Thermoionization and Dissociation of Fullerenes and Endohedral Fullerenes

University of New Hampshire University of New Hampshire Scholars' Repository

Doctoral Dissertations Student Scholarship

Fall 2003

Thermoionization and dissociation of fullerenes and endohedral fullerenes

Rongping Deng University of New Hampshire, Durham

Follow this and additional works at: https://scholars.unh.edu/dissertation

Recommended Citation Deng, Rongping, "Thermoionization and dissociation of fullerenes and endohedral fullerenes" (2003). Doctoral Dissertations. 177. https://scholars.unh.edu/dissertation/177

This Dissertation is brought to you for free and open access by the Student Scholarship at University of New Hampshire Scholars' Repository. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of University of New Hampshire Scholars' Repository. For more information, please contact [email protected]. THERMOIONIZATION AND DISSOCIATION

OF FULLERENES AND ENDOHEDRAL FULLERENES

RONGPING DENG

B.S. Xinjiang University, 1982

M.S. Fudan University, 1988

M.S. University of New Hampshire, 1998

DISSERTATION

Submitted to the University of New Hampshire

in Partial Fulfillment of

the Requirements for the Degree of

Doctor of Philosophy

Physics

September, 2003

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3097783

UMI

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This dissertation has been examined and approved.

/'i, /) / CL 7 Dissertation Director, Olof E. Echt, Professor of Physics

Harvey Shepa ssor of Physics

P ' ^LeprMiller, Professor of Chemistry c ^ ~ \

,Jf,# //^ Lynn Kistler, Associate Professor of Physics

O m A u - f ^ ( Karsten Pohl, Assistant Professor of Physics

r/tz/zso7 Date

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. To my wife, Li Ye and my son, Jason

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGEMENTS

I would like to thank my advisor, Dr. Olof Echt, for providing this opportunity for

me to participate in this research. I am grateful for his inspiration, guidance,

encouragement and input throughout this research and my graduate studies. There are

many other persons who have made contributions to this research work. Among them are

Geoffrey Littlefield, Mark Osgood, Rory McCrimmon, Aaron Clegg and many others. I

also would like to thank every member of my thesis committee, Dr. Harvey Shepard, Dr.

Glen Miller, Dr. Lynn Kistler and Dr. Karsten Pohl, for their valuable time and effort in

examining this thesis and for supportive discussions. Finally, I would like to thank every

faculty and staff in the Physics Department. This work benefits from what they taught

me, and their support. I gratefully acknowledge support for this research by the National

Science Foundation (NSF #9507959).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS

DEDICATION...... iii ACKNOWLEDGEMENTS...... iv LIST OF TABLES...... viii LIST OF FIGURES...... ix ABSTRACT...... xv

INTRODUCTION...... 1

1 FULLERENE RESEARCH...... 3

1.1 The Structure of the Ceo Molecule ...... 3 1.2 Synthesis of Fullerenes ...... 6 1.3 Stability and Fragmentation of Fullerenes ...... 9 1.4 Physical and Chemical Study of Fullerenes ...... 11 1.4.1 Electronic Structure of the Ceo Molecule ...... 12 1.4.2 Chemical Reactions and Fullerene Derivatives ...... 13 1.4.3 Cgo Solid and Fullerides ...... 15 1.4.4 Fullerene Applications ...... 21 1.5 Endohedral Fullerenes ...... 25 1.6 Mass spectrometric Studies of Fullerenes ...... 32 1.6.1 Mass Spectrometers ...... 32 1.6.2 Photon Excitation Mass Spectrometry ...... 33 1.6.3 Ion Collision Mass Spectrometry ...... 34 1.7 Conclusions ...... 37

2 COOLING PROCESSES IN ENERGETICALLY EXCITED C60...... 38

2.1 Molecular Collisions and Energy Redistributions ...... 39 2.1.1 Molecular Collisions ...... 39 2.1.2 Energy Distribution ...... 45 2.2 Review of Theories in Rate Constant Calculations ...... 47 2.2.1 Rate Constant ...... 47 2.2.2 Collision Theory ...... 49 2.2.3 Potential Energy Surface Calculation ...... 52 2.2.4 Transition State Theory (TST) and the RRKM Approach ...... 54 2.2.5 Evaporation from Small Clusters ...... 60 2.2.6 Microcanonical Temperature Approach ...... 65 2.3 Competing Cooling Processes in Hot Cgo ...... 70 2.3.1 Cooling Processes in Hot C6o ...... 70

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.3.2 Radiation from Excited C6o ...... 71 2.3.3 Thermionic Emission from Excited C6o ...... 73 2.3.4 Unimolecular Dissociation from Excited C6o ...... 77 2.4 Conclusion ...... 84

3 THERMIONIC EMISSION FROM MULTIPHOTON EXCITED C60...... 85

3.1 Introduction ...... 85 3.2 Experiment ...... 86 3.2.1 Laser Ionization Time-of-Flight Mass Spectrometer ...... 86 3.2.2 C6o Molecular Flux Measurement ...... 89 3.2.3 Laser Intensity ...... 92 3.2.4 Single Electron Counting ...... 92 3.2.5 Detection Efficiency ...... 94 3.3 Probability of Delayed Electron Emission ...... 94 3.4 Discussion ...... 103 3.4.1 Accuracy of Results ...... 103 3.4.2 Effect of Fragmentation on Delayed Electron Emission ...... 104 3.4.3 Rate Constants ...... 106 3.5 Conclusions ...... 108

4 COLLISIONAL FORMATION OF ALKALI METALLOFULLERENES...... 109

4.1 Introduction ...... 109 4.2 Endohedral Fullerene A@C6o in Collision Experiments ...... 109 4.3 Alkali Metal Ion Sources ...... 114 4.4 Metallofullerene Formation by Ion Implantation into C6o Films ...... 120 4.4.1 LDI-MS Experiment ...... 120 4.4.2 Metallofullerene Products ...... 125 4.5 Metallofullerenes in Gas Phase Collisions ...... 127 4.5.1 Ion-Molecular Collision TOF Mass Spectrometer ...... 130 4.5.2 Ion Optics ...... 135 4.5.3 Collision of C6o with Potassium Ions ...... 139 4.5.4 Collision of C(,o with Sodium Ions ...... 147 4.6 Summary...... 148

5 THEORETICAL ANALYSIS...... 153

5.1 Introduction...... 153 5.2 Formation and Dissociation of Fullerenes with Encapsulated Na...... 154 5.2.1 Experimental Breakdown Curve ...... 154 5.2.2 Modeling the Breakdown Curve ...... 157 5.2.3 Results and Discussions...... 162 5.3 Heat Capacity of C6o ...... 168 5.3.1 Calculation of Caloric Curve ...... 168 5.3.2 Cgo Heat Capacity Measurement ...... 172

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.4 Collision Induced Thermionic Emission ...... 176 5.4.1 Collision Induced Ionization and Efficiency of Energy Transfer 176 5.4.2 Modeling the Ion Product in Collision ...... 178 5.4.3 Results and Discussions ...... 180 5.5 Conclusions ...... 185

BIBLIOGRAPHY...... 186

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF TABLES

T a b l e 1-1. P h y s i c a l P r o p e r t ie s o f t h e C 6o M o l e c u l e a n d C 6o S o l id a ...... 11

T a b l e 1-2. C a l c u l a t e d E l e c t r o n A f f in it ie s (E A ) a n d Io n i z a t io n P o t e n t ia l s (IP ) o f f u l l e r e n e s a n d e n d o h e d r a l fullerenesa ...... 31

Table 5-1. The 46 vibrational frequencies (n ) and their degeneracies (g) of C6o- These param eters are used with equation (5-3-1) to calcu late the caloric c u r v e E{T) of the C6o m olecule. These frequencies and degeneracies are adopted from reference [Jishietal 1 9 9 2 ]...... 1 7 0

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES

F ig u r e 1-1. T h e s t r u c t u r e o f t h e C 6o m o l e c u l e . T h is t r u n c a t e d icosahedral STRUCTURE IS HIGHLY SYMMETRIC. THE CARBON ATOMS ARE LOCATED AT THE 60 IDENTICAL VERTICES. THE STRUCTURE HAS 12 PENTAGONS AND 2 0 HEXAGONS. THE PICTURE IS BASED ON [W EBER 1 9 9 9 ]...... 5

F ig u r e 1 -2 . T h e g e o m e t r y o f a C 86 m o l e c u l e . T h e s t r u c t u r e s o f h ig h e r FULLERENES CAN BE THOUGHT AS ADDING EVEN NUMBER OF CARBON ATOMS, OR HEXAGON RINGS TO THE C6o STRUCTURE. THIS PICTURE IS PRODUCED FROM [WEBER 1 9 9 9 ] 6

F ig u r e 1 -3. T h is T O F m a s s s p e c t r u m s h o w s t h e c a r b o n c l u s t e r io n distribution PRODUCED BY LASER VAPORIZATION OF GRAPHITE [ROHLFING ETAL 1 9 8 4 ] ...... 8

F ig u r e 1-4. M ass spectrum of fragm ent ions form ed by excitation ofC6o+ [O ’B r ie n e t a l 1988]. The fragm ent distribution consists of tw o groups. F ullerene ions w ith sizes n > 30 fullerenes form by statistical evaporation o f C2. Sm aller ions are chains or rings...... 10

F ig u r e 1 -5 . T h e e l e c t r o n ic s t r u c t u r e o f t h e C 6o m o l e c u l e . T h e t r ip l y DEGENERATE LU M O IS LOCATED 1.7 EV ABOVE THE FIOM O ...... 13

F ig u r e 1-6. A w a t e r s o l u b l e fulleropyrrolidine . T h e s o l u b il it y in c r e a s e s u p o n FUNCTIONALIZATION. THIS FULLEROPYRROLIDINE BEARS SOLUBLE PENDANT GROUPS. T h e p e n d a n t g r o u p s n o t o n l y im p r o v e s o l u b il it y b u t a l s o c a n a n c h o r t h e FULLERENE TO SURFACES OR MATRICES ...... 14

F ig u r e 1-7. T h e f c c s t r u c t u r e o f t h e C 60 s o l i d . T h e l a t t ic e c o n s t a n t is 1 4 .1 6 A a t r o o m temperature . T h is p ic t u r e is a d o p t e d f r o m [F u l l e r e n e G a l l e r y ] 16

F ig u r e 1-8. T h is f ig u r e s h o w s t h a t t h e interstitial s it e s in f u l l e r id e s a r e d o p e d BY METAL ELEMENTS FOR THE STRUCTURE OF FULLERIDES. THE LEFT PICTURE IS AN ACeo STRUCTURE WITH ALL THE OCTAHEDRAL SITES FILLED BY A. THE RIGHT PICTURE IS AN A 3C 6 o WITH ALL THE OCTAHEDRAL AND TETRAHEDRAL SITES FILLED. THE LARGE SPHERES REPRESENTC6o- THIS PICTURE IS FROM [FULLERENE GALLERY]...... 17

F ig u r e 1-9. T h e s t r u c t u r e o f a n e n d o h e d r a l f u l l e r e n e [F u l l e r e n e G a l l e r y ], In THIS STRUCTURE, AN ATOM IS ENCAPSULATED AT THE CENTER OF THE CAGE. OFF- CENTER LOCATION OF THE CAPTURED ATOM IS ALSO A POSSIBLE CONFIGURATION.... 26

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure l-l0. The electron distribution map of an endohedralS c @ C82 m o l e c u l e . The map indicates th at the Sc is encapsulated and off-centered inside the C82 cage [Shinohara 2000]...... 2 9

F ig u r e 1 -1 2 . I o n s p r o d u c e d in t h e c o l l is io n o f C 6o- ( a ) In c o l l is io n o f C m w it h L i+ a t 74 e V , C2 loss is the dominant fragm entation pattern [W an et a l1993]. (b ) In c o l l i s i o n o f C60 w i t h C2+ a t 15.6 MeV, significant charge transfer is observed [Nakai e t a l 1997]...... 36

F ig u r e 2 -1 . T h e trajectories o f c o l l is io n i n t h e p ic t u r e o f t h e c l a s s i c a l m echanics, b is the impact param eter ...... 4 3

F ig u r e 2 -2 . T h e r e a c t io n c r o s s s e c t io n f o r t h e c a p t u r e o f H e i n t h e c o l l is io n WITH C 60+ AS A FUNCTION OF THE COLLISION ENERGY [CAMPBELL AND ROHMUND 2 0 0 0 ]. T h e s o l id l in e is a p l o t o f e q u a t io n ( 2 - 1 - 2 1 ) . T h e s q u a r e s y m b o l s a r e experimental d a t a ...... 4 5

F ig u r e 2 -3 . E n e r g y redistribution in a n e x c it e d m o l e c u l a r s y s t e m ...... 4 6

F ig u r e 2 -4 . T h e p o t e n t ia l e n e r g y s u r f a c e o f a c h e m ic a l r e a c t i o n AB + C —► A + BC. In a l l t h e trajectories , o n l y t h o s e t h a t c r o s s t h e s a d d l e p o in t l e a d t o p r o d u c t i o n ...... 53

F ig u r e 2 -5 . T h e a s s u m e d t r a n s it io n s t a t e in a r e a c t i o n . O n c e a s y s t e m a c q u ir e s e n o u g h e n e r g y i n t h e r e a c t io n c o o r d in a t e t o c r o s s t h e c r it ic a l s u r f a c e , it is a t t h e t r a n s it io n s t a t e a n d t h e s y s t e m w il l a d v a n c e t o p r o d u c t s ...... 55

Figure 2-6. Three cooling processes in energetically excited C6o* ...... 71

Figure 2-7 R adiation from gas phase hot C6o. The m olecule is excited by a 193 nm ArF excim er laser. The radiation has the same distribution as radiation FROM A HOT TUNGSTEN FILAMENT [HESZLEREIML 1997]...... 7 2

Figure 2-9. Ion products from m ultiphoton excitedC 60. The TOF mass spectrum SHOWS THE COMPETING CHANNELS OF UNIMOLECULAR DISSOCIATION AND ELECTRON EMISSION IN THE MULTIPHOTON EXCITED C 6o MOLECULES...... 7 8

Figure 2-10. The m icrocanonical rate constants for the com peting processes in e x c i t e d Ceo- D ata are adopted from [Lifshitz 2000]...... 83

F ig u r e 3 -1 . U V l a s e r multiphoton e x c it a t io n T O F m a s s spectrometer f o r t h e STUDY OF DELAYED ELECTRON EMISSION FROM C6o MOLECULES...... 8 8

F ig u r e 3 -2 . D i a g r a m o f t h e arrangement f o r t h e C 6o b e a m measurement ...... 91

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F ig u r e 3 - 3 . D e p e n d e n c e o f e l e c t r o n c o u n t r a t e o n discriminator t h r e s h o l d . T h e s e d a t a s u g g e s t t h a t t h e d e t e c t io n e f f ic ie n c y is l im it e d b y t h e DISCRIMINATOR THRESHOLD, EVEN AT-1 0 M V ...... 9 5

F ig u r e 3 -4 . D e l a y e d e l e c t r o n e m is s io n f r o m l a s e r e x c it e d C 6o m o l e c u l e s . T h e SOLID SYMBOLS ARE RECORDED AT DIFFERENT LASER PULSE ENERGIES BUT IDENTICAL SOURCE CONDITION, T = 370 °C. THE BACKGROUND INTENSITY (DOTTED LINE) IS RECORDED WITH THE C6o BEAM BEING BLOCKED. THE SPECTRUM RECORDED AT 5 20 °C WITH MILDLY FOCUSED LASER (OPEN CIRCLES) SHOWS DELAYED ELECTRON EMISSION OVER 3 0 0 M S...... 9 6

F ig u r e 3-5. N u m b e r o f e l e c t r o n s p e r l a s e r s h o t . T h e d a t a s h o w n in t h e f ig u r e ARE INTEGRALS OF THE SPECTRA IN FIGURE 3 -4 OVER A TIME RANGE FROM 0 TO T. Note the relatively sm all fraction of quasi-prompt electrons em itted FROM EXCITED C 6o DURING THE FIRST 2 0 N S ...... 9 8

F ig u r e 3-6. T o t a l e l e c t r o n y ie l d v s . l a s e r f l u e n c e . T h e n u m b e r o f d e l a y e d ELECTRONS EMITTED FROM THE EXCITED C6o MOLECULES IS INTEGRATED OVER TIME INTERVALS OF 0.1 MS < T< 80 MS. THE FIGURE SHOWS THE TOTAL ELECTRON YIELD AS A FUNCTION OF LASER FLUENCE FOR THREE DIFFERENT C 60 SOURCE TEMPERATURES. 100

F ig u r e 3-7. C o m p a r is o n o f t h e temperature d e p e n d e n c e o f t h e n u m b e r o f DELAYED ELECTRONS WITH THE QUOTIENT OF EQUILIBRIUM VAPOR PRESSURE, P, AND SOURCE TEMPERATURE, T. THIS QUOTIENT IS LINEARLY RELATED TO THE NUMBER DENSITY OF C 6o IN THE MOLECULAR BEAM. VALUES FOR P ARE TAKEN FROM THE REFERENCES LISTED IN THE FIGURE...... 1 0 2

F ig u r e 3 -8 . T im e - o f - f l ig h t m a s s s p e c t r a o f multiphoton e x c it e d C 6o. T h e s p e c t r a WERE RECORDED WITH AN UNFOCUSED LASER AT FLUENCES OF 29 AND 102 Mj/CM2, RESPECTIVELY. THEY ARE REPRESENTATIVE OF THE CONDITIONS CHOSEN FOR COLLECTION OF DELAYED ELECTRONS...... 105

F ig u r e 3 -9 . T i m e - o f - f l ig h t m a s s s p e c t r u m o f multiphoton e x c it e d C 6o a t h ig h LASER FLUENCE. THE SPECTRUM SHOWS THAT FRAGMENTATION IS VERY STRONG UNDER CONDITIONS WHERE DELAYED ELECTRON EMISSION SATURATES...... 1 0 7

F ig u r e 4 -1 . Io n p r o d u c t s in t h e c o l l is io n o f C 6o+ w it h H e a t o m s a t t h e c o l l is io n ENERGY OF 44 EV. THE SPECTRUM IS ADOPTED FROM REFERENCE [ROSS AND C a l l a h a n 1 9 9 1 ]...... 11 0

F ig u r e 4 -2 . Re l a t i v e c a p t u r e c r o s s - s e c t io n s o f L i@C n+ i n t h e c o l l is io n o f C 6o WITH L l+ IONS AT DIFFERENT COLLISION ENERGIES. DATA ARE FROM [WAN ETAL 1 9 9 2 ]...... 113

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F ig u r e 4 -3 . D ia g r a m o f m e t a l io n g u n . A , B , C - E in z e l l e n s ; D - G r o u p o f d e f l e c t o r s ; E - A n o d e ; F - W e h n e l t ; G - B i a s ; H - Ra d i a t i o n s h ie l d a n d io n g u n s u p p o r t . E m it t e r - in t e g r a t e d h e a t e r c a r t r id g e a n d impregnated p o r o u s t u n g s t e n p l u g ...... 115

F ig u r e 4 -4 . N a + a n d K + io n o u t p u t a s a f u n c t i o n o f io n k in e t ic e n e r g y . T h e io n g u n o p e r a t e d in d c m o d e . T h e io n o u t p u t w a s m e a s u r e d w it h a n e l e c t r o d e OF DIAMETER 0 .8 CM AND LOCATED AT 2 .0 CM FROM THE OUTLET OF THE ION GUN. T h e io n e m it t e r c a r t r id g e s a r e h e a t e d b y (2.0 A, 8.0 V) a n d (2.0 A , 8.8 V ) f o r THE SODIUM AND POTASSIUM SOURCES, RESPECTIVELY...... 116

