In the Laboratory
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Quantum Dots: An Experiment for Physical or Materials Chemistry L. D. Winkler, J. F. Arceo, W. C. Hughes,* B. A. DeGraff,** and B. H. Augustine*** Departments of Chemistry and Physics, James Madison University, Harrisonburg, VA 22807; *
[email protected], **
[email protected], ***
[email protected] The Experiment
Synthesis The core experiment consists of synthesizing nanoparticulate CdS (quantum dots) and largely-colloidal (bulk) CdS, both in fluid solution using a similar set of conditions. Aliquots of Cd(NO3)2 and Na2S in water兾methanol are added to a rapidly stirred methanol solution of an ethylenimine polymer that acts to terminate aggregation of the incipient CdS. These polymers are available in several molecular weights (MW) and in both branched and linear configura1700
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tions. The average CdS particle size and distribution of sizes depends on the characteristics of the polymer used. The experiment can be carried out in air at room temperature, although slightly better results are obtained at 10 ⬚C. The preparations can be completed in under an hour. Students can see that a luminescent material is present by simply shining a standard 366-nm black light on the reaction flask at the end of the preparation. Use of a high-MW, branched polymer produces polydisperse nanoparticles of CdS with typical radii in the 3–4 nm range. Using the same polymer, but a different addition sequence, largely-colloidal CdS can be produced for comparison. Black light illumination shows a clear emission color difference between the two preparations.
Characterization The preparations are then characterized by their UV– vis absorption and emission spectra. The absorption spectra exhibit two strong bands in the near- and deep-UV regions, respectively. The near-UV band is between 320–370 nm and can show some structure. The near-UV band’s position and shape depends on the preparation, with nanoparticulate CdS showing a blue shift compared to the more colloidal CdS (Figure 1). The emission spectra resemble skewed Gaussian functions with λ max dependent on the preparation. The nanoparticulate CdS has a λmax near 460–470 nm, while the colloidal material’s λmax is about 545–555 nm. The preparations are allowed to stand overnight. The emission spectra are retaken and overlaid on the spectra taken immediately after synthesis. Several interesting changes have occurred in both the materials. The emission λmax shows a modest blue shift on standing (∼30 nm for both preparations), the overall emission intensity increases (∼30%), and the distribution
1.2
Normalized Absorption / Emission
Semiconductor quantum dots are nanometer-scale aggregates and can exhibit luminescence. They have several interesting properties that have led to diverse applications ranging from labeling biomolecules (1, 2) to harvesting solar energy (3). Their unique photophysical properties derive from quantum confinement of the charge carriers and serve as an excellent solid-state illustration of the classical particle-in-abox concept that is basic to both physical and materials chemistry. The synthesis and characterization of CdS quantum dots can introduce and dramatically illustrate a number of concepts and techniques. This laboratory is suitable for students in either physical or materials chemistry courses and because it involves brightly colored luminescence often generates considerable interest and enthusiasm. Quantum dots can be obtained in a variety of colors, coatings, and functional-group “handles”; a selection of dots with various features is available commercially (4). The basic concepts behind the technology have been reviewed at a number of levels (5–7). A Google search of “quantum dots” will generate over 250,000 hits. Despite the mature nature of some aspects of quantum dots, it is still an active field of research where new materials and more detailed understanding are vigorously pursued (8). While a wide variety of dots have been reported, we will focus on semiconductor dots with binary composition suspended in solution. Broadly viewed, the basic synthetic approach is to combine the two dot components in a solvent in which the product material has limited solubility. The incipient product is allowed limited aggregation before being sequestered with a suitable passivating coating, usually some type of polymer. Constraining the aggregation number and ensuring a relatively narrow distribution of particle sizes have proved to be major synthetic challenges. Unfortunately, the more elegant syntheses that give tight control over both particle size and distribution require conditions that are less suitable for an undergraduate audience (9). This experiment is adapted from a reported synthesis that uses simple, inexpensive, and userfriendly materials and techniques (10). Indeed, this synthesis, which can be completed in a half an hour using simple equipment and inexpensive chemicals, is very robust.
1.0 0.8 0.6 0.4 0.2 0 300
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Wavelength / nm Figure 1. Normalized absorption and emission spectra for nanoparticulate CdS (-----) and colloidal CdS(- - -).
