Temperature near Gold Nanoparticles under Photoexcitation:Evaluation Using a Fluorescence Correlation TechniqueHiroaki Yamauchi,† Syoji Ito,*,† Ken-ichi Yoshida,‡ Tamitake Itoh,§ Yasuyuki Tsuboi,∥,⊥

Noboru Kitamura,∥ and Hiroshi Miyasaka*,†

†Division of Frontier Materials Science, Graduate School of Engineering Science and Center for Quantum Materials Science underExtreme Conditions, Osaka University, Toyonaka, Osaka 560-8531, Japan‡Rexxam Co., Ltd., Kagawa Factory & Kagawa Branch Office 958, Ikeuchi, Konan-cho, Takamatsu, Kagawa 761-1494, Japan§Health Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Takamatsu, Kagawa 761-0395,Japan∥Division of Chemistry, Graduate School of Science, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan⊥JST (Japan Science and Technology Cooperation), PRESTO, Japan

ABSTRACT: Fluorescence correlation spectroscopy was appliedto the measurement of local temperature in the vicinity of goldnanoparticles adsorbed on the surface of glass substrate under thephotoexcitation at a wavelength of 633 nm. From the diffusioncoefficient of fluorescent guest dyes and the temperaturedependence of the viscosity of a solution, the increase in thetemperature was estimated. It was revealed that the temperatureca. 5 μm from the gold nanoparticles linearly increased with anincrease in the incident laser power and an increase in the numberof gold nanoparticles on the substrates. Temperature elevationcoefficients of single gold nanoparticles with 100 and 150 nmdiameters under the irradiation at 633 nm were, respectively, estimated to be (2.3 and 6.9) × 10−3 K·kW−1·cm2. These valuescould be interpreted on the basis of the absorption coefficients of gold nanoparticles and the thermal conduction in the solution.

■ INTRODUCTION

Surface plasmon polariton leads to the compact storage ofphoton energy in electron oscillations at the interfaces of noblemetals and dielectrics.1,2 In particular, a nanoscale gap betweena pair of noble metallic nanoparticles provides significantlyenhanced electric field within the gap under the photoexcitationwith a polarization along the long axis of the dimer particles.This drastically enhanced electric field originates from stronginteraction between photons and nanostructures of noblemetals, called localized surface plasmon resonance (LSPR).Theoretical studies predicted that the enhancement factorattained up to ∼104 to 105 in the intensity of electric fields (|E|2) in a gap between a pair of silver nanoparticles.3,4 Theselocalized and enhanced light fields can induce various chemical/physical phenomena that generally require strong light fieldsaccessible only by large-scale pulsed laser systems and used invarious applications such as SERS (surface-enhanced Ramanscattering) microscopy,5−8 nanoscale optical tweezer,9−11

multiphoton photochemical reaction,12,13 and so forth.Although photoexcitation at plasmon resonance bandsgenerates quite strong electric fields at specific points ofmetallic nanostructures, the strong coupling between photonsand electrons also induces the temperature increase in a smallarea of nanostructures through the electron−phonon relaxationin less than or equal to a few picoseconds time range followed

by the phonon−phonon relaxation in several tens of pico-seconds.14 In actuality, metallic nanostructures have beenapplied to thermal imaging15 and photothermal reactions16−21

as nanoscale heat sources.It is indispensable to quantitatively clarify the effect of the

heat in the field-enhancement by spatially resolved measure-ment of local temperature to precisely elucidate the role ofLSPR in various processes and to optimize the strong electricfield for advanced applications. In general, phenomena sensitiveto temperature change can be used for the estimation of localtemperature, such as fluorescent peak shift of dyes22 andquantum dots,23 fluorescence polarization of probe dyemolecules,24 lateral diffusion coefficient of fluorescent mole-cules,25,26 and refractive index change of the surrounding mediaof photoexposed nanoparticles.27 Several research groupsexperimentally28−30 and theoretically31−33 estimated heatgeneration by plasmonic nanostructures under photoexcitation.Misawa et al. employed Raman spectroscopy to evaluate thelocal temperature on gold nanoblocks on the basis of the ratiobetween Stokes and anti-Stokes Raman scattering intensities inSERS measurements.28 Hashimoto et al. measured the peak-

