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Article 60
Direct Microscopic Analysis of Individual C Dimerization Events: Kinetics and Mechanisms Satoshi Okada, Satori Kowashi, Luca Schweighauser, Kaoru Yamanouchi, Koji Harano, and Eiichi Nakamura J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 26 Nov 2017 Downloaded from http://pubs.acs.org on November 27, 2017
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Direct Microscopic Analysis of Individual C60 Dimerization Events: Kinetics and Mechanisms Satoshi Okada, Satori Kowashi, Luca Schweighauser, Kaoru Yamanouchi, Koji Harano*, Eiichi Nakamura* Department of Chemistry, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan ABSTRACT: Modern transition state theory states that the statistical behavior of a chemical reaction is the sum of individual chemical events that occur randomly. Statistical analysis of each event for individual molecules in a three-dimensional space however is practically impossible. We report here that kinetics and mechanisms of chemical reactions can be investigated by using a one-dimensional system where reaction events can be observed in situ and counted one by one using variable-temperature (VT) atomic-resolution transmission electron microscopy (TEM). We thereby provide direct proof that the ensemble behavior of random events conforms to the Rice–Ramsperger–Kassel–Marcus (RRKM) theory, as illustrated for [2 + 2] cycloaddition of C60 molecules in carbon nanotubes (CNTs). This method gives kinetic and structural information for different types of reactions occurring simultaneously in the microscopic view field, suggesting that the VT-TEM opens a new dimension of chemical kinetics research on molecules and their assemblies in their excited and ionized states. The study carried at 393–493 K showed that pristine CNT primarily acts as a singlet sensitizer of the cycloaddition reaction that takes place with an activation energy of 33.5 ± 6.8 kJ/mol. On the other hand, CNT suffers electron-damage of the conjugated system at 103–203 K, and promotes a reactive radical cation path that takes place with an activation energy of only 1.9 ± 0.7 kJ/mol. Pre-exponential factor of the Arrhenius plot gave us further mechanistic insights.
Introduction Observation of the motions and reactions of molecules, being quantum mechanical entities, has long been an impossible dream. Through advances in transmission electron microscopy (TEM) and methods to anchor molecules on a carbon nanotube (CNT; Figure 1a and b), we can visually study the structural changes of molecules in situ using single-molecule atomic-resolution real-time TEM imaging (SMART-TEM).1,2,3 To go one step further to study reaction kinetics, we need statistical information over time and temperature—information that is so far inaccessible by many of the single-molecule analytical methods,4,5 including TEM imaging.6 Here, a long-standing interest in this context is to know if the behavior of individual molecules conforms to the basic assumption of the Rice– Ramsperger–Kassel–Marcus (RRKM) theory that isolated molecules behave as if all their accessible states were occupied in random order.7,8 To address this question, we chose to study [2 + 2] electrocyclic conversion of a van der Waals (vdW) complex of C60 1 in a CNT to an adduct 2 (step 1, Figure 1b and c)—a well-known reaction without mechanistic information. 9,10 ,11 Through counting reaction events one by one, we could identify four concurrent reactions. One observed at 393–493 K (step 1H), where the CNT maintained its structural integrity, involves a singlet excited state [2 + 2] cycloaddition reaction with an activation energy of 33.5 ± 6.8 kJ/mol. Here the pristine CNT acts as a single sensitizer of the cycloaddition. Another pathway found at 103–203 K (step 1L) to occur after CNT was heavily damaged by the electron beam (cf. Figure 2), 12 is a temperature-insensitive reaction. This reaction takes place with an activation energy of only 1.9 ± 0.7
kJ/mol. Here an ionized form of the damaged CNT is considered to act as an oxidant to generate a reactive radical cation of C60. The third is the further conversion of 2 to a fused dimer 3 (step 2), which is also temperature sensitive as studied at 393– 493 K. The fourth is a purely thermal retro [2 + 2] reaction frequently occurring above 493 K.13 Overall we found that the rate profile of the [2 + 2] dimerization of the vdW complex 1 under the 1D constraints depends heavily on the reaction temperature, the quality of the CNT, and the competing thermal cycloreversion reaction, as controlled by the activation energy, the frequency of the reaction, and the concurrent reactions. In this single molecule study, we needed only 25–70 molecules to analyze the frequency of the reaction events, and several hundred molecules in total to determine the activation energies. The systematic variable-temperature (VT) atomistic TEM study of chemical reactions represents, to our knowledge, a rare example of the kind, and suggests the potential of SMART-TEM imaging for chemical kinetics study on individual molecules and their assemblies in the field of chemistry,14 catalysis,15 materials,16 and biological science.17 ,18
