Gold Nanostars in Plasmonic Photothermal Therapy: The Role of Tip

Article pubs.acs.org/JPCC

Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

Gold Nanostars in Plasmonic Photothermal Therapy: The Role of Tip Heads in the Thermoplasmonic Landscape Hirak Chatterjee,† Dewan S. Rahman,† Mahuya Sengupta,‡ and Sujit Kumar Ghosh*,† †

Department of Chemistry and ‡Department of Biotechnology, Assam University, Silchar 788011, India

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S Supporting Information *

ABSTRACT: Throughout the history of science, comparison among calculated parameters and experimental observables has been considered as obvious to accomplish and reciprocate a fundamental hypothesis. The exploitation of sharp edges toward a plethora of paraphernalia has been continued from the prehistoric evidence to modern nanotechnology. To validate the hypotheses of the sharp edges, gold nanostars that exhibit their localized surface plasmon resonances in the visible−near-infrared region and contain multiple sharp tips have been considered as the model structures. Efficient control on the length and sharpness of the spikes has been achieved by judicious manipulation of the respective synthetic protocol. The electromagnetic simulation considering the topological parameters demonstrates an exotic interplay between the depolarization factor (Pz) and aspect ratio (α) to express the strength of the electric field generated at the tip heads as a function of their sharpness. Subsequent profiling of photothermal response caused by resistive heat exhibits an outstanding proof-of-concept resemblance between the local thermal manipulation and replicated in vitro laboratory experiment. Thus, the present work investigates an interdisciplinary analytical landscape enumerating the role of sharpness on the enhanced field and the temperature distribution localized at the tip head in the realm of plasmonic photothermal therapy.

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INTRODUCTION Sharpness of a tool has been considered as a parameter of mechanical efficiency to the humankind since the Neolithic age.1 From the Stone Age, the philosophy transcends from 50,000 years to the era of modern material sciences, being exploited by scientists for the proliferation of sophisticated technology through the development of exotic materials at the nanometer size regime. Nanoscale morphologies with tipped surfaces that impart significant contributions to the surface energy of the materials are of considerable interest in governing their physicochemical processes. Now-a-days, the manufacturing of architectures with large local curvatures is one of the basic conditions to design efficient heterogeneous catalysts,2 sharp tip to map electrostatic (viz., scanning transmission electron microscopy,3 near-field scanning optical microscopy,4 electron energy loss spectroscopy,5 etc.) and mechanical (viz., atomic force microscopy,6 etc.) properties at the bottom, sharp brush edges to project efficient solar energy harvesting,7 nanoscopic probes to modify the proximal molecular fluorescence,8 and tipped nanoantenna for ultrasensitive detection through surface-enhanced Raman scattering spectroscopy.9 In addition to the amplification of local electromagnetic fields at high curvature points, branched nanoconstructs are indispensable in enhanced human epidermal growth factor receptor 2 (HER 2) degradation,10 protruded nanostars for high loading and controllable cargo release,11 and glowing tips of nanostars as efficient photothermal transducers for cancer theranostic applications.12 Thus, the activity of the © XXXX American Chemical Society

nanostructures is strongly dependent on the morphology of the particles and to determine the properties that govern the structure−activity relationships, we need general equation of the topology under consideration.13 Electromagnetic interaction with such asymmetric manifolds leads to an exodus from the universal scattering behavior that is predicted, for a sphere, by optical scattering theories at Mie14 (R > λ) and Rayleigh− Gans−Debye15

( 20λ < R < λ)

size regime, where R is the

particle radius and λ the wavelength of incident light. Therefore, the topology of nanostructured materials governs their plasmonic properties in a vivid fashion; asymmetric polarization of surface plasmon occurs because of the inhomogeneous surface electromagnetic field decorating associated polarized plasmon wave field, being the genesis of efficient tools in the proliferation of sophisticated technologies.16 The advent of plasmonics of noble metal nanostructures could venture an extensive paradigm of substantial technological applications that could be achieved by careful manipulation of surface morphology for pre-engineering the desired material properties.17 Under the influence of the incident electric field, there occurs collective oscillation of the conduction electrons on the surface with a resonance to the Received: January 12, 2018 Revised: May 28, 2018

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DOI: 10.1021/acs.jpcc.8b00388 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

Figure 1. Transmission electron micrographs with successive higher resolution (upper to lower) of the respective sets of gold nanostars. Insets in the upper panel show the diameter histograms of the corresponding sets of the as-synthesized nanostars. The solid yellow circles in the middle panel specify the average tip distribution boundary, whereas the dashed yellow circles show the average core radius and the blue circles indicate the tips, which correspond to the HRTEM images in the lower panel. Scale bar: (upper) 0.2 μm, (middle) 100 nm, and (lower) 2 nm.

tion between the plasmonic attributes and the plausibility of local thermal manipulation of gold nanostars for photothermal ablation of cancerous cells. Martin,35 in his seminal paper published in 1924, has put forward a notion of interdependence of both geometrical factor (i.e., aspect ratio) and material aspect (i.e., depolarization factor) toward the induced field during the measurement of the scattering of liquid molecules, and to the best of our knowledge, this quest had been borne in our mind amidst the pioneering advancement of electromagnetic theories in the past century. In this article, size-selective gold nanostars with fine-tuning of tip sharpness (viz., aspect ratio and curvature) have been synthesized by judicious manipulation of the stoichiometry of the reactants through the wet chemical approach. A critical condensation between the numerical simulations and experimental results demonstrates an interplay between the depolarization factor (Pz) and aspect ratio (α) to determine the strength of the electric field generated at the tip head of the nanostars. Now, the manipulation of local temperature at the tip head as a result of strong electromagnetic confinement has been investigated through a model based on the Poisson equation that reveals the pervading relationship between the temperature distribution profiles and confined thermal damage of the cancerous cells by the gold nanostars. Therefore, the present investigation offers a proof-of-concept thermoplasmonic landscape correlating plasmonic properties and therapeutic endeavors of size-selective gold nanostars for the photothermal ablation of cancer cells.