Received: November 12, 2012Revised: March 18, 2013Published: March 29, 2013

Article

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© 2013 American Chemical Society 8388 dx.doi.org/10.1021/jp311173j | J. Phys. Chem. C 2013, 117, 8388−8396

wavelength shifts in scattering spectra of gold nanoparticlesunder laser heating in three environments: air, water, andglycerol.29 Although the methods employed by Misawa et al.and Hashimoto et al. could provide information on thetemperature around the surface of metallic nanostructures, theyare not so sensitive to small changes of the temperature. Withan aim to detect small deviation of temperature, Baffou et al.developed a method based on the fluorescence polarizationanisotropy and applied it to the imaging of temperaturedistribution around gold nanostructures.30 This technique issensitive to small changes in the temperature of <1 K, but itrequires using solvent with relatively high viscosity, for example,a mixture (4:1) solution of glycerol and water to slow down therotational motion of fluorescent molecules. Photothermalmicroscopy can also be applied for the detection of slightchange of temperature.34,35 Gaiduk et al. demonstrated that 0.1K surface temperature increase of a 20 nm gold particle couldbe detected by photothermal detection method.34 Although thephotothermal microscopy enables us to detect temperaturechange <1 K, it only detects the temperature around singleparticles and does not generally allow spatial mapping oftemperature. For the mapping of small temperature deviations,Baffou et al. demonstrated 2D mapping of local temperaturearound microscopic heat sources by detecting optical phaseshift of illumination light.27 Although the method is useful toobtain 2D distributions of local temperature at high sensitivity<1K, the inverse problem has to be solved to obtain 3Dmapping of temperature because the method detects opticalphase shift integrated along the optical (z) axis. Measuring thelateral diffusion coefficient of a fluorescence dye in a smallvolume by fluorescence correlation spectroscopy (FCS) can beapplied for local temperature estimation at any distance from aheat source.25 The FCS-based temperature estimation methodhas high enough sensitivity to detect temperature change <1 Kas well as high spatial resolution <400 nm in lateral plane and<2 μm along the z direction. With a view to more generallymeasure the temperature around metallic nanostructures withhigh sensitivity and spatial resolution, we have applied FCS todirectly detect the effect of the heat released from the goldnanoparticles under photoexposure.

■ EXPERIMENTAL SECTIONThe specimen of glass substrates, on which gold nanoparticleswere fixed,36 was prepared in the following manner. Coverslips(Matsunami, Japan) were put into acetone in a small vessel andsonicated for 30 min. They were kept in 5 wt % aqueoussolution of sodium hydrate for 30 min to purify the surface.After they were well rinsed with ultrapure water and dried, thecoverslips were irradiated with UV light at 185 nm todecompose the remaining small amount of contaminant byozone. The surfaces of the well-cleaned coverslips were treatedusing a silane coupling agent, 3-aminopropyltrimethoxysilane(APTMS); 200 μL of the 10 wt % ethanol solution of APTMSwas dropped onto the coverslips and kept for 10 min. After itwas rinsed with ultrapure water and dried with a nitrogen gun,200 μL of colloidal solution of gold nanoparticles (EMGC 150and 100, British Biocell) was dropped onto the surface-modified coverslips to fix the gold nanoparticles on the glasssubstrates. After 2 h, the colloidal solution was rinsed withultrapure water and dried with the nitrogen gun. The schematicillustration of the specimen thus prepared is shown in Figure1a. For the measurement of local temperature by FCS, we useda confocal-microscopic system, of which details were previously

described.25 In brief, the system consists of an inverted opticalmicroscope (IX70, Olympus), two CW lasers with oscillatingwavelengths at 488 (blue) and 633 nm (red), and an avalanchephotodiode (SPCM-AQR14, Perkin-Elmer). The blue laser(Excelsior 488, Spectra Physics, 488 nm output) was used as anexcitation light source for FCS measurement, and the red one(25 LHP 925, Melles Griot) was used for exciting the goldnanoparticle. The output of the laser at 488 nm was focused byan objective (UPlanApo 100X Oil Iris3, NA: 1.35, Olympus)into the diffraction-limited size. Half-wave and a quarter-waveplates for 488 nm were used to ensure the circular polarizationof the laser light at 488 nm under the objective. The detectionvolume (confocal volume) of the FCS measurement wasregulated by a pinhole (diameter, 40 μm) attached to the sideport of the optical microscope. Fluorescence photons emittedfrom dye molecules inside the confocal volume were detectedwith the avalanche photodiode, of which output was sent to acounting board (M9003, Hamamatsu photonics). Scatteredlight from the sampling volume was blocked with a long-passfilter (LP01-488RU, Semrock) and a short-pass filter (SP01-633RU, Semrock). Autocorrelation functions of the detectedfluorescence intensity were obtained using FCS software(U9451, Hamamatsu photonics).The spot size of the 633 nm laser light focused by the