F ig u r e 4 -5 . M a s s s p e c t r u m o f a c o m m e r c ia l s o d i u m io n s o u r c e . T h e s o u r c e is CONTAMINATED BY ABOUT 1 % OF K+...... 1 1 7

F ig u r e 4 -6 . M a s s s p e c t r a o f p o t a s s i u m io n s o u r c e s , ( a ) Io n s d e t e c t e d i n t h e o u t p u t o f a c o m m e r c ia l p o t a s s i u m io n s o u r c e . T h e im p u r it y m e t a l io n s REACH SOME 10% OF THE TOTAL ION OUTPUT. (B) RE-COATING THE ION EMITTER ENHANCED THE PURITY OF THE POTASSIUM ION SOURCE...... 118

F ig u r e 4 -7 . M a s s s p e c t r u m o f a c o m m e r c ia l io n s o u r c e c l a im e d t o b e d o p e d w it h c a l c iu m . T h is io n s o u r c e d o e s n o t e m it a n y Ca + (m a s s 4 0 a m u ), b u t K + ( m a s s 39 AND 41 AMU), AND OTHER ALKALIS ...... 1 19

F ig u r e 4 -8 . L a s e r D e s o r p t io n a n d Io n iz a t io n M a s s S pectrometer (LDI-MS) 122

F ig u r e 4 -9 . T h e r o t a t in g d is c ( l e f t ) o n t o w h ic h t h e C 6o f il m is g r o w n , a n d t h e io n o p t ic s f o r l a s e r d e s o r p t io n io n iz a t io n m a s s spectrometry ...... 123

F i g u r e 4 -1 0 . LDI-MS spectrum of a C6o film . N o fragm ent from C6o is observed. The asym m etric ta il of the C60 peak is due to fullerenes th at contain 13C i s o t o p e s...... 1 2 4

F ig u r e 4 -1 1 . LDI-MS s p e c t r a o f N a + io n i m p l a n t e d C 6o f i l m s . T h e in t e n s it y o f t h e SODIUM METALLOFULLERENE ION DEPENDS ON THE IMPLANTATION ENERGY. THIS FIGURE SHOWS SPECTRA FOR IMPLANTATION ENERGIES FROM 20 TO 100 EV. THE IMPLANTED C6o FILMS ARE PREPARED WITH THE RATIO BETWEEN N A + AND C6o OF ROUGHLY 1:1 ...... 128

F ig u r e 4 - 1 2 . LDI-MS s p e c t r u m o f K+ i m p l a n t e d C 6o f il m . N o p o t a s s i u m METALLOFULLERENE IONS WERE OBSERVED. THE IMPLANTATION ENERGY IS 100 EV...... 12 9

F ig u r e 4 -1 3 . Io n - m o l e c u l e c o l l is io n T O F m a s s spectrometer ...... 131

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F ig u r e 4-14. A x i a l v ie w o f t h e io n c o l l is io n a n d e x t r a c t io n c o m p o n e n t s . A is t h e ION EXTRACTION PLATE; B IS THE C6o OVEN; C IS THE MOLECULAR FLUX MONITOR (MICROBALANCE); AND D IS THE METAL ION GUN...... 132

F ig u r e 4 -1 5 . T o p v ie w o f t h e io n c o l l is io n a n d e x t r a c t io n c o m p o n e n t s . T h e C 6o SOURCE IS ON THE RIGHT; THE MICROBALANCE IS ON THE LEFT. THE ION OPTICS CONSISTS OF A W lLEY-McLAREN LENS AND A SET OF ION DEFLECTOR (SHOWN NEAR TOP OF THE PHOTOGRAPH)...... 1 3 3

F ig u r e 4-16. G e o m e t r y o f t h e t w o -f ie l d W i l e y -M c L a r e n i o n o p t ic s ...... 136

F ig u r e 4 - 1 8(a ). M a s s s p e c t r a o f io n s f o r m e d b y c o l l is io n o f C 6o w it h p o t a s s i u m IONS. A t c o l l is io n e n e r g ie s b e l o w 4 8 E V , n o p o t a s s i u m metallofullerene is o b s e r v e d ...... 141

F ig u r e 4 - 1 8 (b ). M a s s s p e c t r a o f io n s f o r m e d b y c o l l is io n o f C 6o w it h p o t a s s i u m i o n s . F r a g m e n t i o n s , s m a l l e r t h a n K C 5g+, a r e o b s e r v e d a t c o l l is io n ENERGIES ABOVE 5 6 E V ...... 1 4 2

F ig u r e 4 -1 8 ( c ). M a s s s p e c t r a o f io n s f o r m e d b y c o l l is io n o f C 6o w it h p o t a s s i u m IONS. A t c o l l is io n e n e r g ie s h ig h e r THAN 70 EV, C 6o+ a n d KC58+ d o n o t s u r v i v ei\ . 143

F ig u r e 4-19. T h e e n e r g y d e p e n d e n c e o f t h e f u l l e r e n e io n intensities in t h e COLLISION OF C6o WITH POTASSIUM IONS...... 144

F ig u r e 4-20. T h e e n e r g y d e p e n d e n c e o f t h e p o t a s s iu m metallofullerene io n PRODUCTS IN THE COLLISION OF C6o WITH POTASSIUM IONS...... 145

F ig u r e 4-2 1(a ). M a s s s p e c t r a o f p r o d u c t io n s f r o m c o l l is io n s o f C 6o w it h s o d iu m i o n s . NaC60+ IS t h e l a r g e s t ION o b s e r v e d . It is t h e o n l y p r o d u c t o b s e r v e d a t COLLISION ENERGY BELOW 35 EV. THE MASSES OF C60+ AND NaC58+ DIFFER BY ONLY 1 AMU; THEY CANNOT BE RESOLVED SEPARATELY...... 150

F ig u r e 4-2 1 (b ). M a s s s p e c t r a o f p r o d u c t io n s f r o m c o l l is io n s o f C 6o w it h s o d iu m IONS. No NaC60+ IS OBSERVED AT AND ABOVE 55 EV . Cn+ AND NaCN-2+ PEAKS COINCIDE WITHIN OUR MASS RESOLUTION...... 151

F ig u r e 4-22. T h e e n e r g y d e p e n d e n c e o f p r o d u c t io n intensities in c o l l is io n s o f C 60 WITH SODIUM IONS ...... 152

F ig u r e 5-2. Comparison of breakdown curves. The dotted line is the breakdown curve reported by W an e t a l [ W a n e ta l 1993], m easured w ith a kinetic ENERGY SPREAD OF ABOUT 3 EV, AN ORDER OF MAGNITUDE LARGER THAN IN OUR EXPERIMENT (FULL DOTS AND SOLID LINE)...... 165

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F ig u r e 5 -4 . C a l o r ic c u r v e o f C 6o. T h e d a s h e d l in e is f r o m t h e equipartition THEOREM; THE SOLID LINE AND THE DOTTED LINE ARE CALCULATED FROM STATISTICAL MECHANICS WITH THE 4 6 VIBRATIONAL MODES AND THEIR DEGENERACIES...... 171

F ig u r e 5 -6 . H e a t c a p a c it y o f C 6o m o l e c u l e s . T h e h e a t c a p a c it y i s m e a s u r e d b y THE CHANGE IN THE BREAKDOWN ENERGY OF N A @ C 6 o+ IONS AS THE C60 SOURCE TEMPERATURE CHANGES...... 1 7 4

F ig u r e 5 -9 . E f f e c t o f e n e r g y b r o a d e n i n g

xiv

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT

THERMOIONIZATION AND DISSOCIATION

OF FULLERENES AND ENDOHEDRAL FULLERENES

Rongping Deng

University of New Hampshire, September, 2003

Electron emission and unimolecular dissociation of energetically excited

fullerenes and endohedral fullerenes are studied with mass spectrometry. Three

experimental approaches have been developed for these studies. These are UV laser

excitation time-of-flight mass spectrometry (TOF-MS), laser desorption and ionization

mass spectrometry (LDI-MS), and ion-molecule collision mass spectrometry (IMC-MS).

Our first experimental effort is to investigate delayed electron emission from

multiphoton excited C6o molecules. A lower limit of the probability of electron emission

from multiphoton excited C6o molecules is determined to be about 2.6 %. This result

indicates that electron emission is not merely parasitic to dissociation.

The second experimental effort is the study of metallofullerene formation.

Threshold energies were found in the formation of potassium metallofullerenes and

sodium metallofullerenes. The large thresholds indicate that the alkali metallofullerene

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. products have endohedral structure. Sodium ion implantation into C6o films could be a

potential method of producing metallofullerenes in macroscopic quantity.

The ion-molecule collision experiments characterize the dynamical and physical

processes in energetically excited fullerenes. Modeling the breakdown curve of Na@C6o+

in the collision of C6o with sodium ions enables us to extract the activation energy for loss

of C2 from Na@C6o+, which gives the value of 10.17 ± 0.02 eY. The result indicates that

the encaged sodium ion does not significantly change the C-C binding in the fullerene

shell.

Changing the internal energy of the target C6o molecules causes a shift in the

breakdown curve of Na@C6o+. Based on this phenomenon, a method of measuring the

heat capacity of C60 is introduced. The heat capacity is determined to be 0.0126 ± 0.0014

eV/K for temperatures of 500 °C < T< 570 °C.

The C6o+ ion product in the collision of C$q with potassium ions is modeled as

thermionic emission. The C6o+ intensity reaches its maximum at 57 eV. At this collision

energy the efficiency of energy transfer reaches about 78 %. This high efficiency can be

explained using the two-stage collision model.

xvi

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. INTRODUCTION

The discovery of the highly symmetric and closed-shell structure of C6o and

higher fullerenes in 1985 [Kroto et al 1985] inspired intensive and extensive scientific

research on these fascinating carbon clusters. Due to the strong covalent bonding between

carbon atoms, fullerenes have stable structures. The sizes of the fullerenes are between

the size of small molecules and bulk materials. The fundamental research on the physical

and chemical properties of these clusters help us to understand how the physical

properties of a physical entity are related to its structure. It is also important to understand

the physical properties of these clusters in order to develop new materials for

applications. Potentials in fullerene-based applications have already been proposed in

various fields including mechanics, optical devices, electronics, materials, chemical and

biomedical applications. Fullerene study has been one of the most active scientific

research areas.

This dissertation presents fundamental research on the topics of cooling processes

in energetically excited fullerenes and metallofullerenes, the formation of alkali

metallofullerenes and the time-of-flight mass spectrometers employed for the above

studies. This dissertation has five chapters. Chapter 1 is a brief review of fullerene

research as the background for our work presented in this dissertation. Chapter 2 has two

parts. The first part is a review of molecular reaction rate theories. The second part of this

chapter presents the cooling processes in energetically excited fullerenes and the research

progress on the study of the cooling processes in fullerenes. Our research is based on the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. theories and facts presented in this chapter. Chapter 3 presents the method and results of

our study on the thermionic emission from UV laser multiphoton excited C6o molecules.

Chapter 4 describes the apparatus that we have developed to investigate the formation of

alkali metallofullerenes and yields of the metallofullerene products in the studies. Chapter

5 is our research on the ion-molecule collision induced dissociation and electron emission

in fullerenes. It also presents an experimental method to determine the heat capacity of

C6o molecules.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 1

FULLERENE RESEARCH

1.1 The Structure of the C^o Molecule

Carbon clusters display various forms of structures. These structures can be linear

chains, rings or closed shells. The most stable forms of carbon clusters are determined by

their size. It is found that for a cluster of size up to 10 carbon atoms, the stable structure

takes the form of a linear chain. For a size from 10 to 30 carbon atoms, the stable

structure takes the form of a molecular ring, and for a size of 40 and larger, the stable

structure takes a form of a closed shell. The most prominent fullerene, C6o, is the first

type of molecule among the fullerene family to be discovered in 1985. The closed-caged

structure of this molecule was proposed by Kroto [Kroto et al 1985] and was confirmed

by nuclear magnetic resonance (NMR) experiments [Taylor et al 1990]. Not only did the

experiments give direct evidence that the C

they also confirmed that only one type of chemical site exists for the carbon atoms in this

molecule. Ceo has 60 equivalent vertices, 12 pentagons, 20 hexagons and 90 edges. Its

geometry meets the Euler’s rule for polyhedra [Dresselhaus et al 1996],

f + v = e + 2,

where / is the number of faces, v is the number of vertices and e is the number of edges.

There are two different bond lengths in Cgo- The bonds between the pentagon and the

hexagon are single bonds with a length of 1.46 A. The bonds between the two hexagons

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. are double bonds with a length of 1.40 A. A geometric calculation gives a diameter of

7.09 A for this molecule. A consistent experimental value of 7.10 ± 0.07 A is given by

NMR measurement. If we add the electron cloud thickness of 3.3 5 A, a value based on the

spacing between layers in graphite, the outer diameter of C6o is 7.10 + 3.35 = 10.45 A.

Figure 1-1 shows the structure of a Ceo molecule.

It is easily understood that pentagons exist in the closed-caged fullerene

structures. Hexagons can only generate planar structures. Pentagons are needed to create

the curvature. The curvature introduces strain in the stmcture. In the electronic view, sp2

bonds which exist in graphite are planar and trigonal, while sp3 bonds which exist in

diamond are tetrahedral. The stmcture of Cgo requires a mixture of sp 2 and sp 3 bonds. The

binding energy (atomization energy) of Ceo is 7.4 eV/atom.

Besides Euler’s rule determining the geometry of polyhedrons, there is another

mle to geometrically determine the stability of the fullerene structures. This rule is called

the isolated pentagon rale (IPR); it states that a chemically stable fullerene structure

requires that the pentagons are isolated. The isolated pentagon rale can be best

understood as a logical consequence of minimizing the number of dangling bonds and the

steric strains of fullerenes. C 6 o is the smallest fullerene that satisfies the IPR and C 70 is

the next smallest one. and C 70 are very stable in air. The strong C-C bonds inside

these molecules make them strong and resilient structures. There is no IPR fullerene

between C 60 and C 7 0 . Although all chemically stable fullerenes follow this isolated

pentagon rale, fullerene derivatives do not necessarily follow this rale since the

functionalization or doping may change the strain on the shell.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The C 70 structure can be viewed as adding a ring of 10 carbon atoms, or adding a

belt of 5 hexagons, to the C 60 molecule around the equatorial plane of the molecule. In

the synthesis of fullerenes, it is found that C 70 is less abundant than C6o- C 70 has higher

binding energy per atom. However, in kinetics, with higher binding energy the barrier

that must be overcome to reach C 70 upon formation is greater, which makes the formation

less favorable. The structures of higher fullerenes are built by increasing the number of

hexagons, while the number of pentagons remains constant at twelve. Figure 1-2 shows

the geometry of a Cg6 molecule.

Mb* 4 . ^ ^

Figure 1-1. The structure of the C 60 molecule. This truncated icosahedral structure is highly symmetric. The carbon atoms are located at the 60 identical vertices. The structure has 12 pentagons and 20 hexagons. The picture is based on [Weber 1999].

The truncated icosahedral structure of C 60 has very high symmetry. There are 120

symmetry operations for the icosahedral point group h- They are 12 primary fivefold

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. rotations Cj though the center of the pentagonal faces, 20 secondary threefold rotations

through the centers of the 20 hexagonal faces, 30 secondary twofold rotations through the

30 edges joining the two adjacent hexagons. The truncated icosahedron has a shape of a

sphere. Its basis functions for electronic structure calculations are the spherical harmonics

Yim for group Ih.

Figure 1-2. The geometry of a Cg6 molecule. The structures of higher fullerenes can be thought as adding even number of carbon atoms, or hexagon rings to the structure. This picture is produced from [Weber 1999].

1.2 Synthesis of Fullerenes

Fullerenes were first discovered by Smalley’s group in an experiment employing

laser-induced vaporization of graphite and mass spectrometry [Kroto et al 1985], Figure

1-3 shows a mass spectrum of carbon clusters produced by a similar technique one year

before the discovery of fullerenes [Rohlfmg et al 1984], In this spectrum, all larger

clusters, beyond n = 36, contain an even number of carbon atoms. Only later was it

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. realized that all these clusters have caged structures. When fullerenes were newly

discovered, only microscopic quantities were produced using this type of laser

vaporization technique. In a typical apparatus, a pulsed Nd:YAG laser operating at 532

nm wavelength with pulse energy of about 250 mJ would vaporize a graphite target into a

stream of high pressure helium. This method of producing fullerenes is only suitable for

gas phase studies, and mass spectrometry studies. Macroscopic quantities of fullerenes

are produced using the arc discharge technique [Kratschmer et al 1990]. For example, in

a vacuum system, two electrodes are placed in ~ 200 torr He atmosphere. An electric

discharge generated between these two graphite electrodes creates a high temperature of

about 4000 °C at the arc spot to evaporate the graphite and produce fullerenes. The

efficiency of fullerene production depends on various parameters. A total fullerene yield

of ~ 10 % requires a minimum gas pressure ~ 25 torr. Another technique of producing

macroscopic quantity of fullerenes is the plasma arc. In this type of apparatus, the gap

between the two graphite electrodes is fixed. This technique is reported to produce

fullerenes with a yield as high as ~ 40 % [Dresselhaus et al 1996],

The raw products from the electric arc and plasma arc techniques contain various

sizes of fullerenes as well as soot. The fullerene extraction and purification are critical

stages in the production process. Extensive research on fullerenes was possible only after

methods were developed to separate fullerenes from the soot so that macroscopic

quantities of pure fullerenes became available and affordable [Kratschmer et al 1990].

Solvent methods or sublimation methods have been employed for fullerene extractions.

C6o is soluble in benzene or toluene. In certain solvents, only higher fullerenes are

soluble. In the sublimation method, the raw soot is heated in a quartz tube in He or

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vacuum to sublime the fullerenes. The sublimation temperatures are 350 °C and 460 °C

for Cgo and C 7 0 , respectively. Methods of fullerene purification include solvent method,

Liquid Chromatography (LC), and sublimation in a temperature gradient.

100

xio

0 >

•4—*

c 80 oc

0 20 40 60 80 100 120

Cluster Size (Carbon Atoms)

Figure 1-3. This TOF mass spectrum shows the carbon cluster ion distribution produced by laser vaporization of graphite [Rohlfmg et al 1984],

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.3 Stability and Fragmentation of Fullerenes

Structural studies indicate that the growth of fullerenes by adding extra carbon

atoms likely takes place in the vicinity of a pentagon. The addition of one hexagon to a

fiillerene requires two additional carbon atoms. Energetically, absorption of C 2 is

exothermic. In a C 2 molecule, each carbon has two sp a bonds and two % bonds. After

being absorbed, each carbon atom has three a bonds and one n bond. In this process, the

total energy decreases by about ~ 4 eV for each carbon atom [Dresselhaus et al 1996].

The bonds between carbon atoms on the fullerene surface deviate substantially

from the ideal bonds for sp2-hybridized carbon. The pyramidalization angle, defined as

Qan- 90°, is 11.6° for C60, the largest value of any of the fullerenes. This pyramidalization

angle induces strain of 8.5 kcal/mol/per carbon atom [Beckhaus et al 1992]. Exohedral

additions to the fullerene shell will alleviate the strain, while endohedral additions may

cause an increase in strain.