incident frequency, coined as localized surface plasmon resonance (LSPR). 18 Depending on the direction of propagation of planar electric field and orientation of the nanostructures at the same boundary element, the pattern of LSPR modes dictates their characteristic optical absorption and scattering in these subwavelength structures.19,20 Therefore, to understand the optical properties of shape-selective nanostructures, the knowledge of surface topology that provides the location of point dipoles is prerequisite to model the surface electric field distribution and to design the scattering profile of the nanostructures. There have been several theoretical and experimental approaches in the literature to investigate the plasmonics of gold nanostars, for example, polarizationdependent scattering,21 plasmon hybridization of the core and tips,22 orientational effects of the tips,23 selective excitation of individual tips,24 two-photon photoluminescence,25 label-free biosensing,26 and surface-enhanced Raman scattering activity.27 As to the typical anisotropic nanostructures, gold nanostars, possessing sharp protruding tips surrounding the spherical core, could be employed to obtain a general expression describing the sharpness of the tip heads of the nanospikes in the scattering of electromagnetic radiation. On the other hand, localization of the electric field strength on the tip head leads to strong dephasing of coherently oscillated surface electrons, the energy of which is transferred to the atomic lattice effusing strong flux of heat at the metal−dielectric interface.28 Gold nanostars, possessing a high absorption-to-scattering ratio, at their corresponding localized surface-plasmon resonances, are one of the most prolific agents for the transduction of photon energy into heat that makes them emerging alternative12,29 to near-infrared (NIR)-absorbing nanoparticles,30 nanoshells,31 nanorods,32 nanocages,33 or nanomatryoshkas34 in plasmonic photothermal therapy (PPTT). It is, therefore, reasonable to design a thermoplasmonic landscape by picturesque condensa-

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EXPERIMENTAL SECTION

Reagents and Instruments. All the reagents used were of analytical reagent grade. Hydrogen tetrachloroaurate (HAuCl4· 3H2O), silver nitrate (AgNO3), cetyltrimethylammonium bromide (CTAB), L(+) ascorbic acid, sodium borohydride B


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The Journal of Physical Chemistry C Table 1. Fitting Parameters for the Five Different Sets of Gold Nanostars fit parameters set A B C D E

average diameter of nanostars (nm) 200 300 400 450 340

± ± ± ± ±

20 30 20 30 10

average diameter of nanocores (nm) 107 165 200 240 160

± ± ± ± ±

6 10 20 10 10

average length of nanospikes (nm)

length of semimajor axis (nm) (a)

length of semiminor axis (nm) (b)

aspect ratio (α = a/b)

± ± ± ± ±

4.70 6.30 6.80 7.70 8.75

1.50 2.89 3.44 4.84 7.23

3.133 2.200 1.975 1.591 1.211

70 80 90 100 75

6 5 5 15 5

solid yellow periphery represents the average tip circumference and the dotted circle shows the circumference of the core section; the blue circle indicates the region of maximum focus subjected to HR transmission electron microscopy (HRTEM) analysis in the lower panel for measuring the tip sharpness. To explicate the dependence of the spike length as a function of tip ellipticity parameter, an ellipsoidal fit model37 can be adopted, as discussed in Supporting Information 2, and this, in turn, originates the basis of a general form of equations to describe the sharpness of the spikes. Table 1 enunciates the fitting parameters represented as the change in aspect ratio (α) with an average length of the spikes measured from the micrographs of the different sets of nanostars. Figure 2 shows the localized surface plasmon band of the aqueous dispersion of the five different sets of as-synthesized

(NaBH 4 ) 4′,6-diamidino-2-phenylindole dihydrochloride (DAPI), Histopaque-1077, Dulbecco’s phosphate-buffered saline, RPMI 1640 medium, 4-(2-hydroxyethyl)piperazine-1ethanesulfonic acid, and fetal bovine serum were purchased from Sigma-Aldrich and were used as received. Sodium chloride (NaCl), calcium chloride (CaCl2), and Annexin V-FITC conjugates (green) were purchased from Invitrogen and were used without further purification. Double-distilled water was used throughout the course of this investigation. Animals were housed, handled, and euthanized as per the regulations of Institutional Animal Ethics Committee, Assam University, Silchar. All animals were given standard rodent food and water ad libitum. All experiments were approved by Assam University Ethics Committee, Assam University, Silchar (IEC/ AUS/B/2013-015 dated November 27, 2013). Absorption spectra were measured in a PerkinElmer Lambda 750 UV−vis−NIR spectrophotometer by taking the sample in 1 cm quartz cuvette. Transmission electron microscopy (TEM) was performed on a JEOL JEM-2100 microscope with a magnification of 200 kV. Samples were prepared by placing a drop of solution on a carbon-coated copper grid and dried overnight under vacuum. High-resolution (HR) transmission electron micrographs were obtained using the same instrument. Laser heating of the nanospikes was carried out with a continuous-wave infrared diode laser (model: MLL-III-785-1 W, Changchun New Industries Optoelectronics Technology Co. Ltd., China) of wavelength 785 ± 5 nm. Fluorescence microscopic images of the cells staining with DAPI (excitation: 350 nm, detection: 470 nm) were recorded on a Nikon Eclipse TS100 fluorescence microscope. Computational models were developed using FreeCAD, Meshlab, and ImageJ software packages. Different simulation techniques, viz., MATLAB 2011a, COMSOL Multiphysics software package, and DDSCAT code, were used to perform the theoretical calculations.

Figure 2. Surface plasmon absorption of the five different sets of assynthesized gold nanostars.

