Size-Dependent Temperature Effects on PbSe Nanocrystals

Jun 15, 2010 - Daniel Jaque , Blanca del Rosal , Emma Martín Rodríguez , Laura Martínez Maestro , Patricia Haro-González , José García Solé...
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Size-Dependent Temperature Effects on PbSe Nanocrystals )

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Quanqin Dai,†,‡,^ Yu Zhang,†, ,^ Yingnan Wang,§ Michael Z. Hu,‡ Bo Zou,*,§ Yiding Wang, and William W. Yu*,†, †

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Department of Chemistry and Biochemistry, Worcester Polytechnic Institute, Worcester, Massachusetts 01609, ‡Nuclear Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, §State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, China, and State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China. ^ These authors contributed equally to this work Received March 7, 2010. Revised Manuscript Received May 30, 2010 An investigation show that the temperature-induced band gap (Eg) variation of PbSe nanocrystals is strongly sizedependent. The temperature coefficients (dEg/dT ) evolve from negative to zero and then to positive values, with the increase of PbSe nanocrystal sizes. Such phenomena imply that PbSe nanocrystals may be the potential candidate as sensitive temperature markers. Additional analyses disclose that the molar extinction coefficients of PbSe nanocrystals remain unchanged in the investigated temperature range (25-120 C).

Introduction In comparison to II-VI and III-V nanomaterials, the IV-VI lead chalcogenides (PbE, where E = S, Se, or Te) are accessible to the strong quantum confinement, and is of consistent interest in their unique optical properties and potential applications.1-6 These lead chalcogenide nanocrystals shares some identical features,7-9 such as the narrow bulk band gap, large exciton Bohr radius, and nonstoichiometry with a systematic Pb excess. Among the many types of semiconductor nanocrystals, PbSe nanocrystals have become one of the most intriguing. The corresponding exciton Bohr radius of PbSe is 46 nm, approximately eight times larger than that of CdSe.5 Therefore, PbSe nanocrystals may provide unique opportunities for investigating properties in a strongly size-dependent system. Their low energy transitions occur in the technologically important near-infrared wavelength range of the electromagnetic spectrum.10 With the size-dependent band gap, PbSe nanocrystals have recently shown great potentials in telecommunication,10 photodetection,11 *Corresponding authors. E-mail: [email protected] (W.W.Y.); zoubo@ jlu.edu.cn (B.Z.). (1) Ekimov, A. I.; Efros, A. L.; Onushchenko, A. A. Solid State Commun. 1985, 56, 921. (2) Zhu, J.; Wang, H.; Xu, S.; Chen, H. Langmuir 2002, 18, 3306. (3) Darbandi, M.; Lu, W.; Fang, J.; Nann, T. Langmuir 2006, 22, 4371. (4) Dai, Q.; Wang, Y.; Zhang, Y.; Li, X.; Li, R.; Zou, B.; Seo, J.; Wang, Y.; Liu, M.; Yu, W. W. Langmuir 2009, 25, 12320. (5) Wise, F. W. Acc. Chem. Res. 2000, 33, 773. (6) Hines, M. A.; Scholes, G. D. Adv. Mater. 2003, 15, 1844. (7) Dai, Q.; Wang, Y.; Li, X.; Zhang, Y.; Pellegrino, D. J.; Zhao, M.; Zou, B.; Seo, J.; Wang, Y.; Yu, W. W. ACS Nano 2009, 3, 1518. (8) Moreels, I.; Lambert, K.; Smeets, D.; Muynck, D. D.; Nollet, T.; Martins, J. C.; Vanhaecke, F.; Vantomme, A.; Delerue, C.; Allan, G.; Hens, Z. ACS Nano 2009, 3, 3023. (9) Moreels, I.; Lambert, K.; Muynck, D. D.; Vanhaecke, F.; Poelman, D.; Martins, J. C.; Allan, G.; Hens, Z. Chem. Mater. 2007, 19, 6101. (10) Steckel, J. S.; Coe-Sullivan, S.; Bulovi, V.; Bawendi, M. G. Adv. Mater. 2003, 15, 1862. (11) McDonald, S. A.; Konstantatos, G.; Zhang, S. G.; Cyr, P. W.; Klem, E. J. D.; Levina, L.; Sargent, E. H. Nat. Mater. 2005, 4, 138. (12) Weissleder, R. A. Nat. Biotechnol. 2001, 19, 316. (13) Medintz, I. L.; Goldman, E. R.; Uyeda, H. T.; Mattoussi, H. Nat. Mater. 2005, 4, 435. (14) Schaller, R. D.; Klimov, V. I. Phys. Rev. Lett. 2004, 92, 186601. (15) Ellingson, R. J.; Beard, M. C.; Johnson, J. C.; Yu, P.; Micic, O. I.; Nozik, A. J.; Shabaev, A.; Efros, A. L. Nano Lett. 2005, 5, 865.

