Temperature near Gold Nanoparticles under Photoexcitation

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Temperature Near Gold Nanoparticles under Photoexcitation: Evaluation using a Fluorescence Correlation Technique Hiroaki Yamauchi, Syoji Ito, Ken-ichi Yoshida, Tamitake Itoh, Yasuyuki Tsuboi, Noboru Kitamura, and Hiroshi Miyasaka J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp311173j • Publication Date (Web): 29 Mar 2013 Downloaded from http://pubs.acs.org on April 7, 2013

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The Journal of Physical Chemistry

Temperature near Gold Nanoparticles under Photoexcitation: Evaluation Using a Fluorescence Correlation Technique Hiroaki Yamauchi1, Syoji Ito*1, Ken-ichi Yoshida2, Tamitake Itoh3, Yasuyuki Tsuboi4,5, Noboru Kitamura4, and Hiroshi Miyasaka*1 1

Division of Frontier Materials Science, Graduate School of Engineering Science and Center

for Quantum Materials Science under Extreme Conditions, Osaka University, Toyonaka, Osaka 560-8531, Japan. 2

Rexxam Co., Ltd. Kagawa Factory & Kagawa Branch Office 958, Ikeuchi, Konan-cho, Takamatsu, Kagawa 761-1494, Japan

3

Health Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Takamatsu, Kagawa 761-0395, Japan

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Division of Chemistry, Graduate School of Science, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan 5

JST (Japan Science and Technology Cooperation), PRESTO, Japan

ACS Paragon Plus Environment

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Corresponding authors Syoji Ito (at Osaka University), [email protected] Hiroshi Miyasaka (at Osaka University), [email protected]


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Abstract Fluorescence correlation spectroscopy (FCS) was applied to the measurement of local temperature in the vicinity of gold nanoparticles adsorbed on the surface of glass substrate under the photo-excitation at a wavelength of 633 nm. From the diffusion coefficient of fluorescent guest dyes and the temperature dependence of the viscosity of a solution, the rise of the temperature was estimated. It was revealed that the temperature ca. 5 µm from the gold nanoparticles linearly increased with an increase in the incident laser power and an increase in the number of gold nanoparticles on the substrates. Temperature elevation coefficients of single gold nanoparticles with 100- and 150-nm diameters under the irradiation at 633 nm were respectively estimated to be 2.3×10-3 and 6.9×10-3 K·kW-1·cm2. These values could be interpreted on the basis of the absorption coefficients of gold nanoparticles and the thermal conduction in the solution. KEYWORDS: gold nanoparticle, local heating, non-contact temperature measurement, fluorescence correlation spectroscopy


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Introduction Surface plasmon polariton leads to the compact storage of photon energy in electron oscillations at the interfaces of noble metals and dielectrics.1,2 In particular, a nanoscale gap between a pair of noble metallic nanoparticles provides significantly enhanced electric field within the gap under the photoexcitation with a polarization along the long axis of the dimer particles. This drastically enhanced electric field originates from strong interaction between photons and nanostructures of noble metals, called as localized surface plasmon resonance (LSPR). Theoretical studies predicted that the enhancement factor attained up to ~ 104 to 105 in the intensity of electric fields (|E|2) in a gap between a pair of silver nanoparticles.3,4 These localized and enhanced light fields can induce various chemical/physical phenomena that generally require strong light fields accessible only by large scale pulsed laser systems and used in various applications such as SERS

(surface enhanced Raman scattering) microscopy,5-8

nanoscale optical tweezer,9-11 multiphoton photochemical reaction,12,13 and so forth. Although photoexcitation at plasmon resonance bands generates quite strong electric fields at specific points of metallic nanostructures, the strong coupling between photons and electrons also induces the temperature increase in a small area of nanostructures through the electron-phonon relaxation in ≤ a few ps time range followed by the phonon-phonon relaxation in the several tens of ps.14 In actual, metallic nanostructures have been applied to thermal imaging15 and photothermal reactions16-21 as nanoscale heat sources. To precisely elucidate the role of LSPR in various processes and to optimize the strong electric field for advanced applications, it is indispensable to quantitatively clarify the effect of the heat in the field-enhancement by spatially resolved measurement of local temperature. In general, phenomena sensitive to temperature change can be used for the estimation of local temperature,