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gold nanostars. It is seen that for the blunt edge with a smaller tip height (set A), the LSPR appears in the regime of nanospheres (∼554 nm) along with a shoulder in the NIR (∼732 nm). Quite contrary to this observation, with the decrease in sharpness of the spikes (sets B−E), one broad yet well-defined LSPR peak with gradually red-shifted maximum, indicating the contribution of the sharpness to spectral changes and concomitant appearance of certain lumps in the LSPR profile, is seen, pointing out to the possibility of the convolution of complex eigenmodes arising due to the tips and basal core. Therefore, the present synthetic methodology provides nanostars possessing a controlled tip height, which results in concomitant changes in the LSPR pattern. The change in surface plasmon band structure could be ascertained by realistic modeling of the tip surface; first, to model the surface electric field distribution around the whole nanostructure and second, to elucidate their participation in the optical

RESULTS AND DISCUSSION A detailed synthesis of shape-selective gold nanostars possessing multiple tips around the basal core through the wet chemical approach by modification of the reported methods21,36 has been described in detail in Supporting Information 1. Fine-tuning of tip sharpness parameters (aspect ratio and curvature) in five different sets of gold nanostars has been achieved by judicious manipulation of the stoichiometry of the reactants; the decrease in CTAB concentration results in the size decrease of the spikes of the nanostars. Transmission electron micrographs representing the distribution of the particles (upper panel), single particles (middle panel), and tip heads showing their average sharpness (lower panel) of five different sets of gold nanostars are shown in Figure 1. Insets in the upper panel show the diameter histograms of the corresponding sets of the nanostars. In the middle panel, the C


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The Journal of Physical Chemistry C field polarization mechanism. A mechanical computer-aided design of representative nanostar morphology and the finite element (FE) modeling of the surface mapping of the electric field distribution of the gold nanostar are shown in Supporting Information 3. This emancipation from the homogeneity of surface electric field distribution demands a critical analysis of the effect of tip sharpness in governing the optical properties of the anisotropic nanostars. It is noted that the plasmon field adjoins the tip with the core, which is depolarized in terms of surface plasmon field. Thus, a nanostar can be conceived such that the tips are arranged in different orientations perceiving distinctive local symmetries around a void core of least significance in near-field modification but impart a significant contribution toward the effective radius (aeff), which has been taken into consideration in simulation of their scattering behavior. From the basic wave theory, this scattered field corresponds to the frequency of dipolar resonance because of the confinement effect. These frequencies, in turn, have been used to calculate the potential generated at the tip head. The Nordlander group22 has modeled the nanostar as a truncated sphere with protruding tips of prolate spheroidal shape and using the finite-difference time-domain method, it has been shown that the plasmon modes of a nanostar result from the hybridization of plasmons associated with the core and the tips. The nanostar core serves as a nanoscale antenna, dramatically increasing the excitation cross section and the electromagnetic field enhancements of the tip plasmons. In the present work, the aim is to design and simulate the behavior of highly polarized sharp tip heads so that the theoretical model perceived correlates the results which are turned to be abruptly suitable for photothermal experiments. In this context, we have attempted to construct an analytical model for the tip of a nanostar by exact determination of their bent edge obtained from the TEM images as shown in Figure 3. We have employed basic Euclidean geometry to design the twodimensional (2D) slice of the solid cone formed by the protruded spike of a nanostar (panel A). The tip head can be

considered as an elliptical end, where the tangents at some specific points will mimic the sides of the conical tip (panel B). Considering a small unit of the shift constant H, the total tip height hn has been discretized as hn = h1 + nH, where n is the order of shift for the center of the respective tip ellipsoid (a detailed derivation is shown in Supporting Information 4). Now, by setting the value of n as the variable, a sequence of analytical models has been designed by realistic parameterization of the conical tip surfaces, which were subjected to numerical solutions to correctly estimate their scattering properties. The relationship between the intensity and polarization state of the incoherent light can be depicted by the vector elements of the Stokes’ parameters described through the Mueller matrix associated with the optical signals of the nanostructures.38 A discrete dipole approximation (DDA) technique has been employed to determine the Mueller matrix and to compute the scattering coefficients numerically for the finite target, miniaturizing as a dipole array of the lattice elements.39 The DDA simulation has been performed based on the DDSCAT code,40 and all the simulations have been pursued under the constraint of the prescribed boundary condition, |m − 1| < 2, where m is the imaginary part of the complex refractive index of gold provided by Johnson and Christy.41 As to the next condition, to set the dipoles along the axes of the nanotips, the point-in-polyhedron algorithm42 has been used to meet the boundary condition43 for the limiting value of interdipole λ distance (d) given by d < 10 |m| , where λ is the maximum wavelength of the LSPR spectrum. Because there is no hard and fast rule to set the dipoles for a mesh in a regular array, the simulations have been run over and over up to 10 sets of shape files altering d values until a stable numerical output is reached. Furthermore, extensive number of volume elements (dipoles) has been conceived to generate the shape files, which were, further, rendered with LiteBil, a visualizer to achieve dipolar arrays for the perfect depiction of prebuilt meshes avoiding inaccuracies and simulation errors. The series rendered structural arrays based on this conical model characterized by the equivalent tip cone angles, which are displayed in the panel C. Numerical simulations based on DDA and FE method (FEM) techniques elucidate significant attributes on the plasmonic properties of the asymmetric gold nanostars as shown in Figure 4. All the FEM simulations have been performed with the radio frequency (RF) module of COMSOL Multiphysics software package. The calculations were set up as a 2D model in which we invoke the geometric scattering boundary for sharpness to solve Maxwell’s equations for the systems under consideration. Computational details for FE modeling of the tip heads are presented in Supporting Information 5. To obtain the scattering efficiency, we have performed the DDA calculations for each set of the nanotips under consideration. The conditions were set with respect to the unidirectional propagation of wave (x-axis) considering polarization along both the parallel and orthogonal directions to the axis of modeled right circular cone motifs. Polarization angle of the incident wave was set to 0° with respect to the central axis of the cone so that the calculated polarization profile conveys to enumerate the polarization at the tip heads of the synthesized particles. The extinction efficiency calculated from DDA simulation for the ensemble of nanotips (panel A) shows the scattering spectral profiles with the change in tip

Figure 3. Modeling the tip heads of a nanospike: (A) geometrical representation to mimic the nanotip morphology, (B) mesh grid presentation of the resultant tip head, and (C) numerical models of the nanospikes in two dimensions with gradual change in shift order at an interval of 100.5. D


