nanoframe structures were studied, as defined in Table 1. It should be noted that the nanoframe dimensions selected for this analysis were chosen to illustrate representative photothermal behavior and provide an intuitive guide for optimal heating efficiency. The thermofluidic analysis was divided into two phases. In the first phase, a thermal analysis was

performed to predict the power level required to heat the fluid around nanoframes of varying sizes (L and W) from an ambient temperature of 300K to the superheat temperature of water i.e. 580K. The heating process depends on the pulse intensity and duration, which was constrained to be between 3 to 5ns. The nanosecond pulse duration far exceeds the characteristic time constants (femto- to pico-seconds) for nonequilibrium energy transfer mechanisms, that occur in gold nanoparticles, and are therefore consistent with the continuum modeling approach taken here.21-22 Once the preliminary thermal calculations were completed, we performed the second phase of analysis where we applied the power levels obtained in the phase one analysis with a slightly increased pulse duration in order to heat the nanoframes beyond the superheat temperature, which causes vaporization of the surrounding fluid and bubble nucleation. The pulse duration was tuned so that the nanoparticle achieved a temperature that was sufficiently high to generate a sustained nanobubble, but low enough (< 1100K) to avoid melting or vaporizing the nanoparticle. A summary of key simulation parameters, such as power and pulse duration


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Figure 9. 3D perspective of CFD simulation showing nanobubble at maximum expansion for different nanoframe geometries.

required for the nucleation of an explosive nanobubble around each geometry, is given in Table 1. Figures 6, 7 and 8 illustrate simulation results for nanoframes with the following dimensions: L=50nm-W=5nm, L=50nm-W=10nm and L=70nm-W=5nm, respectively. These figures show a plot of the nanoparticle temperature vs. time and inset pictures of the nanoframe and the fluid temperature at various phases of the nanobubble cycle. The photonic analysis indicated that while all the geometries in Table 1 have absorption peaks in the NIR, the two nanoframes with thinner frame elements, i.e. L=50 and 70nm with W=5nm had minor peaks, i.e. their dominant absorption occurred at a longer wavelength. On the other hand, the nanoframe with thicker frame elements (L=50nm, W=10nm) had a dominant absorption in the NIR and a corresponding absorption cross-section that was ~2 orders of magnitude higher than the other geometries. In fact, we found that nanoframes with more densely packed (i.e. thicker and more closely spaced) frame elements provide more efficient photothermal heating and larger nanobubbles due to enhanced LSPR coupling and cooperative heating between the elements. An example of the photothermal-nanobubble heat-cycle for a nanoframe with L=50nm and W=5nm is shown in Fig. 6. The nanoframe and the fluid are initialized at a temperature of 300K.

The nanoframe is illuminated by a nanosecond pulsed laser that is operating that the LSPR wavelength of the nanoframe, in this case, λLSPR=1500nm. The temperature of the nanoframe rises steadily for the first few nanoseconds as indicated in the temperature vs. time plot of Fig. 6. The fluid around the nanoframe reaches its superheat temperature (580K) 2.8ns after the onset of illumination, at which time a homogeneous water vapor bubble is nucleated around it. Upon nucleation, the temperature of the nanoparticle rises rapidly since it is being insulated by a thin sheath of vapor while still being heated by the laser. This continues until the end of the laser pulse, which coincides with the bubble formation and maximum temperature as shown in plot segment and inset (Fig. 6a). The pulse duration is 3.18ns as indicated by the red dashed line. After it is nucleated the nanobubble expands because of its higher pressure compared to the surrounding fluid. The nanobubble reaches a maximum size as shown in inset Fig. 6b. For this geometry, the maximum bubble radius achieved was ~120nm. Eventually, the nanobubble collapses bringing fluid back in contact with the nanoparticle after 7.8ns as shown in plot segment and inset Fig. 6c, reducing its temperature to the ambient temperature (Fig. 6d). An interesting observation of this process is the formation of a hot mass of fluid in the middle of the nanoframe, which only partially evaporates as the nanobubble expands but does not reach superheat temperature. This phenomenon allows for the cooling of the nanoframe during the nucleation of an explosive nanobubble around it, thus maintaining its temperature below melting i.e. 1100K, for the entirety of the photothermal heat cycle. For comparison purposes, we provide a transparent 3D perspective of the maximum expansion of the nanobubbles generated around all the geometries studied in order of maximum size as shown in Fig 9. This figure clearly illustrates that nanoframe geometries with more concentrated metallic mass are capable of generating nanobubbles of larger radius.



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the single nanoparticle system. Moreover, all cooperative heating effects become negligible after a distance of 1 edge length (50nm) in all directions. 7. CONCLUSIONS

Figure 10. Percentage of single nanoframe energy required to achieve multi-nanocage nucleation vs. nanocage separation distance.