Results To obtain event-by-event statistics of the reactions, we monitored the conversion of 1 to 2 and 3 for a given number of C60 molecules packed in CNTs of 1.4-nm diameter (C60@CNT).19 The [2 + 2] dimerization is thermally forbidden,20 and needs electronic excitation.21 The reaction was examined at 103–643 K using a 120-kV electron beam with an electron dose rate (EDR) of 3.1 × 105 e– nm–2 s–1 unless otherwise noted, and recorded continuously on a complementary
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Journal of the American Chemical Society metal oxide semiconductor (CMOS) sensor as a 2k × 2k pixel movie with a frame rate of 1.0 s. At this EDR, electrons are shot from an electron emitter with an interval of 8.1 µs/C60 (area of 0.396 nm2), and each electron passes through C60 in an attosecond period (120-kV electrons travel at 59% of the speed of light).3 a
b
c
e-beam (120 kV)
cycloaddition
1
sample stage
step 1H: 33.5 kJ/mol step 1L: 1.9 kJ/mol
fusion
2
a
10 s (3.1 × 106)
1 2
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5 6 7 8 9 10 11 12
electron beam
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retro [2 + 2]
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5 6
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3 d 8 s (2.5 ×
106)
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197 s (6.1 × 107) 1 2– 3
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4 5– 6 7 8
9 10 11– 12–13 14 15 16 17
402 s (1.2 × 108) 4 5 6 7 8 9 1 2 3
10 11 12 13 14
Figure 1. SMART-TEM imaging of the dimerization of C60@CNT. (a) A schematic illustration of the experiments using C60@CNTs on a temperature-controlled microgrid. (b) TEM images of intermediates in a 1.4-nm CNT. The scale bar is 1 nm. (c) Four types of reactions observed using TEM. (d) Steps 1H and 2 seen for 17 molecules at 443 K under 120 kV acceleration voltage, and with an electron dose rate (EDR) of 3.1 × 105 e– nm–2 s–1. Numbers in parentheses denote total electron dose (TED) of each frame with the unit of e– nm–2. A [2 + 2] cycloadduct is indicated as hyphenated numbers and a fused oligomer as boxed numbers. A defect is shown with a red arrow. The scale bar is 2 nm. The original movie is in Supporting Information (Movie_S1.avi)
Figure 2. TEM imaging of the dimerization of C60@CNT at 298 K. (a) Intact CNT containing C60 molecules. (b) The same CNT heavily damaged after irradiation for 349 s to be compared with the virtually intact CNT at 402 s in Figure 1d. Numbers in parentheses denote total electron dose (TED) of each frame with the unit of e– nm–2. A [2 + 2] cycloadduct is indicated as hyphenated numbers and a fused oligomer as boxed numbers. The scale bar is 2 nm. The original data in Figure S10.
Several key conditions made the present study possible. The highly thermally conductive CNT22 functions as a thermal bath, and the efficiency of heat transfer between the specimen and the heated/cooled TEM grid much affected the reproducibility of the reaction rates. For effective heat control, we therefore optimized sample deposition on a TEM microgrid that is heat-controlled with an instrumental error of a few degrees (see Experimental Section). An as-prepared sample failed to contact well the surface of the grid. A sample softened by sonication for 1 h achieved a good contact and produced reproducible results. On the other hand, when we used extensively debundled C60@CNT prepared by extended sonication of a 1,2,4-trichlorobenzene dispersion (see Experimental Section), the reaction showed little temperature dependency because of poor contact and poor heat transfer. Similarly, we found the efficiency of heat transfer also differs at the different areas of the partially debundled C60@CNTs@grid where we saw some CNTs are isolated entirely from others, and these data were not taken into account in the reaction rate analysis. To ensure reproducibility, we used the same sample of C60@CNTs@grid in a series of experiments. Another key enabler is an aberration-corrected atomicresolution (0.10-nm point resolution) TEM equipped with a CMOS image sensor that allows us to monitor reaction events continuously 23 unlike a charge-coupled device sensor that needs a blinking time for data retrieval during which we cannot monitor the progress of reactions, e.g., a thermal reaction.