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shown by the polarization profiles obtained from the DDA calculation. The multimodal peaks obtained from scattering simulations were inspected through the polarization states obtained from the FEM simulations. The representative surface plots showing two different eigenmodes (for n = 10) obtained in the case of nanostars (set B), at wavelengths 520 and 600 nm, respectively, are shown in the left inset of panel A. The plasmon frequency (ωl,m) of spheroidal nanostructures depends on the modes of resonance through the following relationship, ω l,m =

2l + 1 l + εD(l + 1)

ωB, where ωB is the background frequency

and εD dielectric constant of the medium, which possesses a value greater than unity. Therefore, plasmon energy decreases with respect to the increase in the order (l) of plasmon resonance. These findings are quite similar to those reported by Tabatabaei et al. in the investigation of coupling of nanopyramids.44 Considering electrostatic approximation, a surface wave in xy-plane with a unit background field in xz-direction has been depicted to calculate the interaction with the 2D projection of the tip edge placed in the same plane for the ensemble of particles by FE simulation. A detailed calculation through FEM simulations is presented in Supporting Information 6. The observed pattern illustrates the relative increase in the spread of the intense electric field at the tip head for all sets as displayed in panel B. The series of surface plots exhibits the increase in the spread of the surface electric field that governs the depolarization of surface charge at the tip head as shown in the inset. The field enhancement at the tip head of shape-selective nanospikes shows an exponential decay in the field strength with the decrease in sharpness as calculated from the FEM simulation of the tip array. A quantitative measure of this phenomenon depicts the field strength distribution over the arc length for each of the 2D nanotips under consideration. According to the Gans’ theory, the depolarization factor (Pz) along the z-direction of polarization with respect to the ellipticity (e) of the both ends of the prolate particles can be expressed as45

Figure 4. Modeling the optical properties of the different sets of nanospikes under consideration: (A) normalized extinction efficiency as a function of wavelength by using the DDA method (the right inset shows the orientation of the numerical models of the nanospikes representing a gradual increase in basal radius in the xy-plane as a function of shift order of the tips along the z-axis; the left inset shows the FEM simulation corresponding to dipolar (l = 1) and quadrupolar (l = 2) modes, and an array of the polarization maps color-coded for different peaks arising out from the scattering simulation for different values of sharpness parameter (n) are exhibited at the top of the profile) and (B) electric field strength as a function of arc length (the inset shows an array of surface plots designating the logarithm of electric field strength on the tip head of a nanospike from each set by FE simulation).

Pz =

E0, z − E i, z ⎤ 1 − e2 ⎡ 1 1+e − 1⎥ = ⎢ ln ⎯⎯⎯→ 2 ⎦ 1−e e ⎣ 2e L z

(1)

where E0 is the applied electric field, Ei the z-component of the ⎯⎯⎯→

induced field, and Lz the geometrical factor of depolarization along the z-direction. Substituting the depolarization factor with the aspect ratio (α), the expression for the depolarization factor (Pz) can be modified into the form

sharpness. The right inset shows the orientation of the numerical models of the nanospikes representing gradual increase in basal radius in the xy-plane as a function of shift order of the tips along the z-axis. The field strength of plasmon eigenmodes was determined from both the DDA and FEM simulations setting the modal solution in an RF module of the software package. An array of the polarization maps colorcoded for different peaks arising out from the scattering simulation for different values of sharpness parameter (n) are exhibited at the top of the profile. The results show that all the highest intensity transverse peaks are dipolar (l = 1) in nature. For the sharpest tips, the less intense peaks at the longer wavelength region appear quadrupolar in nature (l = 2), but after losing their sharpness to a certain extent (up to n = 10), all the peaks become dipolar in their scattering characteristics, as

Pz =

1 2 α −

⎡ α+ α ⎢ ln ⎢ 2 1 ⎣ 2 (α − 1) α−

(α 2 − 1) (α 2 − 1)

⎤ − 1⎥ ⎥ ⎦ (2)

Keeping ellipticity of the both ends of the prolate particles constant, the effect of depolarization has been fixed to a constant value with concomitant increase in the overall size as to the formalism of the theoretical model for the different sets of nanospikes under consideration. Under such circumstances, the change in the theoretical spectra can be assumed only due to the effect of orientational robustness of dipole lattices constructing the tip. By comparing the numerically simulated and experimentally observed spectra, it is possible, thereby, to elucidate the effect of geometrical asymmetry in the scattering phenomena of the different sets of as-synthesized nanostars. E


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The Journal of Physical Chemistry C Both the experimental and simulated spectra show a strong peak at the shorter wavelength region and a small shoulder at the longer wavelength region, signifying the presence of a sharp tip with a shorter length, which replicates the anomaly observed in the LSPR spectrum of the smallest nanostars of set A. Because of the short height of the protruded tip, the participation of the basal core in the scattering phenomena increases, giving rise to the presence of a shoulder along with the sharp LSPR peak. With further elongation in the size of the tips (sets B−D), the sharpness decreases; despite having a short peak height, set E shows an extreme blunt tip head. This, in turn, increases the spread and exponentially decreases the intensity of the surface electric field as a function of arc length of the tips, imparting a gradual red shift in the LSPR maximum with simultaneous broadening of the linewidth.46 Polydispersity of the nanostars, as evident from the corresponding diameter histogram, could also be taken into consideration to account for the broadness of the LSPR pattern. Thus, plasmonic effects become more pronounced for the ensembles of nanospikes belonging to the nanostars of sets B−E as their LSPR bands become broadened with the size of spikes providing an anticipated platform to reveal the pervading relationship between the topology and plasmonic properties of nanostar morphology. Further attributes of the experimental results have been elucidated by manipulating the transmission electron micrographs in a vector form into the aforementioned FE modeling protocol. Because all sets of nanostars were synthesized using CTAB as the capping agent, the refractive index corresponding to CTAB has been set to 1.435.47 A detailed calculation through FEM is described in Supporting Information 7. Figure 5 shows the calculated electric field along the edge of the surface by FE modeling concerning the transmission electron micrographs of the different sets of nanospikes (panel A) and field intensity distribution as a function of arc length (panel B). The experimentally observed profiles reveal a strong similarity with the pattern obtained from the simulation results. The profile for the nanostars of set A demonstrates the highest value of electric field intensity with a shallow spread as predicted earlier. The apparent bluntness for the nanospikes of set B becomes clearly visible with widespread electric field having minute increase in field intensity pertaining to the numerical models with higher value of shift order (n = 10). Concomitant increase in the electric field distribution for the nanospikes of sets C−E could be apprehended considering the field pattern arising out with the increase in nanospike basal radius (ymax). With the increase in their size, the number of dipoles also increases and the corresponding extinction maximum appears to be red-shifted. Because of meager increase in intensity with extensive spreading of the surface electric field, the LSPR spectra also appear to be broad in nature. A comparative anatomy for the scattering properties of the simulation results and experimental manifestations of the different sets of nanospikes is depicted in Figure 6. Panels A and B show the profiles showing the plot of ln|E02|, obtained from FE simulation as functions of ln|λext|, calculated by using DDA and ln|λLSPR|, from the experimentally observed spectra for the different sets of nanospikes, respectively. Interestingly, an opposite trend is observed in the spectral band as a function of electric field distribution over a tip head in the simulation as well as experimental observation; the contradiction arises from the basic difference between the simulated and experimental results because of the change in the aspect ratio (α), which has