objective was adjusted using a pair of lenses inserted in theoptical path from the light source to the microscope. Todetermine the diameter of the focal spot, we obtained thefluorescence intensity distribution of a thin amorphous film offluorescent dyes on a well-cleaned coverslip under photo-excitation with the red laser by using a CCD camera (CascadeII 512B, Princeton Instruments). From the analysis of thefluorescence image using a 2D Gaussian function, the spotdiameter, 2w0, was obtained to be 18.7 μm. Here w0 is a beamwaist (1/e2 width radius) of the focal spot. Because thediffraction-limited detection volume of FCS and the beam axisof the 633 nm laser are coaxially located, as shown in Figure 1b,and the distance between the detection volume and the goldparticles (∼5 μm) is smaller than the spot diameter of the 633nm laser (18.7 μm), it is expected that the peak intensity of the633 nm Gaussian beam dominantly affects the measurement ofFCS. Hence in the estimation of average intensity of the 633

Figure 1. (a) Schematic illustration of gold nanoparticles on glasssubstrate and (b) the optical configuration for the local temperaturemeasurement around gold nanoparticles.

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nm laser the 1/e width of the Gaussian distribution, rave, wasemployed as an “averaging width” in the present study.Actually, an average light intensity estimated using theaveraging width (2rave = 13.2 μm) is 74.7% of the peakintensity, while that estimated using 1/e2 width is 59.8%. Toestimate the area covered with the gold nanoparticles, SAu, wecounted the number of pixels corresponding to gold nano-particles inside the exposed area of the 633 nm laser, S633 =πrave

2, in a threshold-filtered (binarized) optical transmissionimage. In the present study, we defined the coverage of the goldnanoparticles as SAu/S633. This procedure will be preciselyexplained later.Figure 1b schematically illustrates the configuration for

measuring local temperature near the gold nanoparticles.Solution containing fluorescent dyes, Rhodamine123 (R123,Acros Organics), was sandwiched with well-cleaned coverslips,one of which has gold nanoparticles. The thickness of thesolution was ca. 30 μm. In the present study, ethylene glycol(99.5%, Wako) was used as a solvent because it has lowvolatility and large temperature dependence of the viscosity.The concentration of the dye was kept low, typically 10−10 to10−9 M. The detection point of FCS was ca. 5 μm orthogonallydistant from the glass surface unless otherwise noted.A scanning electron microscope (SEM) (JSM-6060, JEOL)

was used to obtain the information on precise structures ofnanoparticles on the surface. In the SEM observation, the glasssurface was coated with osmium using an osmium coater (Neo-Osmium Coater, Meiwafosis) to prevent the charge-up effect.For the ensemble measurement of extinction spectra of goldnanoparticles, a UV−visible spectrophotometer (U-3500,Hitachi) was employed.Local temperature in solution was estimated in the following

manner.25 The fluorescence autocorrelation function, G(τ), wasfirst analyzed by a model25,37,38 of FCS represented by eq 1.

τ ττ

ττ

ττ

= + +−

− +

× +

−

−

⎛⎝⎜⎜

⎛⎝⎜

⎞⎠⎟⎞⎠⎟⎟⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

GN

pp

w

( ) 11

11

exp 1

1

T D

1

2D

1/2

(1)

Here N is the average number of molecules in the confocalvolume. p and τT are, respectively, the fraction of thecontribution of the triplet state and the triplet lifetime. w is astructure parameter defined by w = wz/wxy. Here wz and wxy are,respectively, the axial and radial radii of the ellipsoidally shapedconfocal volume (Vconf = π3/2wzwxy

2). τD is the averagedresidence time (diffusion time) of a molecule in the confocalvolume. This residence time of the fluorescent dye is related toits translational diffusion coefficient, D, as represented by eq 2.

