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FULLERENES, NANOTUBES, AND CARBON NANOSTRUCTURES Vol. 12, No. 1, pp. 229–234, 2004 1 2 3 4 5 6 7
2 C60 Mean Lifetime as a Function of Electron Energy and Molecular Temperature
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Y. V. Vasil’ev,1,2,* R. R. Abzalimov,1 S. K. Nasibullaev,3 and T. Drewello4
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Institute of Physics of Molecules and Crystals, Ufa Research Centre of RAS, Ufa, Russia 2 Bashkir State Agriculture University, Ufa, Russia 3 Bashkir State University, Ufa, Russia 4 University of Warwick, Coventry, England
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ABSTRACT 2 The electron autodetachment rate constant of the negative ion C60 has been determined as a function of both electron energy and molecular temperature. The experimental findings provide proof of the statistical 2 . The experimental data nature of the electron auto-emission from C60
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*Correspondence: Y. V. Vasil’ev, Institute of Physics of Molecules and Crystals, Ufa Research Centre of RAS, Ufa, Russia and Bashkir State Agriculture University, Ufa, Russia; Fax: þ1 541 737 2062; E-mail:
[email protected].
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DOI: 10.1081/FST-120027161 Copyright # 2004 by Marcel Dekker, Inc.
1536-383X (Print); 1536-4046 (Online) www.dekker.com
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Vasil’ev et al. have been rationalized within the framework of statistical transition state theory.
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Key Words: Electron capture; Electron autodetachment; Negative ion lifetime; Fullerenes.
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INTRODUCTION
Electron autodetachment (EAD) is the main decay process for a transient molecular negative ion, resulting in the formation of a neutral molecule and a free electron. As a typical unimolecular reaction, EAD is characterized by its rate constant. The reciprocal rate constant represents the negative ion mean lifetime, which can be measured by mass spectrometry when exceeding several 2 microseconds. The EAD from C60 has to a certain extent the same physical origin as delayed ionization of neutral metal-clusters or fullerenes, the nature of which has been extensively discussed over the last decade.[1] In contrast to their positively charged counterparts, the internal energy of negative ions, generated by resonant electron capture, can be estimated precisely. It is, therefore, particularly interesting to note that the experimental and earlier-predicted 2 theoretical mean lifetimes of C60 differ within several orders of magnitude, 2 [1] depending on the internal energy of C60 . This discrepancy led to conjecture[1] 2 that electron autodetachment from C60 does probably not obey the statistical description. However, recent theoretical work[2] showed that under more careful consideration of the experimental details, the discrepancy between theory and experiment becomes less dramatic. 2 The present work addresses the question as to whether the EAD from C60 is a statistical process or not by providing experimental insight into the true 2 nature of the process. For earlier experimental studies covering EAD from C60 [1] we refer to Ref. . By use of a mass spectrometry-based method for 2 the determination of the negative ion lifetime, the EAD from C60 has been studied here for the first time as a function of both the electron energy and the molecular temperature of C60 prior to the electron attachment event. Transition state theory has been applied to the elucidation of the underlying mechanism of the electron autodetachment process and excellent agreement with the experimental data has been obtained.
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EXPERIMENTAL
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All experiments have been conducted with a single-focusing MI-1201 mass spectrometer (Russia) incorporating a custom-built trochoidal electron
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C2 60 Mean Lifetime 85 86 87 88 89 90 91 92 93 94 95 96 97
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monochromator as the electron gun (250 meV electron beam, FWHM). The well-collimated C60 beam has been generated by use of an oven. The temperature of the molecular beam, T, has been varied by the oven heater. The molecular beam has been crossed at right angle with the electron beam 2 inside the ionization chamber of the mass spectrometer. The resulting C60 ion beam has been extracted and accelerated. After passing the magnet-analyzer, the ions were registered by a detection system and the resulting spectrum was stored with the help of a computer. For the determination of the negative ion mean lifetime, total and neutral currents have been measured separately. The total current consists of negative ions of a selected m/z ratio and of a neutral component. The latter is composed of neutrals of the same mass as the ions and results from EAD of the selected negative ions in the second field free region of the mass spectrometer.
