Spectroscopic and Physical Characterization of Functionalized Au

Sep 19, 2014 - Nanoparticles: A Multiweek Experimental Project ... notions of nanotechnology to chemistry students at the graduate level (M.Sc. and. P...
0 downloads 0 Views 3MB Size
Article pubs.acs.org/jchemeduc

Spectroscopic and Physical Characterization of Functionalized Au Nanoparticles: A Multiweek Experimental Project Jean-Francois Masson* and Hélène Yockell-Lelièvre Department of Chemistry, Université de Montréal, Montreal, Quebec H3C 3J7, Canada S Supporting Information *

ABSTRACT: A term project was introduced in teaching advanced spectroscopy and notions of nanotechnology to chemistry students at the graduate level (M.Sc. and Ph.D.). This project could also be suited for an honor’s thesis at the undergraduate level. Students were assigned a unique combination of nanoparticle synthesis (13 nm Au nanospheres, ∼100 nm nanoraspberries or ∼50 nm nanostars) and fluorescent/ Raman-active ligand (HS-PEG-FITC, rhodamine 6G, 4-mercaptobenzoic acid, 4nitrobenzenethiol, and phenanthroline). Characterization with transmission electron microscopy allowed the students to confirm the shape and size distribution of nanoparticles. The ligands immobilized on the surface of the nanoparticles were extensively characterized using a suite of optical techniques. UV−vis was used to observe the plasmonic bands of particles of varying shapes, and fluorescent spectroscopy was used to construct fluorescent pathways with the aid of Jablonski diagrams. The vibrational bands of the ligands were identified using IR and Raman spectroscopy. Performing surface-enhanced Raman spectroscopy (SERS) on the nanoparticle at different excitation wavelength (488, 633, and 785 nm) was used to understand the influence of the surface plasmon on SERS and fluorescence spectroscopies. Students were required to write a full scientific paper for the report of the term project. KEYWORDS: Upper-Division Undergraduate, Graduate Education/Research, Analytical Chemistry, Physical Chemistry, Hands-On Learning/Manipulatives, Problem Solving/Decision Making, Nanotechnology, Raman Spectroscopy, Spectroscopy, UV-Vis Spectroscopy



have been reported despite their numerous advantages.16−21 The series of experiments proposed here aim to strengthen the notions relating to the optical properties of metallic nanoparticles and to teach their synthesis and handling. The characterization of different ligand/nanoparticle couples by each student allowed for autonomy in the laboratory and strengthened spectroscopic data acquisition and interpretation skills. Additionally, submission of the final report helped to demonstrate the notion of scientific writing. The laboratories were implemented in our Advanced Analytical Spectroscopy class at the graduate level. Laboratories were performed the week following a 3 h lecture about a spectroscopic technique (synthesis and properties of nanoparticles, Microscopy, infrared, Raman, fluorescence). Aside from the first laboratory that was performed on consecutive days (total of less than 5 h), all other experiments were completed in a series of 3 h laboratories. Each student was assigned a unique combination of particle and ligand to promote autonomy in the laboratory. In addition, the experiments were assigned in a matrix format (i.e., 15 students = 3 types of nanoparticles × 5 ligands), which favored collaboration between students sharing either the ligand or

INTRODUCTION Research on metallic nanoparticles (NP) and nanostructures has impacted many fields of modern science. Applications of NP encompass colloidal science,1 bioanalytical technologies,2 biosensing,3 nanofabrication in 1 or 2 dimensions4−6 and study of advanced spectroscopy concepts.7 Among the interesting applications, we point out DNA analysis,2−8 sensors for various biomolecules,3−8 cancer therapy,9,10 and anticounterfeiting tags.11 Scholarly articles have now numbered in the thousands per year and it has become one of the main fields of research in science. The properties of matter are strongly influenced by the shape and size. While bulk metals are relatively inert, striking phenomenon occurs in particles of 100 nm or less. Among them, surface-enhancement of Raman scattering (SERS),12 quenching of fluorescence of metal-bound fluorophores,13 local heating14 and strong coloration due to the shape and size of the NP15 are some of the various physical effects commonly observed with nanoparticles. The importance of these phenomena in the various fields of chemical sciences makes it important to include theoretical notions in the curriculum of upper-division undergraduate students and graduate students. While classical lectures on the optical properties of metallic nanoparticles have been increasingly added to curriculums, only a few laboratory experiments based on metallic nanoparticles © 2014 American Chemical Society and Division of Chemical Education, Inc.