Photofragmentation plays an important role in the study of fiillerene

fragmentations. Figure 1-4 shows a mass spectrum of fragment ions formed from laser-

excited Cgo+ [O’Brien et al 1988]. The highly excited C6o+ undergoes a series of C 2 losses

until C 32+ is reached. At this size the strain energy in the fullerene becomes too high, and

it fragments into other structures. If neutral C 60 molecules are photoexcited, they may

emit electrons at some random time after excitation. This type of thermionic emission

will be studied in detail in Chapter 2 and Chapter 3.

Fragmentation of fullerenes and fullerene ions has also been studied by other

experimental methods. Examples are collision of fullerene ions with target gases [Larsen

et al 1999, Caldwell et al 1992, Hvelplund et al 1991, Doyle and Ross 1991, McElvany

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and Callahan 1991, Weiske et al 1991] and collision of fullerene ions with surfaces. In

the gas phase collision experiments, the fragment distribution depends on the collision

energies. For collision energies higher than 100 eV, two groups of fragment ions were

observed, similar to results from photofragmentation experiments. Fragments with sizes n

> 30 are fullerenes, smaller fragments can be chains and rings. Similar fragmentation

patterns were observed in experiments on collisions of fullerenes with surfaces [Lill et al

1996]. Successive C2 fragmentation from excited fullerenes is also observed in the

collision of C 60 and C 70 with alkali metal ion projectiles [Wan et al 1993].

10 20 30 50 6040

Cluster Size (Carbon Atoms)

Figure 1-4. Mass spectrum of fragment ions formed by excitation of Cgo+ [O’Brien et al 1988]. The fragment distribution consists of two groups. Fullerene ions with sizes n > 30 fullerenes form by statistical evaporation of C 2 . Smaller ions are chains or rings.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In order to transfer graphite into the gas phase, it has to be heated up to several

thousands of degrees. Fullerenes can be sublimed at temperatures below 400 °C. This low

sublimation temperature makes the gas phase study of fullerenes easy. One possible

problem is the thermal degradation of fullerenes. Often a nonvolatile residue is found

after sublimation that cannot be dissolved in organic solvents. It has been characterized as

amorphous carbon [Popovic et al 1994] or polymerized carbonaceous material [Piacente

et al 1995].

Table 1-1. Physical Properties of the C6o Molecule and C^o Solid3

Constant Value C-C bond length between pentagon and hexagon 1.46 A C-C bond length between adjacent hexagons 1.40 A Molecular diameterb 7.10 A Binding energy per atom 7.40 eV Electron affinity 2.65 ± 0.05 eV First ionization potential 7.56 eV Second ionization potential 11.5 eV Lattice constant (fee) 14.17 A Intermolecular distance in solid 10.02 A Cohesive energy of Ceo crystal 1.6 eV/Ceo Mass density of solid 1.72 g/cm3 Electron band gap of solid 1.5 eV aValues are adopted from [Dresselhaus et al 1996]. ‘This value is based on the NMR measurement. The geometric calculation gives a value of 7.09 A.

1.4 Physical and Chemical Study of Fullerenes

The physical and chemical properties of fullerenes are determined by their

molecular structures. Fullerenes have potential applications as electronic and optical

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. materials, for chemical and biological products, and in emerging nano-technology. Table

1-1 lists some known physical properties of the C6o molecule and C6o solid.

1.4.1 Electronic Structure of the Cgo Molecule

Reduction and oxidation studies in fullerene electrochemistry provide a pathway

to access the electronic properties of fullerenes and their derivatives. Voltametric

experiments have investigated the electrochemical properties and stabilities of many new

fullerene-based materials [Echegoyen et al 2000], C(,o has 30 bonding molecular orbitals

with 60 n:-electrons [Haddon et al 1986]. Its antibonding lowest unoccupied molecular

orbital (LUMO) is triply degenerate; it is located 1.7 eV above its highest occupied

molecular orbital (HOMO), as shown in Figure 1-5. Higher fullerenes, such as C 7 0 , have

similar electronic structure [Baker et al 1991; Colt and Scuseria 1992], Due to the low

electron affinities, 2.7 eV for C 6 0 and 2.8 eV for C 7 0 , and high ionization potentials, 7.6

eV for Cgo and 7.3 eV for C 7 0 , fullerenes display rich electrochemistry. The low-lying

triplet LUMO states in C 60 give this molecule an exceptionally low reduction potential

and the ability to accept up to six electrons electrochemically. However, oxidation of C< 5o

is relatively difficult due to the high ionization potentials.

The measurement of the difference between the first reduction and oxidation

potentials reveals the HOMO-LUMO energy gaps in fullerenes. The results indicate that

the first one-electron reduction becomes easier as the size of the fullerene increases,

which is in agreement with that electron affinities increase with increasing size of the

fullerenes [Yang et al 1995].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. <-lg

LUMO lu

1.7 eV

HOMO

Electronic Structure of C,'60

Figure 1-5. The electronic structure of the Cgo molecule. The triply degenerate LUMO is located 1.7 eV above the HOMO.

1.4.2 Chemical Reactions and Fullerene Derivatives

Although there are no dangling bonds in fullerene structures, the double bonds at

the junction of the six-membered rings provide fullerenes with the ability to undergo

addition reactions, which promises varied production of fullerene derivatives and many

potential applications based on functionalized derivatives of fullerenes.

The synthesis of fullerene derivatives includes the cycloadditions, hydrogenated

fullerenes, halogenation of fullerenes, nuleophilic additions, and organometallic

fullerenes [Wilson et al 2000]. A large number of functional groups have been covalently

attached to fullerenes. This can be an effort to modify the electronic properties of

fullerenes to produce materials such as three-dimensional electroactive polymers,

molecular wires, surface coatings, and electro-optic devices [Prato 1997], Singly-bonded

functionalized derivatives of C6o include dihydrofullerenes C 60H2 , alkylfullerenes R 2 C60

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and R 4 C6 0 , and fluorofullerenes C 6oF4 8 - Cyclopropanated derivatives of C6o include

epoxyfiillerene CeoO, methanofullerenes, and transition metal derivatives. In the

transition metal derivatives, the electron-rich transition metal complexes attach to the

exterior of the fullerene framework. These fullerene derivatives promise the possibility of

producing crystalline molecular solids [Fagan et al 1992, Balch and Olmstead 1998].

Fullerene derivatives also include the cycloaddition products with the formation of four-,

five-, or six-membered rings and heterocyclic derivatives with rings larger than a

cyclopropane ring. These products can be designed to combine the fullerene electronic

and photophysical properties with those of other electroactive centers and chromophores

such as ferrocene to form conducting salts, photo-induced charge transfer complexes, or

nonlinear optical materials [Guldi et al 1997, Maggini et al 1994, Prato et al 1996, Prato

andMaggini 1998],

(C H 2C H 20 ) 3C

Figure 1-6. A water soluble fulleropyrrolidine. The solubility increases upon functionalization. This fulleropyrrolidine bears soluble pendant groups. The pendant groups not only improve solubility but also can anchor the fullerene to surfaces or matrices.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Functionalization can improve the solubility of fullerenes. Several

fulleropyrrolidines bearing solubilizing pendant groups have been produced [Signorini et

al 1996, Maggini et al 1999], The synthesis of water-soluble fullerene derivatives has

been an essential prerequisite for developing fullerene biomedical applications, such as

singlet oxygen generation, radical scavenging properties, and HIV-1 protease inhibition

[Jensen et al 1996]. Figure 1-6 shows an example of a soluble fulleropyrrolidine [Wilson

et al 2000]. In this fullerene derivative, the pendant groups improve the solubility. On the

other hand, the pendant groups can anchor the fullerene to inert matrices or surfaces,

which open up potentials for various applications.

1.4.3 Cgo Solid and Fullerides

Crystalline Cgohas a face-centered cubic (fee) structure with a lattice constant of

14.1569(5) A at 290 K. Figure 1-7 shows the fee structure of the Cgo solid. Many

experimental techniques have shown that Cgo molecules are disordered in orientation at

room temperature. The effect has been studied by X-ray diffraction (XRD) [Heiney et al

1991], nuclear magnetic resonance (NMR) [Johnson et al 1992a], quasi-elastic neutron

scattering [Neumann et al 1991] and muon spin relaxation [Kiefl et al 1992]. The Cgo

molecules rotate almost freely and randomly without any preferred orientation in space.

The interaction between the Cgo molecules in the solid is relatively weak

compared to the Cgo intramolecular interactions. The electronic structure of fullerene

solids is mainly determined by the electronic levels of the Cgo molecule itself. In the Cgo

solid, the energy bands which are formed when the molecular orbitals of neighboring

molecules mix, are only weakly broadened and result in a set of rather narrow, non-

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. overlapping bands. Since the HOMO hu band is completely filled and the LUMO tju band

is empty, pure solid C6o is an insulator. The local density approximation (LDA) has been

applied to calculate the bandwidths, bandgaps and density of states near the Fermi level

N(Ef ) [Erwin and Pickett 1992], The calculation shows that the bandwidth of tju is about

0.5 eV and the HOMO-LUMO band gap is about 1.5 eV. The HOMO level in the solid

forms the valence band and the LUMO level forms the conduction band.

Figure 1-7. The fee structure of the Cgo solid. The lattice constant is 14.16 A at room temperature. This picture is adopted from [Fullerene Gallery].

Another active research area is the formation of new compounds by reactions of

inorganic compounds with fullerene solids. Fulleride, a solid form of fullerene and

metallic compound, is one of the new materials. Metal ions are at the interstitial sites in

the fulleride solid. AnC6o has a face-centered cubic (fee) structure at temperature above

400 °C [Bommeli et al 1995]. A3 C60 has a fee structure with all octahedral and tetrahedral

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. holes being filled [Tycko et al 1991]. Two structures of fullerides are shown in Figure 1-

8. Fullerides can be prepared by intercalation of metal atoms into the fullerene solid via

vapor transport or by solution techniques. Vapor phase intercalation is a popular and

successful technique for alkali metal fulleride preparations; it is relatively easy due to the

large interstices in the Ceo solid. The intercalation process includes a stage of direct

reaction of a stoichiometric amount of alkali metal vapor with C6o powder and a stage of

annealing [Flebard et al 1991]. The intercalated alkali fulleride powder obtained directly

from the vapor phase transport methods has a small grain size of about 1-3 pm in

average. Preparations of high quality superconducting crystals with exact A 3 C60

stoichiometry, homogeneous dopant distribution and minimum defects are under study

[Haluska et al 1998].

)

Figure 1-8. This figure shows that the interstitial sites in fullerides are doped by metal elements for the structure of fullerides. The left picture is an AC 60 structure with all the octahedral sites filled by A. The right picture is an A 3 C60 with all the octahedral and tetrahedral sites filled. The large spheres represent C 6 0 . This picture is from [Fullerene Gallery],

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Depending on their structure and stoichiometry, fullerides are conducting,

semiconducting, or insulating. The electronic structure of fullerides is mainly determined

by the C6o molecules. Doping with alkali metal leads to charge transfer from the metal

atom to Qo. In A 3 C60 , the three transferred electrons occupy the t\u band to make it half-

filled, thus the fulleride is metallic. Structural symmetry and disorder are two other

factors that can affect the electronic structures, bandwidth, and density of state

distributions [Satpathy et al 1992]. Since the LUMO orbitals are antibonding, electron

transfer may cause expansion of the molecules. This expansion includes distortion in the

molecule’s icosahedral symmetry. The distortion in geometry, in turn, will shift the

energies of molecular orbitals, and change the band gap [Galfand 1994].

Alkali metal fullerides AnCeo (A = alkali metal ion) have received considerable

attention since AnC6o, such as RbCsaCeo and CS 3C6 0 , exhibits superconductivity at a

transition temperature up to 40 K [Rosseinsky 1995, Palstra et al 1995, Haddon 1992,

Gunnarsson 1997, Buntar and Weber 1996, Tanigaki and Prassides 1995]. In the AnC6o

fullerides, n can be as low as 1 and as high as 12, such as CsCeo and LinCgo- The valence

electrons of the alkali atoms transfer to the tiu band, and the tjg band (6 < n < 12), of the

C60 solid. Great efforts have been made to investigate the structural and electronic

properties of fullerides since there exists great interest in this new class of

superconducting materials.

Superconducting fullerides can be classified according to their stoichiometry

[Buntar 2000]. In alkali fullerides, A 3 _xA’xC 6o (A, A’ = K, Rb and Cs, and x < 3), up to

three electrons are doped into the LUMO ( tju). In sodium fullerides Na 2AxCeo with x < 1,

tiu is less than half-filled, and in alkali/alkaline-earth E fullerides A 3 _xExC 6o with x < 3,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the electron doping to tju is larger than 3. The above types of fullerides have fee lattices

with space group Fm3m . In the alkali/alkaline-earth fullerides K^BasCeo, the tju band is

fully filled and the next tig band, which is the triplet LUMO+1 state, is partially filled.

This class of fulleride has the body-centered cubic (bcc) lattice structure. Other fullerides

such as A 4 C6 0 , which has body-centered tetragonal, and AeCeo, which has the bcc

structure, are insulators.

Great efforts have been made to experimentally characterize and theoretically

understand the superconducting properties of fullerides. The mechanism of

superconductivity in fullerides can be explained to a certain extent using the electron-

phonon coupling. It is believed that the intramolecular phonon mode plays a major role in

superconductivity. Other phonon modes, such as C< 5o-C, 5o and alkali-C6o vibrations, are

believed to be not important in superconductivity. Alkali fullerides, such as K 3 C60 and

RbsC6o, are found to be type-II superconductors [Spam et al 1992, Holczer et al 1991].

Transport properties are characterized by measuring the temperature dependent

resistivity. This study of the transport properties provides information about the electron

scattering mechanism, mean free path, electron-phonon coupling, and so on [Hebard et al

1993, Crespi et al 1992, Xiang et al 1993, Erwin and Pickett1992], The transition

temperature Tc was investigated for various fullerides. The measurements demonstrated a

dependence of transition temperature on lattice constant a [Tanigaki et al 1991, Fleming

et al 1991, Yildirim et al 1995]. In the electron-phonon interaction mechanism, the

transition temperature Tc is determined by the phonon energy co and the electron-phonon

coupling parameter A [McMillan 1968].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The energy gap A is another characteristic parameter in superconductivity. The

density of state distribution N(E) is quite different in the superconducting state from that

in the normal state. In the normal state, N(E) is filled up to the Fermi level Ef , but below

Tc, there is an energy gap A. At T— 0 K, all states below the gap are fully occupied. The

energy gap reflects the effect of coupling [Mitrovic 1984], Energy gap measurements

have been performed in many experiments [Zhang et al 1991, Jess et al 1994, Sasaki et al

1994], The experimental results were compared with the BCS theory [Stenger et al

1995], The critical fields, Hci and HC2, were measured to characterize the mixed state of

these type-II superconductors [Bunter and Weber 1996, Holczer et al 1991, Gu et al

1994, Bunter et al 1997, Spam et al 1992],

In the BCS theory, the transition temperature is sensitive to the mass of the

vibrating atoms. Since carbon is rich in isotope 13C, the isotope effect measurements have

been performed to compare with the theoretical rale of Tc oc (m /m ')0'5 [Chen and Lieber

1992, 1993], It is believed that fiillerene superconductors follow the weak intramolecular

electron-phonon coupling mechanism. Relations between the critical fields and the

coupling were established [Tinkham 1975]. However, the discrepancies between the

experimental results and the theoretical predictions [Gunnarsson 1997, Buntar 2000]

indicate that more efforts are needed to better understand this new class of organic

superconducting materials.

Fullerene-surface interactions are another important research topic. Reports on the

fullerene-surface interactions include fullerene-metal, fullerene-semiconductor and

fullerene-insulator interactions, such as the interaction of fullerenes with noble metal

surfaces (Ag, Au, Cu, Al and transition metals, Pt and Ni), with semiconductors Si, Ge,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. GaAs, silicon carbide 6H-SiC(0001), and with insulator surfaces such as TiC >2 and MgO.

Since C^o has a large ionization potential compared with the work functions in metals

(2.3, 4.24, 4.49, and 6.2 eV for Na, Zn, W, and Pt, respectively), electron transfer from

metal surface to fullerenes is expected. The binding of fullerenes to metals is stronger

than to insulators or semiconductors. Charge transfer from semiconductor surfaces would

be difficult because of the band gap barrier. The interactions of fullerenes with

semiconductors, late transition metals, and aluminum surfaces are covalent, but

interaction with insulators is via van der Waals attractions. The interaction with

semiconductor surfaces can be very strong if the surface has dangling bonds to build the

covalent bonding interactions [Sakurai et al 1996, Gensterblum 1996, Dresselhaus et al

1996, Hamza 2000].

1.4.4 Fullerene Applications

Ever since the fullerenes were discovered in early 1985, potential applications

based on fullerenes have been proposed. Fullerene research is expected to bring new

electronic materials, chemical and biological products, new materials for energy storage,

and applications in nano-technology. The development of fullerene applications depends

on our understanding and the ability to manipulate the physical and chemical properties

of fullerenes and their derivatives. The size of fullerenes is between that of small

molecules and bulk materials. One goal of fundamental research is to understand the

change in physical properties in the transition from small molecules to bulk materials.

The formation of fullerene derivatives provides opportunities to make use of their

photoelectronic properties. The low-lying triplet t\u states in fullerenes and their ability to

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. accommodate up to six electrons [Echegoyen et al 1998, Dubios et al 1991] make

fullerenes good candidates in photoconducting applications. Photophysical studies of

fullerenes investigate the energy and electron transfer between the fullerene and the

attached compounds or surfaces [Guldi et al 2000]. Photoactive polymers have important

applications in photoresists, xerography, photocuring of paints and resins, and solar

energy conversion systems [Yu and Heeger 1995, Wang et al 1993, Silence et al 1992,

Bunker et al 1995]. C6o dopants enhance the photoconductivity of polymers. These doped

polymers may have applications due to the formation of excited charge-transfer products

[Wang et al 1993].

Although fullerenes are not water soluble, many fullerene derivatives are water

soluble [Ruoff et al 1993]. The synthesis of water soluble fullerene derivatives and stable

water suspension of fullerenes [Bullard-Dillard et al 1996] opens up promising fullerene

based applications in biochemistry.

Studies have been reported that fullerene derivatives can be used as enzyme

inhibitors. For example, experiment and molecular modeling have shown that a C6o

derivative is a competitive inhibitor of HIV protease [Friedman et al 1993, 1998,

Sijbesma et al 1993]. A report showed that a water soluble N-

tris(hydroxymethyl)propylamido methanofullerene C6o derivative was active against

HIV-1 in acutely infected human peripheral blood mononuclear cells [Schinazi et al

1995]. Some reports claim that fullerene compounds interact with biological receptors

[Wilson et al 1995]. Effects of the water-soluble fullerene compound C 6o(OH )2 4 on

microtubule assembly have been observed [Simic-Krstic 1997], which could lead to

application in anticancer drugs. Under visible or UV irradiation, fullerenes Ceo and C 70

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. can efficiently convert to their excited triplet states. These electronically excited

fullerenes can efficiently sensitize the formation of O 2 . This photochemical property may

be used in photodynamic therapy [Abogast et al 1991], Due to their unique electronic

structures, fullerenes can readily accept up to six electrons. This electron-transfer ability

implies the application of fullerene redox chemistry to biosensor technology. Studies

showed that a C6o-containing bilayer lipid membrane works as a light-sensitive diode

capable of photoinduced charge separation, which is useful in developing electrochemical

biosensor electronics devices [Tien et al 1997, Cardullo et al 1998]. Fullerenes

containing radioactive carbon isotopes nC and 14C may find their applications in biology

as radiotracers. nC-labeled fullerenes Cn (n = 60, 70, 76, 78 and 84) have been produced

[Micth et al 1997]. They can possibly be used as short half-life tracers. Neutron

irradiation of purified holmium metallofullerene, Ho@Cg 2 , and a water-soluble

166Ho@C84(OH)n, have been proposed for medical applications [Thresh et al 1997].