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such as fluorescent peak shift of dyes22 and quantum dots,23 fluorescence polarization of probe dye molecules,24 lateral diffusion coefficient of fluorescent molecules,25, 26 and refractive index change of the surrounding media of photo-exposed nanoparticles.27 Several research groups experimentally28-30 and theoretically31-33 estimated heat generation by plasmonic nanostructures under photoexcitation. Misawa et al. employed Raman spectroscopy to evaluate the local temperature on gold nanoblocks on the basis of the ratio between Stokes and anti-Stokes Raman scattering intensities in SERS measurements.28 Hashimoto et al. measured the peak-wavelength shifts in scattering spectra of gold nanoparticles under laser heating in three environments: air, water, and glycerol.29 Although the methods employed by Misawa et al. and Hashimoto et al. could provide information on the temperature around the surface of metallic nanostructures, they are not so sensitive to small changes of the temperature. With an aim to detect small deviation of temperature, Baffou et al. developed a method based on the fluorescence polarization anisotropy and applied it to the imaging of temperature distribution around gold nanostructures.30 This technique is sensitive to small changes in the temperature of < 1 K but it requires using solvent with relatively high viscosity, e.g. a mixture (4:1) solution of glycerol and water to slow down the rotational motion of fluorescent molecules. Photo-thermal microscopy can also be applied for the detection of slight change of temperature.34,35 Gaiduk et al. demonstrated that 0.1 K surface temperature rise of a 20-nm gold particle could be detected by photo-thermal detection method.34 Although the photo-thermal microscopy enables to detect temperature change < 1 K, it only detects the temperature around single particles and does not generally allow spatial mapping of temperature. For the mapping of small temperature deviations, Baffou et al. demonstrated twodimensional (2D) mapping of local temperature around microscopic heat sources by detecting optical phase shift of illumination light.27 Though the method is useful to obtain 2D distributions


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of local temperature at high sensitivity < 1K, the inverse problem has to be solved to obtain 3D mapping of temperature because the method detects optical phase shift integrated along the optical (z) axis. On the other hand, measuring the lateral diffusion coefficient of a fluorescence dye in a small volume by fluorescence correlation spectroscopy (FCS) can be applied for local temperature estimation at any distance from a heat-source.25 The FCS based temperature estimation method has high sensitivity enough to detect temperature change < 1 K as well as high spatial resolution < 400 nm in lateral plane and < 2 µm along z-direction. With a view to more generally measure the temperature around metallic nanostructures with high sensitivity and spatial resolution, we have applied FCS to directly detecting the effect of the heat released from the gold nanoparticles under photo-exposure.

Experimental Section The specimen of glass substrates, on which gold nanoparticles were fixed,36 was prepared in the following manner. Cover slips (Matsunami, Japan) were put into acetone in a small vessel and sonicated for 30 min. They were kept in 5 wt% aqueous solution of sodium hydrate for 30 min to purify the surface. After well rinsed with ultrapure water and dried, the cover slips were irradiated with UV light at 185 nm to decompose the remaining small amount of contaminant by ozone. The surfaces of the well-cleaned cover slips were treated using a silane coupling agent, 3aminopropyltrimethoxysilane (APTMS); 200 µL of the 10 wt% ethanol solution of APTMS was dropped onto the cover slips and kept for 10 min. After rinsed with ultrapure water and dried with a nitrogen gun, 200 µL of colloidal solution of gold nanoparticles (EMGC 150 and 100, British Biocell) was dropped onto the surface-modified cover slips to fix the gold nanoparticles on the glass substrates. After 2 hours, colloidal solution was rinsed with ultrapure water and