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In the Laboratory
narrows for the nanoparticulate CdS as shown by loss of intensity in the longer wavelength region. The effects of aging can be a point of departure for more detailed discussions. This phenomenon is rather common (10) and is attributed to the removal or termination of dangling bonds at the surface of the particle. These dangling bonds result in traps that allow nonradiative decay of the excited state and their termination enhances the emissive decay path. The mechanism of termination is not completely understood. Hazards Methanol, Cd(NO3)2⭈4H2O, and Na2S⭈9H2O are all toxic so good practice requires use of suitable gloves for all manipulations. The ethylenimine polymer is an irritant. Methanol solutions, even at 10 ⬚C, should be handled in a hood. Proper disposal of reaction products and excess reagents is essential. Discussion The emission energy taken at λmax for the nanoparticulate CdS can be thought of as composed of the band-gap energy, Ebg, and the quantum-confinement energy, ∆Eqc, which is the energy increment due to confinement of the charge carriers in a smaller “box”. When the CdS particle absorbs a photon, an electron–hole pair is created. The electron rapidly loses any excess energy to the lattice and resides at the lowest energy state of the conduction band. If the particle is large (i.e., greater than 10 nm) the electron–hole recombination can result in emission of a photon with energy corresponding to the band gap of CdS. In practice the particles are not perfect so that defects and impurities alter the emission energy and a spread of photon energies is observed, usually centered around the band-gap energy. When the particles are small, less than 10 nm, quantum mechanics predicts a shift in the energy levels owing to the confinement of the electron–hole pair. This energy shift, ∆Eqc, increases with decreasing particle size. Because this preparation results in a variety of particle sizes, ∆Eqc has a range of values. For convenience we select the most probable value of ∆Eqc , which corresponds to λmax in the emission spectrum. Thus
E photon =
hc λ max
= E bg + ∆Eqc
(1)
The Ebg for bulk CdS at room temperature is ∼2.42 eV = 3.85 × 10᎑19 J (11). For a typical λmax = 465 nm, ∆Eqc ∼ 4.25 × 10᎑20 J, which is the additional energy resulting from quantum confinement and can be related to the most probable particle radius through the expression (12) ∆Eqc =
h2 8R
2
1 1 + me* m h*
(2)
where R is the particle radius, me* is the effective mass of the electron, and mh* is the effective mass of the hole. These have values of 0.19 me and 0.80 me respectively, where me is the rest mass of the electron. The use of effective masses is necessary owing to the different behavior of electrons in the solid state versus discrete molecules (holes have no real counterwww.JCE.DivCHED.org
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part in discrete molecules). In short, effective masses are a function of the curvature of the energy bands in the solid state. A good discussion of the physical and mathematical origins of effective masses can be found in Hummel (13). Here we have simplified eq 2 by ignoring the electron–hole correlation effects. A discussion of the approximations used to obtain eq 2 and their limitations is available (14). With λmax = 465 nm, ∆Eqc ∼ 4.25 × 10᎑20 J, eq 2 will yield R ∼ 3.04 nm. This is an approximate value since the spread of emission wavelengths is large. However, even cursory comparison with the largely-colloidal CdS with λmax ∼ 530 nm clearly shows a shift to higher transition energy with smaller particle size. It is quite instructive for the student to construct a plot of λmax versus Rparticle, a task easily done with a mathematical-modeling program such as Mathcad. From this plot it is easily seen that when the average particle radius exceeds 10 nm, the effects of quantum confinement are minimal. Students should note the similarity of eq 2 to the Schrödinger expression for a particle-in-a-box modified for a spherical container. The mechanism for the production of emission in both the nanoparticulate and the bulk CdS material is electron– hole recombination. In the bulk solid state, this electron– hole pair is called an exciton that can be modeled approximately as a hydrogen atom where the hole serves as the nucleus. As with eq 2, effective masses must be used, but one can calculate a radius of separation, aB (Bohr radius), using 2
aB =
h ε 1 1 + m h* π e 2 me*
(3)
where ε = εCdSε0 is the dielectric constant and e is the charge on the electron. me* and mh* have the same meaning as eq 2. Using a value of 5.7 for εCdS at optical frequencies (12a), we predict ∼2.0-nm radius of separation for the exciton pair. This compares favorably with our particle radius of 3.04 nm. As the particle size approaches the exciton separation, the charges are confined to the particle’s surface and quantum confinement becomes a major effect as the charge carriers can not be swept away but can “classically” orbit. It is also useful for students to estimate how many CdS molecules are in the average aggregate. Using ionic radii found in widely-available sources (e.g., Handbook of Chemistry and Physics) and a simple packing model, we estimate that for a ∼3-nm radius particle there are about 1200 CdS molecules per particle, depending on the packing model. The polydisperse nature of this preparation can be vividly illustrated by comparison to the commercial products such as CdSe dots. The emission spectrum for these commercial quantum dots shows a full-width at half maximum of about 30 nm while the same measure for this preparation is ∼125 nm. Despite the smaller intrinsic band gap of CdSe, these dots are more widely used and more readily available at reasonable cost (4). CdSe dots are available in colors ranging from deep red to blue–green with narrow dispersion due to tight aggregation control using a more sophisticated synthetic technique. The polymer-passivation technique used in this experiment is much less efficient than that used in ref 9, but this experiment uses much less hazardous conditions and reagents.
