In the Laboratory
The Laser Synthesis of Linear Polyynes: The Particle in a Box Revisited Bruce D. Anderson* and Christopher M. Gordon Department of Chemistry, Muhlenberg College, Allentown, PA 18104; *
[email protected] The one-dimensional particle in a box is an integral part of the quantum mechanics taught in undergraduate physical chemistry courses. Experiments demonstrating how a series of cyanine dyes serve as models of one-dimensional particle in a boxes are well-known (1, 2). Further, a series of diphenyl compounds have been shown to serve as effective models for quantum mechanical behavior (3). In this experiment, linear polyynes are synthesized and their agreement with quantum mechanical predictions based on the one-dimensional particlein-a-box model is investigated. Linear polyynes are a class of molecules with alternating triple and single bonds such as C8H2: H C C C C C C C C H These molecules are of interest as potential molecular conductors (4), for their role in the chemistry of outer space (5), and even as precursors to the synthesis of larger organic molecules (6). Polyynes are synthesized in a variety of ways including laser ablation of graphite in solution (7), an electrical arc between graphite electrodes in solution (8), and from more exotic sources such as buckyballs (9) and diamond nanoparticles (10). In this experiment, a high power (80 mJ/pulse) Nd:YAG laser is used to synthesize linear polyynes from a solution of graphite in ethanol. The resulting solution is analyzed using GC–MS to identify which polyynes have been created. Then the absorbance spectrum of the reaction mixture containing the polyynes is acquired and used to calculate the length of the carbon chain based upon the quantum mechanical particle-ina-box model. Quantum mechanics predicts that all of the pi electrons are free to move throughout the conjugated portion of the polyyne. Thus, the length of the box, L, (the distance between the terminal carbon atoms) can be calculated from the one-dimensional, particle-in-a-box eigenvalue expression
%E nf 2 ni 2
2
h
8 mL
2
(1)
where h is Planck’s constant, m is the mass of an electron, and n is the quantum number that corresponds to either the initial or final state of the electron. The box length for each polyyne is calculated using three different methods and the results are compared. Synthesis of Polyynes Graphite powder, 16 mg, and 4 mL of absolute ethanol are placed in a large test tube (14 mm × 150 mm). A stir “pea” is placed in the test tube and the test tube is covered with Parafilm. A second test tube is prepared identical to the first to serve as a control for the experiment. For the control experiment, one test tube is clamped in an upright position on a hot plate. The stirrer is turned to a moderate rate and the heater turned to low. The goal is to keep the graphite suspended in the solution but not to create a vortex.
The control sample should be heated until it is warm to the touch, but the solution should not boil. The solution is heated and stirred for one hour. The sample is checked periodically and the temperature adjusted as needed. The other test tube with the graphite solution is clamped upright on a second hot plate. The stirrer is set to a moderate rate, but the heat is not used. The flashlamps for the Nd:YAG laser is started. The laser energy is adjusted with the Q-switch to a low intensity so that the position of the beam on the test tube can be safely aligned. The height and position of the test tube is adjusted as needed. The laser energy is increased and the sample is irradiated for one hour. While a laser energy of 80 mJ/pulse has been shown to be successful, a laser energy of 30 mJ/pulse is not sufficient to initiate the reaction under these conditions. The sample is checked periodically to ensure that everything is aligned, the graphite has not settled out, and so forth. When both the control and laser samples are finished, the laser, hot plate, and stirrers are turned off. Each sample is filtered with a 0.45 μm PVDF membrane syringe filter and the filtrate is collected in a small glass vial. The appearance of each sample is noted. Product Analysis The students analyze both the lased and control samples using GC–MS. Students use the GC–MS data to identify which polyynes are produced in the lased and control samples. A Restek Rtx-1MS column is used (30 m, 0.25 mm i.d., 0.25 μm). The temperature program (80 °C isothermal for 5 min., ramp at 5 °C/min to 130 °C) is a shortened version of that found in the literature (4). During the experiment, only a small concentration of polyynes is produced and thus the detector voltage and sample size may need to be increased significantly to observe the product peaks. Once students know which polyynes are present in their sample, the UV–vis spectrum is acquired from 500–200 nm using ethanol as the blank for both samples. For best results, the strongest peak should have an absorbance of less than 1.0. If the solution has an absorbance higher than this, dilution is recommended. The students record the wavelengths of all peaks present. The observed peaks are compared to the absorbance peaks found in the literature (Table 1). Using the table, students identify which absorbance peak in their spectrum belongs to Table 1. UV–Vis Spectral Data from Polyynes
Polyyne
λ/nm
C4H2
200*
C6H2
208, 218,* 225
C8H2
200, 218, 227*
C10H2
218, 227, 239, 251*
Note: The data was obtained in methanol solution (11). The asterisk marks the most intense peak in the series.
© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 9 September 2008 • Journal of Chemical Education
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In the Laboratory
0
2
4
6
8
10
12
14
Time / min
Figure 1. Total ion chromatogram for the lased solution of graphite in ethanol showing formation of C6H2 (1.83 min) and C8H2 (4.38 min) polyynes. The peak at 1.5 min is due to ethanol.
which polyyne. The longest wavelength peak observed for each polyyne corresponds to the lowest energy transition for the molecule and is used to calculate the box length. For example, if students observe a mass spectral peak with m/z of 98, the presence of C8H2 is confirmed. When the absorption spectrum for the reaction mixture is compared to the peaks in Table 1, the students assign the peak at 227 nm in their acquired absorbance spectrum as the lowest energy transition (ni = 8 to nf = 9)for C8H2.1 Now eq 1 can be used to calculate the box length based upon experimental data. In addition, students calculate the molecular length through the summation of literature bond lengths and from a model constructed with a molecular modeling program. The entire synthesis and analysis is easily completed by a group (2–3) of students in a 3 hour laboratory period. Hazards
50
60
The Nd:YAG laser used is a Class 4 laser product that produces intense visible and invisible radiation. Avoid eye or skin exposure to direct or scattered radiation. Laser goggles are recommended. To minimize scattered radiation in the laboratory, it is recommended that the reaction take place in a sealed sample compartment or at least be covered with a cardboard box or dark cloth. Based on the hazards associated with similar compounds, linear polyynes are most likely to be classified as harmful irritants. Gloves and goggles are recommended. It is recommended that students work in a hood as much as possible when handling the solutions.
70
m/z
Figure 2. Mass spectrum for C6H2 (peak at 1.83 min).
Results and Discussion
60
70
80
m/z
80
100
Figure 3. Mass spectrum for C8H2 (peak at 4.38 min).
216.0 227.0
Absorbance
0.6
0.4
0.2
0.0 200
300
400
Wavelength / nm Figure 4. UV–vis absorbance spectrum for the lased solution.
1280
500
Figure 1 shows a typical student chromatogram for a mixture of graphite in ethanol that was lased for an hour. The peaks at 1.83 min and 4.38 min correspond to the C6H2 (see Figure 2 for the mass spectrum) and C8H2 (see Figure 3 for the mass spectrum) polyynes, respectively. While all student groups observed the C8H2 peak, most (8 out of 9) observed C6H2, some (3 out of 9) reported C10H2 as a product, and another (1 out of 9) reported C4H2. The large peak at 1.5 minutes is from the solvent and is present in the control sample and when ethanol is injected into the GC–MS. Figure 4 shows a typical absorbance spectrum for the lased solution. The peaks observed for the C6H2 (216 nm) and C8H2 (227 nm) polyynes are used in the eigenvalue expression to calculate the length of the quantum mechanical box. Table 2 shows the box lengths for the polyynes as calculated from the quantum mechanical model as well as the molecular lengths obtained from Spartan and from the summation of bond lengths. Clearly, the lengths calculated from Spartan and tabulated bond lengths are in excellent agreement with each other. The calculated quantum mechanical box lengths, however, differ significantly with percent errors ranging from 97% for C4H2 to 11% for C10H2. The large discrepancies between the quantum mechanical values and those calculated from the other methods provide the instructor with an opportunity to engage the students in a conversation about the assumptions of the model. For example, in the particle-in-the-box model, the potential energy is stated to be zero inside the box and infinite everywhere outside the box whereas for the polyynes this is not the case. Given these significant differences between the
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In the Laboratory Table 2. Molecular Lengths Calculated from Different Methods Polyyne
Bond Lengths/Å
Spartan/Å
Quantum Mechanics/Å
C4H2
3.785
3.753
7.39
C6H2
6.364
6.305
9.23
C8H2
8.943
8.856
10.82
C10H2
11.522
11.407
12.62
Acknowledgments The authors would like to thank NASA for the funds to purchase the laser, the students in the physical chemistry classes of 2007 for running through the initial version of the experiment, and the reviewers for their helpful comments. Note 1. For each compound n is determined by counting the number of pi electrons and then filling the energy levels with pairs of electrons.