τ =w

D4xy

D

2

(2)

By using the Stokes−Einstein model in eq 3, we can derive eq4.

πη=D

kTT a6 ( ) (3)

ηγτ

γ π= =⎜ ⎟⎛⎝

⎞⎠

TT

wa

k( )32xy

D

2

(4)

Here η(T) is the viscosity of solution at temperature T, a is thehydrodynamic radius of a probe molecule, and k is Boltzmannconstant. From these relations, we can estimate the localtemperature by comparing τD and the reference value of T/ηunder the assumption that γ was independent of thetemperature in the range of the experiments. This assumptionwas proved to be valid in the previous experiments of theestimation of the local temperature at a focal point of a near-infrared laser for optical trapping.25

■ RESULTS AND DISCUSSIONCharacterization of the Specimen. Figure 2a shows an

optical transmission image of gold nanoparticles with a 150 nm

diameter on the glass substrate. A solid circle in the Figureindicates the irradiation area of the 633 nm laser beam, S633,estimated by the method described in the ExperimentalSection. Figure 2b shows an SEM image of the 150 nm goldparticles. Here we can observe several nonspherical particlesand the overlap of some particles in the aggregated area.Because the light is absorbed only by the top particle in theoverlapped ones owing to the large absorption cross section, wedid not take into account the overlap of nanoparticles in thesubsequent discussions. Similar SEM images were also obtainedfor the nanoparticles with a 100 nm diameter, as shown inFigure 2c. In the aggregated area, however, the number ofnanoparticles in a unit area is larger than that of 150 nmnanoparticles owing to the smaller diameter and well-alignedpacking.Figure 3a shows a typical extinction spectrum of the 150 nm

gold particles adsorbed on the glass surface covered withethylene glycol, while Figure 3b shows the extinction spectrumof the 150 nm gold particles dispersed in a binary solution ofethylene glycol and water (volume ratio, 9:1). The spectralband shape of the aggregate (Figure 3a) is similar to that insolution (Figure 3b). This result suggests that the most of the150 nm gold particles do not show so strong mutual interactioneven after being adsorbed to the glass surface.Figure 3c shows a typical extinction spectrum of the 100 nm

gold particles adsorbed on the glass surface covered withethylene glycol. Figure 3d shows a typical extinction spectrumof the 100 nm gold particles dispersed in the binary solution ofethylene glycol and water. Compared with the spectra of 150nm particles (Figure 3a,b), the difference between the spectraof the adsorbed particles and the colloidal solution is ratherlarge, especially in the wavelength region longer than 600 nm.This large difference is attributable to quadrupole plasmonmode because the 100 nm particles are more closely packed intheir aggregates, as shown in Figure 2c.The extinction spectra of gold nanoparticle generally involve

contributions from scattering and absorption processes, and the

Figure 2. (a) Optical transmission image of gold nanoparticles with a150 nm diameter on the substrate. Open circle shows the irradiationarea of the 633 nm laser light. (b) SEM image of gold nanoparticleswith a 150 nm diameter on the substrate. (c) SEM image of goldnanoparticles with a 100 nm diameter on the substrate.

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absorption takes an important role in the temperatureelevation. Hence, to estimate the contribution of the absorptionin the extinction spectrum, we calculated cross sections for theabsorption and scattering processes of gold nanoparticles inethylene glycol solution on the basis of Mie theory.39 In thecalculation, we employed complex dielectric constants of bulkgold in a literature.40 To calculate absorption and scatteringcross sections of gold nanoparticles on glass surface, we used aneffective refractive index of surrounding media, neff = (1.52 + 2× 1.43)/3.41 Figure 4a,b, respectively, shows calculatedabsorption and scattering cross sections of spherical nano-particles with different diameters. The absorption cross sectionshows no distinguishable dependence on particle diameter from80 to 170 nm, while the scattering cross section clearly dependson particle size. Figure 4c,d shows superimposed spectra ofboth contributions for particles with 150 and 100 nmdiameters, together with the measured spectra of the colloidalsolution shown in Figure 3b,d. The spectra thus calculatedreproduce the experimental results in the solution fairly well.Figure 4e shows the particle-size dependence of absorption

