In the Laboratory
Quantum Dots in a Polymer Composite: A Convenient Particle-in-a-Box Laboratory Experiment Charles V. Rice* and Guinevere A. Giffin Department of Chemistry and Biochemistry, The University of Oklahoma, Norman, OK 73019; *
[email protected] Numerous laboratory exercises seek to increase student understanding of quantum mechanics and the interpretation of spectroscopic data. For decades, UV–vis spectroscopy has been used to study organic dyes, whose absorption spectra are directly related to the electron delocalization in conjugated π-bond networks (1, 2). Quantum mechanical calculations employ a 1-D particle-in-a-box model, which can be difficult for students to grasp (2). Semiconductor nanocrystals provide an opportunity to demonstrate quantum mechanics with a 3-D particle-in-a-box model (3, 4). In the classroom, semiconductor nanocrystals provide a mechanism to explain solid-state crystallography, inorganic chemistry, and nanotechnology (4–7). The background material presented in the cited reports is thorough and not repeated here. Building on these efforts, we have developed a quick and safe laboratory experiment that records photoluminescence spectra of semiconductor nanocrystals embedded in a polymer matrix. This experiment provides a fresh alternative to the classical quantum mechanics experiments typically done in a third- or fourth-year physical chemistry laboratory. Imbedding nanocrystals consisting of a CdSe core surrounded by a layer of ZnS in a matrix of polyurethane/acrylic acid provides a durable sample, resistant to surface oxidation. Oxidation of CdSe alters the size of the quantum “box” and leads to sample degradation over time. This core–shell arrangement also reduces surface defects, forming a true nanocrystalline quantum box (8). Such a robust sample is resistant to photobleaching and can be used repeatedly without damage. Previous laboratory exercises to synthesize semiconductor quantum dots require dangerous chemicals, high temperatures, and inert atmospheres (4, 7). The photoluminescence spectrum consists of a single line, whose frequency is directly related to the particle size. A laboratory experiment with analysis of quantum-sized metal sulfide particles by UV–vis spectrophotometry has been previously published in this Journal (4). These types of experiments are awkward, and the absorption spectra have several broad, overlapping lines. Fitting a tangential line near the onset of absorption is required to measure the particle size. Problems mount if the samples decompose from surface oxidation or the student-led synthesis is imperfect. Simplifying the laboratory exercise allows teaching efforts to be expanded to discuss spectroscopy and line broadening mechanisms. The fluorometer used is a low-cost modular setup that provides students with a hands-on experience of spectrophotometer operation. Calculation of particle size is straightforward using the peak maximum, while the line width can be used to illustrate the effect of a particle-size distribution. Even for laboratories without a fluorescence spectrophotometer, the polymer composite sample eliminates sample preparation needed to collect absorption spectra.
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Theory Ultraviolet light promotes electrons from the valence band into the conduction band where they are delocalized in three dimensions. In a bulk semiconductor, the energy levels in the valence and conduction bands are continuous (9). An electron excited into the conduction band results in a hole in the valence band. This electron–hole pair is called an exciton. The electron–hole pair separates to a distance characteristic of the material and is known as the exciton Bohr radius. In CdSe the exciton Bohr radius is 56 Å (10).When the radius of the quantum dot is smaller than the exciton Bohr radius, the energy of the exciton increases because it is confined within the physical dimensions of the quantum dot nanocrystal. The energy of the excited electron is dependent on the size of the quantum dot, where the valence and conduction bands exist as discrete energy levels (9, 10). Charge recombination results in the emission of light via fluorescence. In bulk materials, numerous energy levels are available and subsequent transitions between these states gives rise to a broad emission peak. In quantum dots, only a few states are allowed, thus the energy transitions are discrete and yield a narrower emission peak compared to the bulk material. The quantum dot emission wavelength is directly related to the exciton energy and therefore size of the quantum dot, which can be modeled with a 3-D box. Energy levels of a particle confined a 1-D box are given by En
n2 h 2
8 m r2 where n is the quantum number related to the energy eigenstate, h is Planck’s constant, m is the mass of the particle, and r is the nanoparticle radius. In an orthogonal 3-D system, the energy levels are described by
En
n2 h 2
1 1 1 2 2 2 Lx Ly Lz
8m
(1)
where L x, Ly, and Lz are the dimensions in each direction. A similar expression was developed by Brus to describe the discrete energy levels that exist due to confinement within a spherical nanocrystal, the quantum dot (10).The energy of the first excited state is
E
h2 8r
2
1 1 me mh
(2)
The effective electron mass within the exciton is me*. For CdSe, me* = 0.13me where me is the electron mass in kg. The effective mass of the hole in the exciton is given by mh*, which is 0.45me (10). The effective masses are only a fraction of the mass of an
Journal of Chemical Education • Vol. 85 No. 6 June 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
In the Laboratory gated spectrofluorometer
electron because the Coulombic attraction between the hole and the electron is screened (11). The emission wavelength from the semiconductor nanocrystal can then be related to the particle size using
h 2
%E r E gap hO
8 r2
1
me
1
mh
cuvette holder LED source
(3)
hc M
which adds the band gap energy of the bulk semiconductor, Egap, to the quantum confinement term. ΔE(r) is the fluorescence emission peak energy in Joules and Egap for CdSe = 1.74 eV.
samples
Figure 1. Ocean Optics modular spectrophotometer.
