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We use Mie theory and discrete dipole approximation method to calculate absorption and scattering efficiencies and optical resonance wavelengths for three commonly used classes of nanoparticles: gold nanospheres, silicaâgold nanoshells, and gold na
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Extraction of Absorption and Scattering Contribution of Metallic Nanoparticles Toward Rational Synthesis and Application Bi-Ju Liu,† Kai-Qiang Lin,†,§ Shu Hu,† Xiang Wang,† Zhi-Chao Lei,† Hai-Xin Lin,† and Bin Ren*,†,‡,§ †
State Key Laboratory of Physical Chemistry of Solid Surfaces, ‡The MOE Key Laboratory of Spectrochemical Analysis and Instrumentation, and §Collaborative Innovation Center of Chemistry for Energy Materials, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
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S Supporting Information *
ABSTRACT: Noble metal nanoparticles have unique localized surface plasmon resonance (LSPR), leading to their strong absorption and scattering in the visible light range. Up to date, the common practice in the selection of nanoparticles for a speciﬁc application is still based on the measured extinction spectra. This practice may be erroneous, because the extinction spectra contain both absorption and scattering contribution that may play diﬀerent roles in diﬀerent applications. It would be highly desirable to develop an eﬃcient way to obtain the absorption and scattering spectra simultaneously. Herein, we develop a method to use the experimentally measured extinction and scattering signals to extract the absorption and scattering spectra that is in excellent agreement with that simulated by discrete dipole approximation (DDA). The heating curve measurement on the three types of gold nanorods, with almost the same extinction spectra but diﬀerent absorption and scattering contribution, convincingly reveals an excellent correlation between the heating eﬀect and the absorption strength rather than the extinction strength. The result demonstrates the importance to obtain the scattering and absorption spectra to predict the potential application for diﬀerent types of nanoparticles, which in turn will screen eﬃciently nanoparticles for a speciﬁc application.
important application in plasmon-enhanced catalysis,33−35 and it was found that metal nanoparticles with strong absorption show great advantages.24,36 Theoretically, it is well-understood that the absorption contributes to the heating eﬀect or produces the hot electron−hole pairs.24,37 In practice, one tends to just measure the extinction spectra of the synthesized nanoparticles and then choose the light with closest wavelength for photothermal therapy or catalysis, according to the peak in the extinction spectra. However, the experimentally obtained extinction spectrum contains both the contribution of scattering and absorption, and if the contribution of scattering process is dominated, this practice may be erroneous or misleading.23 Therefore, it would be highly desirable if the absorption and scattering contribution in the extinction spectrum can be reliably and conveniently obtained. Thereby, one can choose the right type of nanoparticles for a speciﬁc application. Various techniques have been used to characterize LSPR of nanoparticles, including UV−vis and dark ﬁeld spectroscopy (DFS), resonance light scattering (RLS), and photothermal imaging. However, none of them is able to obtain both the
Figure 1. (A) Diagram of the experimental setup for extraction of absorption (IA) and scattering (IS, total) spectra of metallic nanoparticles from the measurable extinction (IT) and scattering signal (I′S, partial). (B) A plot of IS vs I′S at diﬀerent concentrations in the wavelength region of 750−760 nm, with the result of the linear ﬁt (solid line).
the measurable extinction and scattering signals. The signals were obtained on a home-built dual-channel optical ﬁber-based UV−vis spectrometer. The reliability of the method was tested by comparing the spectra obtained in experiment with that by discrete dipole approximation (DDA)43 simulation for gold nanoparticle (with almost ideal spherical shape) of diﬀerent sizes. The temperature rising curve was evaluated for three types of Au nanorods with almost the same extinction wavelength but diﬀerent contributions of scattering and absorption, to obtain a quantitative relationship between the absorption coeﬃcient and heating eﬃciency. This method provides a simple but eﬃcient way to screen metal nanoparticles (of diﬀerent absorption or scattering properties) for the future applications and guide the design of functional metal nanoparticles.