Figure 5. Modeling the TEM images of the different sets of nanospikes under consideration: (A) calculated electric field along the edge of the surface by FE modeling concerning the transmission electron micrographs and (B) field intensity distribution as a function of arc length.

been assumed as constant for all the theoretical models and points out to search for new avenues for further in-depth analysis of shape parameter. Panel C shows an exponential increase in ln|E02| with an increase in aspect ratio (α) of the different sets of nanospikes. Because depolarization factor (Pz) is a function of aspect ratio (α) as depicted in eq 2, this relationship, too, succeeds in the case of the surface plot obtained when depolarization factor is revealed as a logarithmic F


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Figure 6. Comparison of the scattering properties of the simulated and experimental data: (A) plot of ln|E02|, obtained from FE simulation as a function of ln|λext|, calculated by using DDA, (B) plot of ln|E02|, obtained from FE simulation as a function of ln|λLSPR|, from the experimentally observed spectra, (C) aspect ratio (α) as a function of electric field at the tip head obtained from FE simulation, and (D) aspect ratio and depolarization factor as a controlling unit of electric field simulated at the tip head and observed LSPR wavelength for different sets of the nanostars. The white circles in panel D show the minimization of field boundary condition for both the parameters.

function of both FE simulated electric field squared at the tip head of the TEM images and observed LSPR wavelength, as presented in panel D. The analytical model has been conceived from the fit equations appeared in the panels B and C. It is observed that the electric field increases exponentially with increase in depolarization factor and the exponent is steeper at the high wavelength region than that of the lower regime. Physically, this effect confers to the fact that with the increase in LSPR wavelength, the dipolar interaction increases for tip heads possessing equal ellipticity. Because size is the key parameter for a material immersed in a uniform dielectric medium to shift the position of LSPR wavelength, the effect of depolarization can be interpreted as the size effect on the dipolar interaction of the nanostructures. An expression for the polarizability tensor (αj), at any direction j, for an inhomogeneous ellipsoid can be expressed as a linear function of its volume (V = abc) as αj = 4πabc

generalized ellipsoidal geometry, the depolarization factor for the ith axis (Li) can be presented in the form Li =

∫0

∞

ds 2

(s + R i ) (s + a 2)(s + b2)(s + c 2)

(4)

where s and Ri are the surface area and half axis along the ith axis, respectively. From eq 4, it is apparent that with an increase in the aspect ratio, the value of surface integral decreases and surface electron density increases. Therefore, the switch over boundary describes the limiting condition, which points out to the minimum sharpness required to overcome the retardation effect of depolarization of a specific material by accumulating the adequate surface electron density. After crossing the boundary, both depolarization factor and aspect ratio contribute to the increase in potential at the tip head. Thus, by controlling the sharpness of the chosen material, the required potential could be achieved for, further, optoelectronic applications. Although it is possible to synthesize nanostars possessing a variable number of tips arranged in different fashions, the number of tips per nanostar has been manipulated at ca. 10, which corresponds to similar symmetry as well as chirality of the scatterer. The nanostars, however, exhibit a symmetry of low order (S4) than their corresponding nanopods bearing an octahedral or tetrahedral arrangement around the core, and their respective orientation shows angular deviation b = c). From the profiles, it is evident that both the aspect ratio and depolarization factor impart nonlinearity to the conceived electromagnetic field. The observed minima in the electric field strength, marked with white circles in the panel D, exhibit a hyperbolic curvature defining a switch over boundary, which converges toward the minimal value of depolarization factor for the sharper tips. For a G