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dried with the nitrogen gun. The schematic illustration of the specimen thus prepared is shown in Figure 1(a).For the measurement of local temperature by FCS, we used a confocal-microscopic system, of which details were described previously.25 Briefly, the system consists of an inverted optical microscope (IX70, Olympus), two CW lasers with oscillating wavelengths at 488 nm (blue) and 633nm (red), and an avalanche photodiode (SPCM-AQR14, Perkin Elmer). The blue laser (Excelsior 488, Spectra Physics, 488 nm output) was used as an excitation light source for FCS measurement and the red one (25 LHP 925, Melles Griot) was used for exciting the gold nanoparticle. The output of the laser at 488 nm was focused by an objective (UPlanApo 100X Oil Iris3, NA: 1.35, Olympus) into the diffraction-limited size. Half-wave and a quarter-wave plates for 488 nm were used to ensure the circular polarization of the laser light at 488 nm under the objective. The detection volume (confocal volume) of the FCS measurement was regulated by a pinhole (diameter, 40 µm) attached to the side port of the optical microscope. Fluorescence photons emitted from dye molecules inside the confocal volume were detected with the avalanche photodiode, of which output was sent to a counting board (M9003, Hamamatsu photonics). Scattered light from the sampling volume was blocked with a long-pass filter (LP01488RU, Semrock) and a short–pass filter (SP01-633RU, Semrock). Autocorrelation functions of the detected fluorescence 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 the optical path from the light source to the microscope. In order to determine the diameter of the focal spot, we obtained the fluorescence intensity distribution of a thin amorphous film of fluorescent dyes on a well-cleaned cover slip under photoexcitation with the red laser by using a CCD camera (Cascade II 512B, Princeton Instruments). From the analysis of


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the fluorescence image using a two-dimensional Gaussian function, the spot diameter, 2w0, was obtained to be 18.7 µm. Here, w0 is a beam waist (1/e2 width radius) of the focal spot. Because the diffraction-limited detection volume of FCS and the beam axis of the 633-nm laser are coaxially located as shown in figure 1(b), and the distance between the detection volume and the gold particles (~ 5 µm) is smaller than the spot diameter of the 633-nm laser (18.7 µm), it is expected that the peak intensity of the 633-nm Gaussian beam dominantly affect the measurement of FCS. Hence in the estimation of average intensity of the 633-nm laser, the 1/e width of the Gaussian distribution, rave, was employed as an "averaging width" in the present study. Actually, an average light intensity estimated using the averaging width (2rave = 13.2 µm) is 74.7% of the peak intensity, while that estimated using 1/e2 width is 59.8%. To estimate the area covered with the gold nanoparticles, SAu, we counted the number of pixels corresponding to gold nanoparticles inside the exposed area of the 633-nm laser, S633 = πrave2, in a thresholdfiltered (binarized) optical transmission image. In the present study, we defined the coverage of the gold nanoparticles as SAu/S633. This procedure will be precisely explained later. Figure 1(b) 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 cover slips, one of which has gold nanoparticles. The thickness of the solution was ca. 30 µm. In the present study ethylene glycol (99.5%, Wako) was used as a solvent, because it has low volatility and large temperature dependence of the viscosity. Concentration of the dye was kept low, typically 10-10 to 10-9 M. The detection point of FCS was ca. 5 µm orthogonally distant from the glass surface unless otherwise noted. A scanning electron microscope (SEM) (JSM-6060, JEOL) was used to obtain the information on precise structures of nanoparticles on the surface. In the SEM observation, the glass surface


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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 gold nanoparticles, 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), was first analyzed by a model25,37,38 of FCS represented by eq. (1).

(1) Here, N is the averaged number of molecules in the confocal volume. p and τT are respectively the fraction of the contribution of the triplet state and the triplet lifetime. w is a structure parameter defined by w = wz / wxy. Here, wz and wxy are respectively the axial and radial radii of the ellipsoidally shaped confocal volume (Vconf = π3/2wzwxy2). τD is the averaged residence time (diffusion time) of a molecule in the confocal volume. This residence time of the fluorescent dye is related to its translational diffusion coefficient, D, as represented by eq. (2).

(2) By using the Stokes-Einstein model in eq. (3), we can derive eq. (4).

(3)

(4) Here, η (T) is the viscosity of solution at temperature T, a is the hydrodynamic radius of a probe molecule, and k is Boltzmann constant. From these relations, we can estimate the local temperature by comparing τD and the reference value of T / η under the assumption that γ was


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independent of the temperature in the range of the experiments. This assumption was proved valid in the previous experiments of the estimation of the local temperature at a focal point of a near infrared laser for optical trapping.25

