In the Laboratory
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An EPR Experiment for the Undergraduate Physical Chemistry Laboratory R. A. Butera and D. H. Waldeck* Department of Chemistry, University of Pittsburgh, Pittsburgh, PA 15260; *
[email protected] measure the isotropic EPR spectra of two inorganic complexes, Cu(acac) 2 (2) and VO(acac)2 (3). By using DPPH as an internal standard in the study of the EPR spectra of the complexes, students are able to determine their g values. In addition, these complexes have a well-defined spectral structure, which the students must assign by consideration of the molecule’s spin sublevels. O2N N
N
NO2
1
O2 N
O −
2
CuΙΙ
O O −
3
O
− O
O −
V O
O
O
A discussion of EPR spectroscopy may be found in standard sources (2–4) or in the supplemental material for this laboratory exercise.W The Instructional Apparatus and the Measurement of g The organic compound DPPH is a radical possessing one unpaired electron that is distributed throughout the molecule. From the relationship between the resonance frequency ν and the field strength H h ν = ∆E = E2 – E1 = g µB H (1) the g-factor for the spin of the electron can be determined. The students proceed in two steps. First, they calibrate the
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We describe a novel experiment for the physical chemistry laboratory that has been successfully implemented at the University of Pittsburgh for the past 5 years. The exercise uses an unusual approach that both elucidates the principles of an experimental measurement for the students and provides them with experience using research-grade commercial equipment. The dual objective is accomplished by using an “instructional” spectrometer to measure the value of g for an organic radical DPPH and combining this with the measurement of the spectra of two inorganic complexes using a Varian E4 spectrometer. Students use their measured value of g for DPPH to determine the values of g for the two complexes and must provide a qualitative explanation for the characteristics of their spectra. More than 300 undergraduate science and engineering majors have performed this experiment successfully. Although some examples of undergraduate laboratory exercises have been reported (1), electron paramagnetic resonance (EPR, or electron spin resonance ESR) is not commonly introduced to undergraduate students. It is the electronic analogue of NMR spectroscopy, which probes the nuclear spin transitions of molecules. Because the splittings between electron spin sublevels are intrinsically larger than those between nuclear spin sublevels, it is possible to perform EPR spectroscopy with more rudimentary equipment than is required by NMR spectroscopy. This enables one to devise an experimental apparatus in which the physical principles of the measurement are more readily apparent, providing a useful introduction to resonance spectroscopies. EPR spectroscopy is useful for studying the structure of paramagnetic species, which include transition metal ions, organic free radicals and ions, and electronically excited states. Molecules of this type can play important roles in reaction mechanisms. EPR spectroscopy uses microwaves to induce transitions between the electron spin energy levels of the paramagnetic species and is able to provide detailed information on the electronic characteristics of the molecule. This experiment has two experimental components and involves two different experimental apparatuses. The first component uses a Leybold EPR instrument (Pasco Scientific Models S E 9634, 9635, 9636), which is specifically designed as a teaching tool, to study the spectrum of the organic radical 2,2′-diphenyl-1-picrylhydrazyl (DPPH [1]). By measuring how the resonance frequency of DPPH shifts with the magnitude of the applied magnetic field, the student is able to measure the value of its g-factor. The value of g provides a quantitative measure of the molecule’s magnetic moment—that is, how much the applied magnetic field shifts the energies of the molecule’s electron spin energy sublevels—and is sensitive to the details of the molecule’s electronic structure. The g value is the primary empirical parameter that characterizes the molecule’s response and is loosely analogous to a chemical shift in NMR spectroscopy. The second component of the laboratory exercise uses a Varian E4 EPR spectrometer to
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JChemEd.chem.wisc.edu • Vol. 77 No. 11 November 2000 • Journal of Chemical Education
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Figure 3. Absorption data for DPPH acquired with this instrument.