cross sections at the wavelength of 633 nm. The absorptioncross section is in the range of (3 to 8) × 10−15 m2 for theparticles with diameters from 80 to 170 nm. Figure 4f showsthe ratio of the absorption cross-section to the extinction cross-section at the wavelength of 633 nm as a function of particlediameter. This Figure indicates that the fraction of absorptioncross-section is not so strongly dependent on particle size in thediameter range of 100−150 nm.It should be noted, however, that 100 nm gold particles

adsorbed on the glass substrate showed different extinctionspectra from that of colloidal solution of 100 nm particles,although the extinction spectrum of 150 nm particles adsorbedon the surface was close to that in solution. Hence, the fractionof the absorption cross-section for the 150 nm particle may beused for the discussion of the temperature elevation of the 150nm particle, but it seems inadequate for the 100 nm particle.We will discuss this point later.Estimation of the Temperature Elevation. To estimate

local temperature of ethylene glycol in the vicinity of the goldnanoparticles upon the photoexposure of the 633 nm laser, weobtained the diffusion time of the guest dye molecule. Beforediscussing the dependence of diffusion time on the excitation

intensity of the 633 nm laser, we first show the effect of thepresence of the nanoparticles on the diffusion profile of thefluorescent dye without 633 nm laser excitation. Figure 5a

shows a fluorescence autocorrelation curve of the dye solutionmeasured at the position 5 μm distant from the goldnanoparticles with a 150 nm diameter. The solid line is thecurve analyzed with eq 1. As shown in this Figure, theexperimentally obtained autocorrelation curve is well-repro-duced by the analytical model (solid line), even in the presenceof the gold nanoparticles. The diffusion coefficient of the dye

Figure 3. Extinction spectra of gold nanoparticles for (a) particles with150 nm diameter adsorbed on the substrate, (b) those dispersed inethylene glycol−water (9:1) solution, (c) those with 100 nm diameteradsorbed on the substrate, and (d) those dispersed in ethylene glycol−water (9:1) solution.

Figure 4. Dependence of extinction spectra on the diameter ofspherical gold nanoparticles in ethylene glycol, calculated on the basisof the Mie theory. (a) Absorption and (b) scattering cross sections. Inboth figures, the diameter is (from bottom to top) 80, 90, 100, 110,120, 130, 140, 150, 160, and 170 nm. (c) Calculated spectrum for a150 nm particle (solid line) and an experimental one (dotted line). (d)Calculated spectrum for a 100 nm particle (solid line) and anexperimental one (dotted line). (e) Calculated result on the diameterdependence of absorption cross sections at 633 nm. (f) Calculatedresult on the fraction of absorption cross sections in the totalextinction cross section.

Figure 5. Fluorescence autocorrelation curves of Rh123 in ethyleneglycol solution sandwiched with coverslips, one of which has goldnanoparticles adsorbed on the surface: (a) without the 633 nm laserirradiation and (b) with the 633 nm laser irradiation at 4 mW power.

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thus obtained was 1.2 × 10−11 m2/s, which is in goodagreement with that obtained in the area without nanoparticles.The result indicates that the presence of the gold nanoparticlesdoes not seriously affect the Brownian motion of the dye at thedetection point.Figure 5b shows a fluorescence autocorrelation curve of the

dye solution under photoexcitation of the gold nanoparticleswith the 633 nm laser at the incident power of 4 mW. Theincident laser power of 4 mW is the highest value employed inthe present experiment. The solid line is the curve analyzedwith eq 1. Although slight deviation is observed in the residualcurve, the autocorrelation could be reproduced by eq 1. Adiffusion coefficient, 2.3 × 10−11 m2/s, obtained from the curve,is two times larger than that obtained without 633 nm laserexposure. Usually, rather strong lasers can lead to the opticaltrapping of the small particles. In actuality, we recentlydemonstrated by computational simulation methods42 thatoptical trapping potential larger than the thermal energy of kTat a room temperature can affect the diffusion of the smallobjects such as molecules. However, in the present case, thephotoexcitation at 633 nm did not increase the diffusion time ofthe dye. This is due to the loose focusing of the 633 nm laser sothat the effective trapping potential was not produced.Figure 6a−c shows fluorescence autocorrelation curves with