Published: September 19, 2014 1557

dx.doi.org/10.1021/ed500067u | J. Chem. Educ. 2014, 91, 1557−1562

Journal of Chemical Education

Article

nanoparticle. A full scientific paper was requested for the report in order to improve writing skills of students. As a large size and research-oriented University, we have access to a large range of analytical techniques to characterize nanoparticles: Advanced surface interrogation (UV−vis, Raman, XPS, infrared, fluorescence, light scattering, among others) or high-resolution imaging techniques (electron microscopyTEM, SEMor dark-field microscopy). The selection of techniques depends on the instrumentation available at hand. For example, characterization can be undertaken with simple laboratory equipment, such as UV− vis, standard spectrofluorimeters and infrared spectroscopy, which is typically available in all teaching laboratories. In this paper, we have targeted UV−vis spectroscopy, infrared, Raman, fluorescence and transmission electron microscopy (TEM), which are available in our institution and corresponded to the skills we intended to strengthen in our analytical and physical chemistry curriculum.

■ ■

Figure 1. UV−vis spectra of nanospheres (blue), nanostars (red), and nanoraspberries (black) as synthesized, before functionalization with the ligand. The concentration and extinction coefficient of the different nanoparticles were extracted from the UV−vis and TEM images.

the concentration (a factor of 5 concentration and 5 fractions was sufficient). The sample was then sonicated to resuspend the nanoparticles in the same volume and centrifuged again. The ligand assigned to the student was then added to the nanoparticle suspension. Solutions of Rhodamine 6G and 4MBA were prepared at 100 mM in water and ethanol, respectively, PEG-FTIC was dissolved to obtain a final concentration of 1−2 mg/mL, and these solutions were added at 1% (v/v) to the nanoparticle suspensions and reacted overnight to form a layer on the nanoparticle. Solutions of 4NBT and phenanthroline were prepared at 10 mM in dichloromethane and the nanoparticles were reacted by vigorously shaking 1:1 volumes of the ligand solution and nanoparticle suspensions for 15 min. The reacted phenanthroline nanoparticles were collected at the interface by careful pipetting. The nanoparticles modified with 4-NBT and phenanthroline were resuspended in ethanol. The nanoparticles were washed once again three times by repeating the centrifuge and wash cycles. Another UV−vis spectrum was acquired with the same spectral range. Writing Prompt: • Discuss the color changes observed during the synthesis with the mechanism of formation of the nanoparticles. • Note and explain the changes in the shape and intensity of the UV−vis spectrum of the functionalized AuNP. • Correlate the number of plasmonic bands with the shape of the nanoparticles. • Why does the same reagents lead to nanostars or nanoraspberries depending on the stoichiometry?

MATERIALS Detailed lists of materials required for each experiment are provided in the Supporting Information. EXPERIMENTAL DETAILS

Week 1: Nanoparticle Synthesis

Preliminary Step: Detailed protocols are provided in Supporting Information. All glassware to be used was cleaned in aqua regia. The glassware was rinsed multiple times with ultrapure water to wash off any trace of aqua regia. Caution! Aqua regia is highly corrosive and protective gear must be worn. During nanoparticle synthesis, please observe and note color changes. Nanosphere: In an Erlenmeyer flask or a reflux setup if available, 50 mL of ultrapure water and 0.700 mL of 17 mM sodium citrate were brought to a boil while stirring. When boiling, 0.100 mL of a 250 mM solution of chloroauric acid trihydrate was added. Heating and stirring were maintained until the solution turned red. The nanoparticle suspension was then removed from the heating plate and was let to cool to room temperature. If needed, water was added to maintain the volume constant when using an Erlenmeyer flask. Nanostar: To 100 mL of ultrapure water was added 0.100 mL of chloroauric acid trihydrate. The solution was stirred at room temperature for 1 min. Then, 40 mL of 100 mM HEPES solution was added while stirring. When mixing was completed after a few seconds, stirring was stopped and the reaction was leaved to proceed overnight. Nanoraspberry: To 100 mL of ultrapure water was added 0.100 mL of chloroauric acid trihydrate. The solution was stirred at room temperature for 1 min. Then, 6.25 mL of 100 mM HEPES solution was added while stirring. Stirring was maintained for the reaction to proceed overnight. Common Procedure for All Nanoparticle: UV−vis spectrum was acquired following the synthesis of the nanoparticle suspension between 300 and 850 nm (Figure 1). Nanoparticles were then recovered by centrifugating at 14 000 rpm for 15 min for nanospheres or 10 min for nanostars or nanoraspberries and washed with water three times. To wash the nanoparticles, the supernatant was gently pipetted and the same volume of water was added. Smaller concentration of nanostars was collected; thus, they were resuspended in a smaller volume and several fractions were combined to increase