strength at the sample when the current through both coils is known. They determine the current by means of a calibrated shunt resistor and Ohm’s law. They use a gaussmeter (Model 907, Magnetic Instrumentation Inc.) to measure the magnetic field strength. To determine the value of g for DPPH, the students measure the change in frequency for the resonance as a function of the applied magnetic field. Experimentally, they set the frequency of the applied rf and scan the magnetic field to find the value at which absorption occurs. After a spectrum is obtained (see Fig. 3), they assign the field strength for the peak of the absorption. They repeat this procedure for a number of frequencies (typically 5 to 10). From the slope of the line in a plot of the frequency versus the magnetic field, they determine the value of g (see Fig. 1). The Research/Commercial Instrument Figure 2. The “instructional” EPR apparatus. Top: photograph of the apparatus; bottom: schematic diagram.
apparatus for field strength according to the equation H = mi + b, where i is the applied current through the Helmholtz coils that generate the magnetic field. Second, they measure the “spectrum” of DPPH at 5 to 10 different field strengths and radio frequencies. By plotting the observed frequency of the transition as a function of the applied field strength (see Fig. 1), they can calculate g for DPPH. They should find that the value for DPPH is close to that for the free electron, but slightly larger (2.0038, as compared to 2.00232). The instructional apparatus (Pasco Scientific Models S E 9634, 9635, 9636) uses a radio frequency source rather than a microwave source and consists of six primary components: (i) a radio frequency (rf ) control unit (probe holder), (ii) a magnetic field (mf) control unit, (iii) a pair of Helmholtz coils, (iv) a multimeter, (v) a phase shifter, and (vi) an oscilloscope. A photograph and a schematic diagram of the apparatus are shown in Figure 2. The apparatus is interfaced to a personal computer. The open and modular structure of this instrument allows the students to clearly observe the different features of the measurement. For example, they manually control the strength of the magnetic field by adjustment of the current through the Helmholtz coils. They align the coils and the rf probe (containing the sample) so that it lies on an axis through the centers of both coils. The coils are placed symmetrically about the rf probe and separated by 2.5 inches, the radius of one coil. In this arrangement, the students can calculate the field 1490
The inorganic compounds Cu(acac)2 2 and VO(acac)2 3 are both EPR active. The copper compound is a d9 species and the vanadium compound is d1. Both compounds have one unpaired spin and display hyperfine splittings in their spectra. However, the vanadium compound has an unpaired electron, whereas the copper compound behaves as if a positive charge (the hole) is unpaired. In the experiment the students synthesize the two inorganic complexes and determine their EPR spectra. (Details of the sample preparation may be found in the supplemental materials.W) In the spectral measurement they place a solid sample of DPPH (encapsulated in a quartz capillary tube) inside the solution and use its EPR spectrum as an internal reference. In this way, they are able to determine the g-factor for the inorganic complexes.
EPR Sample Preparation and Measurement The students are provided with a synthetic preparation for the two inorganic compounds.W They dissolve their samples in a solvent that is 40% chloroform (CHCl3) and 60% toluene, by volume. The concentration of VO(acac)2 or Cu(acac)2 should be 10᎑3–10᎑2 M. Students then pipet a small amount of the solution(s) into an EPR tube(s). Inside each sample tube, they place the DPPH reference. They then use the E4 EPR spectrometer to measure the spectrum of the complexes. First they tune the spectrometer cavity, finding the signal and optimizing it. The derivative spectra are recorded by a plotter and the spectral transitions (magnetic field) are manually assigned on the basis of the spectrometer settings. Sample spectra for the two species are provided in Figure 4. The students assign two major characteristics of the spectrum. First, they determine the number of transitions and
Journal of Chemical Education • Vol. 77 No. 11 November 2000 • JChemEd.chem.wisc.edu
In the Laboratory
Others are more involved:
A Signal
Given that the Hamiltonian of such a system may be written as ∆E = ᎑ ⭈ H, where = g µB (S + L), they are asked to rationalize how the orbital angular momentum L affects the measured value of g. DPPH
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They are asked to explain why they do not see hyperfine splitting in DPPH, and what they might do experimentally to obtain hyperfine structure. 4000
They are asked to explain why the spectra for the inorganic complexes are not symmetrically shaped and, in particular, why the linewidths of the observed transitions are different from one another.