Results and Discussion Characterization of the specimen Figure 2(a) shows an optical transmission image of gold nanoparticles with a 150-nm diameter on the glass substrate. A solid circle in the figure indicates the irradiation area of the 633-nm laser beam, S633, estimated by the method described in the experimental section. Figure 2(b) shows an SEM image of the 150-nm gold particles. Here, we can observe several non-spherical particles and the overlap of some particles in the aggregated area. Because the light is absorbed only by the top particle in the overlapped ones owing to the large absorption cross section, we did not take into account the overlap of nanoparticles in the subsequent discussions. Similar SEM images were also obtained for the nanoparticles with a 100-nm diameter as shown in Figure 2(c). In the aggregated area, however, the number of nanoparticles in a unit area is larger than that of 150-nm nanoparticles owing to the smaller diameter and well-aligned packing. Figure 3(a) shows a typical extinction spectrum of the 150-nm gold particles adsorbed on the glass surface covered with ethylene glycol, while figure 3(b) shows the extinction spectrum of the 150-nm gold particles dispersed in a binary solution of ethylene glycol and water (volume ratio, 9:1). Spectral band shape of the aggregate (figure 3(a)) is similar to that in solution (figure 3(b)). This result suggests that the most of the 150-nm gold particles do not show so strong mutual interaction even after being adsorbed to the glass surface.


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Figures 3(c) shows a typical extinction spectrum of the 100-nm gold particles adsorbed on the glass surface covered with ethylene glycol. Figure 3(d) shows a typical extinction spectrum of the 100-nm gold particles dispersed in the binary solution of ethylene glycol and water. Compared to the spectra of 150-nm particles (Figs. 3(a) and 3(b)), the difference between the spectra of the adsorbed particles and the colloidal solution is rather large, especially in the wavelength region longer than 600 nm. This large difference is attributable to quadrupole plasmon mode because the 100-nm particles are more closely packed in their aggregates as shown in figure 2(c). The extinction spectra of gold nanoparticle generally involve contributions from scattering and absorption processes and the absorption takes an important role in the temperature elevation. Hence, in order to estimate the contribution of the absorption in the extinction spectrum, we calculated cross sections for the absorption and scattering processes of gold nanoparticles in ethylene glycol solution on the basis of Mie-theory.39 In the calculation, we employed complex dielectric constants of bulk gold in a literature.40 To calculate absorption and scattering crosssections of gold nanoparticles on glass surface, we used effective refractive index of surrounding media, neff = (1.52 + 2×1.43)/3.41 Figures 4(a) and 4(b) respectively show calculated absorption and scattering cross-sections of spherical nanoparticles with different diameters. The absorption cross-section shows no distinguishable dependence on particle diameter from 80 nm to 170 nm, while the scattering cross section clearly depends on particle size. Figures 4(c) and 4(d) show superimposed spectra of both contributions for particles with 150- and 100-nm diameters, together with the measured spectra of the colloidal solution shown in figures 3(b) and 3(d). The spectra thus calculated reproduce the experimental results in the solution fairly well.


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Figure 4(e) shows the particle-size dependence of absorption cross sections at the wavelength of 633 nm. The absorption cross section is in the range of 3 - 8 ×10-15 m2 for the particles with diameters from 80 nm to 170 nm. Figure 4(f) shows the ratio of the absorption cross-section to the extinction cross-section at the wavelength of 633 nm as a function of particle diameter. This figure indicates that the fraction of absorption cross-section is not so strongly dependent on particle size in the diameter range of 100 - 150 nm. It should be noted, however, that 100-nm gold particles adsorbed on the glass substrate showed different extinction spectra from that of colloidal solution of 100-nm particles, although the extinction spectrum of 150-nm particles adsorbed on the surface was close to that in solution. Hence, the fraction of the absorption cross-section for the 150-nm particle may be used for the discussion of the temperature elevation of the 150-nm 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 gold nanoparticles upon the photoexposure of the 633-nm laser, we obtained the diffusion time of the guest dye molecule. Before discussing the dependence of diffusion time on the excitation intensity of the 633-nm laser, we first show the effect of the presence of the nanoparticles on the diffusion profile of the fluorescent dye without 633-nm laser excitation. Figure 5(a) shows a fluorescence autocorrelation curve of the dye solution measured at the position 5-µm distant from the gold nanoparticles with a 150-nm diameter. The solid line is the curve analyzed with eq. (1). As shown in this figure, the experimentally obtained autocorrelation curve is well reproduced by the analytical model (solid line) even in the presence of the gold nanoparticles. The diffusion