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biomedical labeling and imaging,12,13 and solar energy conversion.14-16 Remarkably in the solar cell application, PbSe nanocrystals exhibit a unique “carrier multiplication”, in which up to seven electron-hole pairs can be excited by the absorption of one single high-energy photon.14 To facilitate the performance of these promising applications, the relevant fundamental investigations are extensively undergoing. For example, the relationship of the band gap and the particle size of PbSe nanocrystals has been experimentally measured, and their size-dependent extinction coefficients have also been determined.7,9 It is worth noting that these fundamental investigations have been conducted at room temperature, and thus the obtained data need to be examined prior to their practical application at a temperature other than room temperature. For the nanomaterial-based application at different temperatures, the low spatial resolution of conventional temperature measurement techniques makes it extremely challenging to measure the exact temperature at the micro- and nanoscale.17-19 To solve this technical difficulty, nanosized semiconductors, such as CdSe nanocrystals,18 have been recently proposed to be temperature markers for measuring the virtual temperature in micro- and nanoscaled devices and applications. The typical II-VI and III-V nanomaterials, however, have limited resolution in the temperature sensitivity (e.g., 0.1 nm/C for CdSe nanocrystals).18 In addition, the intraband electron-phonon terms of II-VI and III-V nanomaterials are much larger than their interband terms, indicating that the intraband energy difference cannot reach the energy gap of the corresponding bulk materials. Accordingly, the temperature coefficients of these nanomaterials are close to the values of their bulk materials (e.g., -0.28 meV/K for bulk CdSe).5,20 We here report the temperature effect on the band gap of a series of high-quality PbSe nanocrystals, which exhibit a strong (16) Koleilat, G. I.; Levina, L.; Shukla, H.; Myrskog, S. H.; Hinds, S.; Pattantyus-Abraham, A. G.; Sargent, E. H. ACS Nano 2008, 2, 833. (17) Jorez, S.; Laconte, J.; Cornet, A.; Raskin, J. P. Meas. Sci. Technol. 2005, 16, 1833. (18) Li, S.; Zhang, K.; Yang, J. M.; Lin, L. W.; Yang, H. Nano Lett. 2007, 7, 3102. (19) Zhou, J.; Yan, H.; Zheng, Y.; Wu, H. Adv. Funct. Mater. 2009, 19, 324. (20) Dai, Q.; Song, Y.; Li, D.; Chen, H.; Kan, S.; Zou, B.; Wang, Y.; Deng, Y.; Hou, Y.; Yu, S.; Chen, L.; Liu, B.; Zou, G. Chem. Phys. Lett. 2007, 439, 65.

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Figure 1. (a) Temporal evolution of the absorption spectra of high-quality PbSe nanocrystals. (b) Typical TEM image of the monodisperse PbSe nanocrystals.

size dependence on their temperature coefficients and may potentially act as the temperature marker. In addition, the molar extinction coefficients of PbSe nanocrystals are found to be constant in a temperature range of 25-120 C.