The CFD simulations presented here were performed on a stand-alone 24-core workstation with 128 GB of RAM. The time for the simulations varied from 124 to 530 hours depending on the dimensions of the nanoframe and the size of the ensuing nanobubbles. 6. COOPERATIVE HEATING We performed thermal simulations of a colloid system comprising of nanoframes to examine the effects of cooperative heating. We studied an evenly spaced 3D array of nanoframes with an edge length of 50nm and an edge thickness of 5nm. We systematically varied the surface-tosurface spacing between the nanoparticles from 0 to 100 nm, uniformly in the x-, y- and zdirections. We completed 3D CFD thermal analysis (without phase change) using the same amount of power in each nanoparticle as in the single nanoframe case described above. We then calculated the pulse duration and energy that is required to heat the array of nanoframes to the superheat temperature. The results of this parametric analysis are presented in Fig. 10. Based on our calculations, it can be concluded that for a distance of 10nm between the outer edges of the nanoframes (which corresponds to an Au concentration of approximately 1.16x1028 ng/nm3), only 50% of the energy is required to reach the nucleation temperature as compared to

We have used a combination of 3D computational electromagnetic and fluid dynamic analysis to study the fundamental photothermal behavior of colloidal gold nanoframes under nanosecond-pulsed laser heating. We have found that the unique morphology of the nanoframes offers significant advantages for a variety of photothermal and theranostic applications. Specifically, the LSPR wavelength of a nanoframe can be broadly tuned from the visible to NIR by controlling its dimensions during synthesis. The ability to tune LSPR to the NIR is especially important for in vivo applications where the incident light should fall within the NIR optical window for more effective tissue penetration. Moreover, we have shown that Au nanoframes have a substantial absorption crosssection in the NIR that is essentially independent of orientation. This is also important as it implies that nanoframes can provide efficient photothermal heating for in vitro, in vivo or any colloidal application where they can be randomly oriented. Overall, we have found that Au nanoframes have photothermal properties that can be leveraged for a variety of bioapplications by enabling enhanced theranostics: imaging, spectroscopy, drug delivery, photothermal therapy and explosive nanobubble cancer treatment. The thermofluidic analysis indicates that by carefully tuning laser irradiance and pulse duration, the generation of controlled nanobubbles around nanoframes is potentially possible without melting the nanoparticle. We have found that nanoframe geometries with more densely packed frame elements can provide enhanced photothermal heating due to electromagnetic coupling and cooperative heating between the elements. Moreover, since cooperative heating between nanoframes reduces


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the power required for nucleation, nanobubble generation selectivity could be manipulated for localized cancer cell destruction when adequate uptake is achieved. A more comprehensive analysis of these effects is part of our future work. Finally, in addition to our new findings of nanoframe behavior, the modeling approach that we demonstrate broadly applies to arbitrary photothermal nano-transducers and should prove useful in the development and rational design of novel applications.



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Funding Sources ASSOCIATED CONTENT N/A N/A Notes AUTHOR INFORMATION

None

Corresponding Author Edward P. Furlani Dept. of Electrical Engineering Dept. of Chemical and Biological Engineering 113B Davis Hall University at Buffalo (SUNY) Buffalo, New York 14260-4200 Email: [email protected]; Phone: (716) 645-1194; Fax: (716) 645-3822.

ACKNOWLEDGMENT N/A

Author Contributions The manuscript was written through contributions from all authors. All authors have given approval to the final version of the manuscript. These authors contributed equally: Ioannis H. Karampelas1 and Kai Liu2 1

Dept. of Chemical and Biological Engineering,

University at Buffalo SUNY, NY 14260 2

Dept. of Electrical Engineering, University at

Buffalo SUNY, NY 14260


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Figure 1. Nanoframe structure and characteristic dimensions (Edge length L and edge thickness W). 164x100mm (149 x 149 DPI)



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Figure 2. Photonic analysis of an Au nanoframe (L=28nm and R=4) with parallel alignment to the incident polarization: (a) computational domain, (b) in plane spatial plot of electric field intensity enhancement (|E|2/|E0|2) (plane shown in inset). 84x127mm (300 x 300 DPI)


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Figure 3. Nanoframe absorption spectra as a function of geometric parameters: (a) absorption spectra vs. L(W=7nm) (b) absorption spectra vs. R=L/W (L=28nm). 44x18mm (300 x 300 DPI)



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Figure 4. Pulsed laser heating of colloidal Au nanoparticles. Nanoparticle orientation is defined by angles θ and φ. Inset plot illustrates a laser pulse profile, irradiance I vs. t 157x126mm (149 x 149 DPI)


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Figure 5. Optical absorption cross section σabs vs. orientation. Plot of the dependence of σabs on the orientation of Au nanoframe. The p-polarized light is employed to illuminate the nanoparticle at different orientations. 47x37mm (300 x 300 DPI)



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Figure 6. Photothermal heat cycle of a nanoframe (L=50nm, W=5nm) (cutaway perspective of heated nanocage): plot of nanocage temperature vs. time, pulse duration indicated by red arrow and dashed line and inset plots showing various phases of the thermal cycle; (a) nanobubble formation, (b) nanobubble (maximum size), (c) nanobubble collapse, (d) cooling. 490x217mm (149 x 149 DPI)


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Figure 9. 3D perspective of CFD simulation showing nanobubble at maximum expansion for different nanoframe geometries. 411x337mm (149 x 149 DPI)



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Figure 10. Percentage of single nanoframe energy required to achieve multi-nanocage nucleation vs. nanocage separation distance. 175x136mm (149 x 149 DPI)


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Plasmonic Nanoframes for Photothermal Energy Conversion - The

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