Side Project

A UV−vis spectrum was acquired each week and the changes were noted to the shape and intensity of the peak(s). Important! All dilution or concentration factors were tracked throughout the experiments. Volumes were accurately pipetted at all times. Solutions were stored in the refrigerator at all times. Week 2: Transmission Electron Microscopy

A drop of nanoparticle suspension was deposited on a TEM grid coated with a Formvar film. Careful when handling the TEM grid, they are fragile! The TEM grid was held with tweezers when the solution was pipetted. The grid may flip upside down otherwise. The nanoparticle suspension was let to dry overnight and the TEM grid was placed in a storage box dedicated to TEM grids. The position of the TEM grid in the 1558

dx.doi.org/10.1021/ed500067u | J. Chem. Educ. 2014, 91, 1557−1562

Journal of Chemical Education

Article

Figure 2. TEM images for the different types of nanoparticles: (left) nanospheres, (center) nanoraspberries, (right) nanostars. The scale bar is 20 nm for each image.

Figure 3. Raman spectra of AuNP with 4-nitrobenzenethiol (4-NBT). Different lasers show fluorescence quenching (488 nm−left) or SERS (633 nm, center; 785 nm, right). See the Supporting Information Figure SI1 for the other Raman spectra.

Figure 4. (Left) Infrared spectra acquired in ATR of a standard of 4-NBT (black) and on nanoparticles (red). Good agreement was observed between the IR spectra on the nanoparticles and for the standards. (Right) Infrared spectra of the reducing agents and of the capping molecule during the synthesis of the nanoparticle. The presence or absence of the vibrational bands of these reagents shows the extent of reaction of the functionalization reaction. See the Supporting Information Figure SI2 for the other IR spectra.

Week 3: Raman Spectroscopy

box was noted. A trained professional did the TEM measurements. Images were acquired at different locations and at different magnifications. Images were acquired with large areas and others images were zoomed on single (or a small cluster of) nanoparticles to observe the shape and size distribution (Figure 2). Writing Prompt:

A volume of 100 μL of AuNP solution was deposited on a goldcoated glass slide (a standard uncoated glass slide also works). The drop was dried with a jet of N2 to concentrate the drop in a small area of the surface. The procedure was repeated with 100 μL of the standard solution of the ligand. When dried, the areas of the surfaces where the drop had dried were measured with a Vernier caliper. The number of AuNP and ligands contained per unit area was estimated. The Raman spectra of the standard and of the AuNP were measured between 500 and 3200 cm−1 with several lasers (Figure 3): for example, one can use 488, 633, and 785 nm. The integration time and laser power were adjusted to have excellent signal-to-noise ratio. Writing Prompt:

• Calculate the average diameter of the nanoparticles ImageJ was employed to analyze TEM data (http:// rsbweb.nih.gov/ij/). • Construct a size distribution histogram. • Calculate the concentration of AuNP in the solution. • Determine the extinction coefficient of the AuNP. 1559

dx.doi.org/10.1021/ed500067u | J. Chem. Educ. 2014, 91, 1557−1562

Journal of Chemical Education

Article

Figure 5. (Left) Excitation−emission matrix (EEM) spectra of 4-nitrobenzenethiol. The intensity was plotted in natural logarithm scale to clearly show the regions of fluorescence due to 4-NBT. Diagonal lines are due to incomplete filtering of different orders of Rayleigh scattering. (Right) Reconstruction of the Jablonski diagram of 4-NBT with the EEM spectra. See the Supporting Information Figure SI3 for the other 3D fluorescence spectra.