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The Journal of Physical Chemistry C context, we have formulated the way to reticulate the plasmonic response as a function of aspect ratio of the fitting ellipsoid at the tip head. The formulation involves the calculation of polarization based on DDA because it would be appropriate for such kind of asymmetric nanostructures. Next, we follow up a basic scattering theory to enumerate the depolarization factor, which has been achieved both through DDA and Gans’ modification proposed for ellipsoidal particles. On the other hand, the potential generated at the tip head has been calculated by solving Maxwell’s equations explicitly. Now, it is the basic philosophy to bridge up two different perspectives of plasmonics that govern the optoelectronics of the nanostars. In addition, the experimentally observed plasmonic attributes have also been taken into consideration. Thus, all the prerequisites to bridge the both viewpoints have been accomplished in three steps as depicted in Figure 6. We have mapped the change in experimentally observed plasmon wavelength (panel A), simulated scattering wavelength obtained through DDA (panel B), and aspect ratio of the tip obtained through synthesis and perceived through the analytical model (panel C) as a function of their simulated field strength (obtained by solving Maxwell’s equation using FE modeling) satisfying each other in an analytical relationship as depicted by the blue line in Supporting Information 8. Thus, the separate avenues can be reconciled into a singular scale to account for the plasmonic response of the nanostar geometry. Taking all these factors together, we have shown that there exist two basic limitations that have to be overcome to acquire the desired maximum possible electric field strength for any sharp tip and to obtain more delicate quantum information arising through tunnelling (panel D). The first factor is the structure in the realm of sharpness and the second one is optical properties of the material, which is governed by the aspect ratio at the tip head and depolarization factor at the resonance wavelength, respectively. Depolarization bears an important signature of the morphology of a scatterer, which is often coined as the “hard problem” of the scattering simulation.38 The scattering characteristics could be obtained from the DDA simulations for each set of modeled nanotips. It is, therefore, a straightforward technique to describe linear, circular, and elliptical polarization at the wavelength of interest from the respective Muller matrix components. Because the sum of the polarization and depolarization is always unity, with the help of the identity and the calculated polarization values obtained from DDA simulation (considering the resultant polarization angle, θ = 90°), the depolarization contributing to the overall asymmetric structure can easily be perceived. Each of this depolarization at the tip head should also follow the analytical solution provided by Gans’ modification for the ellipsoidal particles because the tip heads are also consisted of an ellipsoid placed on the top. In this realm of analytical design, we have found that both these techniques produce similar results to account for the plasmon field at the tip head. Meanwhile, depolarization is the ratio between charge displacement and polarizability; it also corresponds to the fact that blunt tips show higher retardation through the depolarization field, which is quite evident from Figure 7. It is seen that there is an exponential decrease of the electric field factor with the increase in depolarization factor. The inset shows DDA simulation for azimuthal polarization of the nanotips. Considering the basic definition of depolarization factor as shown in eq 4, the

Figure 7. Optoelectronic effects arising due to the polarization of surface charge; depolarization factor as a function of electric field. The inset shows the azimuthal polarization profile using DDA calculation for theoretical models under consideration. ⎯⎯⎯→

geometrical factor, Lz , increases with the increase in the length of the vertex, giving rise to a greater dipole volume, and consequently decreases the difference between applied and induced field strengths. A similar effect is pertinent to the tips with a constant aspect ratio, the maximum polarization of which coincides at 90° and 270°, respectively, but the minima at 0° and 180° increase significantly with the volume of the nanotips. The volume of nanotips is a function of the vertex length; thus, with the increase in shift parameter, the volume of the tips increases and tip heads become more and more flattened. It is noted that for the relatively blunt tip head (n = 102.5 to 102), isotropic polarization is observed in all scattering angles and becomes maximized at orthogonal orientation to the incident field with the increase in sharpness (n = 101.5 to 100). It is, thus, apparent that the change in polarizability for the sharpest tip can exhibit the maximum change in polarization with the incident light. Therefore, the coherent control of polarization for tip heads flanked around the nanostars could pave an avenue for prolific and precise control in extreme light concentration and so as the thermal manipulation, which could be exploited, further, for mapping their photothermal efficacy. Plasmonic nanostructures have emerged to be highly promising photoabsorbing agents as alternative to conventional light-absorbing dyes for the photothermal ablation of cancerous cells.48−53 Because metallic nanostructures are very inefficient fluorophores, high absorption-to-scattering ratio of plasmonic gold nanostars offers a noninvasive photon excitation modality in the NIR “theranostic window” (700−1300 nm).54 Although the difficulty of the surface functionalization limits the utility of gold nanostars in several biomedical applications, significant plasmonic and thermodynamic attributes offer a unique opportunity as efficient and selective photothermal transducers, considerably damaging the cancerous cells.55 When gold nanostars accumulated at the tumor site are exposed to an impinging laser beam resonant with their surface plasmon oscillations, the absorbed light is converted to thermal energy, as a result of nonradiative relaxation of electron oscillations in the nanoparticle lattice.56 The nanostars have been modeled by using the anatomical dimensions from the transmission electron micrographs as depicted in Figure 1. Although it is seen that for each set of the H


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Pennes, first, introduced the model for hyperthermia simulation through his famous bioheat-transfer equation (BHTE) as59

nanostars, the core-to-tip size ratio alters significantly as presented in Table 1, but their number ratio remains, nearly, similar (typically within 1:8 to 1:10). For the simulation purpose, we have selected asymmetric nanostars bearing 10 tips around the core, which are being heated up ideally with the interaction of both the cellular media and incident radiation, that has been mapped experimentally by the Bardhan group.57 The formalism of the tips involves a restriction that their circumference on the spheroidal basal core has to be such that protrusions should not intersect with each other eventually, which will form a blunt cone at the tip head. This restriction, thus, derives to the condition that involves the height-to-solid angle ratio to design the nanospikes as has been discussed earlier.37 Following our previous design, we have modified the topological solution for the nano tip head to a more sophisticated formalism through which all the attributes of a nanospike (viz., height, sharpness, area of basal core, and basal circumference of the tips) could be concealed together. Throughout the discourse, the individual nanospikes could be described, solely, by the sharpness parameter (n) based on which their thermoplasmonic behavior has been elucidated. Therefore, the thermoplasmonic attributes become a sensitive function of the number of tips bearing particular sharpness showing the orientation average photothermal response and the fraction of the cellular uptake of the nanostars for the destruction of cancerous cells. Through these considerations, the nature of sharpness could be apprehended to the selective photothermal behavior of gold nanospikes in which the volume term is not included. Thus, we have interconnected the photothermal activity to the tip shape by ignoring the contribution of the depolarized core, by taking their weighted-average photothermal response into consideration. Because the laser beam is coherent and unidirectional toward the embedded nanostructures, it could be easily perceived that conduction of heat generated by the electromagnetic field could be approximated as unidirectional flow of heat across the surface. One-dimensional mapping of the heating power density, q(x), around the nanostars can be calculated using an FE modeling technique. Indeed, the temperature distribution, T(x), generated by heating power density, q(x), is governed by the Poisson equation58 ⎡ d ⎛ d ⎞⎤ ⎢ ⎝⎜kx ⎠⎟⎥T (x) + q(x) = 0 ⎣ dx dx ⎦

ρCp ,tis(T )

ρCp ,tis(T )

1 Re[(σ − jωε)EE*] 2

δT δ ⎡ δT ⎤ = Q ext + ⎢k tis(T ) ⎥⎦ δt δx ⎣ δx − ω blCp ,bl(T )[T (t )−Tbl]

(9)

where ktis is the thermal conductivity of the tissue and Tbl and ωblCp,bl(T) are the temperature and the perforation constant of blood, respectively. Now, from the computed value of Qext, obtained by solving eq 7, it is possible to determine the rate of heat flow in the x-direction, in temperature,

( δδTx ) as well as the temporal change

( δδTt ), because of strong plasmonic interaction.