Due to the higher hydrogen storage capacity of C 60 relative to metal hydrides, it is

expected that fullerene-based batteries should be lighter per unit of stored charge than the

present Ni-Cd batteries, and they should have a longer lifetime [Dresselhaus et al 1996].

As a storage medium for hydrogen, fullerenes are potentially a key factor in the

development of new batteries.

Fullerenes have large nonlinear electric susceptibility and nonlinear optical

response. These characteristics may find application as optical limiters [Tutt and Kost

1992, Wray et al 1994] to protect sensors and materials from being damaged by high

intensity light. In space, the high intensity light may come from the sun. In industry,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. fullerene material may protect sensors and eyes of workers that are exposed to lasers and

other intense light sources.

Fullerene research has helped to initiate an interesting and promising field of

science and technology, nano-technology. Carbon nanotubes were first discovered in

1991 when studying Cm using transmission electron microscopy (TEM) [Iijima 1991],

Carbon nanotubes are hollow single- or multi-wall cylindrical carbon structures with

inner diameter ranging from 7 A to ~ 10 nm and lengths up to several hundreds of

micrometers. Nanotubes can be prepared by laser vaporization of a carbon target in a

furnace at 1200 °C. A cobalt-nickel catalyst promotes growth of the nanotubes,

presumably because it prevents the ends from being "capped" during synthesis. About 70

- 90 % of the carbon target can be converted to single-wall nanotubes. In another method,

carbon nanotubes can be produced from ionized carbon plasma [Dresselhaus et al 1996].

Theoretical studies predict that the electrical behavior of a nanotube is related to the

specific geometry of the tube [Hamada et al 1992]. Depending on its radius and chirality,

a carbon tube can be metallic or semiconducting. Since a carbon tube can be thought of

as a sheet of graphite rolled up to form a tube, the electronic band structure of a carbon

tube can be directly derived from the band structure of graphite with an extra

confinement of the periodic boundary conditions around the tube circumference.

Although the curvature of a tube introduces a-n hybridization, this hybridization

significantly affects only small diameter tubes.

Nanotubes are very strong in the axial direction [Ovemey et al 1993]. Carbon

nanotubes have potential application in nanometer-sized electronics. For example, carbon

nanotubes are excellent field emitters and can be used in devices [de Heer et al 1995,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Collins and Settle 1996, Bonard et al 1998]. Carbon nanotubes could find use in

spectroscopic enhancers or chemical sensors [Garcialvidal et al 1998] and polymer

materials. Efforts have been taken to incorporate different materials inside the carbon

nanotubes, such as metal oxides [Ajayan and Iijima 1995, Ebbesen 1996, Ugarte et al

1996], metals, gases [Dillon et al 1997], proteins [Tsang et al 1995], and so on. Filling

carbon tubes with materials could make it possible to manipulate the physical property of

the tubes and bring new applications.

1.5 Endohedral Fullerenes

The large size of fullerenes with hollow cages makes it possible to encapsulate

atoms, molecules or even small clusters. The new species of the fullerene family,

endohedral fullerenes, were synthesized in laboratories after the discovery of C

1-9 demonstrates the structure of an endohedral fullerene. LaCgo was the first

metallofullerene to be detected in a mass spectrometer. In that experiment, the ion source

was prepared by laser vaporization of a LaCl2-impregnated graphite rod [Heath et al

1985]. The LaC< 5o+ ions were supposed to be endohedral. In similar experiments, group II

elements Ca, Sr, Ba and group III elements Sc, Y, La, Ti and Fe, and all the lanthanide

metal series elements except Pm, have been encapsulated by fullerenes [Shinohara 2000].

Fluorine atoms and methyl radicals within the Cgo shell are predicted to be chemically

inert [Mauser et al 1992], An isolated nitrogen atom inside the Cgo shell remains

spectroscopically indistinguishable from nitrogen atoms in vacuo [Pietzak et al 1997].

Macroscopic quantities of metallofullerenes Sc@C 82 [Inakkuma et al 1995],

Y@C82 [Kikuchi et al 1994], La@Cg2 [Kikuchi et al 1993], Gd@Cg2 [Funasaka et al

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1995], La2@C8 o [Suzuki et al 1995], Sc2 @Cg4 [Shinohara et al 1993a, b] and Sc 3 @Cg2

[Shinohara et al 1994] have been isolated and purified. The availability of macroscopic

quantities of these materials makes it possible to investigate their electronic properties

and chemical reactivity. Although the most stable and abundant empty fullerenes follow

the isolated pentagon rule (IPR), it is not necessarily the case for metallofullerenes.

Unconventional caged structures can be significantly stabilized by the caged metal atoms

[Nagase et al 2000]. Therefore, violating IPR cage structures of metallofullerenes are

possible.

Figure 1-9. The structure of an endohedral fullerene [Fullerene Gallery], In this structure, an atom is encapsulated at the center of the cage. Off-center location of the captured atom is also a possible configuration.

Alkali metal endohedral fullerenes A@C 6o (A = K, Li, Na) are the products in the

collision of C 6o with ion projectiles; they have been detected in mass spectrometers [Wan

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. et al 1993, Deng and Echt 2002a]. Noble gas atoms have also been trapped inside the

fullerene cages. Endohedral fullerenes would lead to new fullerene-based materials.

Many experimental techniques have been employed to obtain evidence of

endohedral structures. In gas phase studies, the kinetic analysis of the collisional

formation of metallofullerenes revealed that their formation requires large collision

energies; this is evidence of an encaged structure [Wan et al 1993, Deng and Echt 2002,

Deng et al 2003]. In gas-phase studies it was shown that LaC 6o+ ions do not react with

H2 , O 2 , NO and NH 3 ; this was taken as evidence that the chemically active metal ion was

protected from the surrounding gases and located inside the C 60 shell [Weiss et al 1988],

The stability of metallofullerenes has been investigated by laser

photoffagmentation of KC 6o+, CsC 6 o+, La@C 82 and Sc 2 @Cg4 [Weiss et al 1988,

Wakabayash et al 1996, Suzuki et al 1997], collisional fragmentation with atomic and

molecular targets for Ar@C 6 o [Brink et al 1998], La@Cg 2 and Gd@Cg 2 [Lorents et al

1995] and fragmentation induced by surface (for example, gold and silicon surfaces)

impact for La 2 @Cgo [Yeretzian et al 1992a, b], La@Cg2 [Alvarez et al 1991], La2@Cioo

[Beck et al 1996], La@C6 o [Kimura et al 1999a, b], Ce@Cg2 and Ce 2 @C1.00 [Beck et al

1996], Y@C82 and Ca@C 84 [Kimura et al 1999b]. All these experiments have the

common behavior that fragmentation proceeds by consecutive C 2 loss, and finally ends

up with M@Cn+ ions before they break apart.

High-resolution transmission electron microscopy (HRTEM) of purified Sc 2 Cg4

metallofullerenes provided evidence that two scandium atoms are encapsulated inside the

Cg4 cage [Beyers et al 1994], Similar results were reported for Gd@Cg 2 [Tanaka et al

1996]. Ultra-high vacuum scanning tunneling microscopy (UHV-STM) studies on

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Sc2 @Cg4 and Y@Cg 2 displayed the spherical STM images of those metallofullerenes

[Wang et al 1993, Shinohara et al 1993b, Sakurai et al 1996].

The experiments summarized above provide evidence for an endohedral structure,

but the evidence is rather indirect. Direct evidence has been provided by synchrotron x-

ray diffraction experiments. In these experiments, the measured data were analyzed using

a technique of Rietveld analysis and the maximum entropy method (MEM). MEM can

produce an electron density distribution map from a set of x-ray structure factors. The

powder of solid Y@Cg 2 and Sc@Cg 2 was measured and analyzed by this technique

[Takata et al 1995, 1998]. The result in Figure 1-10 shows the electron density

distribution map of the encaged structure of Sc@Cg 2 - The maximum electron density is

located inside the Cg 2 cage corresponding to the Sc atom. By comparison, the electron

density distribution of an empty Cg 2 is relatively uniform. But the MEM electron density

distributions of Y@Cg 2 and Sc@Cg 2 have many local maxima along the shells. This is

believed to be an indication that in the solid, the rotation of the Cg 2 cage is limited around

a certain axis. The off-centered position of the yttrium atom is consistent with theoretical

analysis [Laasonen et al 1992, Nagase 1993, Nagase and Kobayashi 1994a, Guo et al

1994, Andreoni and Curioni 1996]. The nearest-neighbor Sc-C distance calculated from

the MEM map is 2.53(8) A, and 2.9(3) A for Y-C. ESR [Weaver et al 1992] and

theoretical [Nagase and Kobayashi 1993, Schulte et al 1996] studies suggested that a

strong charge transfer interaction between the Y3+ and the Cg 2 3' may cause the aspherical

electron density distribution of the endohedral complex. This may give some explanation

of the off-centered position of the yttrium atom.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The charge density distribution of a La atom encapsulated in a Cs 2 cage has been

revealed by MEM/Rietveld analysis using synchrotron powder diffraction data

[Shinohara 2000, Nishibori et al 2000]. The derived La atom charge density shows that

the La atom locates at an off-centered position adjacent to a six-membered ring of the

carbon cage. The nearest La~C distance is 2.55(8) A. An electron density distribution

with a feature almost like a bowl or a hemisphere is discovered, which suggests that the

La atom has a large amplitude motion inside the Cg 2 cage at room temperature. The

amount of charge transfer from the La atom to the carbon cage is about 3.2 e, which

corresponds to the nominal electronic structure, La @Cs 2 *. The dynamic motion of

metal atoms inside the fullerene cages have been theoretically predicted based on

molecular dynamics simulations on La@C 6 o and La@Cg 2 [Andreoni and Curioni 1996,

1997, 1998],

Figure 1-10. The electron distribution map of an endohedral Sc@Cs 2 molecule. The map indicates that the Sc is encapsulated and off-centered inside the Cs 2 cage [Shinohara 2000].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The synchrotron x-ray diffraction technique also provides other interesting

features of endohedral fullerenes. The di-metallofullerene of La 2 @Cso has a particularly

interesting configuration. Due to the fact that the h-Cso cage has only two electrons in the

fourfold degenerate HOMO level and can accommodate six more electrons to form the

stable closed-shell electronic state of (La 3 +)2@Cso6" with a large HOMO-LUMO gap, the

encapsulation of two La atoms inside the h -Cso cage is most favorable [Kobayashi et al

1995]. 13C NMR and 139La NMR data for La2@Cgo show that the two caged La atoms

move in a circular pattern inside the h -Cso cage [Akasaka et al 1995, 1997],

The first example of a metal cluster being trapped inside a fullerene was reported

by a synchrotron x-ray diffraction study on Sc 3 @Cs2 [Takata et al 1999]. The study

reported that three Sc atoms are encapsulated inside the C 3v-C 82 fullerene cage. The three

Sc atoms form an equilateral triangle with a Sc-Sc distance of 0.23(3) nm. The charge

state of the encaged Sc 3 cluster is 3+ leading to a formal molecular charge state of

(Sc3)3+@Cg23’ as a result of an intrafullerene electron transfer. The presence of the Sc 3

trimer in the cage is consistent with an extended Hiickel calculation [Ungerer and

Hughbanks 1993].

Two quantities, electron affinity (EA) and ionization potential (IP), characterize

the electronic properties and chemical reactivity of molecular clusters. There has been no

report for the direct measurement of EA and IP for metallofullerenes. Only calculated

values are available [Nagase and Kobayashi 1994a, b]; some are listed in Table 1-2. They

show that the ionization potentials of metallofullerenes are lower than those of the empty

fullerenes, while the electron affinities are higher than those of empty fullerenes. The

calculations also found that when M@Cs 2 either gains or loses an electron, the net charge

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. change on the metal atom M is little, which gives a picture of a “superatom” that M acts

like a positive core and the charge change only takes place on the carbon shell.

C6o is the most abundant fullerene produced in either the arc discharge or the laser

furnace method, but extraction of the M@C 6o metallofullerenes has been difficult for

reasons that are still debated. There is lack of solvent for the extraction process. The

stability in solvents and air is also a problem [Tellgmann et al 1996, Campbell et al

1997]. The high reactivity of M@C 6o remains to be explained.

Table 1-2. Calculated Electron Affinities (EA) and Ionization Potentials (IP) of fullerenes and endohedral fullerenes 3

EA (eV) IP (eV) C60 2.7 7.8 C70 2 . 8 7.3 C82 (C2 isomer) 3.5 6 . 6 Sc@C82 3.08 6.45 y @ c 82 3.20 6 . 2 2 La@C82 3.22 6.19 Ce@C82 3.19 6.46 Eu@C82 3.22 6.49 Gd@C82 3.20 6.25

aValues for fullerenes are adopted from reference [Echgoyen et al 2000], and values for endohedral fullerenes are adopted from reference [Nagase et al 2 0 0 0 ],

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.6 Mass spectrometric Studies of Fullerenes

1.6.1 Mass Spectrometers

Mass spectrometers differ greatly in the techniques of ion generation and mass

selection. In general, a mass spectrometer includes an ion source, ion extraction, ion

selection, ion detection and data process. The diagram in Figure 1-11 indicates these

major components in a typical mass spectrometer. Techniques used in ion generation

include laser ionization, ion collision, electron impact, electrospray and others.

Techniques of ion selection are based on measuring the ratio of ion mass to its electric

charge. This can be accomplished by time-of-flight mass selection, quadrupole mass

selection, sector instruments with magnetic and electrostatic analyzers, and others.

Ion Detection

Mass Signal Extraction Selection Process

Figure 1-11. Diagram of a mass spectrometer. A typical mass spectrometer has five key components: ion source, ion extraction, mass selection, ion detection and signal analysis.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Mass spectrometry plays an important role in fullerene research. In fact,

fullerenes were first discovered by laser ionization mass spectrometry study [Kroto et al

1985]. Many new fullerene derivatives were also first detected by mass spectrometry. For

example, orafullerenes, niobiumfullerenes, and azafullerenes were first detected in mass

spectrometric systems [Guo et al 1991, Chai et al 1991, Clemmer et al 1994, Lamparth et

al 1995, Averdung et al 1995]. Knudsen cell mass spectrometry has been employed to

measure the vapor pressure of C^o [Popovic et al 1994].

Mass spectrometers are not only employed to determine the mass of fullerenes

and fullerene derivatives; they are essential tools in the study of the dynamics in

fullerenes and fullerene derivatives. The availability of macroscopic quantities of pure

C6 o makes it possible to investigate this molecule in detail. There have been many

approaches for preparing Ceo ions, such as laser desorption [Ehlich et al 1996], electron

impact [Doyl and Ross 1991], plasma [Hvelplund et al 1992], electrospray [Liu et al

1995] and sputtering ion sources [Hekansson et al 1996], In mass spectrometry, the

molecules are in the gas phase. An advantage of gas phase study is that the intermolecular

interaction is minimized so that interpretation of results is less ambiguous.

1.6.2 Photon Excitation Mass Spectrometry

Multiphoton ionization mass spectrometry revealed the phenomenon of delayed

ionization which is believed to be the analogue of thermionic emission, i.e. a statistical

process. The experiments provide information about the intramolecular interactions, i.e.

the energy relaxation from electronic excited states to the vibrational states and energy

redistribution within the system. Multiphoton absorption mass spectrometry has also been

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. employed to study the competition between electron emission and fragmentation in

excited C 6 o [Deng and Echt 1998].

Photoabsorption mass spectrometry has been used to study the electronic states in

fullerenes. In this type of experiment, two pulsed lasers with different wavelengths are

employed. A visible or UV laser provides photons to pump the molecule to its excited

states, and a second laser with different photon-energy provides the ionizing photon. The

two-photon absorption process can be used to determine energy and lifetime of excited

states. One specific result is that the lowest triplet state is located at 1.7 eV above the

ground state and has a long lifetime in vibrationally cold Cm [Abogast et al 1991, Haufler

et al 1991]. The lifetime of this state decreases with increasing internal energy [Hedin et

at 2003, Deng et al 2003].

1.6.3 Ion Collision Mass Spectrometry

Ion-molecule or ion-atom collisions have been used to investigate the physical

properties of fullerenes. Collision induced charge transfer, energy transfer and

dissociation are topics of interest.

The fragmentation pattern depends on the collision parameters. The most

important parameters are the masses of the fullerene and the colliding atom/molecule,

and the internal energy of fullerene. Many experimental techniques have been employed

in the study, such as time-of-flight mass spectrometry (TOFMS) [Ehlich et al 1996],

quadrupole mass spectrometry (QMS) [Tuinmann et al 1992], sector instrument with

magnetic and electrostatic analyzers [Lorents et al 1995], instruments combining mass

analysis with ion traps [Cameron and Parks 1997], and ion storage rings [Andersen et al

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1996]. Molecular dynamics simulations of the collision of fullerene ions with atoms

[Ehlich et al 1997] show that, for heavy atoms, prompt energy transfer to a large group of

carbon clusters may lead to a collective release of a group of atoms. For light atoms,

energy is transferred predominantly into the vibrational excitation of the fullerene, and C 2

emission is the dominating decay process. In this case, positive fullerene fragment ions (n

> 30, even) dominate the fragment spectrum. The simulation agrees with the

experimental result.

The internal energy of fullerenes or fullerene ions is an important parameter

determining fragmentation patterns. However, in most gas phase experiments, it is

difficult to control or to determine. Generally, the internal energy distribution is broad.

For fragmentation to occur on the time scale of ~ 10'5 s, the internal energy has to be

about 40 to 50 eV, corresponding to a vibrational temperature around 3500 K. It is

possible to start with a beam of cold C 60 which has a narrow energy distribution, and then

to add a well-defined amount of energy by collision. For example, room temperature

fullerene ions have been created for collision experiments by using electrospray ion

sources [Dupont et al 1994], Hot fullerene molecules can be cooled down in an ion trap

filled with a buffer gas [Wang et al 1991],

The mechanism and outcome of collisions between atoms and fullerenes depends

on the center-of-mass collision energy. Nuclear excitation dominates at low energies. For

example, in the 74 eV Li+ + C 60 collision [Wan et al 1993], C60 is heated via the

transferred collision energy. As shown in Figure l-12a, the energetically excited C 60

undergoes evaporative cooling via successive emission of C 2 dimers.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. At high energies, electronic excitation dominates, and the Cm fragmentation

process depends strongly on how electronic excitation couples to vibrational degrees of

freedom which results in emission of different size of fragment ions with a distribution of

charge states. Results from collisions between C2+ and Ceo at 15.6 MeV are shown in

Figure l-12b [Nakai et al 1997]. Main product ions are C 6oq+ withl < q < 4 , and some

very small carbon cluster ions. Little, if any, evidence for sequential loss of C 2 is seen.