scattering and absorption spectra. To our best knowledge, it seems the combined photothermal imaging and DFS is the only method that can simultaneously obtain the absorption and scattering information.38−40 However, since the photothermal imaging has to be done wavelength by wavelength with a pulse laser and can only be performed on nanoparticles immobilized on a support, the experimental eﬃciency still needs to be improved. In addition, it requires a pulse laser and complicated measurement procedures. Therefore, it is urgent to develop a reliable method that can obtain simultaneously the individual contribution of absorption and scattering for nanoparticles right after wet chemical synthesis in a way as eﬃcient and routine as the measurement of extinction spectrum in ordinary laboratories. Surprisingly, we have found only two works addressing this issue in the literature. In 1999, Collings et al.41 proposed a method to extract absorption and scattering contribution for a molecular species in the aqueous solution. The key point of the method is to obtain the correction factor to calibrate the impact of absorption on scattering. Such a correction factor can only be obtained by changing the concentration of absorbers in the solution followed by curve ﬁtting. Separation of the absorption and scattering can only be achieved by tediously solving the self-consistent equation, which is diﬃcult to be applied for routine measurements. Later in 2001, Micali et al.42 proposed a relatively simple formula and neglected the impact of absorption on scattering. This method has been applied to separate the absorption and scattering of gold nanoparticles. However, due to the neglect of the impact of absorption on scattering, huge deviation was found in the experimentally obtained spectra with the simulated spectra, as will be shown later. Therefore, this method was limited to systems with extinction less than 0.4. Furthermore, the above two methods need a UV−vis spectrometer and a ﬂuorescence spectrometer or resonance light scattering spectrometer. The use of two diﬀerent instruments requires a tedious calibration of the diﬀerent responses of spectrometers. Therefore, it is highly desirable to develop a method that can be conveniently applied for routine measurement of the scattering and absorption signals. With this information, one may be able to choose the right types of nanoparticles for a speciﬁc application. In this paper, we developed a formula to extract the contribution of absorption and scattering of nanoparticles from
EXPERIMENTAL SECTION Chemicals. Pd(II) acetylacetonate (Pd(acac)2), poly(vinylpyrrolidone) (PVP, MW = 30 000), and sodium oleate (NaOL) were purchased from Aldrich. Cetyltrimethylammonium bromide (CTAB), ascorbic acid, N,N-dimethylformamide, ethanol, acetone, trisodium citrate dihydrate (C6H5Na3O7·2H2O), choloroauric acid (HAuCl4·4H2O), hydrochloric acid, and silver nitrate (AgNO3) were purchased from Sinopharm Chemical Reagent Co., Ltd. All the above chemicals were of reagent grade and used without further puriﬁcation. Ultrapure water (Milli-Q, 18.2 MΩ) was used throughout the study. Synthesis of Nanoparticles. All the nanoparticles were synthesized following the literature methods. The uniform gold spheres were synthesized following ref 44, and the gold nanorods were synthesized after ref 45. Instruments. The setup used for extraction of absorption and scattering contribution of metallic nanoparticles includes a light source (AvaLight-DH-S-BAL, Avantes), a four-channel cuvette holder (CUV-ALL-UV, Ocean Optics), ﬂuorescence cuvette (Hitachi), a spectrometer (Acton 2300, Princeton Instrument), and a CCD detector (Pylon 100B, Princeton Instrument). In experiment, as shown in Figure 1A, we ﬁrst obtained I0 by measuring the blank solvent through the transmission light path, and the solvent was replaced by the sol of nanoparticles to obtain IT. Then, IS′ was obtained in the optical path perpendicular to the axis of the main optical path. 1059