When gold nanostars in a cellular medium are illuminated, the abrupt local temperature increase between the hot nanostructured surface and the cooler surrounding biological medium causes the death of the oncogenic cells. Because resistive heat acts as the source of photothermal therapy, under a particular extrinsic laser power, the harnessed energy at the nanostructured tip−cytosol interface could be exploited as the selective agent for the ablation of the oncogenic cells. The sharpness of the tips leads to strong confinement of the electric field that not only increases the energy for the photothermal transduction but also reduces the side effect of excess exposure, shrinking the possibility of damaging noncancerous cells. On the basis of this perspective, we have performed a combined simulation and experimental approach to investigate the photothermal transduction efficiency of gold nanostars accumulated to the splenic macrophages of mice. After 5 decades of extensive investigation, it has been found out that the effectiveness of radiological efficacy resembles to the Arrhenius equation of first-order reaction kinetics, and the transient degree of tissue ablation with time can be related through the Arrhenius damage equation as61

(5)

−ΔEa 1 d(α(x)) = A exp α(x ) d t RT (t )

(10)

where αx is the transient degree of tissue ablation at any time t, ΔEa the activation energy, R the universal gas constant, and A the pre-exponential factor. In the limit of T(t) to the threshold temperature, Tth, at time τ, the integrated form of the Arrhenius equation depicts the fractional damage coefficient (Ω) as the dose parameter given by the relationship62

(6)

The amount of plasmonic heat, Qext, generated by the resistive light−matter interaction with the electromagnetic field can be calculated as Q ext =

(8)

where ρ and Cp,tis represent the density and specific heat of the tissue, respectively. After a long time interval, Incropera and Dewitt modified the equation in the context of Poisson equation as60

where kx is the thermal conductivity of gold (=318 W/m K). Thus, the heating power density, q(x), along the x-axis could be represented as q(x) = −kx∇T (x)

δT = k∇T + ω bl(ρCp)bl δt

(7)

Ω = ln

where σ is the optical conductivity, j the current, ε the optical dielectric constant at the angular frequency (ω) of the incident wave, and E and E* are the respective real and imaginary field components considered as a plane wave interaction with the electromagnetic radiation, which could be solved easily by FE modeling of the nanospikes at the laser wavelength.

α(x)t = 0 = α(x)t = τ

∫0

τ

A exp

−ΔEa dt RT (t )

(11)

and the percentage of cell damage can be calculated as F(α(x)) = 1 − exp( −Ω)

(12) 61

On the other hand, Saparato and Dewey proposed an empirical, simple, and elegant equation in their seminal paper I


Article


Figure 8. Comparative account of the simulated and experimental results of the PPTT of size-selective gold nanostars accumulated at the splenic macrophages of mice: (A) surface plots representing the rate of temperature increase per unit length, (B) profile showing the temporal increase in temperature at the tip heads as a function of time, (C) percent damage of the cells during different time intervals illustrating the size-selective efficacy, and (D) histological evaluation showing the fractional cell death represented by the time development of fluorescence using representative gold nanostars (set A). The percentage of cell death as a function of time fits in the sigmoidal growth curve, as represented by the dashed line in the panel C.

( f) can be expressed with the simple first-order partial differentiation

to express T as a function of t through the simple relationship that holds extremely well for practical theranostics at lowtemperature regime. They invoked the idea of equivalence by normalization through a meticulous analysis of the slope obtained from the Arrhenius plot over a large amount of time− temperature data for different cell lines and append to this simple realization that “The evidence clearly indicates that, for both in vitro and in vivo systems, an exponential relationship exists between temperature and exposure time”. In most of the systems, this relationship can be simply stated: “a one degree increase in temperature requires a two-fold decrease in time for the same effect above 43 °C and a three-to-four fold decrease in time for an iso-effect below 43 °C”.63 This model, though empirical, has become celebrated as CEM 43 °C model, where CEM stands for cumulative equivalent minutes required to obtain the equivalent time of exposure for the samples irradiated in different temperatures. In the simulation, we have considered this model to elucidate a formulation for comparing and normalizing the time and temperature required for the clinical method of radiation. The linear function of the dose parameter, CEM43, has been depicted as ∂CEM43(tn) = min(CEM43(tn)) ∂t

∂CEM43(tn) ∂Ω = f (t ) = ∂t ∂t

Now, solving eq 9 for the temperature increase in the electromagnetic field and the carrying out the integrals for the model eqs 11 and 13, the fractional cellular damage could be obtained, which elucidates the thermoplasmonic efficacy for the nanospikes of different sharpness. The method relies on a minimal penetration of the nanostructures by passive targeting that occurs through an enhanced permeation and retention effect64 at the tumor site. Laser heating of the nanostructures incubated at the tumor site was carried out with a continuouswave infrared diode laser (5.0 mW) with the wavelength at 785 ± 5 nm for 20 min. A detailed experiment of photothermal ablation of cancerous cells using representative gold nanostars (set A) is described in Supporting Information 9. The photothermal response of all sets of gold nanostars can be estimated by FE modeling that is consistent with the optical interactions and the thermal transport of the nanostructures at the intracellular environment. A detailed description showing the complementary analytical steps of computation to account for the photothermal response of the nanostructures has been enunciated in Supporting Information 10. Figure 8 summarizes a comparative account of the simulated and experimental results of the PPTT of shape-selective gold nanostars accumulated at the splenic macrophages of mice. The surface plots (panel A) showing the rate of temperature increase per unit length depict the generation of the highest amount of heat around the sharpest tip and decreases as the bluntness of the tip head increases. From the simulation results, a profile represents the temporal increase in temperature at the tip heads (panel B), and it is apparent that with increase in the time of laser irradiation, the steepest rise in temperature occurs for the sharpest tip. Now, considering temperature increase inside the nanostructures as uniform in the homogeneous biological medium and setting the threshold temperature at Tth