Ion Mass ( amu )

C60

Ceo2+

Ion Mass ( amu12)

Figure 1-12. Ions produced in the collision of Ceo- (a) In collision of Ceo with Li+ at 74 eV, C 2 loss is the dominant fragmentation pattern [Wan et al 1993]. (b) In collision of Cm with C2+ at 15.6 MeV, significant charge transfer is observed [Nakai et al 1997].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. At collision energy about 1 keV, the energy transfer in the collision of fullerene

and the target atom results in the prompt ejection of smaller or larger clusters of carbon

atoms followed by evaporative cooling via C 2 emission from the remaining hot fullerene

daughters, and C 3 emission from the hot chain or ring fragments. The relative population

of the two fragment groups, n > 30 and n < 30, depends on the target atom mass [Larsen

etal 1999],

Charge transfer has been studied in the collisions of C 60 with multicharged

projectile ions. The ionization potentials of fullerenes are lower than those of most atoms,

and charge transfer is relatively easy. For example, it was reported that in the collision of

C<5o with Bi44+ at 500 keV, C6o+q with q up to 9 could be created [Jin et al 1996]. In the

collision of 625 MeV Xe35+ with C 60 , excitation of the giant dipole plasmon resonance

was found to be the dominant mechanism of energy transfer to C 60 molecules [Cheng et

al 1996],

1.7 Conclusions

This chapter presented a review of physical and chemical properties of fullerenes,

it provides the background for the discussion of our research in the following chapters.

The structures of fullerenes are well known today. However, many physical properties of

this new family of carbon cluster still remain to be investigated. Applications promised

by fullerene material demonstrate the importance of continued research in this field.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 2

COOLING PROCESSES IN ENERGETICALLY EXCITED C60

Molecular dynamics studies the physical and chemical rate processes in molecular

systems. It provides a pathway to investigate the molecular structures, the electronic

states of molecules, intermolecular interactions and intramolecular interactions. These

properties are investigated through the means of molecular collisions and photon

excitations. In molecular collisions, the kinetic energy can be transferred from the

colliding reagents to the energetically excited reagent complex, which may lead to

molecular dissociation or polymerization and other decay processes. Under visible or

ultraviolet laser irradiation, a molecule absorbs photons and is electronically excited. The

molecule will then undergo rapid energy redistribution via electron-phonon coupling

followed by molecular dissociation or ionization. The first part of this chapter will review

the theories used to calculate the reaction rates. These theories can be used to characterize

the decay processes in excited fullerenes. The second part of this chapter will describe the

cooling processes in excited C6o- Analysis of our research results, which will be presented

in the following three chapters, is based on the theory discussed in this chapter.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.1 Molecular Collisions and Energy Redistributions

2.1.1 Molecular Collisions

From the energetic view, when a molecular collision leads to a chemical process

that forms new stable species, the collision complex must correspond to an energetically

accessible potential well in the potential energy surface (PES). Also, the collision

complex should have a lifetime longer than a vibrational period (a typical vibrational

period is ~ 10'13 s). This may be the qualitative criterion to judge whether or not a

chemical process can create new species. In order to quantitatively describe the formation

of new species in a dynamical process, two parameters are studied. They are collision

cross section a and reaction rate constant k.

In the gas phase, the probability of a particle A traveling a distance Ax through a

gas of particles B without colliding B depends on the density Suppose the probability

of particle A traveling a distance x without collision with a particle B is P{x), this

probability changes to P(x + Ax) = P(x) + AP at position jc + Ax. The net change in the

probability is given by

AP oc nBP(x)Ax ,

or AP = - o ABnBP(x) Ax ,

thus,

P(x) = P(0)exp(-aABnBx) (2-1-1)

where the proportionality constant gab is called the total collision cross section. It has a

dimension of area. The total collision cross section reflects the nature of the interaction

between the incident particle A and the target particle B. In gas kinetics, the mean free

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. path X is often used instead of the cross section a. The mean free path relates to the cross

section,

X — {

In experiments, incident beams are used instead of a single particle. Suppose the

beam intensity is I(x), equation (2-1-1) can then be written as

I{x) = I(0)exp(-crABnBx). (2-1-3)

On the other hand, when an incident molecule A undergoes an inelastic collision with a

target molecule B, chemical reaction may take place and produce a new complex AB. In

this case, the rate of producing AB depends on the reaction cross section, the intensity of

the incident beam IA = nAv, and the target gas density

where v is the velocity of the incident particle relative to the target particle. Since not

every collision will lead to the production of a new complex AB, the reaction cross

section oa,b ^ ab is always less than the total collision cross section oAb - In the actual

experiment, either the target particles or the incident particles may be generated from a

diffusion source such as a Knudsen cell. Thus the velocity v has a thermal distribution,

and equation (2-1-4) should be averaged over the thermal distribution,

A,B—>AB B A ’ (2-1-5)

where < oa>b ^ ab v> is called the reaction rate Ka,b -*ab (T) of the chemical reaction

A + B -» AB,

K a,B->AB (7 1) - (CTA,B-yABV'} ■> (2- 1-6)

Ka,b ^ ab (T) has unit of [mV1].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In quantum mechanics, the collision cross section can be calculated as follows.

Considering an incident atom or molecule A colliding with a target molecule B, in the

center-of-mass (CM) system, the equation of the collision can be written as

- ^ V 2A'{r,0,

where U(r,6,(p) is the interaction potential of A and B, /u is the reduced mass of the

colliding system ju = mAmB /(mA + mB).

If the incident particle is characterized by a plane wave, the asymptotic form of

the wave function ¥(r,9,

A>(r,e,(p)^C eik | f(6,

where C is the normalization coefficient, z = rcosd is the collision coordinate as shown in

Figure 2-1. The second term in the square bracket in equation (2-1-8) is the scattering

wave function with an angular function f(9,(p). The differential cross section is expressed

as [Schiff 1999]

+g,

For a spherical symmetric potential U(r), the wave function and the cross section

are independent of angle

co T(r,e)=yr-‘*(r)/>(cos«) (2-1-10) 1=0

where P;(cos 6) is the Legendre Polynomial of order I which is the quantum number of

the system’s angular momentum, xi satisfies the equation

d2xM ) 2 2 nU{r) 1(1 + 1) kl - Xl(r) = 0. (2-1-11) dr2 n 2 r 2

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The wave function vF(r,0) is the sum of all partial waves over all I. The differential cross

section a{6) can be obtained by solving the equation (2-1-7) with the asymptotic form of

(2-1-8), which gives

cr(eHf{ef=^ X (2 / + l)e''*'sin<^(cos0j . (2-1-12) /=o

The total cross section for elastic scattering is the integral over the polar angle 6, which

gives

n Arr 00 a - 2 n ^

The parameter <5/ is called the phase shift of the /th partial wave. <5/ is determined by

equation (2-1-11).

In the collision-induced reaction, the reaction cross section can be expressed in a

similar form as

ct* = 7 7 2 7 2Z+» p « ' (2-M 4 > k i=o

where P{T) is the probability of reaction for a given angular component I [Levine and

Bernstein 1987]. Since not every collision will lead to reaction, the reaction cross section

is smaller than the collision cross section.

In classical mechanics, a physical parameter called impact parameter b is used to

measure how close the incident particle comes to the target particle in the collision. This

is explained in Figure 2-1. The total cross section is expressed as

a = ^iTtbdb. (2-1-15)

For a hard sphere model, classical mechanics gives the total cross section of

^(rA+rg)2 which is the circular area with a radius of ta+tb . Beyond this radius, there is no

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. impact between the incident and target particles. The angular momentum of the system

with impact parameter b is L = fivb in which v is the velocity of the incident particle

before it collides with the target particle. The angular momentum is one of the factors that

determine the collision cross section and reaction cross section. For an elastic collision,

the total collision energy of the system is

E , „ , = ^ 2- T + V(r) (2-1-16)

Figure 2-1. The trajectories of collision in the picture of the classical mechanics, b is the impact parameter.

The kinetic energy of the system T can be expressed as

\ (2-1-17) /

with co -bv/r2 = (blr2\j2Etotal I ju ,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and the total collision energy can be written as

(2-1-18)

with

Veff(r) = V(r) + ^ - (2-1-19)

This effective potential can be thought as the sum of V(r) and a centrifugal barrier. In a

collision-induced reaction, the system needs to overcome this effective potential in order

to produce new species. With a given energy Etotai and impact parameter b, the effective

potential has a maximum Ve/j(rmax) at rmax. For example, if a reaction has a threshold

energy V(r) = Eo at r < d, the reaction requires that the energy of the system satisfy

1 - A '' =Etotai-V eff{rm ax)>0. (2 - 1-20)

There exists a reaction barrier (E0 + Etotalb2 / d2) as determined by equation (2-1-19).

This reaction barrier determines the maximum impact parameter hmax = d (l-E 0/Etotal)V2

for a system with given energy Etotai > Eq. The reaction cross section is then

total) = = nd2(l - EJE total) , (2- 1-21)

at Etotai ^ Eq and or{Etotal) 0 at Etotai — Eo.

In a collision of Ceo with an atom, the system should overcome a certain potential

barrier Eo in order to form an endohedral complex. As a simplified model of an absorbing

sphere with a diameter d, as given by equation (2-1-21), the reaction cross section of the

formation of the endohedral fullerene as a function of the collision energy Etotai is plotted

as the solid line in Figure 2-2. One example is the collision of C6o+ with helium. The

figure also shows the experimental data of the C6o+ collision with He at low collision

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. energies. The experimental result can be roughly fitted into the model of equation (2-1-

21) with the diameter of the absorbing sphere d = 0.5 A. It is believed that the mechanism

is insertion through the six-membered ring leading to the He capture at these collision

energies [Campbell and Rohmund 2000],

^ 0.9 □ exprmnt C 0.8 — model C O 0.7 o aR=*d2(1-E0/ET) CD 0.6 w d = 0.5 A

0.0 0.06 0.08 0.10 0.12 0.14 0.160.18 0.20 1/ET(eV-1)

Figure 2-2. The reaction cross section for the capture of He in the collision with C6o+ as a function of the collision energy [Campbell and Rohmund 2000]. The solid line is a plot of equation (2-1-21). The square symbols are experimental data.

2.1.2 Energy Distribution

In a molecular system at thermal equilibrium, the probability P(e;) of a molecule

in energy level at temperature T follows the Boltzmann distribution

O'-22)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where g* is the degeneracy of the ith energy state and so is the ground state energy of the

molecule. The denominator on the right side of equation (2-1-22) is the partition function

q ,

« = f2 4 ’23)

Vibrational Intersystem Crossing Relaxation ^ r > - — i— r

t-400 Cl) / C W 7 V \ \hv2 hvl / Transition /

Reaction Coordinate

Figure 2-3. Energy redistribution in an excited molecular system.

which is effectively the number of quantum states accessible to the molecule at

temperature T. The motion of atoms is a combination of translational, vibrational and

rotational motions. The partition function can be expressed ^ Qtrans^ivib tyrot°

Counting all the states in a molecule gives the partition function as [Barrow 1979]

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where I is the moment of inertia of the molecule and a>, is the vibrational normal mode

frequency.

When a molecule is under photon irradiation or involved in a collision, there will

be an energy perturbation to the thermal equilibrium system. The molecule will undergo

energy redistribution and tend to reach a new equilibrium. When a molecule is excited to

a higher electronic state, it can either release its energy by radiation or randomize its

electronic energy via electronic-vibrational coupling, or intersystem crossing. Figure 2-3

sketches possible energy relaxations in an excited molecule. The electronic-vibrational

coupling process makes the molecule remain in a highly excited state which may cause

the molecule to finally dissociate or emit electrons as channels of energy dissipation.

These reactions are exothermic and cool down the molecule.

2.2 Review of Theories in Rate Constant Calculations

2.2.1 Rate Constant

In order to observe the unimolecular dissociation or isomerization in a system of

molecules, some molecules must have energies higher than certain activation energies.

For an isolated system, one way for a molecule to get the required energy is through

molecular collisions. This process can be expressed as

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. M + M<=>M + M *, K_x \Z~Z~l) M* ——> products,

where M* is the molecule in the excited state. Ki, k_i and k are reaction rate constants

which have unit of [s'1]. Certain conditions are required to maintain the system in a

chemical balance in the above reaction. In physical chemistry, these conditions are called

the Lindemann conditions [Baer and Hase 1996]. It is supposed that, (i) there is an

equilibrium high-energy reservoir in the gas system; (ii) the above chemical reaction

never proceeds too fast to deplete the reservoir. In this case, the reaction rate K is

proportional to the number of energetic molecules M*,

dN K = -= ^ ~ = kN ., (2-2-2) d t M

where Nm and Nm* are the concentrations of molecule M and molecule M*, respectively.

By applying the balance condition of equation (2-2-1), the reaction rate can be written as

K = kN , = — iff*— . (2-2-3) W K ^ + K

The expression (2-2-3) may be useful in measuring the reaction rate constant in a

chemical experiment. It does not give information about the reaction mechanism.

Theories are needed to explain the physical reaction.

The rate constant k is found to be a function of temperature. The reaction rate

constant k is often expressed in Arrhenius form,

k(T)= vo exp (2-2-4) v kBT j

In this expression, v

energy. Study of the rate constants is one of the main topics in molecular reaction

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dynamics. If the rate constant can be measured directly in the experiment as a function of

temperature, equation (2-2-4) may be applied to obtain the activation energy and the pre

exponential factor. These quantities reflect the physical mechanism of the reaction.

2.2.2 Collision Theory

Considering a collision in a molecular gas, the probability density of the incident

molecule A having a translational velocity between u and u+du relative to the target

molecule B is given by the Maxwell-Boltzmann distribution

( V /2 P(u) = An u2e E!kJ (2-2-5)

1 where // is the reduced mass and E = —/ju is the collision energy. Using equation (2-1-

5), the reaction rate for the collision-induced reaction will be

n 3/2

A,B-+AB

Using the collision energy in the above expression, we have

(2-2-6 )

The reaction cross section is usually energy dependent. With the energy threshold

model of equation (2-1-21),

0, E

E > E0 E

the reaction rate turns out to be

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. rSkBT^1'2 . - E J k . T (2-2-7) K (r)=a AB K m )

The temperature dependence of the reaction rate in this model has an exponential

behavior since the last term in the above equation dominates the T-dependence.

In general, in a molecular system, the canonical reaction rate calculation needs to

sum over all the applicable final states and average over all initial states. Let us write the

state-to-state reaction rate as K(i—+f 1),

K (r ) = J > ,K ( i - > / , r ) , (2-2-8) i j

where the indexes i and j refer to initial and final states, pt is the probability of the

molecule in the initial state with energy level

~s,lk„T

Pi = ~e,/k„T ' (2-2-9)

The equation (2-2-6) can be rewritten as

\3/20 h2 f k P \d E h ' <7 (2-2- 10) v2 n p k j j K 71 J

Substituting (2-2-9) and (2-2-10) into (2-2-8), we obtain

K (J) = — \dE (2-2- 11) Q f

with

«■'(£) = 2 > , Mi-+f) (2-2- 12) UJ V n J

and Q is the translational partition function

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. r 2 TTjukJ^12 Q = (2-2-13) v h2

Using equation (2-2-4), the Arrhenius activation energy is expressed as

E = - d ln-Ki r j , (2-2-14) d(l/kT)

Substituting (2-2-11) into the above equation, we obtain

Ea=(E*)-{E), (2-2-15)

where

\EN*{E)eElkBTdE E*) = JL------(2-2-16) \tf*(E )eElk‘TdE

and

(E) =------(2-2-17) X ' d{l/kBT)

According to equations (2-2-15) and (2-2-16), can be interpreted as the average

energy of those collision reactants that lead to products and 5V%E0 is the number of

reaction pairs that do react. Comparing to transition state theory (discussed in 2.2.4),

7V%E) is equivalent to the number of reacting systems at the transition state. $t(E)

includes the dynamical parameters. As expressed in equation (2-2-12), OHJE) can be

calculated from the reaction cross section OR(i—+j).

For a dissociation process, it may be difficult to measure the dissociation cross

section. Instead, the corresponding absorption cross section for the reverse reaction is

easier to be measured. It is possible to calculate the dissociation cross section if the cross

section of the reverse process is known. At thermal equilibrium, the forward and reverse

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. reactions are at balance and this yields a so-called detailed balance equation [Levine and

Bernstein 1987]

gikfcrR(i - > / ) = gf k)aK{f -> i). (2-2-18)

In the above equation, gi is the degeneracy factor of the energy level e,-, and

where Etotai is the total energy of the reactants and Etotai - e is the relative kinetic energy of

the reactants, that

Etotal ~ Et + £ — ET + £ + AE , (2-2-19)

where (Et, e) and ( ET, s ) are translational and internal energies of the reacting system

before and after the reaction, respectively. EE is the energy absorption or release in the

reaction.

2.2.3 Potential Energy Surface Calculation

In collision theory, the reaction rate depends on the reaction cross section. It

would be difficult to obtain the precise reaction cross section by calculations or by

experiment for certain molecular systems. Another way of calculating the rate constant

for a given potential energy surface (PES) is by molecular dynamics [Levine and

Bernstein 1987].

The potential energy surface can be calculated by ab initio methods. This is

complicated for most reaction systems. For a given potential energy surface, the

generalized coordinates, x((t), which decide the motion of a molecule, can be calculated

according to Newton’s law

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A B + C — 5* A + BC

R(AB)

Figure 2-4. The potential energy surface of a chemical reaction AB + C —► A + BC. In all the trajectories, only those that cross the saddle point lead to product ion.

Figure 2-4 shows the potential energy surface of a chemical reaction

AB+C-^A+BC. Only those trajectories that pass through the saddle point (an energy

barrier) can produce BC. The outcome of a trajectory depends on the initial conditions of

the trajectory. These initial conditions include the impact parameter b, angle of approach

0 and collision energy E. In a chemical process, all angles of approach and impact

parameters can occur with a collision energy distribution. The rate of reaction is the

average over all these initial conditions. Simulating the reaction by calculating

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. trajectories for a large number of all possible initial conditions, the ratio of the productive

trajectories to the total of the trajectories gives the rate constant of the reaction. One

useful method in these calculations is the Monte Carlo method. Suppose the productive

probability of a trajectory is P(b, 6, E), the opacity function P(b, E) is

(2-2-21) 0

The reaction cross section would be

(2-2-22) o

The reaction rate K(T) can be calculated by the reaction cross section as expressed in

equation (2-1-5). The potential energy surface calculation is generally complicated and

the rate calculation in this method is difficult.

2.2.4 Transition State Theory (TST) and the RRKM Approach

A statistical theory to calculate the rate constant is the transition state theory. This

theory assumes that for a reaction A+B^Products, there exists a so-called transition state

(ABf through which the product is created. This process can be expressed as

A + B —> (AB)* —> products .

To reach the transition state, the reactants need to overcome a critical energy Eo which is

essentially the same as the activation energy shown in equation (2-2-4). It also assumes

that once the system is at the transition state, there is no return to the initial state. This is

sketched in Figure 2-5. By applying statistical methods, the rate constant k is given by

k T O* (2-2-23) *r = T " 7 ^ r exP ( - W ’)- h QaQb

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In the expression, Qa and Qb are partition functions for reactant A and B, respectively. <^f

is the partition function for all degrees of freedom in the activated complex except the

motion along the reaction coordinate. For a unimolecular reaction, the rate constant will

JrT (1* K = — — exp (~E0/kBT) . (2-2-24) h Q

Critical Surface Reactants

Product

CD I__ c0 LU

i Reaction Coordinate

There are a few theories based on the transition state theory to calculate the

formation of the activated complex. For example, the Slater theory analyzes the vibration

of a molecule in terms of normal modes. It supposes that no energy flows between

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. different modes of vibration and not all molecules with total energy greater than E0 are

able to react [Robinson and Holbrook 1972], The Slater theory is generally not in

agreement with experimental rate constants. A more successful theory is called RRKM

theory, which is a statistical theory developed by Rice, Ramsperger, Kassel and Marcus

[Baer and Hase 1996].