result indicates that we should not neglect the contribution of the absorption process in considering the scattering process. On the basis of this idea, we consider a system with a low concentration of nanoparticles, in which the scattering will not lead to an obvious change of the incident light I0 for absorption and the secondary and multiple scattering can be neglected. Under such kind of conditions, we introduce an empirical formula to calculate A:
Because the detected scattered light is only a small proportion of the total scattered light, the detected I′S intensity was very weak, and the signal was measured at full power to ensure a high detection sensitivity, whereas we applied two ﬁlters of OD = 2 in the output of the light source to prevent the saturation of detector. The diﬀerence has been strictly calibrated when we used the light intensity to extract the scattering and absorption signals. Photothermal Eﬀect Experiment. We diluted the solutions of nanorod sample to ensure that all the samples have a same extinction value of one. In the heating experiment, we took 1 mL of each diluted nanorod sol and ﬁlled it into a standard 10 mm quartz cuvette. The thermal eﬀect was measured using the setup shown in Supporting Information Figure S1. The temperature proﬁles were obtained through a thermocouple inserted into Au nanorod sols that were kept stirring to achieve a uniform temperature distribution upon laser illumination. A CW laser (Torsana Starbright 785 nm, ∼476 mW) was used as the heating source. Discrete Dipole Approximation (DDA) Calculation. We used DDSCAT source code developed by Draine and Flatau for DDA calculation.43,46 The dielectric constants of gold were taken from the experimental data of Johnson and Christy.47 All the nanoparticles were supposed to be dispersed in water (n = 1.33). Morphological Characterization of Nanoparticles. The morphology of all the nanoparticles was analyzed by scanning electron microscopy (SEM) (Hitachi S4800) and transmission electron microscopy (TEM) (Tecnai F-30).
⎛ I − IA ⎞ A = −log10⎜ 0 ⎟ ⎝ I0 ⎠ ⎛ I + IS ⎞ = −log10⎜ T ⎟ ⎝ I0 ⎠
and the scattering (S): S=E−A ⎛I ⎞ ⎛ I + IS ⎞ = −log10⎜ T ⎟ + log10⎜ T ⎟ ⎝ I0 ⎠ ⎝ I0 ⎠ ⎛ I ⎞ = −log10⎜ T ⎟ ⎝ IT + IS ⎠
RESULTS AND DISCUSSION To propose a method to extract the scattering and absorption contribution, it is better to revisit the principle of UV−vis absorption spectrometry. For those systems with a low concentration and weak scattering, when a light (with an intensity of I0) is illuminated in the system, the intensity of the transmitted light (IT), also called extinction (E), can be written as follows: (1)
The relationship among incident light I0, transmission light IT, scattering IS, and absorption IA is as follows: I0 − IS − IA = IT
Thus, eq 1 can be rewritten as ⎛ I − IA − IS ⎞ E = −log10⎜ 0 ⎟ I0 ⎠ ⎝
⎛I ⎞ E = −log10⎜ T ⎟ ⎝ I0 ⎠
⎞ ⎛ I S = −log10⎜ T ⎟ ⎝ IT + IS ⎠
⎛ I + IS ⎞ A = −log10⎜ T ⎟ ⎝ I0 ⎠
The above empirical deduction process is from the absorption point of view, and we can also obtain a same expression from the scattering point of view (Supporting Information section 2). Therefore, from eq 9, the only unknown parameter is the total scattering light (IS). However, it is almost impossible to collect all the scattered light experimentally, because the light is scattered toward all possible directions while it passes through the cuvette. A practical way is to collect the scattered light at a ﬁxed angle (e.g., 90°, see Figure 1) and from the center of the cuvette. The light intensity collected will be I′S, and the total scattering intensity (IS) can be obtained via a scaling factor N.