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Additional Experiments
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There are a number of modifications and extensions that can be considered. Water can be used as the only solvent, but the emission intensity drops and the average particle size increases. A better substitution is 95% ethanol, which gives particles only slightly less emissive and larger than methanol. There are four different polyethylenimines available from Aldrich. Each gives a slightly different dominant particle size and distribution. The particle suspensions are stable in air at room temperature for several days. Our attempts to narrow the distribution of particle sizes by ultra-centrifugation were inconclusive and this could be further pursued. As noted by others (15), the suspensions of nanoparticles scatter visible light. This can easily be seen by eye with a 10-mW DPSS Nd兾YAG laser at 532 nm (while any laser will do, the eye is most sensitive to green light). Unfortunately, the higher-MW passivating polymers also scatter light, so the interpretation of this experiment is not crisp. Finally, it is possible to make cast luminescent thin films of the nanoparticles in suitable polymer hosts such as polyvinylalcohol or a sol-gel glass. These films are stable in air for at least a week.
Instructions for the student laboratory writeup, notes for the instructor, suggestions for supplemental work, and a Mathcad template are available in this issue of JCE Online.
Conclusion This experiment has been used successfully for three years in a senior physical chemistry laboratory. It follows the traditional particle-in-a-box cyanine dye experiment and serves to both reinforce the basic concept of quantum confinement as well as providing a useful bridge between the molecular and solid-state world. Acknowledgments The authors gratefully acknowledge the support of the National Science Foundation (Grants DMR-0071717, DMR-0097449, CHE-97-26999 ). Additionally, the good humor of three classes of Chem. 438L is appreciated.
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Supplemental Material
Literature Cited 1. Henry, C. Chem. Eng. News 2003, June 9, 10. 2. Bruchez, M., Jr.; Moronne, M.; Gin, P.; Weiss, S.; Alivisatos, A. P. Science 1998, 281, 2013–2019. 3. Hanson, T. Squeezing More Juice Out of Solar Pannels. http:/ /www.lanl.gov/worldview/news/releases/archive/04-040.shtml (accessed Jul 2005). 4. Nano Materials. http://www.evidenttech.com/products/quantumdot-nanomaterials.php (accessed Jul 2005). 5. Murphy, C. J.; Coeffer, J. L. Appl. Spectroscopy 2002, 56, 16A– 26A. 6. Gammon, D.; Steel, D. G. Physics Today 2002, 36–41. 7. Bimburg, D.; Grundmann, M.; Ledentsov, N. N. Quantum Dot Heterostructures; Wiley: Chichester, UK, 1999. 8. van Stark, W. G. J. H. M; Frederix, P. L. T. M.; van den Heuvel, D. J.; Bol, A. A.; van Lingen, J. N.; de Mello Donega, C.; Gerritsen, H. C.; Meijerink, A. J. Fluorescence 2002, 12, 69–76. 9. Kippeny, T.; Swafford, L. A.; Rosenthal, S. J. J. Chem. Educ. 2002, 79, 1094–1100. 10. Huang, J.; Sookal, K.; Murphy, C. J.; Ploehn, H. J. Chem. Mater. 1999, 11, 3595–3602. 11. CRC Handbook of Chemisty and Physics, 71st ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1991. 12. (a) Brus, L. E. J. Chem. Phys. 1983, 79, 5566–5571. (b) Brus, L. E. J. Chem. Phys. 1984, 80, 4403–4409. 13. Hummel, R. E. Electronic Properties of Materials, 3rd ed.; Springer Verlag: New York, 2001; pp 70–73. 14. Steigerwald, M. L.; Brus, L. E. Acctn. Chem. Res. 1990, 23, 183– 188. Wang, Y.; Herron, N. J. Phys. Chem. 1991, 95, 525–532. 15. Sooklal, K.; Hanus, L. H.; Ploehn, H. J.; Murphy, C. J. Adv. Mater. 1998, 10, 183–188.
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