Experimental Section Chemicals. Trioctylphosphine (TOP, 90%), oleic acid (OA, 90%), 1-octadecene (ODE, 90%), and selenium (100 mesh, 99.99%) were ordered from Aldrich. Lead(II) oxide (99.99%) was purchased from Alfa Aesar. Methanol, acetone, tetrachloroethylene, chloroform, hexane, and toluene were bought from VWR. Synthesis. PbSe nanocrystals were synthesized by modifying our previous approach;7,21 lower injection/reaction temperatures and fewer OA ligands were employed. Typically, PbO (0.892 g, 4.00 mmol), OA (2.260 g, 8.00 mmol), and ODE (12.848 g) were loaded into a three-neck flask and heated to 170 C. After PbO powder was completely dissolved under a nitrogen flow, 6.400 g of TOP-Se solution (containing 0.640 g of Se and prepared in a glovebox) was swiftly injected into the vigorously stirred solution. Subsequently, the temperature was kept at 140 C for the nanocrystal growth. At different reaction intervals, aliquots were taken out for measurements. Purification. Prior to the measurement, the aliquot samples have to be purified to remove excessive reaction precursors and solvents, for which we resorted to our well-established purification approach.21-23 After an aliquot was quickly taken from the reaction flask and quenched by room-temperature toluene, methanol solution with an equal volume to the sample solution was added for extraction. The extracted PbSe nanocrystals were redispersed in chloroform, where excess acetone was poured to precipitate the nanocrystals via centrifugation. Finally, the purified nanocrystals were dispersed in solvents (e.g., tetrachloroethylene) for further measurements. All the purification procedures above and the following measurements should be performed under the inert gas protection to avoid the possible oxidation.4 Measurement. Transmission electron microscope (TEM) specimens were made in nitrogen atmosphere, where two drops of the diluted sample solution were evaporated onto the carboncoated copper grids. TEM images were taken by a JEOL FasTEM-2010 TEM on several different areas of each grid. On the basis of the obtained TEM images, an Image-Pro Plus 6.0 software was utilized to analyze the particle size and size distribution (21) Yu, W. W.; Falkner, J. C.; Shih, B. S.; Colvin, V. L. Chem. Mater. 2004, 16, 3318. (22) Yu, W. W.; Wang, Y. A.; Peng, X. Chem. Mater. 2003, 15, 4300. (23) Yu, W. W.; Peng, X. Angew. Chem., Int. Ed. 2002, 41, 2368.

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of the resulting PbSe nanoparticles. A Perkin-Elmer Lambda 9 UV-vis-NIR spectrometer and a NIR spectrometer (Spectral Products CM110) were respectively employed to record the absorption and photoluminescence spectra of nitrogen-protected PbSe nanocrystal samples. For the optical measurement at different elevated temperatures, the purified PbSe nanocrystal sample in solution was sealed in nitrogen and heated to specific temperatures, at which temperature the corresponding optical spectra were measured. Such measurements were stared at room temperature (25 C). Subsequently, the temperature was set at 40, 60, 80, 100, and 120 C, respectively. When the sample was heated to a certain temperature (e.g., 60 C), it was maintained for 1020 min. During this maintenance period, the measurement was repeatedly taken. For the investigation of reversibility in the temperature-induced band gap change of PbSe nanocrystals, the multiple heating and cooling cycles were utilized. The PbSe nanocrystal sample was first measured at room temperature. It was subsequently measured again, after being heated to 60 C and then cooled down back to room temperature. At the third and fourth times of measurement, the sample was respectively heated to 80 and 100 C and cooled down back to room temperature.

Results and Discussion Synthesis of High-Quality Nanocrystals. Following the pioneering synthetic work by Murray and his colleagues,24 many research groups reported the successful preparation of PbSe nanocrystals in the solvent phenyl ether, where TOP-Se and lead oleate precursors were employed.25-27 With ODE (a noncoordinating solvent) as the substitute of phenyl ether, Yu and coworkers presented a synthetic scheme to prepare high-quality PbSe nanocrystals with a wide size range.21 Yu et al.’s scheme, compared to the previous ones, was reported to readily produce PbSe nanocrystals with narrower size distributions.21 To minimize the effect of size distributions on our current work, we preferred to select Yu et al.’s scheme and made a suitable modification, as shown in the Experimental Section. Figure 1 shows the absorption spectra of a series of PbSe nanocrystals and a TEM image of the monodisperse PbSe nanoparticles. The resulting nanocrystals have very narrow size distributions (∼6%), analyzed by the Image-Pro Plus 6.0 software. (24) Murray, C. B.; Sun, S.; Gaschler, W.; Doyle, H.; Betley, T. A.; Kagan, C. R. IBM J. Res. Dev. 2001, 45, 47. (25) Wehrenberg, B. L.; Wang, C.; Guyot-Sionnest, P. J. Phys. Chem. B 2002, 106, 10634. (26) Du, H.; Chen, C.; Krishnan, R.; Krauss, T. D.; Harbold, J. M.; Wise, F. W.; Thomas, G.; Silcox, J. Nano Lett. 2002, 2, 1321. (27) Sapra, S.; Nanda, J.; Pietryga, J. M.; Hollingsworth, J. A.; Sarma, D. D. J. Phys. Chem. B 2006, 110, 15244.