Apparently, the extinction (E) contains the contribution of both absorption (A) and scattering (S):
According to eqs 1, 5, and 6, we can obtain the extinction, scattering, and absorption as follows:
⎛I ⎞ E = −log10⎜ T ⎟ ⎝ I0 ⎠
IS = IS′N
Therefore, it is the key to the method to obtain N. Our DDA calculation (Supporting Information Figure S4) indicates that the spatial angle distributions of scattering are nearly the same for nanoparticles with a diameter less than 200 nm. Therefore, within this range, the N can be considered a constant. If we can ﬁnd a sample showing a negligible absorption at a certain wavelength, then the extinction will be totally contributed by scattering, and the scattering can be written as
The absolute expression of either the absorption or scattering is rather complicated. In experiment, if we directly present the scattering, absorption, and extinction spectra using the deﬁnition of the UV−vis spectrometry and consider scattering, absorption as independent parameters, we will ﬁnd that the absorption spectra resemble to the theoretical calculation and are not inﬂuenced by the scattering process. However, the scattering spectra are badly inﬂuenced by the absorption process (see Supporting Information Figures S2 and S3). The
IS = I0 − IT
Thus, N can be obtained by simply taking the ratio of IS with I′S. It has been pointed out that the absorption contribution can 1060
Figure 2. Extracted absorption and scattering spectra for nanoparticles with diﬀerent diameters using diﬀerent methods. Panels A−D are the results obtained by our method, panels E−H are by DDA, and panels I−L are by the method of ref 42. The diameters are 16.5 ± 1.5 nm (for panels A, E, and I), 41 ± 2 nm (for panels B, F, and J), 72 ± 3.8 nm (for panels C, G, and K), and 162 ± 9 nm (for panels D, H, and L). The insets in panels A− D are the corresponding SEM images of the four types of nanoparticles.
the pure solvent and the solution containing nanoparticles through the transmission light path to obtain I0 and IT, respectively, while, IS′ was obtained by measuring the light at 90° to the incident light path, see Figure 1A. The high N value means a low collection eﬃciency in the scattering path. Therefore, to ensure a good signal-to-noise ratio in the scattering path, we increased the power of the light source and used two ﬁlters of OD = 2 in the output of the light source to prevent saturation of the detector. The intensity of the transmitted light should then be multiplied by 104. To prove the reliability of the above method, we synthesized a series of uniform Au nanospheres with diameters of 16.5 ±
be neglected for gold nanoparticles with a diameter >155 nm at wavelengths >750 nm,39 which can be used as an ideal standard sample to obtain N. To avoid the change in the scattering angle distribution and to have a negligible contribution of absorption, we synthesized gold nanoparticles of 180 nm. To reduce the error in the measurement, we measured both IS and IS′ at diﬀerent concentrations (max concentration is lower than 4.3 × 109 NP/mL) of nanoparticles (Figure 1B). By plotting IS against IS′ , we can obtain the N value from the slope, which is about 149 030 and used in the following experiments. After we measured the IT, IS′ , and I0, we can obtain E, S, and A. For this purpose, we used a ﬂuorescence cuvette to measure 1061
Figure 3. Extinction, scattering, and absorption spectra of various types of nanoparticles: (A) 60 nm gold spheres; (B) 60 nm silver spheres; (C) gold nanorods; (D) gold nanocages; (E) palladium nanosheets. The insets are the corresponding SEM images (A−D) and TEM image (E).