diffusion times depending on incident 633 nm laser power atthree different coverages of the 150 nm gold particles. Thelaser-power dependence becomes pronounced with increasingcoverage of gold nanoparticles. The insets of the Figures arecorresponding optical transmission images of gold nano-particles on the glass substrates. Solid circles in the insetsindicate the irradiation area of the 633 nm laser beam. Thelateral position of the measurement was located in the centersof the white circles. The decay of the autocorrelation curvesbecame fast with an increase in the incident laser power at 633nm. This result clearly demonstrates that the residence time ofthe guest dye in the confocal volume decreases owing to the

increase in its translational diffusion coefficient due totemperature elevation caused by the 633 nm laser irradiation.Figure 7 shows the local temperature estimated by the

analysis with eq 4 as a function of the incident laser power at633 nm. The temperature in the confocal volume linearlyincreases with incident laser power under the presentexperimental condition. The slope, ΔT/ΔI, almost linearlyincreases with an increase in the coverage of gold nanoparticles.To quantitatively clarify the relationship between temperatureelevation and coverage of nanoparticles, we measured the localtemperature at several areas with different coverages ofnanoparticles. As shown in Figure 8, almost linear relation

between the temperature elevation coefficient, ΔT/ΔI(K·kW−1·cm2), and the coverage was obtained. This resultindicates that the temperature increase is in proportion to thenumber of the nanoparticles in the exposed area. Because thethickness of the gold particle layer (100 or 150 nm) is muchsmaller than the average size of SAu (typically 5−10 μm indiameter), these experimental results can be approximatelyanalyzed with a planar heat-source model. The heat conduction

Figure 6. Dependence of the autocorrelation curves on the power of the incident He−Ne laser light. The coverage of 150 nm gold particles, SAu/S633,is (a) 0.16, (b) 0.27, and (c) 0.61. The insets show optical transmission image of gold nanoparticles on the substrate. Open circles in the insets showthe irradiation area of the 633 nm laser light.

Figure 7. Temperature at the point of 5 μm from the aggregates of 150 nm gold particles. The coverage of the gold nanoparticles, SAu/S633, is (a)0.16, (b) 0.27, and (c) 0.61.

Figure 8. Relation between the temperature elevation coefficient, ΔT/ΔI, and the coverage of gold nanoparticles. The diameter ofnanoparticle is (a) 150 and (b) 100 nm.

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from a planar heat-source is expressed by a 1D heat-conductionequation (eq 5).

λ= −qTx

dd (5)

Here q is heat flux (W m−2) vertically from a planar heatsource; λ is thermal conductivity (W m−1 K−1); T is thetemperature (K); and x is the distance vertically from the planarheat source. Solving the equation with a boundary condition, T= TRoom at x = lLL (lLL is the thickness of a liquid layer), leads tothe following equation that shows temperature distributionalong the x axis.

λ= − +T x

ql x T( ) ( )LL Room (6)

Here we assume that the temperature decreases to a roomtemperature, TRoom, at the opposite end of a liquid layer with athickness of lLL. By assuming that the heat flux, q, isproportional to the incident power of laser light, I, and thecoverage of gold particles, SAu, the following relation betweentemperature rise at a certain position ΔT(x = l) and SAuI/λ isobtained.

λΔ = ∝ ∝T x l

S Iq S I( ) ( )Au

Au (7)

From eq 7, the following relation is immediately obtained.

λΔ =

Δ∝T x l

IS( ) Au

(8)

Equation 7 predicts that the temperature at a certain positionlinearly increases with increasing incident laser power, while eq8 predicts a linear relation between ΔT/ΔI and SAu. Thesepredictions show very good agreement with experimentalresults shown in Figures 7 and 8.To further estimate the temperature elevation coefficient,