particle-in-the-box model and the real molecules, students find it interesting that the quantum mechanical box lengths calculated for the polyynes are at all close to those found by Spartan and the sum of bond lengths. When surveyed after performing the experiment, the students found the experiment to be informative and interesting. In particular, the length of the quantum mechanical box (the conjugated pi system) is easy for them to visualize and the students see clear evidence that the laser light is driving the reaction when the heated control fails to produce any product. Further, students pointed to the use of all the instrumentation (laser, GC–MS, UV–vis) in a single experiment as a positive experience. Finally, 95% of the students thought this experiment should become part of the regular laboratory curriculum. A slight majority (55%) felt this experiment should replace the particle-in-a-box experiment based on the series of diphenyl compounds (3) while 41% thought it should be done in addition to the diphenyl compound particle-in-a-box experiment. Other variations on the experiment that may be of interest for further studies include using a shorter wavelength laser to initiate the reaction, trying different solvents, and using an LC with a diode array detector to acquire spectra for each polyyne peak as it elutes from the column (7). Conclusion Linear polyynes can be synthesized in the laboratory and although they are not a particle in a box, they do provide another system that can be studied experimentally to further enhance the students’ understanding of an abstract quantum mechanical topic. Students find the experiment interesting as it combines theory, experiment (especially the laser), and molecular modeling all in the same exercise. The experiment described can be used in addition to one of the more traditional particle-in-a-box experiments (1–3) or it can be used to replace them if space in the curriculum is tight.
Literature Cited 1. Garland, C. W.; Nibler, J. W.; Shoemaker, D. P. Experiments in Physical Chemistry, 7th ed.; McGraw Hill: New York, 2003; pp 380–385. 2. Sime, R. J. Physical Chemistry: Methods, Techniques, and Experiments; Saunders College: Philadelphia, 1990; pp 687–694. 3. Anderson, B. D. J. Chem. Educ. 1997, 74, 985. 4. Morales, R. G.; Gonzalez-Rojas, C. J. Phys. Org. Chem. 2005, 18, 941–944. 5. Shindo, F.; Benilan, Y.; Chaquin, P.; Guillemin, J.-C.; Jolly, A.; Raulin, F. J. Molec. Spect. 2001, 210, 191–195. 6. Morisaki, Y.; Luu, T.; Tykwinski, R. Organic Letters 2006, 8, 689–692. 7. Tsuji, M.; Tsuji, T.; Kuboyama, S.; Yoon, S.; Korai, Y.; Tsujimoto, T.; Kubo, K.; Mori, A.; Mochida, I. Chem. Phys. Lett. 2002, 355, 101–108. 8. Cataldo, F. Carbon 2004, 42, 129–142. 9. Tsuji, M.; Kuboyama, S.; Matsuzaki, T.; Tsuji, T. Carbon 2003, 41, 2141–2148. 10. Tabata, H.; Fujii, M.; Hayashi, S. Chem. Phys. Lett. 2004, 395, 138–142. 11. Heymann, D.; Cataldo, F. Polyynes: Synthesis, Properties and Applications; Cataldo, F., Ed.; CRC Press: Boca Raton, FL, 2006; pp 371–424.
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