1.5, 41 ± 2, 72 ± 3.8, and 162 ± 9 nm following ref 44. The use of uniform gold nanospheres allows a reliable comparison of experimentally obtained spectra with the simulated spectra. For clarity, we present in Figure 2A−D the experimentally obtained absorption and scattering spectra using our method, Figure 2E−H the calculated results by DDA, and Figure 2I−L the experimentally obtained absorption and scattering spectra following the method of ref 42. From Figure 2, parts A and B, we can see that the dipole scattering and absorption peak positions of 16.5 nm nanoparticles are at 532 and 519 nm, respectively. It is clear that absorption is dominated in the extinction spectra, and the peak positions of scattering and absorption are close to each other. With the increase of the diameter, both scattering and absorption peaks become broader and the scattering intensity signiﬁcantly increases accompanied by a huge red shift, whereas the contribution of absorption to extinction decreases accompanied by a small red shift. As a result, obvious separation in the peak position of scattering and absorption was observed with the increase of the particle size. At the size of 162 nm, obvious quadrupole scattering peak can be observed at 543 nm. Interestingly, the absorption, scattering, and the extinction spectra produced by DDA calculation agree excellently with the experimental result, in not only the peak position, but also the relative intensity. A small deviation in the wavelength region from 400 to 450 nm is due to the low quantum eﬃciency of CCD and the low intensity of the light source in the wavelength range below 450 nm. (All spectra have been smoothed with 20 points average without aﬀecting the spectral features. The original spectrum of 72 nm nanospheres is shown in Supporting Information Figure S5.) Our experimental results, including the peak position, relative peak intensity for nanoparticles of diﬀerent sizes, are in a surprisingly good agreement with simulated result of ref 39. However, the results (Figure 2 I−L) obtained with the method of ref 42 show a clear deviation to the DDA simulation and our method, indicating the importance of considering the absorption eﬀect in deduction of the scattering, absorption, and extinction
formulas. In a word, the above result indicates that our method can be used as a simple, reliable, and practical way to eﬀectively extract absorption and scattering spectra compared with the reported methods.40−42 With the extracted absorption and scattering spectra, we can also easily obtain the absorption and scattering cross section (σabs and σsca) by A = σabscl and S = σscacl, where c is the concentration of nanoparticles, l is the optical path length. It is surprising to observe that the bandwidth for the size of 72 nm obtained in experiment is as narrow as the theoretical simulation. The main reason may be that the particles in this size range produce nearly the same peak position, which will not lead to the broadening of the spectra even if there is a small size distribution of the nanoparticles (see Supporting Information section 6 and Figure S6 for detailed discussion). It should be noted that our method was proposed with the assumption that the secondary scattering and multiple scattering can be neglected. However, they are unavoidable in real systems and they may become severe with the increase of concentration. A recent work indicates that the secondary scattering and multiple scattering should be taken into account when the concentration of nanoparticle is higher than 1010 and 1011 NP/mL for nanoparticles with strong scattering and absorption, respectively.48 The upper concentration limit may diﬀer for nanoparticles of diﬀerent shapes and sizes. We did the concentration dependence study, and a good linear relation was found between the concentration and the scattering, absorption, and extinction spectra (see Figure 1 and Supporting Information Figure S7). It should be pointed out that the highest concentration used here is the concentration of assynthesized Au nanoparticles, which has the practical application signiﬁcance. It indicates that the secondary and multiple scattering can be neglected when using our method, even for most of the nanoparticles directly obtained from the wet chemical synthesis. In principle, our method is based on the dipolar scattering pattern (Supporting Information Figure S4) and should be limited to the dipolar system. Surprisingly, we 1062
Figure 4. Absorption, scattering, and extinction spectra obtained using our method for nanorods with diﬀerent aspect ratios: (A) 85.6 ± 5.5 nm/22.4 ± 2.1 nm; (B) 116.3 ± 6.5 nm/34.6 ± 1.7 nm; (C) 129.9 ± 5.4 nm/45.8 ± 2.3 nm. The insets are the corresponding SEM images. (D) The heating curves obtained under 785 nm laser illumination and the cooling curves obtained when the laser was turned oﬀ.