In a reaction, the system has to overcome a barrier in order to produce new

complexes. The barrier is a saddle point in the system’s potential energy surface; it

corresponds to a critical surface in the system’s phase space. Once the critical surface is

crossed, the system is in a transition state. Suppose a system has N atoms; it has 2N

coordinates ( q i, q2, ..., qn, Pi, P2, ■■■>Pn) in phase space. If the system’s energy is greater

than the critical energy E0, it could cross the critical surface. It is assumed that the

reaction path at the saddle point is perpendicular to all other coordinates. Assuming that

the system before the reaction is in a thermal equilibrium, i.e. the energy is equilibrated,

the density on the surface of phase space is uniform. Statistically, we consider a

microcanonical system with Wreaction systems. If ( qp*) is the reaction coordinate in

phase space, the ratio of the reaction systems at the transition state to the total of the

reaction systems is

dq*dp* [• • • [••• \dq* ■ ■ ■ dqn^*dp* ■ • ■ dpn_* d2T{q ,p ) _ h = e - s , - e 0 (2-2-25) TV

H-E

In the above equation, et is the translational energy associated with the momentum in the

reaction coordinate above the critical energy Eo. The reaction rate is then d9i (q*, p*)/dt.

Considering dq^/dt = p^/p, where p is the reduced mass of the reaction system, and s f -

p /2p, the reaction rate can be written as

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. M < J- • • \dq* • • • dqn_*dp* • • • dpn^ d m * , p i H =- E E --e s t.-E - E ,q (2-2-26) dt {••• j ' '’\dqx • • • dqndpx •■■dpn

The microcanonical rate constant of the reaction system with st, k(E, st), is defined by

(2-2-27)

Therefore, the rate constant is

K H = E -e , (2-2-28)

In the above equation, the denominator equals hnp(E) and the numerator equals

hn~xp{E - E 0 - £ t), thus

(2-2-29)

Summing over all translational energies gives the microcanonical rate constant

W *(E -E 0) (2-2-30) hp(E) ’

where ?t(E-Eo) is the sum of the states at the transition state with translational energies

from 0 to Eo.

The canonical rate constant k(T) can be derived from the microcanonical rate

constant k(E). The reaction system’s energy depends on its translational energy and its

angular motion. In quantum mechanics, two quantum numbers n and j are generally used

to identify the states Enj. It is also supposed that the system is at thermal equilibrium. The

initial energy distribution is not important in this theory. What is needed is that the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. system has a mechanism for rapid energy redistribution, which requires that the system

has strong intramolecular vibrational coupling; this can be accomplished by anharmonic

interaction. In thermal equilibrium, the energy distribution is

- E ,j / k 8T P„, = z , , r = ------gte E'J'kBT. (2-2-31) ' Z s / ~ ‘ Q m A ? ) n j

The canonical rate constant is expressed as

« # •)- • n,j(E>Ea) z^total v ) nJ(E>E0)

k(t )= A(T)e~E°lksT,

< 2 ' 2 ' 3 2 ) zltolaiy ) n,j(E>E0)

To give a physical explanation of the pre-exponential term A(T), let us replace the sum by

integration

A(T) = -r1 — \K(E)p(EVC-E''IVdE- E totai ' ) E>E0

Substituting (2-2-30) into the above, we have

A(T) = ------— - W*(E - EQY (E~Eo)lkBTdE. hQtotal{T) J Eo

1 ® A(T) =------fw * (E y E/k*TdE. (2-2-33) h Q to ta l( T ) 0

The partition function Q(T) is

Q(T) = X g ‘e~E/kBT = )p{EyE/vdE. i 0

Let /? = 1/k.BT., Q{fi) can be written as the Laplace transform of p(E).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Q (j))= \p (E yv

Also, the total number of states is

5V(£)= ]p{E)m = C 'W )I Pi 0

Therefore,

A(T) = ^ ^ - 1 , (2-2-34) hQtotal{T)

where Q*totai(T) is the partition function for the system in the transition state without

counting the motion along the reaction coordinate. The canonical rate constant can then

be written as

k{t ) = kT-Q*(~T)- e~Ea,ksT. (2-2-35) hQtotal (T)

As an example, the vibrational partition function for a system in the transition

state is

e v 4 r ) = q t(t ).

If ksT is much larger than ho)RC, then

1 , ks T l _ e-f>o>RC/kBr ~ '

We can write the rate constant as

K(f\ = 0)RcQ*total(^') e-E„/kBT 2x 8 „ J t )

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where vRc is the vibrational frequency along the reaction path. The rate constant

calculation requires knowledge of the vibrational frequencies for the reacting system.

These vibrational frequencies are determined by the molecular structures. The ab initio

molecular orbital calculation [Hehre et al 1986] and density functional theory (DFT)

[Scott and Radom 1996] are two of the commonly used methods to calculate vibrational

frequencies. For example, an ab initio molecular orbital calculation combined with

RRKM theory has been applied to the molecular dissociation of dimethylformamide

cations, (CH 3 )2NCHO+. The calculated rate constant is in excellent agreement with the

experimental data which were obtained by Photoelectron-Photoion Coincidence

(PEPICO) technique [Riley and Baer 1993],

The magnitude of the Arrhenius pre-exponential factor of the rate constant can be

used to identify the so-called tightness of a transition state. Loose transition states

correspond to simple bond cleavages and their rate constants have a high pre-exponential

factor. Tight transition states correspond to reactions in which rearrangements may be

involved, they have low pre-exponential factor [Lifshitz 2001]. Typical values of pre

exponential factor range from 1013 to 1016 s'1.

2.2.5 Evaporation from Small Clusters

Once a cluster acquires enough energy from collisions or laser excitation,

electrons, monomers, or dimers may evaporate from the cluster. A common method of

cluster excitation is multiphoton absorption. When a cluster is under irradiation by a

high-intensity laser beam, the cluster-photon interaction can be very large, making

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. multiphoton absorption possible. In the energy rich cluster, intramolecular energy

redistribution takes place. When the cluster is in higher excited levels, the density of

states increases. The increase in the density of states makes energy equilibration fast.

A quantitative description of dissociation is possible only if the excitation energy

is not too high, and fully equilibrated. This may be true if dissociation happens

microseconds after excitation; this is similar to evaporation from bulk material. A widely

used theory of cluster evaporation is the finite heat bath theory developed by Klots [Klots

1989, 1990]. The following is a summary of this theory.

Using the Laplace transform theorem and the steepest descent approximation, the

density state of a cluster can be expressed as [Hoare and Ruijgrok 1970]

p(E) = Q(T)eE,k*T / 4lrtCkBT , (2-2-37)

where E is the energy of the cluster as a microcanonical ensemble and C is the heat

capacity in unit of ks- The total number of states with energy lower than or equal to E is

N{E) = kTp(E). (2-2-38)

In this expression, T is the temperature at which the canonical energy of the system

equals the particular energy of E. This temperature is defined by

E = - kBT. (2-2-39)

In statistical mechanics, the entropy of the system is

S{T) = k,lnQ(T)+k J ^ 2 S i

The canonical thermodynamic energy is

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Thus, we have

S(T) = kB In [kBTp(E)\ + kB ln(2 n C f2 . (2-2-40)

Applying (2-2-38) to the above equation, we obtain the approximation

S(r) = kB ln[A(£)]+ kB ln(2 n C f2. (2-2-41)

The microcanonical rate constant is expressed in (2-2-30), which gives

ln[*:(£)] = ln A * (£ -£ 0)~ In p (E )-\n h ,

where E0 is the activation energy at T = 0 K. Taking the derivative with respect to the

energy yields

d ln(y(£)) = d In N*{E - E0) d In p(E) (2-2-42) dE dE dE

Again, using (2-2-30), we have

d\nN{E)= 1 dN{E) __ p(E) _ 1 (2-2-43) dE N{e ) dE N(e ) kBT'

From equation (2-2-37), we have

In P(e ) = In Q{t ) + El kBT — \A^bt 42ttC),

and

d In p(E) _ 1 dE " kBT '

Equation (2-2-42) becomes

d ln(x(f)) _ 1 1 (2-2-44) ds kBT* kBT

In the above equation, is the temperature of the cluster at the transition state with the

microcanonical energy E -Eg. can be determined by

E-E,=[E*(T*)). (2-2-45)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. is always less than T. is the transition state energy. Equation (2-2-44) can be

written as

d ln(/r(^)) _ T-T* ds kBT*T

In a large cluster, the loss of monomer or dimer will not significantly change the heat

capacity. In the above equation, the numerator on the right hand side can be replaced by a

heat capacity C in units of kB, and the energy change in the system A E,

AT - T - T * = AE/(CkB) . We can write

d In(*:(£■)) _ AE (2-2-46) ds ~ C(kBT*)(kBT )'

Using the temperature definition E = - kBT and

AE = CkiAT- ksAT = (C - l)kBAT,

we obtain

d\nK{s) C - l Ea (2-2-47) dT ~ C*kR TT* '

In the above equation, we define an activation energy of evaporation as

Ea = C*kB(r -T*), (2-2-48)

The microcanonical rate constant can be expressed in Arrhenius form

/c(f) = A(T )exp (2-2-49)

The temperature Tb is determined as that of a heat bath that has the same rate constant

K(Tb) as a microcanonical ensemble of energy E{Tb) with a rate constant x{E{Tb)), thus

k(T ) = A(T )exp {2-2-50)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where

2 1 AEvmvap 1 f AEvap II r ur J 1 + + (2-2-51) 2 CTb 1 2 I CTb j

The pre-exponential factor A can also be expressed as the change of the system’s entropy

AS?(T) = S*(Tb) - S(T), hence

AS* exp (2-2-52) \ kBT j

where a is the reaction degeneracy.

Klots suggested [Klots 1991a] that the ratio of Ea/ksTb is approximately constant

for all clusters containing some 10 to 100 atoms. This ratio is called the Gspann

parameter y

y = Ea/kBTb. (2-2-53)

Gspann first proposed that the rate of cluster evaporation could be expressed in the form

of an Arrhenius law with Ea, though this is just an approximation [Gspann 1982],

Equation (2-2-50) and (2-2-53) can be combined to

In A - In K(Tb) = y . (2-2-54)

For most atomic clusters, the value of the Gspann parameter is about 25 [Klots 1990].

However, the value appears to be significantly larger for fullerenes [Lifshitz 2000],

Klots also applied this finite heat bath theory to thermionic emission from small

clusters. For a hard-sphere model [Klots 1991b], the canonical rate constant for electron

emission is obtained as

' 2 V , V KI(A % r l l + E ^ + Q.,,fYE-'k'T‘, (2-2-55) V y^ib J

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where Ea is the energy threshold for electron ejection, QVjb and Q°Vib are the vibrational

partition functions after and before the thermionic emission, and

Qsmf = 2jub2kBTb/h 2 (2-2-56)

is the surface vibrational partition function. The pre-exponential frequency factor is

obtained to be 2.0 x 1016 s'1 as calculated by equation (2-2-55).

2.2.6 Microcanonical Temperature Approach

The finite heat bath theory of thermal evaporation from clusters developed by

Klots is based on transition state theory. The theory is not very transparent for reasons

such that, the transition state is a hypothetical state, and Tb is the temperature of a

hypothetical heat bath defined such that its canonical rate constant x{Tb) is equal to the

microcanonical rate constant ic{E{Tb)).

An alternative statistical theory has been proposed by Andersen, Bonderup and

Hansen [Andersen et al 2001, 2002], The theory is analogous to the fragmentation theory

in nuclear physics developed by Weisskopf [Weisskopf 1937, Blatt and Weisskopf 1952],

The ABH theory introduces a microcanonical temperature Tm that is defined in terms of

the derivative of the logarithm of the energy density of the isolated finite system. The

microcanonical temperature is significantly different from the canonical temperature T

for a small system. Without introducing the transition state and many other hypothetical

parameters, the ABH model gives the rate constant in an expression that is similar to the

finite heat bath theory. For electron emission from clusters, the transition state theory

requires a model of energy exchange between electrons and atoms. It is argued by

Andersen et al [Andersen et al 2002] that the large mass difference between the two

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. makes the energy exchange inefficient, thus the transition theory may not be suitable to

describe thermionic emission from clusters.

A system with well defined density of energy states p(E) and excitation energy E

can be represented by a microcanonical ensemble. Suppose that p(E) is smoothed over an

energy interval larger than the spacing of the energy levels, then a microcanonical

temperature Tm can be defined as

(2-2-57)

and a partition function

(2-2-58) 'o

where s is the internal energy of the system. The most probable value of s equals E. The

average energy of the corresponding canonical system at Tm is

(2-2-59)

The microcanonical heat capacity is

(2-2-60) C™ dTm

and the canonical heat capacity is

(2-2-61) m

By applying a Gaussian approximation to Qifim) with E as the most probable energy of e,

(2-2-62)

Substituting (2-2-62) into (2-2-59), the average energy of the canonical ensemble

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. thus, we obtain

(2-2-63)

If the temperature dependence of Cm on Tm is small and can be ignored, then the

microcanonical heat capacity Cm is related to the canonical heat capacity Cc as

(2-2-64)

The emission from clusters is analogous to particle emission from nuclei

[Weisskopf 1937, Blatt and Weisskopf 1952]. In statistical equilibrium, a detailed

balance is maintained between the emission and absorption of particles. This detailed

balance can be expressed as

^emsPparent ^absPproducts> (2 2 65)

where p parent and p products are energy densities of the reaction parent and its daughters,

respectively. For electron or monomer/dimer emissions, the rate can be expressed as

[Andersen et al 2002, Hansen 1999]

a c{E)seelksTdd s ,

The temperature Td is the microcanonical temperature of the daughter at energy E - Ea

where Ea is the activation energy. Integrating the above equation over e, the rate constant

can be obtained as

(2-2-66 )

with

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The cross section is the average over a thermal energy distribution at the microcanonical

temperature T

uu Jdsac(s)se -E / kBTd <7, =• (2-2-68 ) jdsse £lks

The capture cross section of (2-1-14) at energy s can be rewritten as

a R{e) = nX1 £ (2 1+1 )P(l, s ) . (2-2-69) ;=o

In this expression, the reduced de Broglie wavelength X replaces the wave vector in

equation (2-1-14). The angular momentum Ih is associated with an impact parameter

ranging from IX to (/ + l)X and the corresponding classical cross section is xX2(2l + 1).

lmax is the effective cut-off angular momentum beyond which the probability P(l, e) is

small [Blatt and Weisskopf 1952].

The Arrhenius form of the microcanonical rate constant can be obtained by a

Taylor expansion of

p ( e - E j In -E,-i-\np(E-EJ2)-~El^--\np(E-EJ2). . p (e ) . dE 24 a dE2 '

Approximating the microcanonical heat capacity as a constant, this yields

P (E ~ E ,) ______-E. _ e _: In 1 + - (2-2-70) p(E) ) kB(T „ -E J2cX " l2C2m(T„-EJ2C„)

where Tm is the microcanonical temperature before the emission. By substituting equation

(2-2-70) into equation (2-2-66), the microcanonical rate constant takes the form

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where Te is called the emission temperature given by the expansion in equation (2-2-70).

To second order of Eal2CmTm, this emission temperature is

T * T ------^ — . (2-2-72) e m 2 Cm 12 C2T m

Comparing equations (2-2-71) and (2-2-72) to the rate constant obtained from the

finite heat bath theory (2-2-49) and (2-2-51), it is seen that these two theories formally

give the same expression for the evaporation from clusters, though they introduce

different models.

The total emission rate from an ensemble with energy distribution g(E, t) at time t

l{i)= \dEK{E)g(E,t). (2-2-73)

There are two limits for g(E, t). If the clusters are in thermal contact with a heat reservoir

at temperature T, the energy distribution is canonical, and constant in time, thus

g{E,t)x-p{EyBlk°T. (2-2-74)

This will give an exponential decay. In the other limit, the cluster ensemble is isolated,

and g(E, t) will depend on time, because hot clusters will dissociate more quickly than

cold ones. The cluster emission rate will be

l{t)= \dEic{E)g(E$yK{E)t . (2-2-75)

If the initial distribution g(E, 0) is broad compared to K(E)exp[-K(E)t\, it can be extracted

out of the integral. K(E)exp[-K(E)t] is peaked at k(E) = 1/t, and the emission rate will

follow a power law I(t) ~ 1/t. This assumes that no decay other than dissociation occurs.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. We will discuss the situation in which other competing processes are involved in Section

2.3.4.

2.3 Competing Cooling Processes in Hot Ceo

2.3.1 Cooling Processes in Hot Ceo

Cooling processes in fullerenes and some other clusters are quite different from

those in small molecules. Energetically excited fullerenes, or, in short, “hot” fullerenes

C60*, can undergo three different processes to release their excess energies. They are

evaporation of neutral fragments (mostly C 2 ), thermionic emission, and black-body-like

radiation. The corresponding reactions are

(2-2-76)

Css —» C(5o+ + e , (2-2-77)

C(,o —+ C^o + hv. (2-2-78)

Figure 2-6 illustrates these decay processes. Hot C6o*+ cations can undergo the following

(2-2-79)

C6o+ - C60+ + hv. (2-2-80)

Thermionic emission from C6o*+ is quenched because the second ionization potential

(11.4 eV) of C 60 is much higher than the first ionization potential (7.6 eV) of C6o-

Generally, all possible cooling processes may take place at the same time in an

ensemble of hot fullerenes. This presents a challenge to the analysis of data from

experiments that usually monitor only one channel, and to the development of theoretical

models.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Radiation

hv +

Electron Emission ► e~ + ffC

Unimolecular dissociation ► I +

Figure 2-6. Three cooling processes in energetically excited C< 5o*-

2.3.2 Radiation from Excited C< 5o

Experiments on laser excited neutral C6o* revealed that the photon emission from

the hot molecules is structureless. Continuous, black-body-like light emission has been

observed upon irradiation of gas phase C6o at 193 nm at fluences from 3 to 80 mJ/cm2 in

Ar and He ambient [Heszler et al 1997]. Experiments have been performed to obtain the

radiation rate for neutral C6o [Kolodney et al 1995a], C6o* anions [Andersen et al 1996]

and C6o+ cations [Lemaire et al 1999]. The experiments were modeled with consideration

of competing decay channels. At an internal energy of 19 ± 3.5 eV, or a temperature of

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. about 2000 K, the mean radiative rate is Krad = (3.3 ± 1) x 102 photons per second

[Lifshitz 2001]. The microcanonical radiation rate can be expressed as [Lifshitz 2000]

Io%k( e ) = 0.082E + 1.045, (2-2-81)

where E is in unit of eV and k in unit of photon per second.

CD +-»> as ©

c« ©

400 700 800500600

Wave length (nm)

Figure 2-7 Radiation from gas phase hot C 6 0 - The molecule is excited by a 193 nm ArF excimer laser. The radiation has the same distribution as radiation from a hot tungsten filament [Heszler et al 1997],

As discussed later, sufficiently hot Ceo molecules, having roughly excess energy E

= 40 eV, undergo fragmentation and electron emission on the time scale of microseconds.

In this case, the rate of photon emission, expressed in equation (2-2-81), is much lower

than that of electron emission and Cj loss.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.3.3 Thermionic Emission from Excited C6o

Delayed ionization refers to the process that electrons are emitted from a hot

cluster microseconds or even milliseconds after the cluster has been energetically excited.