Figure 6. (Left) Excitation and (right) emission spectra of 4-nitrobenzenethiol for a standard solution (black) and 4-NBT immobilized on AuNP (red). The excitation spectra were collected at 388 nm emission wavelength, and the emission spectra were collected at 240 nm excitation, which are the wavelengths of highest intensity. See the Supporting Information Figure SI4 for the other fluorescence excitation and emission spectra.

• Explain the differences in the Raman spectra with different lasers. • What optical phenomenon is observed with the 488 nm laser? • Calculate the area density of the ligand on the AuNP and on the surface of the standard. • Determine the amplification factor of the ligand on the nanoparticle.

Week 5: Fluorescence Spectroscopy

A 1 mM standard solution of the ligand was prepared in water (Rh6G, PEG-FITC, and 4-MBA) or ethanol (phenanthroline and 4-NBT). For highly fluorescent molecules such as rhodamine 6G or FITC, the solution was further diluted by 100-fold to 10 μM. The solutions were filtered through a 0.45 μm filter to minimize diffusion from large particles in suspension. An UV−vis spectrum was measured to determine the concentration of nanoparticles in solution. An excitation− emission matrix spectrum of the standard solution of the ligand was acquired between 200 and 500 nm excitation wavelength and 240 and 600 nm emission wavelength (Figure 5). Please note that you will see Rayleigh scattering! The optimal excitation and emission wavelength were determined for your ligand. Then, an emission spectrum was acquired at the optimal excitation wavelength and an excitation spectrum was also acquired at the optimal emission wavelength for the standard solution and for the nanoparticle suspension (Figure 6). Writing Prompt: • Construct the Jablonski diagram for the ligand. • Identify excitation−emission pathways. • Plot the diagram to scale using eV energy scale in the yaxis. • Calculate the concentration of ligands assuming a full coverage of the ligand on the nanoparticle (or the coverage determined by the vibrational spectroscopy experiments). • Estimate the quenching factor of the AuNP on the fluorescence of the ligand.

Week 4: Infrared Spectroscopy

With the use of the same gold-coated slides as prepared for the Raman spectroscopy experiment, the IR spectra of the standard and the AuNP were measured between 500 and 4000 cm−1 using an ATR configuration or a diffused reflectance instrument (Figure 4). The resolution was set at 4 cm−1. The IR spectra of the reactants (HEPES and sodium citrate) were also measured. The number of scans was adjusted to achieve a suitable signalto-noise ratio. The gold-coated slides were more efficient due to the minimization of the IR absorption of glass. Writing Prompt: • Compare the IR spectra (both the standards and the ligand on the AuNP) with the Raman spectra. • Why are some vibrations activated in Raman and/or in infrared? • Using standard tables or references, identify the vibrations activated with each vibrational spectroscopy technique. • Estimate the presence of starting materials and the extent of the ligand exchange reaction on the AuNP. 1560

dx.doi.org/10.1021/ed500067u | J. Chem. Educ. 2014, 91, 1557−1562

Journal of Chemical Education



Article

HAZARDS Aqua regia is highly corrosive. Personal protective gear for handling acid solution should be worn: eye protection and face shield, lab coat plus acid apron and acid resistant gloves. A laboratory assistant can do this procedure prior to the laboratory. AuNP are currently considered safe to handle. However, students must be aware that it is not the case of all nanoparticles. Lasers are handled during Raman spectroscopy measurements. Protective glasses are to be worn if the laser has an open path.

nanoparticles can be estimated from the area of the ligand and the area of the nanoparticle knowing the diameter from TEM. The students are asked to either find in the literature the area occupied on the nanoparticle by their ligand or estimate it from logical assumptions. The concentration of nanoparticles is known from UV−vis (see above). For fluorescence, the concentration of ligand in solution for the nanoparticle suspension is equal to the product of the number of ligand per nanoparticles and the concentration of nanoparticle in solution. For SERS, N is equal to the number of nanoparticles multiplied by the number of ligand on each NP or the number of ligand in the volume pipetted on the glass slide. These assumptions provide a good relative measurement of the QF or EF.



STUDENTS RESULTS Students obtained all results presented above. At the end of the semester, a discussion was organized to compile the results and produce comparative tables for different aspects of the project. For example, tables of the LSPR resonance wavelength and AuNP size are suggested. The students can then clearly observe the reproducibility of their work and the effect of the different AuNP and ligand on the results obtained by themselves and others.