by the absorption, and the scattering can be neglected, which is attributed to the ultrathin thickness (ﬁve atomic layers of palladium). This unique property of palladium nanosheet makes it even a better material than the gold nanorod and gold nanocage for photothermotherapy. Among all these materials, the gold nanorod is the most interesting. It has a very sharp peak in the long wavelength and has tunable scattering to absorption contribution depending on the size and aspect ratio. Therefore, it has found wide application in photothermal therapy as well as SERS,63 bioimaging,64 and diagnosis of diseases. In a word, the proper separation of the scattering and absorption contribution in the extinction spectra enables us to obtain the optical properties of speciﬁc nanoparticles and to predict their potential application. Up to now, quite a large amount of metal nanoparticles have been used in thermal therapy.26,28,54,60,65 As stated in the introduction, the common practice in the literature by now is still using the peak in extinction spectra to determine whether they are appropriate for the thermal therapy. However, as it is shown above that the extinction contains the contribution of absorption and scattering, and if the relation between the heating eﬀect and the optical properties cannot be reliably established, the use of extinction peak alone may mislead the selection of proper nanoparticles for the photothermal application. To address this issue, we carefully synthesized three kinds of gold nanorods with almost the same longitudinal LSPR peaks near 785 nm. The experimental extinction, absorption, and scattering spectra are given in Figure 4A−C, which match with the DDA calculation result in Supporting Information Figure S3. It can be clearly seen from the ﬁgures that, although they
found that even for 324 nm gold nanospheres, in which the quadrupole contribution is quite signiﬁcant, the experimental result still agreed well with the simulation (see Supporting Information Figure S8). After demonstrating that our method can be reliably used for extracting the absorption and scattering spectra, we further extend this method to other widely used metallic nanoparticles to obtain their absorption and scattering properties, which may guide the selection of suitable nanoparticles for the end application. We synthesized various types of metallic nanoparticles, including 60 nm gold nanospheres,49 60 nm silver nanospheres,50 gold nanorods,45,51 gold nanocages,52,53 and palladium nanosheets54 following the literature methods. The extracted scattering, absorption, and their extinction spectra are shown in Figure 3A−E. For the ease of comparison, their extinction values were normalized to 1. It is obvious that silver nanospheres show the strongest scattering among all the nanoparticles, and scattering dominates in the extinction. It is generally accepted that nanoparticles with a strong scattering may have strong surface enhancement eﬀect in surfaceenhanced Raman scattering (SERS).55,56 Thus, it is no wonder that silver nanoparticles have been demonstrated to be the best candidates of SERS substrates.57 Moreover, the high scattering eﬃciency of silver nanospheres makes them excellent probes for bioimaging.17,58,59 In addition, gold nanorods, gold nanocages, and palladium nanosheets (seen in Figure 4C−E) show extremely strong absorption contribution to the extinction, making them promising materials for photothermal therapy, as shown in a large amount of work in literature.28,29,54,60−62 Most interestingly, the extinction spectrum of the palladium nanosheets is almost totally contributed 1063
absorption eﬃciency through the extracted absorption spectra by our method. Thereafter, we can directly calculate the heating curve and the equilibrium temperature that the nanoparticle system can reach during heating. Therefore, we can now quickly screen for the nanoparticles suitable for photothermal treatment by simply checking the absorption eﬃciency of the extracted absorption spectra. This study provides a method to quickly screen for nanoparticles with strong absorption eﬃciency for photothermal therapy, which may eﬃciently accelerate the discovery and synthesis of the most suitable nanoparticles for a speciﬁc purpose, on the basis of either the absorption or scattering properties. If the extinction and scattering can be measured during the heating process, we may be able to investigate the eﬀect of temperature on the LSPR properties.