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a
# of [2 + 2] events
Figure 1d illustrates an example of the reaction (443 K), where dimer 2 (step 1, or specifically step 1H; see below) formed first, followed by conversion (step 2) to fused dimer 3 or oligomers (molecules 6–14 at 402 s). Thus, 17 molecules connected initially via 16 vdW bonds gave one dimer for molecules 5 and 6 (6.3% conversion) after 8 s, and five dimers (31%) after 126 s. Notably, the 5–6 dimer (2) had undergone cycloreversion to the vdW complex 1 at 402 s. This reaction predominated above 493 K, as discussed later. In each experiment in Figure 2, we studied 25–70 molecules in several CNTs concurrently for 5–10 min. After a long observation time, CNTs gradually suffered damage, as seen by deformation of the outline of CNT after 197 s (Figures 1d) and defect formation at total electron dose (TED) of 1.0 × 108 e– nm–2 (402 s, red arrow). CNTs suffered damage much more quickly at 298 K (Figure 2a vs. 2b where the outlines of CNTs are largely lost), and very quickly below 203 K.
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200
Figure 3. Reaction kinetics of steps 1H, 1L, and 2 at 120 kV and EDR of 3.1 × 105 e– nm–2 s–1. (a) The occurrence of random reaction events of step 1H integrated over every five-second period at 443 K plotted against TED (every 1.6 × 106 e– nm–2 s–1 = five seconds). (b) Reaction progress (1 – P, where P is C60 conversion normalized to one) at 120 kV vs. TED (black) and the data were taken at 80 kV (298 K, red). (c) Reaction progress vs. TED studied at 203–643 K.
Figure 3a illustrates a typical time course of conversion of 1 to 2 over TED at 443 K with a frame rate of 1.0 s for 54 molecules encapsulated in several CNTs. The dimerization events occurred randomly zero to five times every five seconds at various locations in several CNTs. From this data, we
calculated an average interval of reaction events to be 58 s; that is, 7.1 × 106 electrons/C60 cause one dimerization event. We observe no statistically meaningful rate difference among the molecules in different CNTs. Despite the randomness of the events, the reaction progress (1 – P, where P is the conversion of C60 normalized to one) plotted against TED suggested a first-order decay (Figure 3b and c). A semilogarithmic plot (black line in Figure 4a) indeed showed first-order decay up to 60% conversion, indicating that the random events conform to the RRKM theory.7,8 The red dotted line in Figure 3b shows that, at 80-kV acceleration voltage at 298 K the reaction is extremely slow, approximately 100 times slower than at 120 kV– an observation relevant to the reported mildness of TEM observation with a less than 80 kV electron beam.24 This rate difference probably originates from the lower frequency of excitation of C60 by the CNT under the 80-kV irradiation as discussed in the Discussion section below. Interestingly, the representative data on the reaction progress at 203–643 K (Figure 3c) reveal two different rate profiles. Above 393 K, the reaction occurred with no induction time and at 203 K with a very long induction time, during which the CNTs largely lost their tubular outline by electron damage (cf. Figure 2b). Upon closer analysis, we found that the reaction at 298 K shows an intermediary behavior between high and low temperature reactions, and hence the data set at 298 K was not analyzed further. Figures 4a summarizes the semilogarithmic plots of the reaction profiles observed at high temperatures (393–493 K) under 120 kV and EDR of 3.1 × 105 e– nm–2 s–1. Figure 4b shows the rate constants obtained against TED at various temperatures. The magnitude of the error found in this table is small enough to ensure the credibility of the subsequent analyses. From these data we determined the activation energy of step 1H to be 33.5 ± 6.8 kJ/mol (Figure 5 black line) through least-square fitting described in Figure S7, and the PEF of 3.9 × 10-4 e– nm2. This activation energy compares favorably with a reported theoretical value of 25 kJ/mol for C60 dimerization via S1 state,25 and suggests that reaction goes through the S1 excited state of C60. An experimental value of 23 kJ/mol has been reported for photodimerization of crystalline C60.13 The rather large error in our experiment probably originates from the variation of the temperature felt by the molecules, and needs to be reduced further in the future studies. The dimerization at 543 K and 643 K slowed down significantly because of visually observed, competitive thermal cycloreversion (2 to 1).13 These two data point are shown in the summary of kinetics in Figure 5 (purple circle). As shown Figure 1d, we saw one such event at 443 K—an illustration of the probabilistic behavior of individual reaction events. Step 2 took place with similar ease as step 1H (Figure 5, red dots). Only five data points could be taken at 393–493 K, because the rate constant coupled with that of step 1H could be determined only with very large uncertainty. Nonetheless, an activation energy of 23 ± 17 kJ/mol and a small PEF of 7.1 × 10-6 e–1 nm2 were obtained (Figure S9). Similarly, we analyzed the reaction at 103—203K that occurred only after significant damage of CNT (step 1L; Figure 4c and d). As the temperature was lowered, the CNT damage became quicker and the induction time shorter. The kinetic analysis in Figure 4d is based on the data after the induction