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coefficient of the dye thus obtained was 1.2 × 10-11 m2/s, which is in good agreement with that obtained in the area without nanoparticles. The result indicates that the presence of the gold nanoparticles does not seriously affect the Brownian motion of the dye at the detection point. Figure 5(b) shows a fluorescence autocorrelation curve of the dye solution under photoexcitation of the gold nanoparticles with the 633-nm laser at the incident power of 4 mW. The incident laser power of 4 mW is the highest value employed in the present experiment. The solid line is the curve analyzed with eq. (1). Although slight deviation is observed in the residual curve, the autocorrelation could be reproduced by eq. (1). A diffusion coefficient, 2.3 × 10-11 m2/s, obtained from the curve, is twice larger than that obtained without 633-nm laser exposure. Usually, rather strong lasers can lead to the optical trapping of the small particles. In actual, we recently demonstrated by computational simulation methods42 that optical trapping potential larger than the thermal energy of kT at a room temperature can affect the diffusion of the small objects such as molecules. However, in the present case, the photoexcitation at 633 nm did not increase the diffusion time of the dye. This is due to the loose focusing of the 633-nm laser so that the effective trapping potential was not produced. Figures 6(a) – 6(c) show fluorescence autocorrelation curves with diffusion times depending on incident 633-nm laser power at three different coverages of the 150-nm gold particles. The laser-power dependence becomes pronounced with increasing coverage of gold nanoparticles. The insets of the figures are corresponding optical transmission images of gold nanoparticles on the glass substrates. Solid circles in the insets indicate the irradiation area of the 633-nm laser beam. The lateral position of the measurement was located in the centers of the white circles. The decay of the autocorrelation curves became fast with an increase in the incident laser power at 633 nm. This result clearly demonstrates that the residence time of the guest dye in the


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confocal volume decreases owing to the increase in its translational diffusion coefficient due to temperature 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 at 633 nm. The temperature in the confocal volume linearly increases with incident laser power under the present experimental condition. The slope, ∆T/∆I, almost linearly increases with an increase in the coverage of gold nanoparticles. To quantitatively clarify the relationship between temperature elevation and coverage of nanoparticles, we measured the local temperature at several areas with different coverages of nanoparticles. As shown in figure 8, almost linear relation between the temperature elevation coefficient, ∆T/∆I (K·kW-1·cm2), and the coverage was obtained. This result indicates that the temperature increase is in proportion with the number of the nanoparticles in the exposed area. As the thickness of the gold particle layer (100 nm or 150 nm) is much smaller than the average size of SAu (typically 5-10 µm in diameter), these experimental results can be approximately analyzed with a planar heat-source model. The heat conduction from a planar heat-source is expressed by a one-dimensional heat conduction equation (eq. (5)). (5) Here, q is heat flux (Wm-2) vertically from a planar heat-source; λ is thermal conductivity (Wm1

K-1); T is temperature (K); and x is distance vertically from the planar heat-source. Solving the

equation with a boundary condition, T = TRoom at x = lLL (lLL is the thickness of a liquid-layer), leads to the following equation that shows temperature distribution along the x-axis. (6) Here, we assume that the temperature decreases to a room temperature, TRoom, at the opposite end


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of a liquid layer with a thickness of lLL. By assuming that the heat flux, q, is proportional to the incident power of laser light, I, and the coverage of gold particles, SAu, the following relation between temperature rise at a certain position ∆T(x = l) and SAuI/λ is obtained. (7) From eq. (7), the following relation is immediately obtained. (8) Eq. (7) predicts that the temperature at a certain position linearly increases with increasing incident laser power, while eq. (8) predicts a linear relation between ∆T/∆I and SAu. These predictions show very good agreement with experimental results shown in figures 7 and 8. In order to further estimate the temperature elevation coefficient, ∆T/∆I, of the single gold nanoparticle, we obtained the relationship between the coverage and the number of nanoparticles in the following manner. From an SEM image of aggregated gold nanoparticles on the glass surface, of which typical example is shown in figure 9(a), we counted the number of gold nanoparticles, NAuNP, and determined the positions of their centers. Then we allocated the detection point spread functions (PSFs) of the microscope on the centers of individual gold nanoparticles to obtain a superimposed image of the detection PSFs. The detection PSF used in the procedure was estimated from an optical transmission image of a single gold nanoparticle. By threshold-filtering the superimposed image we obtained a binarized image as shown in figure 9(b). The white area of a constructed (binarized) image approximately corresponds to an optical transmission image of the aggregate of gold nanoparticles. This white area in a binarized image was defined as the area occupied by gold nanoparticles, SAu_bin. Constructed images thus obtained were divided into small squares of which individual sizes are corresponding to the size