ΔT/ΔI, of the single gold nanoparticle, we obtained therelationship between the coverage and the number ofnanoparticles in the following manner. From an SEM imageof aggregated gold nanoparticles on the glass surface, of whichtypical example is shown in Figure 9a, we counted the numberof gold nanoparticles, NAuNP, and determined the positions oftheir centers. Then, we allocated the detection point spreadfunctions (PSFs) of the microscope on the centers of individualgold nanoparticles to obtain a superimposed image of thedetection PSFs. The detection PSF used in the procedure wasestimated from an optical transmission image of a single goldnanoparticle. By threshold-filtering the superimposed image, weobtained a binarized image, as shown in Figure 9b. The whitearea of a constructed (binarized) image approximatelycorresponds to an optical transmission image of the aggregateof gold nanoparticles. This white area in a binarized image wasdefined as the area occupied by gold nanoparticles, SAu_bin.Constructed images thus obtained were divided into smallsquares of which individual sizes are corresponding to the sizeof a single pixel of the CCD camera, SCCD_pix, as shown inFigure 9b. Because the size of the single pixel is too small to bedrawn, the mesh in Figure 9b is drawn every 14 pixels. Thenumber of pixels included in an apparent occupied area,Npix_AuNP is expressed by Npix_AuNP = SAu_bin/SCCD_pix. NAuNP/SAu_bin gives the number density of gold nanoparticles(particles/μm2). Figure 9c shows the relation betweenNAuNP/SAu_bin and Npix_AuNP. In the plot, the density isdependent on the number of pixels in the range of Npix_AuNP

< 7 × 103. This is quite reasonable because the effect of thediffraction limit is pronounced in small aggregates. With anincrease in the number of pixels, the number density, NAuNP/SAu_bin, gradually increases and reaches a plateau in the regionwhere the number of pixels is larger than 7.0 × 103. The valueof NAuNP/SAu_bin at the plateau is 10 particles/μm2 for the 150nm gold particles, whereas it is 27 particles/μm2 for the 100 nmgold particles. From these values, the temperature elevationcoefficients, ΔT/ΔI, for single gold particles with the 150 and100 nm diameters on the glass substrate were, respectively,estimated to be (6.9 and 2.3) × 10−3 K·kW−1·cm2. In thecalculated extinction spectra of gold nanoparticles in solution, itwas observed that the absorption cross-section of a 100 nmparticle at the wavelength of 633 nm was almost the same asthat of a 150 nm particle (Figure 4e). Scattering contributedless to the extinction at 633 nm of a 100 nm particle than thatof a 150 nm particle (Figure 4f). However, the actual extinctionspectrum of the 100 nm particles adsorbed on the glass surface(Figure 3c) showed rather large difference from that in solution(Figure 3d). Hence, the contribution from scattering might bepronounced in the extinction spectrum of 100 nm particlesadsorbed on the surface, and as a result the smaller ΔT/ΔI wasobtained.To elucidate the mechanism of the temperature rise, we

carried out a simple calculation on the basis of the steady-stateheat conduction from the nanoparticle to the surroundingmedia. In this calculation, it was assumed that thermalconduction occurs from a small spherical heat source with aradius of r1 to the homogeneous surrounding media and theeffect of a coverslip was ignored. These approximations lead toa 1D heat conduction equation25,43,44 as represented by eq 9.

πλ= −T

r

Q

rdd 4

1abs2 (9)

Figure 9. (a) SEM image of an aggregate of gold nanoparticles with a150 nm diameter. (b) Optical transmission image constructed bytaking into account the diffraction-limited size. The mesh in the Figurecorresponds to 14 × 14 pixels in the optical microscope. (c) Density of150 nm nanoparticles in aggregates as a function of the number ofpixels in the constructed optical transmission images. (See the text.)The dotted line is a guide to the eye.

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Here Qabs is photon energy absorbed by the nanoparticle, λ isthe thermal conductivity of the surrounding medium(W·m−1·K−1), T is temperature (K), and r is the distancefrom the center of the nanoparticle. By solving eq 9 under theboundary conditions of T = T1 at r ≤ r1 and T = TR (roomtemperature) at r = ∞, temperature distribution T(r) is derivedas eq 10.