Delayed ionization was first observed in metal oxide clusters in 1986 [Nieman et al

1986]. Delayed ionization of fullerenes was first observed by Smalley and co-workers

[Mamyama et al 1991]. Delayed electron emission from C6o continues to receive great

attention. It is widely believed to be a statistical process. However, experiments have

shown that delayed electron emission from C®) cannot be characterized as a single rate

process [Walder et al 1993, Walder and Echt 1992], There is evidence that mechanisms

other than statistical processes may play a role in the delayed electron emission

[Campbell and Levine 2000].

Most of the experimental studies on delayed electron emission were done by mass

spectrometry with multiphoton-excited Ceo- Delayed ionization is also observed after

energetic collisions of C6o with electron impact [Bekkerman et al 1998, Gallogly et al

1994], atomic collisions [Wan et al 1992] and surface collisions [Yeretzian and Whetten

1992, Weis et al 1996]. The first experiment on the delayed ionization of UV

multiphoton excited Ceo was performed in 1990 [Campbell et al 1991]. In this

experiment, Cgo ions were produced by laser desorption from a film, followed by UV

multiphoton excitations. Ceo cations were observed up to 20 ps after the laser pulse.

Following this experiment, there have been many studies on delayed ionization from

multiphoton excited C6o [Zhang and Stuke 1993, Ding et al 1993, 1994, Wurz and Lykke

1992, Campbell et al 1992, Walder et al 1993, Walder and Echt 1992, Deng and Echt

1998], Figure 2-8 shows delayed electron emission from UV laser excited Ceo in the gas

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. phase. This electron emission was observed in our lab. The delayed electron observation

window in experiments can be extended up to 100 ps. It is seen that the decay is non

exponential; it cannot be fitted by a sum o f just a few exponential decays [Walder et al

1993, Walder and Echt 1992]. This result can be understood because the C6o molecules

have a broad initial energy distribution and the observed rate constant is the ensemble-

averaged rate.

Electron Emission From Excited Cfin o.i £ (J) c c

c o . o i oi— tJ0J LU

0.001

0 10 20 30

Delay Time (ps)

Figure 2-8. Delayed electron emission from hot Ceo- The C6o molecules are excited by a Nd:YAG laser at 355 nm. The delayed electron emission was observed in our experiment.

In the multiphoton excitation experiments, photon energies range from UV to IR,

such as ArF excimer laser (193 nm), Nd:YAG laser of 2nd, 3rd and 4th harmonic (532 nm,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 335 nm, 266 nm), and CO 2 laser (IR wave length, i.e. 1.06 pm). In CO 2 laser excitation,

the photon energy is far below electronically excited states. Experiments showed that

even a low-intensity CO 2 laser pulse could cause substantial delayed ionization but no

fragmentation [Loepfe et al 1993, Hippier et al 1997].

Ultrashort laser pulses have also been used to investigate the ionization and

fragmentation mechanisms in C 60 molecules. Electron-phonon coupling time is of order

of picoseconds, laser pulses below ps are expected to be a probe to investigate the

coupling process. In an experiment, a 100 fs laser pulse was used to study the ionization

and fragmentation [Hunsche et al 1996]. The experiment suggested that plasmon

resonance might play an important role in the ionization and fragmentation in Ceo- In a

more recent experiment, sub-50 fs laser pulses at wavelengths of 795 nm and 400 nm

were used [Tchaplyguine et al 1999]. The experiment did not support the suggestion of

direct multiphoton plasmon excitation. Instead, it showed that, for laser intensities below

the threshold of multiple ionization and fragmentation, single ionization can be described

by a direct multiphoton ionization with the order of the process corresponding to the

number of photons needed to overcome the ionization potential.

Photoelectron spectra indicate that there are three different ionization mechanisms

in C 60 molecules [Campbell et al 2000]. In the experiment, neutral C 60 effusive beam was

produced from an oven at temperature of 450 - 500 °C. The C 60 molecules were ionized

by a pulsed laser with a wavelength of 790 nm and different pulse durations. For laser

pulses less than 100 fs, the ionization is a direct multiphoton ionization or threshold

ionization. For laser pulses wider than 100 fs but less than ps, the observed ionization is

statistical after energy equilibration among the electronic degrees of freedom. For laser

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. pulses longer than ps, the ionization has the characteristics of thermionic emission. This

shows that full energy randomization over all electronic and vibrational degrees of

freedom needs a time of picoseconds.

The role of the low-lying triplet state of C6o in the thermionic emission is still

controversial. The lowest triplet state (LUMO) in Ceo is located at about 1.7 eV above the

ground state (HOMO) [Zhang and Stuke 1993, Ding et al 1993]. Direct two photon

ionization will be the dominant process when using photons with energy of 5.9 eV (first

IP- 1.7 eV) or higher in the multiphoton ionization experiment. In this direct two photon

ionization process, the reaction pathway is believed to be that the first photon is absorbed

to excite the Ceo into the singlet manifold, then the photoexcited singlet state rapidly

relaxes to the triplet manifold from which it is ionized by absorption of a second photon.

The process can be observed in experiment. The mechanism changes to delayed

ionization when the photon energy is reduced below the 5.9 eV threshold. [Wurz and

Lykke 1994, Jones et al 1993].

There was a suggestion that the intramolecular interaction of many triplet states

may give rise to delayed ionization by a mechanism similar to the fusion of excitons in

solids [Zhang and Stuke 1993]. There is no further experimental evidence to confirm this

claim. The suggestion is thought not necessary [Campbell and Levine 2000],

A later experiment provided other evidence that the low-lying triplet state plays a

significant role in thermionic emission [von Helden et al 1998]. In the experiment, the

tunable IR radiation from a free electron laser was used to excite Ceo molecules

vibrationally, but not electronically. Alternatively, the molecules were excited in IR and

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UY irradiation. The experimental result showed that vibronically excited C6o undergoes

thermionic emission much more readily than C6o that is only vibrationally excited.

2.3.4 Unimolecular Dissociation from Excited C6o

On the time scale of microseconds, dissociative decay is the dominant decay

channel of excited C6o as well as excited C6o+. Mass spectrometry studies have revealed

that the primary dissociation reaction for hot C6o is sequential loss of C 2 units, as shown

in Figure 2-9. Therefore, the activation energy Ea of C 2 loss from Ceo is of major interest.

A survey of the activation energies obtained from different experimental and theoretical

methods can be found in [Matt et al 1999b, 2001]. For many years, experiments

suggested values of Ea ~ 5 - 7 eV, while theoretical values would range from 10 to 12

eV. More recently, it has become widely accepted that the activation energy has a value

of about 10 eV and a pre-exponential frequency factor of roughly 5 xlO19 s'1 for C 2 loss

from Ceo+ [Matt et al 2001].

Many methods have been used in theoretical studies of the Ceo dissociation

energy. Among these methods are high level density functional theory (DFT) [Boese and

Scuseria 1998], Hartree-Fock (IFF) calculation [Eckhoff and Scuseria, 1993], tight-

binding theory [Xu and Scuseria 1994, Zhang et al 1992], methods using local spin

density approximation with plane-wave basis [Yi and Bemholc 1992], and the modified

semi-empirical method [Stanton 1992], These calculations gave the activation energy of

C2 loss with a value between 10 and 12 eV. The high level density functional theory

calculation [Boese and Scuseria 1998] gave the lowest value that is considered to be the

most reliable theoretical value.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Most experiments determine the activation energy of C 2 loss from C 6 o+, while

theoretical studies refer to neutral C 6 o- Fortunately, the ionization potentials of C 58 and

Ceo are accurately known, and from the difference in their value, the C 2 loss activation

energy of neutral Ceo is determined to be 0.54 eV higher than that of C 6 o+ [Sandler et al

1992a, Lifshitz 1993],

460 C, 29 mj/cm

8 0.8 - a> W) Ss § 0.6 » o

& 0.4 - c/> c CD c 0.2 - c _o 0.0 -

50 52 54 56 58 60 62 64 66 68 70 72 74 Time (microsecond)

Figure 2-9. Ion products from multiphoton excited C 6o- The TOF mass spectrum shows the competing channels of unimolecular dissociation and electron emission in the multiphoton excited Ceo molecules.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The activation energy for C 2 loss from C6o+ cannot be measured directly.

Generally, certain models are required to be applied to the experimental data in order to

derive the activation energy.

One method in investigating the dissociation energy is the kinetic energy release

distribution (KERB) measurement. In a so-called model free approach [Sandler et al

1992b, Klots 1991a], the KERD is expressed as

c \ p{e) = s l exp ^ (2-2-82) V B )

where s is the total kinetic energy of all reaction products in the CM system, I is a

parameter ranging from 0 to 1, and 7^ is the transition state temperature (see Section

2.2.4). Both these parameters / and T* are determined by fitting equation (2-2-82) to the

experimental data. The activation energy Ea is related to the Gspann parameter y as

defined in equation (2-2-53) and the heat bath temperature Tb,

Ea= y kBTb,

The value of Tb is calculated by fitting transition state temperature 1* and y [Klots 1991a]

(2-2-83)

where C is the heat capacity of C6o+ in unit of kB. Several KERD measurements gave the

activation energy with values ranging from 7.2 eV to 10.6 eV [Laskin et al 1999, Matt et

al 1999b, c]. The strong correlation between the Gspann parameter y, and the pre

exponential frequency factor (see equation (2-2-54)), is the major source of error in the

experimental values for activation energy Ea.

Another approach is the analysis of metastable fractions. Metastable fraction is

defined by the ratio of daughter ions D to the total of ions, D+P, in a fragmentation

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. process. Mass spectrometers are suited for the measurement of the metastable fraction by

setting a time window U - tj. Based on Klots’ finite heat bath theory, the metastable

fraction is expressed as [Baer and Hase 1996]

(2-2-84)

Usually, for a given instrument and ion mass, ti and t2 have fixed values of a few tens of

microseconds. By using a mass spectrometer combined with ion trap and reflectron, the

time window can be varied and extended up to 100 /is [Laskin and Lifshitz 1997],

However, for this range, radiative decay needs to be considered in the modeling to derive

the activation energy. Another complication arises from the unknown internal energy

distribution in the C6o+ ions. A fit to the experimental data using equation (2-2-84) gave a

value of 9.5 eV for the C 2 dissociation from C< 5o+ [Laskin and Lifshitz 1997]. The

metastable fractions have also been measured by other groups [Hansen and Campbell

1996, Lifshitz 1993, Campbell et al 1990]. Equation (2-2-84) shows that the Gspann

parameter may be deduced from these data. They do, indeed, suggest that C 60 or C6o+

have a much higher Gspann parameter, and pre-exponential frequency factor, than other

atomic clusters.

Another method is to study the energy dependent fragmentation, i. e. the so-called

breakdown curve. In an experiment [Worgotter et al 1996], breakdown curves were

measured with a double-focusing, sector-field mass spectrometer with electron impact

ionization. The analysis used the finite heat bath theory to model the breakdown curve.

The results suggested a loose transition state model with an activation energy Ea — 9.20

eV and a frequency factor A — 7.1><1019 s'1.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The above experimental studies had to use models based on the transition state

theory and poorly known parameters, such as the Gspann parameter y, or pre-exponential

frequency factor, to derive the activation energy Ea. Hansen and Echt were able to obtain

the dissociation energy of neutral C6o without assuming a value for the Gspann parameter

y, or pre-exponential frequency factor [Hansen and Echt 1997]. Their method is based on

the measurement of the yield of delayed electron emission from multiphoton-excited

in a time-of-flight mass spectrometer. The analysis is similar to the one in Section 2.2.5,

which gave a power law I{t) ~ t However, since the dissociation competes with the

thermionic emission, the ensemble-averaged electron emission rate is now given by

OD (k) x jdEice(E)exp{- [kc{e) + Ka(e )]}, (2-2-85) o

where Ka is the dissociation rate and Ke is the electron emission rate. Both rates can be

expressed in Arrhenius form

Ke{E) = Ae exp(-

Ka(E) - Aa exp(- EaC/E). (2-2-87)

where Ae and Aa are frequency factors for ionization and C 2 loss, respectively.

ionization energy, and C is the heat capacity of C6o- Substituting equations (2-2-86) and

(2-2-87) into equation (2-2-85) and performing some approximations will yield

A t K„) cc (2-2- 88 ) M A jjf (A‘f

where T is the gamma function. The second term in the above equation is of the order of

Ke / Ka. Since the dissociation channel is the dominant channel in the considered time

scale of about 10 microseconds [Deng et al 1998], the second term in the above equation

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. is small, and the time dependence is dominated by t 4>/£“. The measured yield of electron

emission follows

l(t) = Iorp, (2-2-89)

with p =

channel were active as discussed in Section 2.2.5. Since the ionization energy

to be 7.6 ±0.1 eV [de Vries et al 1992], the activation energy Ea is determined to be 11.9

± 1.9 eV for C

larger than all previously published values. It initiated a re-consideration of the value for

the pre-exponential frequency factor Aa. Earlier experimental values were re-examined;

the average of some 20 experimental values is now Ea = 10. 0 ± 1.9 eV for C60+ [Matt et

al 2001].

The above analysis based on the power law has been criticized [Rohmund et al

2001] because, as discussed in Section 2.3.3, photo-excited C6o may relax into the lowest

triplet state which could have a long lifetime [Etheridge et al 1995]. The activation

energy for electron emission out of the triplet state is only

This value would reduce the derived activation energy of Cj loss from C6o from 11.9 eV

to 9.2 eV.

However, the lifetime of the triplet state depends on the vibrational temperature of

C6 0 - In a recent pump-probe experiment, we could show that the lifetime decrease from

milliseconds for cold Cgo to about 40 ns when the vibrational energy reaches 10 eV

[Deng et al 2003]. Such a short lifetime would ensure that electronic and vibrational

degrees of freedom are in equilibrium for a time scale of 1 ps and longer. It should be

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. mentioned, though, that another experimental group claims to observe much longer

lifetimes in highly excited Ceo [Heden et al 2003].

The microcanonical rate constants for the three decay processes discussed in this

chapter are plotted in Figure 2-10 for comparison. The rate constants are calculated based

20-1 • on the following parameters: for C 2 loss, Aa = 8x10 s , Ea = 10 eV; for thermionic

emission, Ae - 2*1016 s'1, IP = 7.6 eV; for radiation, log k(E) = 0.082Z? + 0.744. These

data are adopted from reference [Lifshitz 2000]. It can be seen that for internal energies

higher than 35 eV, or an equivalent temperature higher than 3000 K, dissociation is the

main decay process.

1 2 C60

Dissociation

6 D) Radiation

3 Thermionic emission

0 20 30 40 50 60 70 80

Internal Energy (eV)

Figure 2-10. The microcanonical rate constants for the competing processes in excited C6o- Data are adopted from [Lifshitz 2000],

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.4 Conclusion

Excited fullerenes release their excess energy via unimolecular dissociation,

electron emission, and radiation. The first two processes are thermally activated

reactions. Dissociation and electron emission can be described by statistical theories such

as the transition state theory. The evaporation from clusters is generally described by the

finite heat bath theory which is a thermodynamic calculation. Many experimental efforts

have been made to characterize these cooling processes. However, details of these

processes are still not fully understood. Some experimental evidence exists that delayed

electron emission from photo-excited fullerenes is not a statistical process with complete

randomization of the excess energy [Campbell and Levine 2000]. Further efforts in this

field are expected to give clearer pictures for these processes.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 3

THERMIONIC EMISSION FROM MULTIPHOTON EXCITED C60

3.1 Introduction

Delayed electron emission from energetically excited neutral C6o molecules has

been studied ever since 1990. It is generally believed that delayed electron emission from

Cgo and other atomic clusters is a statistical process similar to thermionic emission from

bulk materials. Therefore, delayed electron emission from clusters is also called

thermionic emission. The mechanism of thermionic emission from clusters, including

fullerenes, is complicated and not yet fully understood. Statistical theories based on

energy equipartition among all degrees of freedom have been developed to calculate the

rate constants for delayed electron emission from atomic clusters. However, the

excitation processes in experiments of multiphoton absorption Ceo molecules are more

complicated. The existing theories cannot be used to well explain the observed delayed

electron emission from multiphoton excited C(,q molecules [Campbell and Levine 2000].

For example, some experiments suggest that excited electronic states might play a

significant role in the delayed electron emission process [von Helden et al 1998].

The complication in the analysis of delayed electron emission from excited Ceo is

also due to the phenomenon that other competing processes of unimolecular dissociation

and radiation take place at the same time in a hot fullerene. In experiments, the individual

processes cannot be separated from each other. It has been claimed that delayed electron

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. emission is an insignificant process compared with unimolecular dissociation [Sandler et

al 1992], This conclusion was based on a poorly known activation energy of the

unimolecular dissociation. This chapter presents an experimental study on the probability

of delayed electron emission from multiphoton excited C6o molecules. This study will

help to understand the competing decay processes in a hot Ceo molecule.

3.2 Experiment

3.2.1 Laser Ionization Time-of-Flight Mass Spectrometer

A laser ionization time-of-flight mass spectrometer was built to study delayed

electron emission from multiphoton excited Ceo molecules. Figure 3-1 is a diagram of this

apparatus. The system is equipped with two sets of drift tubes and ion detectors. The

shorter drift tube is 4 cm in length; it is for delayed electron detection. The longer drift

tube is 190 cm long. This ion flight tube is mounted anti-parallel to the electron flight

tube. It can be used to analyze mass distributions of prompt or delayed cations and

anions. The Ceo molecular beam, the laser beam and the extracted electron/ion beam are

perpendicular to one another. The crossed-beam arrangement is designed to collect

prompt and delayed photoelectrons with nearly 100% efficiency, at least for electrons

emitted within less than 10 ps. The Ceo powder (MER, purity 99.5%) is loaded in a

copper cell (Knudsen cell) with orifice diameter of 1.4 mm. During the experiment, a C6o

molecular beam effuses from this resistively heated cell. At a distance of about 3.3 cm,

shortly before the intersection with a pulsed laser beam, the low-density molecular beam

is collimated by a rectangular slit of 2.0 mm width and 5.0 mm length. The longer side of

the slit is parallel to the laser beam. The unfocused laser beam is generated from a

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nd:YAG laser operating at the third harmonic at a wavelength of 355 nm (photon energy

3.49 eV). The laser beam has a diameter of 6 mm, pulse duration of about 7 ns and

repetition rate of 50 Hz. The beam is collimated by a circular aperture. Strong electron

intensity may cause the saturation of the detector and thus loss of detection efficiency.

Laser beam collimators with apertures of either 1.0, 2.0 or 4.0 mm diameter are used to

keep the detector count rate within a narrow range to avoid the loss of detecting

efficiency due to saturation of the detector. All data presented in this chapter are scaled to

a laser beam diameter of 2.0 mm.

The C6o molecular beam and the laser beam intersect at a right angle between the

first two ion extraction plates, as shown in Figure 3-1. Photoelectrons are extracted by a

weak static electric field (10 V/cm) into the short flight tube toward the detector. At the

end of the tube, electrons with kinetic energy of 300 eV impinge on a micro-channel-

plate detector (MCP, Hamamatsu model 1552-2IS) which has an effective diameter of

2.7 cm. A solenoid is mounted outside the vacuum chamber to generate a homogeneous

static magnetic field parallel to the axis of the electron flight tube to guide the

photoelectrons to the detector. Electrons will be detected as long as their emitting parent

Cgo molecules have not moved away from the tube axis by more than about 1.3 cm along

the direction of the molecular beam. The magnetic field also helps to suppress electrons

originating from other regions of the spectrometer, such as electrons emitted from

electrodes hit by scattered laser light.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. | Quartz Microbalance

MCP Detector For Electrons MCP Detector Electron / ion Extraction For Positive or Solenoid Negative Ions ion Deflector

[( '

ljJ

Positive or Negative Ion Extraction Collimator Collimator

YAG Laser Data Processing 355 nm Preamplifier & Discriminator TDC

f = — I □ □ 0

Figure 3-1. UV laser multiphoton excitation TOF mass spectrometer for the study of delayed electron emission from C6o molecules.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.2.2 Ceo Molecular Flux Measurement

In order to determine the electron emission probability per photo-excited Ceo, we

need to determine the number density of Ceo in the interaction region with the laser beam.