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RESULTS AND DISCUSSION
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Figure 1 shows the effective yield curves (relative cross-sections) of the total current and its neutral component obtained at T ¼ 525 and 870 K, respectively. The temperature influence on the cross-sections has been found particularly pronounced in the case of neutrals, leading to an energy shift of the maximum yield of neutrals of approx. 3.6 eV. In order to rationalize this temperature dependence, the C60 internal energy distribution has been calculated. These calculations reveal that a temperature change from 525 to 870 K would in fact account for a shift of the energy distribution of 3.6 eV. Consequently, the temperature dependence of the resonant curves of the C60 neutrals is entirely determined by the C60 beam temperature prior to the electron capture event. One may further conclude that electron emission from 2 C60 is dependent upon the internal energy content, irrespective of the means of activation, which may be achieved here by increasing the kinetic energy of the incoming electron and/or by enhancing the temperature of the C60 molecular beam. Therefore, a meaningful comparison of different experimental data on 2 the C60 mean lifetime must involve the conversion of electron energy and molecular temperature into the total internal energy, while also taking into account the electron affinity of C60. The result of such a procedure is shown in 2 Fig. 2. Indeed, the C60 mean lifetime curves measured at the two different temperatures (Fig. 1) are in excellent agreement on the internal energy scale (Fig. 2). As a consequence, unprecedented experimental proof is provided for 2 the statistical nature of the C60 negative ion EAD phenomenon.
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2 Figure 1. Effective yield curves of the total current (C60 negative ions and their neutrals after EAD) recorded at two C60 beam temperatures: 525 K (4) and 870 K (W) (top panel). Effective yield curves of the neutral component at the same conditions 2 (middle panel). Experimental C60 lifetime curves together with their theoretical predictions on the basis of Klots theory[3] (bottom panel).
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Rice – Ramsperger – Kassel – Marcus (RRKM) theory has been applied to 2 calculate the EAD rate constant of C60 , k(E), on the basis of Eq. (1):
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k(E) ¼
sN z (E E0 ) hr(E)
(1)
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where s is the ratio of the symmetry numbers, N‡(E 2 E0) is the sum of states of the transition state in the energy range from 0 to E 2 E0, E0 is the activation energy (here representing the electron affinity), h is Planck’s constant, and r(E) 2 is the density of states of C60 with the internal energy E. The sum of states and the density of states have been calculated using the Beyer–Swinehart algorithm[4] for harmonic oscillators. Based on our earlier investigation into the “forward” reaction of electron attachment to C60, the Jahn–Teller active vibrational modes Hg(2) and Hg(8) have been chosen as reaction coordinates for the inverse/“backward” process (i.e., EAD). Curve 3 in Fig. 2 represents
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C2 60 Mean Lifetime
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2 Figure 2. Experimental C60 mean lifetime curves (the same as in Fig. 1) at 525 and 870 K (Curve 1 (4) and 2 (W), respectively) displayed as functions of the total internal energy. Curves 3 (—) and 4 ( ) have both been calculated using Eq. (1), curve 4 takes 2 also into account the real internal energy distribution of C60 .
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2 this “purely theoretical” mean lifetime curve of C60 as a function of the internal energy derived from Eq. (1), whereby the rate constant was transformed into 2 lifetime. In a real experiment, however, the C60 ion beam consists of a set of ions that are characterized by the energy distribution, which has been taken into account for the mean lifetime curve 4. It is obvious from Fig. 2 that as a result of these considerations a very reasonable agreement between theory and experiment has been obtained. Future work will focus on further improvements of our theoretical treatment by considering further influential features of the real experiment. These will include, for instance, the experimental time frame, ion beam depletion over time, and negative ion neutralization through rest gas collisions in the second field free region of the instrument. Work in this direction is in progress and will be published elsewhere.
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ACKNOWLEDGMENTS
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The work has been supported by the Russian Foundation for Basic Research (Grant #01-02-16561) and The Leverhulme Trust (UK).
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REFERENCES
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1. Campbell, E.E.B.; Levine, R.D. Delayed ionization and fragmentation en route to thermionic emission: statistics and dynamics. Annu. Rev. Phys. Chem. 2000, 51, 65 –98. 2. Andersen, J.U.; Bonderup, E.; Hansen, K. Thermionic emission from clusters. J. Phys. B: At. Mol. Opt. Phys. 2002, 35, R1 – R30. 3. Klots, C.E. Quasiequilibrium rate constants for thermionic emission from small particles. Chem. Phys. Lett. 1991, 186, 73 – 76. 4. Beyer, T.; Swinehart, D.F. Algorithm 448: number of multiply restricted partitions [A1]. Commun. Assoc. Comput. Mach. 1973, 16, 379.
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Submitted July 4, 2003 Accepted August 10, 2003