have almost the same extinction spectra, their absorption and scattering contribution extracted by our method are obviously diﬀerent: for nanorod 1, absorption is dominated in the extinction spectrum; for nanorod 2, absorption and scattering almost contributes equally to extinction; and for nanorod 3, scattering is dominated. The following three properties of these three nanorods are especially important: (1) the absorption, scattering, and extinction peaks of each nanorod are at the same wavelength; (2) the wavelengths of the above peaks for the three types of nanorods are almost at the same position; (3) they are of the same material, gold. These properties can be fully utilized to eﬀectively avoid the complicate conversion of wavelength or absorption coeﬃcient for diﬀerent nanorods. Therefore, the control experiments can be done and demonstrated in a straightforward way. We used a 785 nm laser as the heating laser and monitored the heating eﬀect of diﬀerent nanorods. It may be more straightforward to control the concentration of the nanoparticles so that the optical properties can be normalized to one nanoparticles. However, in practice, it is more common to use the extinction intensity as a criterion. For this purpose, we adjusted the extinction values of each type of nanorods to 1 by controlling the concentration. Then, we took 1 mL of sols from the above solution and tested their photothermal eﬀects using the setup shown in Supporting Information Figure S1, following the literature method.66 The laser power used for heating is 0.48 W. The heating and cooling curves are shown in Figure 4D. From the ﬁgure, we can ﬁnd that nanorod 1 shows the strongest thermal eﬀect and nanorod 3 shows the least thermal eﬀect. Since the study was done with the same extinction value, the excellent correlation of the photothermal eﬀect with the absorption strength clearly indicates that absorption is dominated in the photothermal eﬀect. To understand the correlation in a more quantitative way, we adopted Newton cooling law to describe the heating curve: T (t ) = T0 +
Iσ (1 − e−αt ) Cmα
CONCLUSIONS In summary, we have proposed a novel method, including formulas and experimental setup, to extract the scattering and absorption contribution from the experimentally measured extinction spectra and part of the scattering signal of metal nanoparticle sol solution. We used gold nanospheres of diﬀerent sizes as a model system and convincingly demonstrated that the extracted spectra of absorption and scattering are in excellent agreement with the DDA calculation. We further veriﬁed, using real but important systems, such as gold nanospheres, nanorods, nanocages, silver nanospheres, and palladium nanosheets, the applicability of using absorption and scattering spectra to predict the possible application of nanoparticles. We in purpose, synthesized three types of gold nanorods with almost the same extinction spectra but diﬀerent absorption and scattering contribution, to convincingly demonstrate that the sole use of extinction spectra to predict the potential application of nanoparticles may be erroneous. The excellent correlation between the absorption, rather than the extinction strength, and the heating eﬀect shows the importance to obtain the scattering and absorption spectra. The dual-channel optical ﬁber-based UV−vis spectrometer can be easily set up in ordinary laboratories, oﬀering a simple routine method to screen for nanoparticles for a speciﬁc application, and even to guide the synthesis of nanoparticle for a certain purpose highly eﬃciently, demonstrating the reliability of the present method. The method provides an opportunity to correlate the absorption or scattering contribution to photochemistry of plasmonic strong coupling systems.67
where T0, I, σ, C, and m are the initial temperature of the system before heating, the input laser power, the absorption eﬃciency, the average speciﬁc heat capacity, and the average mass of the system, respectively. In the present system, σ was obtained from the extracted absorption spectra, which is 0.832, 0.682, and 0.535 for nanorods 1, 2, and 3. Cm can be considered a constant under a deﬁned experimental condition. α is the heat transfer coeﬃcient of the system and can be obtained by ﬁtting the experimental cooling curve using the following equation for any of the nanorod system: T (t ) = T0 + (T ′ − T0)e
S Supporting Information *
The deduction of the formulas from the scattering point of view, calculation of the spatial distribution of scattering and optical properties of gold nanorods, concentration dependence study, and the experimental setup for heating experiment. This material is available free of charge via the Internet at http:// pubs.acs.org.
where T′ is the temperature right before the cooling of the system. By ﬁtting the cooling curves of nanorod 1, nanorod 2, and nanorod 3 using eq 13 and the heating curve of nanorod 3 using eq 12 with the experimentally measured T0, T′, and σ obtained from the absorption spectra, we obtained Cm = 7.4 J·°C−1 and α = 2.8 × 10−3 s−1. The Cm obtained here is the heat capacity of the whole system, which is higher than that of pure water (4.179 J·°C−1). This is understandable, because both water and the cuvette contribute to it. With the obtained Cm and α values, we can obtain a heating curve of nanorods 1 and 2, in excellent agreement with the experimentally obtained data. For a system with known Cm and α, we can obtain the
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ACKNOWLEDGMENTS We acknowledge support from MOST (2013CB933703 and 2011YQ03012406), NSFC (21021120456, 21321062, and 21227004), and MOE (2010121019 and IRT13036). We also thank Professors Nanfeng Zheng and Xiaoqing Huang for kindly providing the Pd nanosheets.
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