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Journal of the American Chemical Society time ended at each temperature. Thus, we found that step 1L takes place with an activation energy of 1.9 ± 0.7 kJ/mol (Figure 3c), and a PEF of 1.4 × 10-7 e–1 nm2. The latter value is 1/2800 of the one found for step 1H, suggesting that step 1L occurred much less frequently that step 1H, while the reaction itself occurs with a much lower activation energy, probably, via a radical cation of C60. 0
393 K 443 K 453 K 463 K 473 K 493 K
ln(1 - P)
–0.2 (25%) –0.4
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103 128 153 203
0.0178 ± 0.0008 0.017 ± 0.001 0.026 ± 0.002 0.054 ± 0.004
step 1L (103–203 K) 1.9 ± 0.7 kJ/mol
0.08
step 1H (393–493 K) 33.5 ± 6.8 kJ/mol
0.06 step 2
0.04 0.02
retro [2+2] 0
100 200 300 400 500 600 700 R
Figure 5. Reaction rate vs. temperature correlation illustrated for four reaction types: step 1H (black), step 1H, retro [2 + 2] cycloaddition (purple), step 1L (blue) and step 2 (red). Activation energies for step 1H and step 1L are shown in the plot.
–1.0
0
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0.0123 ± 0.0006 0.0445 ± 0.0008 0.093 ± 0.004 0.052 ± 0.005 0.0612 ± 0.0008 0.108 ± 0.003
(25%) –0.5 (50%)
In Figure 5, we plot the rate constants against the stage temperature, and summarize the results of the present kinetic studies. We found four distinct reactions: An S1 excited state pathway (step 1H; black) taking place between 393 K and 493 K, retro [2 + 2] cycloaddition prominent above 543 K (purple), a radical cation pathway (step 1L; blue) that requires very small thermal activation, and step 2 at 393–493 K that follows step 1H. 0.12
–0.6 (50%)
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induction time, from the data after which we calculated the firstorder rate constant.
rate constant [10–6 e–1 nm2]
a
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Discussion To put the observations into perspective, we illustrate in Figure 6 the time scale of the events associated with step 1H , which we consider to occur via S1 excited state of C60. Under our standard condition of EDR = 3.1 × 105 e– nm–2 s–1, incident electrons pass through a C60 molecule in CNT every 8.1 µs, and the dimerization occurs every 58 s. Namely, one electron out of 7.1 × 106 electrons/C60 causes one reaction event, and the vast majority of the electrons contribute only to TEM imaging, while a small portion may cause only electron excitation and atomic vibrations.26 This picture therefore indicates that the frequency of the reaction events per given time is proportionate to the number of electrons/time. This was indeed found to be the case. The reaction rates/TED was independent of different EDRs (2.1 × 105 to 2.4 × 106 e– nm–2 s–1; under 120-kV acceleration; Figures 7a and b). This data also indicates that multi-electron excitation is unlikely, as one would expect from the large difference of the time scales between the 8.1-microsecond interval of the electron arriving at C60@CNT and the femto- to nanosecond time scales of the chemical reactions (Figure 6).
Figure 4. Rate constants of steps 1H and 1L at 120 kV. (a) A semilogarithmic plot of Figure 3c above 393 K, and first-order kinetics fitting shown as solid lines. (b) The rate constants of step 1H at 393–493 K obtained from a. (c) A semilogarithmic plot of the reaction progress vs. TED. First-order kinetics are fitted to each plot with the same color. (d) The rate constants of step 1L at 103 K obtained from fitting shown in c. The data at 203–643 K was taken with EDR of 3.1 × 105 e– nm–2 s–1 and the data at 103–153 K with 1.3 × 106 e– nm–2 s–1. The reaction at 203 K showed a long
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8.1 µs: interval of electron passage through C60@CNT 58 s: interval of reaction events e–
e–
e–
e–
e–
e–
e–
e–
no electron excitation -TEM image formation chemical electronic atomic and reactions excitation molecular (fs-ps) vibrations (ps) (ps-ns) Figure 6. Time scale of electron impacts and chemical events caused by incident electrons.
a
EDR = 2.1 × 105 e– nm–2 s–1 7.1 × 105 e– nm–2 s–1 2.4 × 106 e– nm–2 s–1
0 –0.2 (25%) ln(1 - P)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
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–0.4 –0.6 (50%) –0.8 –1.0
0
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20 30 TED [106 e– nm–2]
40
b EDR (e– nm–2 s–1)
rate constant (10–6 e–1 nm2)
2.1 × 105 7.1 × 105 2.4 × 106
0.0394 ± 0.0008 0.043 ± 0.002 0.039 ± 0.001
Figure 7. The rate constants of step 1H obtained under different EDRs. (a) A semilogarithmic plot of the reaction progress at 298 K against TED at different EDRs shown. (b) The rate constants at different TEDs obtained from a.