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Figure 2. Temperature-induced spectral shifts of the resulting PbSe nanocrystals with different particle sizes.

Temperature-Induced Band Gap Variation. As illustrated in Figure 2a, when temperature increased, the corresponding absorption spectra of 3.9 nm PbSe nanocrystals shifted to red, accompanied by a gradual decrease of absorbance. This temperature-induced red shift became less obvious as the particle size of PbSe nanocrystals increased to 4.6 nm (Figure 2a-c). For the 5.1 nm PbSe nanocrystals, no obvious shifts could be observed (Figure 2d). When PbSe nanocrystals became further larger (e.g., 6.4 nm in Figure 2e), their absorption spectra switched to blue shifts with the increase of temperature applied. These blue shifts became more apparent in Figure 2f, where the particle size was 6.9 nm. It should be noted that the experimental results in Figure 2 are reproducible. Thus, it can be concluded that, for the PbSe nanocrystals with a medium particle size (e.g., 5.1 nm), their spectra do not shift with the increase of temperature; but the spectra shift to red and blue for relatively small and large PbSe nanocrystals, respectively. The temperature coefficient, dλ/dT, is depicted in Figure 3a, where λ is the lowest absorption peak position of the PbSe sample, and T is the temperature applied. From Figure 3a, it can be seen that with the increase of nanocrystal sizes, the initially positive dλ/dT becomes zero, and then negative. This size-dependent temperature coefficient is different from the cases of II-VI and III-V nanomaterials with constant dλ/dT values close to those of their bulk counterparts.5,20 Figure 3b gives the temperature coefficient in the term of dEg/dT, where dλ/dT = (-λ2/1240) dEg/dT, and Eg is the band gap energy of the corresponding PbSe nanocrystals. There are three main factors to affect the temperature-induced change of energy gap (Eg) in PbSe nanocrystals: dEg0 dE conf dJe - ph dEg ¼ þ þ dT dT dT dT

ð1Þ

The first term, dE0g/dT, is the temperature dependence of the band energy of bulk materials (E0g) induced by thermal expansion of the lattice constant a,

Figure 3. Temperature coefficients versus particle sizes of the PbSe nanocrystals in the form of (a) dλ/dT and (b) dEg/dT.

dEg0 dEg0 da ¼ dT da dT

where a is the lattice constant of the bulk material. Schl€uter et al. have reported that the calculated value is 230 μeV/K, which results

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ð2Þ

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in the increasing band gap of PbSe bulk materials at elevated temperatures.28 The second term, dEconf/dT, is the temperature-related change of the quantum-confined energy (Econf) induced by thermal expansion of nanocrystal size (R, nanocrystal radius). It is known that Econf  1/R2;29 therefore, dE conf dE conf dR 2E conf dR ¼ ¼ dT dR dT R dT

ð3Þ

If the thermal expansion coefficient of the nanocrystals material R is used, dR/dT = RR, eq 3 can be expressed as dE conf ¼ - 2RE conf dT

ð4Þ

Generally, the confinement energy increases with the decrease of nanocrystals size. The third term, dJe-ph/dT, is the temperature-related change of electron-phonon coupling energy (Je-ph) induced by temperature dependence of phonon density and energy. According to Wise et al.’s work,29 dJe - ph dn T f ¥ f - SðRÞkB ¼ - SðRÞ < pω > dT dT