Experimental
Hazards The matrix of polyurethane/acrylic acid removes many hazards associated with the handling of semiconductor nanocrystals. Evident Technologies provides small vials filled with CdSe in the matrix, eliminating any danger posed by in-house synthetic procedures. Although the light source is low power, appropriate eyewear should be used at all times, and the light source turned off when moving the fiber-optic cables.
red–orange Mmax = 617.8 nm
250
200
Intensity
Seven samples of CdSe/ZnS nanocrystals dispersed in a composite of polyurethane/acrylic acid, each containing different sized crystals, were used as received from Evident Technologies (Troy, NY). The nanocrystal concentration was < 3%. A sample of polymer composite without nanocrystals was used to obtain a background spectrum. Fluorescence spectra were taken using a modular spectrophotometer (USB 2000 FLG, Ocean Optics Inc., FL), as shown in Figure 1. The setup consisted of a gated spectrofluorometer (350–1000 nm), a 380 nm LED excitation light source (45 mW output), two fiber-optic cables, and a cuvette holder with four optical windows. The optical cables were positioned at a 90° angle on the cuvette holder. Each spectrum was collected in a few seconds. The peak maximum and line width were determined using the Ocean Optics software (OOIBase32).
green #1 Mmax = 524.0 nm
150
100
50
FWHM = 30.3 nm
FWHM = 35.5 nm
0 400
450
500
550
600
650
700
Wavelength / nm Figure 2. Photoluminescence spectrum of two core–shell CdSe/ ZnS quantum dots. The nanocrystals are embedded in a matrix of polyurethane/acrylic acid. Peak maximum and line width are determined by the Ocean Optics software.
Table 1. Peak Frequency and Line Width Data for CdSe Quantum Dot Samples
Results
Color
λ/(nm)
FWHM/(nm)
Diameter/(Å)
The peak frequency and full-width at half-maximum (FWHM) are easily determined from the photoluminescence spectrum (Figure 2). The CdSe quantum dot radius was calculated using eq 3, and the results for the samples, each containing different sized quantum particles, are presented in Table 1. Over 80 students, in 7 lab sections, have performed this laboratory exercise over 4 semesters. The student data gave diameters that are within 5% of those provided by the manufacturer, Evident Technologies, Inc. The diameters given by Evident Technologies were estimates based on sizing curves generated from TEM measurements and the first absorption maximum of CdSe nanocrystals by Yu, Qu, Guo, and Peng (12). Many students noted that the concepts of quantum mechanics are quite abstract,
Blue
488.0
37.5
43
Green #1
524.0
35.5
48
Green #2
549.0
34.7
53
Yellow
565.9
32.0
57
Orange #1
586.5
31.2
63
Orange #2
600.8
30.8
67
Red–orange
617.8
30.3
74
Note: Dot samples were excited with the same wavelength. Data were calculated using eq 3.
© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 6 June 2008 • Journal of Chemical Education
843
In the Laboratory
particularly a 1-D box and the differences between adsorption and emission of energy. Students also struggle to grasp the meaning of line width and its relationship to the chemical system under investigation. The transition between two energy levels should, in theory, be a very narrow delta function with infinitesimal line width. The quantum dot/polymer composite samples studied have minimal line broadening from rotational or vibrational perturbations (10). The observed line width arises from the effects of inhomogeneity, mainly a distribution of particle sizes. Students tend to overlook the distribution of particle sizes within the quantum dot samples and therefore struggle to explain the line width. Using 3-D quantum dots, particularly those with current technological relevance, we have been able to clarify these concepts. Acknowledgment This work is supported by The University of Oklahoma and a CAREER Award from the National Science Foundation (CHE-0449622). Literature Cited 1. Soltzberg, L. J. J. Chem. Educ. 2001, 78, 1432–1432. 2. Anderson, B. D. J. Chem. Educ. 1997, 74, 985–985. 3. Lynch, W. E.; Nivens, D. A.; Helmly, B. C.; Richardson, M.; Williams, R. R. Chem. Educ. 2004, 9, 159–162.
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4. Nedeljkovic, J. M.; Patel, R. C.; Kaufman, P.; Joycepruden, C.; Oleary, N. J. Chem. Educ. 1993, 70, 342–344. 5. Kippeny, T.; Swafford, L. A.; Rosenthal, S. J. J. Chem. Educ. 2002, 79, 1094–1100. 6. Lagally, M. G. J. Chem. Educ. 1998, 75, 277–279. 7. Lasher, D. P.; DeGraff, B. A.; Augustine, B. H. J. Chem. Educ. 2000, 77, 1201–1203. 8. Reiss, P.; Bleuse, J.; Pron, A. Nano. Lett. 2002, 2, 781–784. 9. Klimov, V. I. J. Phys. Chem. B. 2006, 110, 16827–16845. 10. Nirmal, M.; Brus, L. Acc. Chem. Res. 1999, 32, 407–414. 11. Brus, L. E. J. Chem. Phys. 1984, 80, 4403–4409. 12. Yu, W. W.; Qu, L. H.; Guo, W. Z.; Peng, X. G. Chem. Mater. 2003, 15, 2854–2860.
Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Jun/abs842.html Abstract and keywords Full text (PDF)
Links to cited JCE articles
Color figures
Supplement
Student handouts
Instructor notes
Journal of Chemical Education • Vol. 85 No. 6 June 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