Table 1. Summary of activation energies and PEFs
step 1H step 1L step 2
activation energy (kJ/mol)
ln(PEF)
PEF (e–1 nm2)
33.5 ± 6.8 1.9 ± 0.7 23 ± 17
–7.8 ± 1.8 –15.8 ± 1.1 –11.9 ± 4.3
3.9 x 10–4 1.4 x 10–7 7.1 x 10–6
While the PEF in a usual Arrhenius analysis reflects the frequency of collision and the steric factor, collision can be neglects in the present study. Instead, the PEF reflects the frequency of the activation of C60, and the steric factor of the reaction of this active species, and the frequency of the activation may be the most influential. The energetics relevant to this discussion is shown in Figure 8a, where we show the HOMO-LUMO gaps and the ionization potentials (IP = -HOMO) of CNT and C60 together with coronene as a model of damaged CNT.3 Given the near zero HOMO-LUMO gap and densely populated exited state energy levels, CNT easily excites under an electron beam. Likewise, CNT (IP = 5.0 eV) easily ionizes under the conditions where C60 (6.2 eV) and coronene (7.2 eV) do not ionize. On the other hand, coronene radical cation can ionize C60 readily, and hence we expect that cation of the damaged CNT can easily oxidize C60. With this data set combined with the data in Table 1, we suggest a few mechanistic implications below. Figure 8b illustrates plausible paths associated with step 1H at 398—498 K. The first step is excitation of CNT by 120-kV electron, the excited CNT transfers energy to C60, and the excited C60 dimerizes to produce 2.21 Note here that thermal relaxation of excited CNT and C60 always compete with the forward reactions. Cycloreversion shown in Figure 8b bottom was visually observed above 493 K (cf. Figure 1d, 402 s), and is reflected in the slow rate of the forward reaction (Figure 5, purple dots). Given an equally large magnitude of maximum transferable energy of 15.8 and 24.5 eV/carbon atom from a 80- and 120kV to a carbon atom (See Supporting Information),14 one would expect nearly equal ability of 80- and 120-kV beams to promote dimerization, which however contradicts with the experiments (Figure 3b; red dots). We suggest that this discrepancy stems from exhaustive thermal relaxation of the 80kV, which reduces the efficiency of the energy transfer to C60. Figure 8c illustrates a radical cation mechanism of step 1L at 103—203 K, which occurs only after extensive degradation of CNT with low activation energy and very low PEF. The data suggest that ionization of C60 occurs infrequently, but the ionized C60 react quickly once formed. The mechanistic dichotomy found for step 1H at high temperatures, and step 1L at low temperatures may give us a clue to understand the known instability of CNT at low temperatures and high stability at high temperature.27 Unlike steps 1H and 1L, step 2 involves a series of C–C skeletal rearrangement. The current resolution of the TEM however does not allow us to study further details of the reaction. Extensive fusion of the molecules to form a double-walled CNT is the terminal point (cf. Figure 1d, 402 s) where the ring strain of C60 is mostly released.
In Table 1, we summarize the activation energies and PEFs of steps 1H, 1L and 2. Not only the energies differ much, but also the PEFs differ as much as 2800 times among the three paths, suggesting that three different mechanisms operate here.
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a
2 energy level [eV]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
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3 4 5 6
HOMO-LUMO gap coronene C60 CNT 0
2.87
5.0
7
6.2
8
IP = -HOMO
4.08
coronene
7.2
Singlet excited state path: activation energy, 33.5 ± 6.8 kJ/mol; PEF 3.9 x10-4 e–1 nm2 excitation by 120 kV e-
vdW dimer (1)
thermal relaxation (>393K)
*
energy transfer
*
excited CNT
excited C60
(1) cycloaddition (2) relaxation
thermal relaxation cycloreversion at >493 K fused products (3)
c
[2 + 2] dimer (2)
Radical cation path: activation energy, 1.9 ± 0.7 kJ/mol; PEF 1.4 x 10-7 e–1 nm2 ionization degradation
vdW dimer (1)
(