ð5Þ

where S(R) is a dimensionless electron-phonon coupling strength which relies on the nanocrystals size; Æhω 9æ is an average phonon energy; and kB is Boltzmann constant. This contribution depends on both temperature and size. With the increase of temperature, the average phonon energy and density will increase. Thus, the absolute value of electron-phonon coupling energy increases and induces larger temperature coefficients. The first contribution, which also takes effect in bulk materials,20 is dominant in large-size nanocrystals. However, this contribution becomes weaker with the decrease of particle sizes because the increasing spacings between quantum confined energy levels in small-sized nanocrystals are more dominantly determined by the particle size rather than by the lattice constant or the electron-phonon interactions. When the first sizedependent contribution diminishes to the lowest level, the last two contributions start to dominate the temperature dependence of the nanocrystal band gap. Thus, the temperature coefficients corresponding to the very small PbSe nanocrystals are sizedependently negative in the term of dEg/dT (Figure 3b). As discussed above, the size-dependent temperature coefficient in PbSe nanocrystals is attributed to their nature, including dE0g/dT, dEconf/dT, and dJe-ph/dT. Such temperature coefficients have no effect from the solvent that is used to disperse PbSe nanocrystals. Not only tetrachloroethylene shown here, but also other solvents (such as hexane, toluene, and chloroform), can be used to disperse PbSe nanocrystals, not affecting the results in Figure 2. However, unlike tetrachloroethylene, these solvents have very strong absorption signals in the infrared range, which tend to cover the absorption from PbSe nanocrystals. In addition to the absorption spectra, the photoluminescence spectrum was also utilized to investigate the temperature-induced band gap shift of PbSe nanocrystals (Figure S1 in the Supporting Information). It should be noted that such investigation could not be applicable to the (28) Schl€uter, M.; Martinez, G.; Cohen, M. L. Phys. Rev. B 1975, 12, 650. (29) Olkhovets, A.; Hsu, R. C.; Lipovskii, A.; Wise, F. W. Phys. Rev. Lett. 1998, 81, 3539. (30) Pietryga, J. M.; Werder, D. J.; Williams, D. J.; Casson, J. L.; Schaller, R. D.; Klimov, V. I.; Hollingsworth, J. A. J. Am. Chem. Soc. 2008, 130, 4879.

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relatively large PbSe nanocrystals (e.g., 6.9 nm), because large nanocrystals exhibited extremely poor photoluminescence.30 In an early publication,29 Wise et al. reported the temperatureinduced variation of energy gap in the lead-salt quantum dots. They focused on PbS nanocrystals in a glass matrix, whereas PbSe nanocrystals were simply mentioned. When carefully comparing their and our temperature coefficients (dEg/dT) for PbSe nanocrystals, we found that the trend of temperature coefficients in their and our studies is consistent, but these coefficient values are not exactly the same. It may be attributed to, but not limited to, the following aspects. First, different research groups reported significant discrepancies in the relation between the first absorption peak position and the particle size of PbSe nanocrystals (Figure S2 in the Supporting Information); such discrepancies would eventually bring differences to temperature coefficients [dEg/dT = (-1240/λ2) dλ/dT] versus particle sizes. In our experiments, the first absorption peak position (the lowest bandgap energy) of each PbSe nanocrystal sample was precisely obtained from the measurement of its absorption spectrum. Comparatively, it was lengthy to accurately determine the particle size of the corresponding sample. To do so, we utilized an ImagePro Plus 6.0 software to analyze the particle size and size distribution of PbSe nanoparticles. A total of 10000-20000 individual PbSe nanoparticles from several calibrated TEM images were counted for each sample, so that the error in the nanocrystal particle size could be minimized. Second, the temperature coefficient (dEg/dT) of PbSe nanocrystals was demonstrated to be sensitively size-dependent. Thus, their particle size needs to be maintained in a narrow range to minimize the effect of size distributions on dEg/dT. As shown above, the PbSe nanocrystal samples studied here have a size distribution as narrow as ∼6%, narrower than that in Wise et al.’s work.29,31 Temperature Markers. Semiconductor nanocrystals, such as CdSe quantum dots, have been demonstrated to be capable of sensing temperature changes and reporting the virtual temperature through optical readouts.18 The experimental results shown in Figure 2 illustrated that PbSe nanocrystals also have the ability to work as temperature markers. In comparison to CdSe nanocrystals with a temperature coefficient (sensitivity) of ∼0.1 nm/C,18 PbSe nanocrystals have higher sensitivity to temperature for their small and large sizes. As shown in Figure 4a, 3.9 nm PbSe nanocrystals were examined to respond linearly to temperature in a range of 25-120 C, in which the spectral peaks shifted to red. The corresponding sensitivity of this spectral shift was ∼0.16 nm/C, 60% higher than that of CdSe nanocrystals. Large-sized PbSe nanocrystals also exhibited sensitive temperature coefficients, e.g. ∼0.15 nm/C for the 6.9 nm nanocrystals (Figure 4b). PbSe nanocrystals with a medium particle size, such as 5.1 nm, were not appropriate for the applications of temperature markers, because the corresponding spectra shifted little or not at all. It was further found that the temperature-induced shifts were reversible when the sample was cooled down (Figure S3 in the Supporting Information). This reversibility, together with the sensitive spectral shift to temperature, enables PbSe nanocrystals to be suitable for temperature measurements. Compared to CdSe nanocrystal-based temperature markers, PbSe nanocrystals are possible for in vivo biological measurements at the near-infrared wavelengths, where biological fluids have the significantly reduced absorption.32 Accurate localized (31) Lipovskii, A.; Kolobkova, E.; Petrikov, V.; Kang, I.; Olkhovets, A.; Krauss, T.; Thomas, M.; Silcox, J.; Wise, F. W.; Shen, Q.; Kycia, S. Appl. Phys. Lett. 1997, 71, 3406. (32) Evans, C. M.; Guo, L.; Peterson, J. J.; Maccagnano-Zacher, S.; Krauss, T. D. Nano Lett. 2008, 8, 2896.