πλ

πλ

= = + ≤ ≤

= + <

T r TQ

rT r r

Q

rT r r

( )4

1(0 )

41

( )

1abs

1Room 1

absRoom 1

(10)

The photon energy absorbed by the single nanoparticle Qabs isrepresented by Qabs= CabsI, where Cabs and I are, respectively,the absorption cross-section of the particle and the laserfluence. In the calculation, the absorption cross sectioncalculated on the basis of the Mie theory was used.Figure 10 shows calculated temperature distribution around

the single gold nanoparticle with a 150 nm diameter under

photoexcitation at a laser fluence of 1 kW/cm2. The calculationshows ΔT = 2.9 K on the surface of the gold nanoparticle andΔT = 3.5 × 10−2 K at 5 μm distant from the center of the goldnanoparticle. This value is five times larger than that obtainedin the present experimental estimation, ΔT = 6.9 × 10−3 K.This difference might be due to the ignorance of the thermalconduction through the coverslips in the calculation. Thecalculated ΔT at 5 μm distant from the center of a goldnanoparticle with a 100 nm diameter was 3.5 × 10−2 K. This is15 times larger than that obtained experimentally, 2.3 × 10−3

K·kW−1·cm2. As discussed in the previous sections, thecontribution from scattering seems larger for the 100 nmparticle adsorbed in the surface and hence the difference fromthe simple estimation of the temperature increase may bepronounced in the 100 nm particle adsorbed on the surface.However, it is worth noting that the temperature elevationestimated on the basis of the simple thermal conduction is onthe same order of the experimentally obtained values. Thisresult indicates that the temperature increase at 5 μm from thegold nanoparticle is mainly due to the thermal conduction fromthe heat source of gold nanoparticles under the excitation of thesurface plasmon band.For the estimation of ΔT/ΔI, most of investigations

concentrated the temperature on the surface of nanostructures.

Oddershede et al. reported the temperature of gold nano-particles under photoexcitation by detecting the gel-to-fluidphase transition in lipid bilayers.45 They estimated ΔT/ΔI onthe surfaces of gold particles with a 100 and 150 nm diameterupon laser irradiation at 1064 nm; the estimated values are,respectively, 452 and 732 K/W. By using the focal spot size ofthe 1064 nm laser, ΔT/ΔI at the unit area corresponds to (1.15and 1.86) × 10−2 K·kW−1·cm2 for the 100 and 150 nmparticles, respectively. By taking into account the difference ofthe absorption cross sections,46 it is possible to estimate thecoefficient of temperature increase at 633 nm from their data;the estimated ΔT/ΔI of a 100 and 150 nm gold particles are,respectively, 0.28 and 0.11 K·kW−1·cm2. The analysis ofexperimental data based on the 1D heat conduction equation(eq 10) estimated ΔT/ΔI on the surfaces of the 100 and 150nm particles at 0.23 and 0.45 K·kW−1·cm2, respectively.Although the present values were slightly different from thoseestimated by the phase transition, the difference of crosssections between the experimental and calculated results mightlead to the difference in ΔT/ΔI values. These results supportthat the simple 1D heat conduction equation could beapplicable to the estimation of the temperature at the pointdistant from the surface of nanoparticles.

■ CONCLUSIONSIn the present work, we have applied FCS to quantify localheating in the vicinity of gold nanoparticles. The temperatureincreased with increasing laser power and the temperatureelevation coefficient per unit power ΔT/ΔI was linearlydependent on the number of gold nanoparticles on thesubstrates. Temperature elevation coefficients of single goldnanoparticles with 100 and 150 nm diameters under theirradiation at 633 nm were, respectively, estimated to be (2.3and 6.9) × 10−3 K·kW−1·cm2. Model calculation based on thethermal diffusion equation reproduced the experimental results.Compared with other methods for the estimation of thetemperature of nanoparticles under the excitation, the presentmethod can provide more precise information with spatialresolution and is applicable to other plasmonic nanomaterials invarious solvents.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: sito@chem.es.osaka-u.ac.jp (S.I.) and miyasaka@chem.es.osaka-u.ac.jp (H.M.).

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was partially supported by Grand-in-Aid forScientific Research (A) (23245004) and Grand-in-Aid forYoung Scientists (A) (23681023) from the Ministry ofEducation, Culture, Sports, Science, and Technology(MEXT), Japan.

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Figure 10. Temperature distribution around the gold nanoparticlewith a 150 nm diameter calculated on the basis of the thermal diffusionequation. (See the text.)

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Nanoparticles on Supported Lipid Bilayers. ACS Nano 2010, 4, 2256−2262.(46) For the estimation of the absorption coefficient at 1064 nm, thesame calculation performed in Figure 4 was employed.

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