DISCUSSION Fifteen graduate students successfully completed the project. The goals were to strengthen notions taught in classroom, provide hands-on experience with analytical tools, improve autonomy in research and assess the ability to interpret data. Thus, the students were given just enough information to be able to carry the experiments and were left to search literature to extract information and interpret data to answer the questions enumerated above. The students were asked to make reasonable assumptions and estimates in the calculations. Their ability to do so was assessed in the logical argumentation in the final report. Students learned to collaborate in a research project by creating a network of consultation between them due to interconnected experiments. Lastly, they were asked to submit a full paper at the end of the semester using a journal template, which had them learn (and struggle!) with editing a manuscript. This will be highly beneficial for their future research papers. For upper-division graduate students, the guidance can be increased by providing further information and discussing the assumptions that are logical with the students.

Concentration and Extinction Coefficient of the AuNP

Calculating the concentration of nanoparticles relies on the assumption that the reaction proceeds with 100% yield and that there is no loss of AuNP on the walls of the container. The nanoparticle diameter is approximated as spheres for nanoraspberries and nanostars. If other nanoparticle shapes such as cubes or rods are employed, the volume of a cube or of a cylinder can estimate the actual volume of the nanostructure. The factor π/6 D3 must be replaced in eq 1 by the appropriate volume formula for the shape employed. Using the calculations proposed by Liu et al.,22 one obtains the concentration of AuNP and extinction coefficient with eqs 1−3: N=

π ρD 3 6 M

(1)

C=

Ntotal NVNA

(2)

A = εbC



ASSOCIATED CONTENT

S Supporting Information *

(3)

where N is the number of Au atoms per NP, ρ is the density of Au (19.3 g/cm3), D is the diameter of the NP calculated by TEM, M is the atomic weight of Au (196.967 g/mol), Ntotal is the number of Au atom available in the reaction vessel, V is the reaction volume, b is the optical path, C is the concentration, A is the absorbance, and ε is the extinction coefficient.

Experimental details; complete set of IR, SERS, and fluorescence spectra. This material is available via the Internet at http://pubs.acs.org.

Quenching (Fluorescence) or Enhancement (SERS) Factor

*E-mail: [email protected].



Corresponding Author

The quenching (QF) or enhancement factor (EF) can be estimated by calculating the number of molecules excited in the laser beam of the standard solution and for the nanoparticles. QF =

EF =

INP Nligand Iligand NNP

(4)

ISERS NNR INR NSERS

(5)

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS The authors would like to thank the chemistry department of Université de Montréal for providing funds to realize the experiments, Jean-Philippe Massé of École Polytechnique for valuable TEM support, and the group of students involved in the CHM6160Advanced Analytical Spectroscopy Winter 2013 semester: A. Atashi; A. Aubé; M. Couture; L. A. DiazLozada; M. Dufresne; C. R. Elie; C. Falcucci; E. Fournaise; J. Gravel; S. Maillette; A. Moreau; K. L. Nguyen; H.P. PoirierRichard; K. Proulx; and H. Zhu.

where I is the intensity and N is the number of molecules in fluorescence for the ligand (standard solution) or the ligand on the nanoparticle (NP), or for SERS, normal Raman (NR) or SERS. The intensity must be corrected for the difference in power of illumination. The number of molecules per 1561