Magnetic Field / G
Signal
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Figure 4. EPR spectra taken on the Varian E4 instrument. A: Cu(acac)2; B: VO(acac)2.
hyperfine splittings, and the nuclear spin of Cu and V. Next, they determine the g-factor by comparison with their internal DPPH reference. The E4 EPR spectrometer operates at a fixed resonance frequency and scans the magnetic field. The students assign the center of the spectrum for each compound and determine its field value. If the transitions occur at different magnetic field strengths, then the g-factors must also be different. In general,
g sample = g DPPH
H DPPH H sample
(2)
Students should find that the g-factors for the complexes are quite different from the g-factor of a free electron. Furthermore, they will find that one of the complexes has a g-factor less than that of the free electron and the other has a g-factor larger than that of a free electron. The shifts in the g value are caused by the influence of spin-orbit coupling and the students are asked to explain these trends (3, 5). To demonstrate their understanding of the laboratory exercise, students are required to answer a number of questions. Some of the questions are straightforward—for example, the following. They are required to explain the splitting pattern in 2 and 3, and the shift in the center frequency of the spectra between the three species (1, 2, and 3). They are asked to explain why the splitting of the electron spin energy levels is larger than that of the nuclear spin sublevels, at the same magnetic field strength. Along this same line they are asked to predict the frequency of the proton NMR transitions of DPPH at the experimental magnetic field strength in the instructional apparatus and at the magnetic field strength of the Varian E4 spectrometer. They are asked to compute the population difference between the two electron spin sublevels of the DPPH molecule in the two spectrometers.
This laboratory exercise provides a useful introduction to resonance spectroscopies (EPR and NMR). The students are able to measure the EPR spectra for a number of species, assign the spectra, and explain the differences in the g values. It is not essential that the systems described here be used; however, systems should be chosen with proper consideration. For example, the hyperfine interaction in DPPH is small enough that contributions from the Breit–Rabi effect at these low fields are safely ignored (3a). Although the two components of the experiment (measurement of g for DPPH and measurement of the spectra for the inorganic complexes) are independent and could be implemented independently, the combination of an “instructional” apparatus with a commercial apparatus allows one to illustrate the underlying concepts of the spectrometric method and to provide experience with a more sophisticated instrument. Hazards The sample preparations require hot acid solutions and proper precautions must be taken. Acknowledgments We thank the University of Pittsburgh for support of this work. We thank R. Shepherd for assistance with the synthesis and D. W. Pratt for advice and discussion. We thank the undergraduate students and graduate teaching assistants who have helped ‘debug’ this experiment over the past few years. W
Supplemental Material
Details concerning the experimental design and implementation are available in this issue of JCE Online. Literature Cited 1. Sojka, Z.; Stopa, G. J. Chem. Educ. 1993, 70, 675, and references therein. 2. Atkins, P. W. Physical Chemistry, 6th ed.; Freeman: New York, 1998. 3. (a) Wertz, J. E.; Bolton, J. R. Electron Spin Resonance: Elementary Theory and Practical Applications; McGraw-Hill: New York, 1972. (b) Poole, C. P. Jr. Electron Spin Resonance, 2nd ed.; Wiley: New York, 1983. 4. Drago, R. S. Physical Methods in Chemistry; Saunders: Philadelphia, 1977. 5. (a) Gersmann, H. R.; Swalen, J. D. J. Chem. Phys. 1962, 36, 3221. (b) Rogers, R. N.; Pake, G. E. J. Chem. Phys. 1960, 33, 1107.
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