(13)

where the statistical factor (RCEM ) obtained from an experimentally determined function of the activation energy, ΔEa, can be expressed as R CEM = exp

−ΔEa RT (t )(T (t ) + 1)

(15)

(14)

The value of RCEM is determined through the experiment, which shows the value 0.5, when Tn ≥ 43 °C and 0.25, when Tn < 43 °C. The parameters, Tn and tn, are the threshold temperature and the time of measurement, respectively, and Δt is the time step of measurement. To couple both of these equations with the transient frequency domain calculation, the change in both of the dose parameters with the forcing function J


Article

The Journal of Physical Chemistry C = 43 °C,65 a critical value in the temperature range to be effective for photothermal ablation, the percent damage of the cells showing the shape-selective efficacy has been illustrated (panel C). To substantiate the simulated results, subsequent experiments have been conducted to determine the therapeutic efficacy in vitro for the representative nanostars (set A). Histological evaluation shows the fractional cell death signified by the time development of fluorescence, and after a particular time, complete ablation of the oncogenic cells was observed (panel D). According to the principle, the theranostic efficacy is proportional to the fluorescent dots, which is, further, an indirect measure of the amount of heat flux passing through the center of laser beam. After a prolonged time of laser irradiation (900 s), when the fluorescence intensity does not change appreciably, the thermodynamic process of cell ablation can be considered as equilibrated, similar to the fundamental concept of reaction kinetics, where the concentration of the product is approximated as constant at the end of the reaction. Because the uptake of the nanostars is nonscalable, the concept of normalization could be applied subjected to the scaling statistics of the CEM 43 °C model, which makes the calculation free from ambiguities. The change in the number of fluorescent dots during different time intervals of in vitro fixed cell imaging is analyzed, of which the maximum value can be accounted for 100% of the cell death. The percentage of cell death as a function of time fits in the sigmoidal growth curve, as represented by the dashed line in the panel C. To obtain a comparative analogue, the observed results are plotted in the same axis with the computed results, which corresponds almost to the sharpness configuration of n = 31, with a considerable accuracy (R2 = 0.986). The dose−response equation can be formulated as F(αx(t )) − k1 =

Scheme 1. Schematic Presentation Showing the Gradual Charge Accumulation and Plasmonic Heating as the Bluntness of the Tip Head Decreases

of the fundamental laws of nature to the welfare of life that merges physics, chemistry, materials sciences, and biology at the nanoscale.

■

CONCLUSIONS In conclusion, the ellipticity of the tip heads has been invoked as an intrinsic physical parameter in governing the scattering of electromagnetic radiation and subsequently in profiling the thermoplasmonic efficacy of the particular nanostar morphology. The scaling of charge accumulation corroborates to the sophisticated optimization of sharpness of the tip heads to transduce the plasmonic heat in achieving minimally invasive therapeutics for the photothermal ablation of cancerous cells. The problem has been formulated by careful manipulation of ellipticity of the tips of shape-selective gold nanostars synthesized by variation of the reaction conditions by a wet chemical technique. Geometrical formalism of the topological parameters of the protruded conical spikes has been rationalized through numerical solutions, which enunciate the effect of both optical and geometrical factors that govern the localization of electric field intensity on nano tip heads. This most important physical insight is that the desired voltage at the tip heads could be achieved by, simply, manipulating the geometry of the architecture for technological applications. On the other hand, it is obvious to exploit the exotic possibilities at the present state-of-the-art research of the several anisotropic nanostructures in PPTT from both theoretical and experimental perspectives. The present article forges a background through critical condensation of the experimental realizations and numerical solutions that provide a quantitative and pragmatic attribution to the paradigm of nano-sharpness toward the advent of plasmonics, catalysis, energy conversion, and spectroscopy.

k 2 − k1 1 + 10(log t0− t )p

(16)

where k1, k2, and p are arbitrary parameters, the values for which can be set to 3.423, 100.712, and 0.006, respectively, and the center of the sigmoid is represented by the coordinates (log t0, (k1 + k2)/2); t0 corresponds to 546.9 s during the course of laser exposure. Therefore, the simulation results based on the Poisson equation, accounting the photothermal heat generation at the tip heads of gold nanostars, correlate well with the experimental observations of the transduction efficacy toward the oncogenic cells. The concept of charge accumulation on a sharp edge has been considered as the cornerstone of electrostatics since its inception. On the other hand, the thermal ablation of tumor dates back to 1700 BC when a glowing tip of a fire drill had been used for breast cancer therapy. In the present investigation, it is observed that charge accumulation on a sharp edge increases and the tip head becomes more and more heated as the bluntness of the tip head decreases as presented in Scheme 1. The present investigation, thus, designs a thermoplasmonic landscape through a critical condensation of the plasmonic and thermodynamic features of gold nanostars toward PPTT. During the last 50 years of journey, materials sciences have become a common platform to bring all domains of natural sciences together. From the design of benign topologies to the synthesis of anisotropic nanostructures, from the radiance of light−matter interaction to the localization of surface plasmons, from the physics of laser heating to the exotic application of PPTTthe chronological sequence of fascinating adventures describes the philosophy of myriad combination

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b00388. K


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Experimental details for the synthesis of gold nanostars, photothermal ablation of cancerous cells, and some aspects of numerical solution (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +91-3842270848. ORCID

Sujit Kumar Ghosh: 0000-0001-6657-7396 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support from DBT, New Delhi (project no. BT/277/NE/TBP/2012). H.C. is grateful to UGC, New Delhi, for Senior Research Fellowship. The authors are thankful to SAIF, North Eastern Hill University, Shillong, for providing facilities for transmission electron microscopic measurements.

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Gold Nanostars in Plasmonic Photothermal Therapy: The Role of Tip

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