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Figure 4. Spectral shifts of the (a) 3.9 and (b) 6.9 nm PbSe nanocrystals over temperature. Table 1. Molar Extinction Coefficient of the 3.9 nm PbSe Nanocrystals at Different Temperatures temperature (C)

measured absorbancea

calibrated absorbanceb

virtual extinction coefficientc (105 M-1 3 cm-1)

actual extinction coefficientd (105 M-1 3 cm-1)

25 0.299 0.278 1.103 1.103 40 0.294 0.275 1.091 1.108 60 0.284 0.269 1.067 1.105 80 0.274 0.264 1.048 1.107 100 0.266 0.259 1.028 1.107 120 0.247 0.253 1.004 1.101 a The measured values were directly obtained from the corresponding absorption spectra. b The calibrated absorbance values were based on Ac = AmWHWHM/K. c The virtual molar extinction coefficients were calculated using Ac = εCL, where C and L were 2.52 μM and 1.0 cm, respectively. Note the concentration of 2.52 μM was used without counting the volume thermal expansion of solvents at higher temperatures. d The actual molar extinction coefficients were calculated using Ac = εCL, where L was 1.0 cm, and C = 2.52/[1 þ (T - 25)  0.00102] μM. Note the actual concentration of PbSe nanocrystals was used, considering the volume expansion of solvents at higher temperatures (T).

temperature measurements for different parts of a living cell may help to disclose the intrinsic biological phenomenon mechanisms and to facilitate the development of future diagnosis and treatment.33 Recent reports showed that the hydrophobic PbSe and PbS nanocrystals could be transferred into aqueous solution by replacing the oleate capping ligand with (1-mercaptoundec-11yl)tetra(ethylene glycol) (MTPEG).32,34 These MTPEG-capped nanocrystals could well maintain their original properties, and were stable over 5 days in the biologically relevant buffers with physiological pHs. Therefore, the small-sized PbSe nanocrystals with the superior temperature sensitivity may be preferable for temperature measurements in the biological and diagnostic systems. Temperature Effect on Molar Extinction Coefficients. As discussed above, PbSe nanocrystals have the potential to be temperature markers as well as other applications. For many of these applications, it is required to know the accurate particle concentration of nanocrystals. The most convenient way to determine the nanocrystal concentration, as demonstrated in literature,7,9,35-38 is to utilize Lambert-Beer’s law A ¼ εCL

ð6Þ

where A is the absorbance at the lowest exciton absorption peak position of the nanocrystal sample, which can be conveniently obtained from the nanocrystal absorption spectrum; ε and C are (33) Gota, C.; Okabe, K.; Funatsu, T.; Harada, Y.; Uchiyama, S. J. Am. Chem. Soc. 2009, 131, 2766. (34) Hinds, S.; Myrskog, S.; Levina, L.; Koleilat, G.; Yang, J.; Kelley, S. O.; Sargent, E. H. J. Am. Chem. Soc. 2007, 129, 7218. (35) Yu, W. W.; Qu, L.; Guo, W.; Peng, X. Chem. Mater. 2003, 2854. (36) Striolo, A.; Ward, J.; Prausnitz, J. M.; Parak, W. J.; Zanchet, D.; Gerion, D.; Milliron, D.; Alivisatos, A. P. J. Phys. Chem. B 2002, 106, 5500. (37) Leatherdale, C. A.; Woo, W. K.; Mikulec, F. V.; Bawendi, M. G. J. Phys. Chem. B 2002, 106, 7619. (38) Cademartiri, L.; Montanari, E.; Calestani, G.; Migliori, A.; Guagliardi, A.; Ozin, G. A. J. Am. Chem. Soc. 2006, 128, 10337.