dx.doi.org/10.1021/ed500067u | J. Chem. Educ. 2014, 91, 1557−1562

Journal of Chemical Education



Article

REFERENCES

(1) Fendler, J. H.; Meldrum, F. C. The colloid-chemical approach to nanostructured materials. Adv. Mater. 1995, 7 (7), 607−632. (2) Katz, E.; Willner, I. Integrated nanoparticle-biomolecule hybrid systems: Synthesis, properties, and applications. Angew. Chem., Int. Ed. 2004, 43 (45), 6042−6108. (3) Willets, K. A.; Van Duyne, R. P. Localized surface plasmon resonance spectroscopy and sensing. Annu. Rev. Phys. Chem. 2007, 58, 267−297. (4) Aizawa, M.; Buriak, J. M. Block copolymer templated chemistry for the formation of metallic nanoparticle arrays on semiconductor surfaces. Chem. Mater. 2007, 19 (21), 5090−5101. (5) Boeker, A.; He, J.; Emrick, T.; Russell, T. P. Self-assembly of nanoparticles at interfaces. Soft Matter 2007, 3 (10), 1231−1248. (6) Srivastava, S.; Kotov, N. A. Nanoparticle assembly for 1D and 2D ordered structures. Soft Matter 2009, 5 (6), 1146−1156. (7) Lal, S.; Link, S.; Halas, N. J. Nano-optics from sensing to waveguiding. Nat. Photonics 2007, 1 (11), 641−648. (8) Penn, S. G.; He, L.; Natan, M. J. Nanoparticles for bioanalysis. Curr. Opin. Chem. Biol. 2003, 7 (5), 609−615. (9) Hirsch, L. R.; Stafford, R. J.; Bankson, J. A.; Sershen, S. R.; Rivera, B.; Price, R. E.; Hazle, J. D.; Halas, N. J.; West, J. L. Nanoshellmediated near-infrared thermal therapy of tumors under magnetic resonance guidance. Proc. Natl. Acad. Sci. U.S.A. 2003, 100 (23), 13549−13554. (10) Huang, X. H.; El-Sayed, I. H.; Qian, W.; El-Sayed, M. A. Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods. J. Am. Chem. Soc. 2006, 128 (6), 2115−2120. (11) Ying Hui, N.; Li, D.; Simon, G. P.; Gamier, G. Paper surfaces functionalized by nanoparticles. Adv. Colloid Interface Sci. 2011, 163 (1), 23−38. (12) Stiles, P. L.; Dieringer, J. A.; Shah, N. C.; Van Duyne, R. P. Surface-enhanced Raman spectroscopy. Annu. Rev. Anal. Chem. 2008, 1, 601−626. (13) Dulkeith, E.; Morteani, A. C.; Niedereichholz, T.; Klar, T. A.; Feldmann, J.; Levi, S. A.; van Veggel, F.; Reinhoudt, D. N.; M?ller, M.; Gittins, D. I. Fluorescence quenching of dye molecules near gold nanoparticles: Radiative and nonradiative effects. Phys. Rev. Lett. 2002, 89 (20), 203002. (14) Jain, P. K.; Huang, X.; El-Sayed, I. H.; El-Sayed, M. A. Noble metals on the nanoscale: Optical and photothermal properties and some applications in imaging, sensing, biology, and medicine. Acc. Chem. Res. 2008, 41 (12), 1578−1586. (15) Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz, G. C. The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment. J. Phys. Chem. B 2003, 107 (3), 668−677. (16) Campbell, D. J.; Xia, Y. Plasmons: Why should we care? J. Chem. Educ. 2007, 84 (1), 91−96. (17) Dungey, K. E.; Muller, D. P.; Gunter, T. Preparation of Dppestabilized gold nanoparticles. J. Chem. Educ. 2005, 82 (5), 769−770. (18) Gerber, R. W.; Oliver-Hoyo, M. Building a low-cost, sixelectrode instrument to measure electrical properties of self-assembled monolayers of gold nanoparticles. J. Chem. Educ. 2007, 84 (7), 1177− 1179. (19) Keating, C. D.; Musick, M. D.; Keefe, M. H.; Natan, M. J. Kinetics and thermodynamics of Au colloid monolayer selfassemblyUndergraduate experiments in surface and nanomaterials chemistry. J. Chem. Educ. 1999, 76 (7), 949−955. (20) Njagi, J.; Warner, J.; Andreescu, S. A bioanalytical chemistry experiment for undergraduate students: Biosensors based on metal nanoparticles. J. Chem. Educ. 2007, 84 (7), 1180−1182. (21) Sharma, R. K.; Gulati, S.; Mehta, S. Preparation of gold nanoparticles using tea: A green chemistry experiment. J. Chem. Educ. 2012, 89 (10), 1316−1318. (22) Liu, X.; Atwater, M.; Wang, J.; Huo, Q. Extinction coefficient of gold nanoparticles with different sizes and different capping ligands. Colloids Surf., B 2007, 58 (1), 3−7.

1562

dx.doi.org/10.1021/ed500067u | J. Chem. Educ. 2014, 91, 1557−1562