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of single pixel of the CCD camera, SCCD_pix, as shown in figure 9(b). The number 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 (particle/µm2). Figure 9(c) shows the relation between NAuNP/SAu_bin and Npix_AuNP. In the plot the density is dependent on the number of pixels in the range of Npix_AuNP < 7×103. This is quite reasonable because the effect of the diffraction limit is pronounced in small aggregates. With an increase in the number of pixels, the number density, NAuNP/SAu_bin, gradually increases and reaches a plateau in the region where the number of pixels is larger than 7.0 × 103. The value of NAuNP/SAu_bin at the plateau is 10 particles/µm2 for the 150-nm gold particles, while that is 27 particles/µm2 for the 100-nm gold particles. From these values, the temperature elevation coefficients, ∆T/∆I, for single gold particles with the 150- and 100-nm diameters on the glass substrate were respectively estimated to be 6.9 × 10-3 and 2.3 × 10-3 K·kW-1·cm2. In the calculated extinction spectra of gold nanoparticles in solution, it was observed that the absorption cross-section of a 100-nm particle at the wavelength of 633 nm was almost the same with that of a 150-nm particle (figure 4(e)). On the other hand, scattering less contributed to the extinction at 633 nm of a 100-nm particle than that of a 150-nm particle (figure 4(f)). However, the actual extinction spectrum of the 100-nm particles adsorbed on the glass surface (figure 3(c)) showed rather large difference from that in solution (figure 3(d)). Hence, the contribution from scattering might be pronounced in the extinction spectrum of 100-nm particles adsorbed on the surface and, as a result the smaller ∆T/∆I was obtained. To elucidate the mechanism of the temperature rise, we carried out a simple calculation on the basis of the steady-state heat conduction from the nanoparticle to the surrounding media. In this calculation, it was assumed that thermal conduction occurs from a small spherical heat source


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with a radius of r1 to the homogeneous surrounding media and the effect of a cover slip was ignored. These approximations lead to a one-dimensional (1D) heat conduction equation25, 43, 44 as represented by eq (9).

(9) Here, Qabs is photon energy absorbed by the nanoparticle, λ is the thermal conductivity of the surrounding medium (W·m-1·K-1), T is temperature (K), and r is the distance from the center of the nanoparticle. By solving eq. (9) under the boundary conditions of T = T1 at r ≤ r1 and T = TR (room temperature) at r = ∞, temperature distribution T(r) is derived as eq. (10).

(10) The photon energy absorbed by the single nanoparticle Qabs is represented by Qabs= Cabs I, where Cabs and I are respectively the absorption cross-section of the particle and the laser fluence. In the calculation, the absorption cross section calculated 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 calculation shows

∆T = 2.9 K on the surface of the gold nanoparticle, and ∆T = 3.5 × 10-2 K at 5 µm distant from the center of the gold nanoparticle. This value is 5 times larger than that obtained in the present experimental estimation, ∆T = 6.9 × 10-3 K. This difference might be due to the ignorance of the thermal conduction through the cover slips in the calculation. The calculated ∆T at 5 µm distant from the center of a gold nanoparticle with a 100 nm diameter was 3.5 × 10-2 K. This is 15 times larger than that obtained experimentally, 2.3 × 10-3 K·kW-1·cm2. As discussed in the previous sections, the contribution from scattering seems larger for the 100-nm particle adsorbed in the


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surface and hence the difference from the simple estimation of the temperature rise may be pronounced in the 100-nm particle adsorbed on the surface. However, it is worth noting that the temperature elevation estimated on the basis of the simple thermal conduction is in the same order of the experimentally obtained values. This result indicates that the temperature rise at 5 µm from the gold nanoparticle is mainly due to the thermal conduction from the heat source of gold nanoparticles under the excitation of the surface plasmon band. For the estimation of ∆T/∆I, most of investigations concentrated the temperature on the surface of nanostructures. Oddershede et al. reported the temperature of gold nanoparticles under photoexcitation by detecting the gel-to-fluid phase transition in lipid bilayers.45 They estimated ∆T/∆I on the surfaces of gold particles with a 100-nm and 150-nm diameter upon laser irradiation at 1064 nm; the estimated values are respectively 452 and 732 K/W. By using the focal spot size of the 1064-nm laser, ∆T/∆I at the unit area corresponds to 1.15×10-2 and 1.86×102