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the molar extinction coefficient and the particle concentration of the corresponding sample, respectively; and L is the length of the light pathway, which is known from the cuvette used. Thus, if the molar extinction coefficient of a nanocrystal sample is known, its particle concentration can be readily calculated by combining eq 6 and its absorption spectrum. Recently, we have determined the molar extinction coefficient of PbSe nanocrystals,7 where it can be fitted into a power function of the nanocrystal diameter (D, nm), ε ¼ 0:03389D2:53801

ð7Þ

As stated above, once ε is determined, eq 6 can be readily used to calculate nanocrystal concentrations. For the accurate calculation, the absorbance in eq 6 needs to be calibrated through Ac ¼ Am WHWHM =K

ð8Þ

where Ac and Am are the calibrated and measured absorbance, respectively; WHWHM (nm) is the measured half-width-at-halfmaximum (HWHM) value to the long wavelength side of the first absorption peak; and K is an average HWHM, equal to 60 nm. It should be noted that eq 7 was established at room temperature, and it needs to be verified whether it is applicable at a temperature different from room temperature. As shown in Figure 2, when the elevated temperature was applied to PbSe nanocrystals, the measured absorbance Am monotonously decreased. After the calibration via employing eq 8, the calibrated Ac still had a slight decrease with the increase of temperature (Table 1, the third column), resulting in the gradually decreasing molar extinction coefficient of PbSe nanocrystals (Table 1, the fourth column). It should be noted that these extinction coefficients in the fourth column of Table 1 were based on the same particle concentration of 2.52 μM, which was the particle concentration at 25 C without the consideration of volume thermal expansion of solvents. The solvent, tetrachloroethylene, has a volume thermal DOI: 10.1021/la101545w

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expansion coefficient of 0.00102 C-1.39 Upon heating, its volume increases monotonously, and thus the actual particle concentration decreases monotonously at higher temperatures. For example, at 120 C, the actual particle concentration should be (120-25)  0.00102 = 9.69% lower than it was at 25 C. Therefore, after consideration of the volume thermal expansion of the solvent, the actual molar extinction coefficient for 3.9 nm PbSe nanocrystals does not change when the temperature varies (Table 1, the fifth column). Further experimental investigation on the PbSe nanocrystals with other particle sizes also showed that their actual molar extinction coefficients kept unchanged with the variation of temperature.

Conclusions An investigation at elevated temperatures has been performed on the high-quality PbSe nanocrystals, displaying a strong size dependence in their temperature-induced band gap variation. Accordingly, the temperature coefficient (dEg/dT) of PbSe nanocrystals evolves from initially negative values to zero and then to positive values with the increase of nanocrystal sizes. The smallsized PbSe nanocrystals with high temperature sensitivity may be (39) Smallwood, I. M. Solvent Recovery Handbook, 2nd ed.; CRC Press: Boca Raton, FL, 2002; p 201.

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appropriate for temperature markers, especially for in vivo biological applications. In addition, the molar extinction coefficients of any given sized PbSe nanocrystals are the same in the temperature range from 25 to 120 C. Acknowledgment. This work was supported by the Worcester Polytechnic Institute, the National 863 Projects of China (2007AA03Z112, 2007AA06Z112), NSFC (20773043), and the National Basic Research Program of China (2005CB724400 and 2007CB808000). Also, this work is sponsored partially by the Laboratory Directed Research and Development (LDRD) program at the Oak Ridge National Laboratory and the Nanomanufacturing project under the Industrial Technology Program of the U.S. Department of Energy. Supporting Information Available: Figures showing the temperature-induced shifts of the photoluminescence spectra of PbSe nanocrystals, first absorption peak positions versus particle sizes of the PbSe nanocrystals collected from our experiment and the literature, and room-temperature measurements of absorption spectra of the PbSe nanocrystal sample before and after multiple heating/cooling cycles. This material is available free of charge via the Internet at http:// pubs.acs.org.

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