K·kW-1·cm2 for the 100- and 150-nm particles respectively. By taking into account the

difference of the absorption cross sections,46 it is possible to estimate the coefficient of temperature rise at 633 nm from their data; the estimated ∆T/∆I of a 100-nm and 150-nm gold particles are respectively 0.28 and 0.11 K·kW-1·cm2. On the other hand, the analysis of experimental data based on the 1D heat conduction equation (eq. (10)) estimated ∆T/∆I on the surfaces of the 100- and 150-nm particles at 0.23 and 0.45 K·kW-1·cm2 respectively. Although the present values were slightly different from those estimated by the phase transition, the difference of cross sections between the experimental and calculated results might lead to the difference in ∆T/∆I values. These results support that the simple 1D heat conduction equation could be applicable to the estimation of the temperature at the point distant from the surface of nanoparticles.


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Conclusion In the present work, we have applied FCS to quantify local heating in the vicinity of gold nanoparticles. The temperature increased with increasing laser power and the temperature elevation coefficient per unit power ∆T/∆I was linearly dependent on the number of gold nanoparticles on the substrates. Temperature elevation coefficients of single gold nanoparticles with 100- and 150-nm diameters under the irradiation at 633 nm were respectively estimated to be 2.3 × 10-3 and 6.9 × 10-3 K·kW-1·cm2. Model calculation based on the thermal diffusion equation reproduced the experimental results. Compared to other methods for the estimation of the temperature of nanoparticles under the excitation, the present method can provide more precise information with spatial resolution and is applicable to other plasmonic nanomaterials in various solvents.

Acknowledgment This work was partly supported by Grand-in-Aid for Scientific Research (A) (23245004) and Grand-in-Aid for Young Scientists (A) (23681023) from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan.


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in

figure

4


was

employed.

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Figure Captions Figure 1. (a) Schematic illustration of gold nanoparticles on glass substrate and (b) the optical configuration for the local temperature measurement around gold nanoparticles. Figure 2. (a) Optical transmission image of gold nanoparticles with a 150-nm diameter on the substrate. Open circle shows the irradiation area of the 633-nm laser light. (b) SEM image of gold nanoparticles with a 150-nm diameter on the substrate. (c) SEM image of gold nanoparticles with a 100-nm diameter on the substrate. Figure 3. Extinction spectra of gold nanoparticles for, (a) particles with 150-nm diameter adsorbed on the substrate, (b) those dispersed in ethylene glycol – water (9:1) solution, (c) those with 100-nm diameter adsorbed on the substrate, and (d) those dispersed in ethylene glycol – water (9:1) solution. Figure 4. Dependence of extinction spectra on the diameter of spherical gold nanoparticles in ethylene glycol, calculated on the basis of the Mie theory. (a) Absorption and (b) scattering cross-sections. In both figures, the diameter is (from bottom to top) 80, 90, 100, 110, 120, 130, 140, 150, 160, and 170 nm. (c) Calculated spectrum for a 150-nm particle (solid line) and an experimental one (dotted line). (d) Calculated spectrum for a 100-nm particle (solid line) and an experimental one (dotted line). (e) Calculated result on the diameter dependence of absorption cross sections at 633 nm. (f) Calculated result on the fraction of absorption cross sections in the total extinction cross section. Figure 5. Fluorescence autocorrelation curves of Rh123 in ethylene glycol solution sandwiched with cover slips, one of which has gold nanoparticles adsorbed on the surface; (a) without the 633-nm laser irradiation and (b) with the 633-nm laser irradiation at 4-mW power.


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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 show the 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, ∆T/∆I, and the coverage of gold nanoparticles. The diameter of nanoparticle is (a) 150 nm and (b) 100 nm. Figure 9. (a) An SEM image of an aggregate of gold nanoparticles with a 150-nm diameter. (b) Optical transmission image constructed by taking into account the diffraction-limited size. The mesh in the figure corresponds to the pixel size in the optical microscope. (c) The density of 150nm nanoparticles in aggregates as a function of the number of pixels in the constructed optical transmission images. (see text). The dotted line is a guide to the eye. Figure 10. Temperature distribution around the gold nanoparticle with a 150-nm diameter calculated on the basis of the thermal diffusion equation (see text).


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Figure 1

Figure 2


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Figure 3

Figure 4


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Figure 5

Figure 6


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Figure 7

Figure 8


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Figure 9

Figure 10


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Temperature near Gold Nanoparticles under Photoexcitation

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