This number density is determined by several factors, such as the source temperature,

orifice diameter of the source, the geometry of the Knudsen cell, and the vapor pressure

in the source. In a Knudsen cell, the orifice diameter is small compared with the size of

the cell so that there is no bulk mass flow out of the orifice. In this case, the gas leaks out

very slowly, and the pressure and temperature in the cell are well defined. Under this

condition, the number of Ceo molecules escaping from the orifice in a time duration t can

be calculated by

(3-2-1)

where N is the number of gaseous Ceo molecules inside the cell, V is the volume of the

cell, A is the cross section of the orifice and is the average speed of the C6o

molecules inside the cell. This average speed can be calculated from the Boltzmann

distribution; it is

(3-2-2)

The temperature of the cell is kept sufficiently low such that the Cgo gas can be

approximately regarded as an ideal gas. Therefore,

where p is the vapor pressure of C< 5o inside the cell. By substituting equation (3-2-2) and

(3-2-3) into equation (3-2-1), we obtain

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. N, (3-2-4) escape 4 kBT

The Ceo beam travels a distance Z, from the cell to the region where it intersects

the laser beam. The number of C6o molecules during the time t at position Z; within a

laser beam cross-section as shown in Figure 3-2, is given by

escape (3-2-5)

The vapor pressure of Ceo has been determined by several groups [Abrefah et al 1992,

Mathews et al 1992, Korobov et al 1994, Piacente et al 1995, Popovic et al 1994,

Popovic 1996], Figure 3-7 shows the published vapor pressures p vs. the oven

temperature T. The reported values disagree with each other by as much as an order of

magnitude. Significant uncertainties arise from the determination of temperature and

apparatus geometry. These parameters introduce significant error into the calculation of

molecular density if equation (3-2-5) is used.

To avoid these uncertainties, we use a quartz microbalance to directly measure the

C(so molecular flux. In the experiment, the C6o molecules emerge from the Knudsen cell

which is maintained at a temperature of 460 °C. The flux density at the ionization region

is corrected for difference in the distances of source-to-microbalance, Zm, and source-to-

laser beam, Z,. According to equation (3-2-5), the correction is

(3-2-6)

where, TV,- and Nm are C6o number densities at the microbalance and at the ionization

region, respectively. Am is the area of the microbalance surface and Ai is the area of the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. molecular beam cross-section corresponding to Am. This geometry is illustrated in Figure

3-2.

Laser Beam Q>o Source Microbalance

Beam Intersection

Figure 3-2. Diagram of the arrangement for the C6o beam measurement.

The flow velocity of Cgo is needed in order to convert flux density into number

density. This flow velocity is given by equation (3-2-2), which is determined by the

source temperature. Any error of a few degrees in the source temperature leads to

insignificant uncertainty in the flow velocity as we can see from equation (3-2-2). For a

source temperature of 460 °C, the C6o number density at the ionization region is found to

be nc 60 = 1.11x 107 cm'3 with an estimated error of 10%.

The use of the quartz microbalance would underestimate the beam flux if the

sticking coefficient of C< 5o were less than one. A lower limit of 0.85 has been determined

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. experimentally [Maltsev et al 1993]. At the worst case, we would underestimate the flux,

and the number density, by some 15 %.

3.2.3 Laser Intensity

The Nd:YAG laser at wavelength 355 nm has a pulse duration of 7 ns. The

average laser pulse energy is measured with a thermopile sensor after the laser beam exits

the vacuum chamber. Due to reflection by the vacuum window, the value displayed by

the sensor is about 10% less than the actual value in the intersection region of laser beam

and C6o molecular beam. Our laser system creates a rather stable average laser fluence

during the experiment. However, there are shot-to-shot fluctuations. Using a fast

photodiode, we see shot-to-shot fluctuations of 5 to 10%.

The laser fluence can be varied by inserting thin quartz plates into the laser beam

at 45° to attenuate the laser intensity without changing the spatial profile of the laser

beam. In the experiment, we use laser fluences ranging from about 20 to 100 mJ/cm .

This corresponds to power densities of 3 to 14 mW/cm , or pulse energies of 0.6 to 3 mJ

for a laser beam diameter of 2.0 mm. In a few cases we use a mildly focused laser beam

in order to cause strong fragmentation of Cqo and to test the detection efficiency of our

system.

3.2.4 Single Electron Counting

The electron and ion detection in our system are operated in single-ion counting

mode. This is accomplished as follows. The output signal from the micro-channel-plate

(MCP) is amplified by a preamplifier with a gain of 10. The amplified signal then passes

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. through a discriminator which has a bandwidth of 300 MHz and a threshold o f-10 mV.

The output from the discriminator is fed into a time-to-digital converter (TDC) with 20 ns

bin width, about 2 bins dead time and multi-hit capacity. Electron spectra are acquired for

100 to 1000 seconds.

This system is well suited for low-count rate applications, but peak count rates

exceeding about 0.1 per laser shot and bin (equivalent to 5 MHz) will lead to noticeable

spectral distortions because of dead time effects in the electronics and the TDC. Also at

high event rates, the gain of the detector will drop due to the temporal reduction of the

high voltage, and an increasing fraction of events will fall below the discriminator

threshold. Excessive peak count rates were avoided as much as possible by either

reducing the laser beam diameter, laser fluence, or the flux of C^o molecular beam (by

reducing the source temperature).

One problem in this experiment is caused by secondary electrons that do not

originate from C6o- Cations formed in the extraction region will be accelerated by the

extraction field and hit some surfaces. Secondary electrons emitted by this ion

bombardment are then accelerated toward the electron detector. To avoid this effect, the

ion extraction field is set to a low value of 10 V/cm, thus limiting the kinetic energy of

cations within the ion extraction region.

The laser pulse also creates anions which will be accelerated towards the electron

detector. However, the kinetic energy of electrons and anions is only 300 eV when they

hit the MCP detector. This value is near the optimum energy for electron detection, but

far below the optimum energy for ion detection. Therefore, detection of anions is strongly

suppressed. The time-of-flight in this setting is about 20 ns for electrons.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.2.5 Detection Efficiency

The detection efficiency is an important parameter in our system designed for

electron counting. The MCP detector used in this experiment has a detection efficiency of

70 ± 10 % for electrons at a kinetic energy of 300 eV. However, the system of MCP-

preamplifier-discriminator does not necessarily reach this maximum efficiency. In an

ideal case, all output signals from the MCP created by real “events” are well above the

electronic noise level, and above the threshold of the discriminator. This ideal situation

could not be realized in our experiments, primarily because of the electronic noise

generated by the laser. To filter this noise, the discriminator threshold was raised, which

caused some loss of signals from real events. This is apparent from the data shown in

Figure 3-3. The system displays a continuous decrease in electron count rate with

increasing threshold.

3.3 Probability of Delayed Electron Emission

Delayed electron emission was observed in the experiment with different laser

fluences. Some spectra are shown in Figure 3-4. Three spectra are recorded at a source

temperature of 370 °C. These spectra demonstrate that changes in laser fluence only

affect the overall electron intensity by some factor, but they do not change the time

dependence of the electron emission from photo-excited C6o molecules. Delayed

electrons were observed for up to 150 ps. Delayed electron emission up to 300 ps has

been observed when we used a mildly focused laser and a C<>o source temperature of 520

°C. This spectrum is shown in Figure 3-4 with open symbols. The intensity is scaled by

an arbitrary factor to fit the spectrum into the figure.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Q.5 E q delayed electrons CN 60 3 5 5 nm, unfocused, 2.9 mJ in CO N ^— o T = 350 °C o tfi " ‘c

-Q •

• O x : (0 L_ 0) W d • ro u . CD Q. W • C60 beam on c O C60 beam off • o3D O • • o © O i . , i i i t I -10 -20 -30 Discriminator threshold (mV)

Figure 3-3. Dependence of electron count rate on discriminator threshold. These data suggest that the detection efficiency is limited by the discriminator threshold, even at -10 mV.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. delayed electrons

▼ 0.7 mJ, 370 °C — 0.7 mJ, C60 beam off o 8 mJ focused, 520 °C O CM ~o

0 50 100 200 250150 T im e (|js)

Figure 3-4. Delayed electron emission from laser excited Cgo molecules. The solid symbols are recorded at different laser pulse energies but identical source condition, T = 370 °C. The background intensity (dotted line) is recorded with the Ceo beam being blocked. The spectrum recorded at 520 °C with mildly focused laser (open circles) shows delayed electron emission over 300 ps.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A background spectrum was recorded at low laser fluence and by blocking the C6o

molecular beam with a mechanical shutter. This background spectrum, shown in Figure

3-4, demonstrates that some electrons originate from sources other than C6o, such as

prompt photoelectrons from background gas, or photoelectrons generated at surfaces, but

this background is weak compared to the signal from excited C6o-

In another set of experiments using laser wavelength of 266 nm, significantly

larger background was observed. This may be due to the increase in photoelectrons

emitted from surfaces when the photon energy is higher.

The total number of electrons emitted from the ensemble of excited Cgo molecules

per laser pulse is obtained by integrating the spectrum from the onset of the delayed

electron signal to some time t. A representative set of integrated data, based on raw

spectra recorded at a source temperature of 370 °C, is shown in Figure 3-5. The figure

displays data recorded with laser pulse energy ranging from 0.7 to 2.5 mJ per laser shot.

These data demonstrate several interesting features, (i) Higher laser pulse energies yield

larger total number of emitted electrons, (ii) The cumulative intensities increase rather

uniformly from time 0.1 /us to about 10 /us. This is roughly a linear increase on a log-log

scale, which indicates that the electron emission follows a power law in time in this

range. This behavior reflects the broad internal energy distribution of the multiphoton-

excited C6o molecules in the experiment [Hansen and Echt 1997], For large delays, the

cumulative intensities reach constant values, (iii) The cumulative intensity during the

early 20 to 40 nanoseconds includes all the prompt electrons. This cumulative intensity is

less than the asymptotic value by nearly two orders of magnitude.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. delayed electrons T = 370 °C 355 nm, unfocused

1.9 mJ 1.6 mJ 1.3 mJ 1.1 mJ

0.01 0.1 1 10 100 Tim e ((js )

Figure 3-5. Number of electrons per laser shot. The data shown in the figure are integrals of the spectra in Figure 3-4 over a time range from 0 to t. Note the relatively small fraction of quasi-prompt electrons emitted from excited C6o during the first 20 ns.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The integrated yields of delayed electrons are extracted from the recorded spectra

by integrating the electron intensity over a range of 0.1 ps < t < 80 ps. This range

excludes the prompt electrons. Spectra recorded at high laser fluence and high C6o

molecule source temperature show mild distortion during the first 1 to 2 ps due to the

high count rates. The delayed electrons are extracted from these spectra over a slightly

narrower range of 5 ps < t < 80 ps. Figure 3-6 displays the dependence of the total

number of delayed electrons per laser shot on the laser fluence and the C

source temperatures at 370 °C, 400 °C and 460 °C. All three curves show an initial steep

slope of 6.0 ± 0.4. If we express the laser fluence as I and the total number of electrons

per laser shot as Ne, then

N e ozIa, a = 6.0 ±0.4. (3-3-1)

This result suggests that the electrons are emitted from Ceo molecules that have absorbed

at least 6 photons, or an energy of about 21 eV. The total internal energy of the Ceo

molecule reaches a value of about 26 eV. At this and higher internal energy, delayed

electron emission and unimolecular dissociation are observable in experiments.

The electron yield, shown in Figure 3-6, increases with source temperature

because a larger number of Cgo molecules are exposed to the laser beam. At constant laser

fluence, the electron yield should scale as the number density of C6o molecules in the

beam. This dependence is demonstrated (left coordinate) in Figure 3-7. The solid symbols

are the measured electron yields. They are linked with a dotted line.

The measured electron yield can be compared with vapor pressure data. As

discussed in equation (3-2-4), the number density of Ceo molecules is proportional to the

vapor pressure p, and so is the electron yield Ne,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o o o 460 °C

400 °C

370 °C

o 0) 03 CD **—»o H o delayed electrons 355 nm, unfocused

o o 20 3040 50 60 70 80 90 100 Laser fluence (mJ/cm^)

Figure 3-6. Total electron yield vs. laser fluence. The number of delayed electrons emitted from the excited C

100

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. N oc £&T . (3-3-2)

The temperature dependence of the vapor pressure p(T) has been studied by several

groups [Abrefah et al 1992, Mathews et al 1992, Korobov and Sidorov 1994, Piacente et

al 1995, Popovic et al 1994, Popovic 1996], The p(T)/T data from those reports are

compiled and shown as lines in Figure 3-7 ( right ordinate, in units of pascal/kelvin).

Analytical expressions have been plotted rather than individual data points. They are

either taken from the reports or obtained by least-square fits to the reported vapor

pressure data. Figure 3-7 shows that our electron yield does increase linearly with p(T)/T

over a wide range of temperatures. This agreement demonstrates that the measured

probability of delayed electron emission per Cgo molecule is not significantly affected by

the source temperature. Deviations near the lower and upper ends of the temperature

scale are probably caused by insufficient signal-to-background ratio and by detector

saturation, respectively.

With the measured delayed electron emission data, we are able to extract the

lower limit of the electron emission probability per excited C6o molecule. At a source

temperature of 460 °C and the laser fluence of 100 mJ/cm2, by integrating the electron

spectra over a range of 0.1 ps < t < 80 ps, an average total number of electrons Ne - 860 ±

200 per laser shot is obtained. The probability Pe of delayed electron emission per

photoexcited C^o molecule is derived as

N Pe= ^ ’ (3-3-3) W c J

101

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C60 number density ■

delayed electrons p/T, Abrefah 1992 p/T, Mathews 1992 p/T, Pan 1992 p/T, Popovic 1994 p/T, Piacente 1995 delayed electrons

300 350 400 450 500 550 Temperature (°C)

Figure 3-7. Comparison of the temperature dependence of the number of delayed electrons with the quotient of equilibrium vapor pressure, p, and source temperature, T. This quotient is linearly related to the number density of Ceo in the molecular beam. Values for p are taken from the references listed in the figure.

102

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where rje < 10± 10 % is the detection efficiency of the MCP detector for electrons at the

kinetic energy of 300 eV (see section 3.2.5), nc = (1.11 + 0.1) xlO7 cm'3 is the number

density of C6o in the molecular beam at 460 °C, and V= (4.1 ± 1.3)xl0'3 cm'3 (see Figure

3-2) is the interaction volume of the C6o molecular beam and the laser beam. These data

show that the probability of delayed electron emission per photoexcited C6o molecule

reaches Pe> 2.6 ± 1.1 % for laser fluence about 100 mJ/cm .

3.4 Discussion

3.4.1 Accuracy of Results

Several factors affect our measurement of delayed electron yields. The limited

integrating time duration of 0.1 ps < t < 80 ps leads to an underestimate of the measured

number of delayed electrons. There are other factors that need to be considered.

In our equipment, the electrostatic extraction field and the magnetic guiding field

enhance the electron collection efficiency. However, this does not completely avoid the

possibility of some electrons from escaping detection. At a C6o molecule source

temperature of 460 °C, Ceo molecules move parallel to the extraction plates with an

average velocity of 173 m/s. Electrons emitted from these C

tens of microseconds after the laser pulse will not be extracted to the detector with 100%

efficiency due to their drifting away from the extraction axis. The loss of these electrons

adds an uncertainty, thus no attempt has been made to correct for this loss. This is one of

the reasons that our measurement presents a lower limit of the delayed electron yield.

The electron yields are analyzed under the laser fluence at which the total number

of emitted electrons per laser shot shows saturation. This is supposed to guarantee that all

103

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ceo molecules in the interaction region absorb several photons to reach the average

excitation energy. However, the C6o molecules are not prepared as microcanonical

ensembles. The internal energy may have a broad distribution. For this reason, the

number density of photoexcited C6o in the interaction region nc6o in equation (3-3-3) is an

upper limit.

3.4.2 Effect of Fragmentation on Delayed Electron Emission

Unimolecular dissociation is the major fragmentation process as observed under

our experimental conditions. At high laser fluence, prompt destructions may take place in

the internally super-hot Ceo molecules. Though this destruction probability is kept low in

our experiment, this may still be considered as a factor of overestimating the number

density of photo-excited C6o molecules as the parents of the delayed electrons. Figure 3-8

shows TOF mass spectra of fullerene cations. The laser fluences used for these spectra

are similar to those under which electron spectra were recorded. The laser has a

wavelength of 355 nm and is unfocused with fluences of 29 and 102 mJ/cm ,

respectively. Under low fluence, only Css+ and Cse fragments are observed. The peak

intensities of smaller fragment ions are less than 1% of that of C6o+. At a maximum

fluence of 102 mJ/cm , fragmentation is much more intense. The time-integrated total

number of fullerene fragment ions, Cn+ of size 40 < n < 58, reaches 30% of the total

number of C6o+ (including both prompt and delayed C6o+ up to 20 ps delay time). Smaller

carbon fragment ions with size less than 30 are not observed.

104

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 460 C, 29 mJ/cm 360 C, 102 mJ/cm

Time of Flight (microsecond)

Figure 3-8. Time-of-flight mass spectra of multiphoton excited C6o- The spectra were recorded with an unfocused laser at fluences of 29 and 102 mJ/cm2, respectively. They are representative of the conditions chosen for collection of delayed electrons.

105

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A test at high laser fluence is accomplished by mildly focusing the laser beam at

the interaction region. In this experiment, fullerene fragment ions with peak intensities

close to the intensity of C6o+ are observed as shown in Figure 3-9. In this case, the total

intensity of large fragment ions, 40 < n < 58, approaches the intensity of C6o+ including

the prompt and delayed ions up to 20 ps. Smaller fragment ions, 1 < n < 30, are also

abundant. Their integrated intensity is about 25% of that of C6o+- These ion spectra

indicate that the saturation of delayed electron emission coincides with the onset of

strong fragmentation.

3.4.3 Rate Constants

Our estimate of the lower limit of delayed electron emission indicates an

approximate upper limit for the rates of other competing decay processes. As measured,

the electron emission probability is about 2.6%. This probability can be expressed as

where Ke is the rate constant for delayed electron emission, Ka is the rate constant for the

unimolecular dissociation, and Kt stands for rate constants for other cooling processes.

The sum of the probabilities of all cooling processes is normalized, I>AH- (3-4-2)

If unimolecular dissociation and electron emission are the two dominant processes in the

excited Ceo molecule,

(3-4-3)

106

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. - 400 C, 2.0 J/cm

■O c o o 0) 53C/5 c 3 0.1 O o

w c CD _c c o 0.01

50 55 60 65 70 Time of Flight (microsecond)

Figure 3-9. Time-of-flight mass spectrum of multiphoton excited C6o at high laser fluence. The spectrum shows that fragmentation is very strong under conditions where delayed electron emission saturates.

107

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In a multiphoton excitation experiment, the internal energy of the excited Ceo has a broad

distribution, and the ensemble-averaged rate constant Kj is proportional to Pj [Hansen and

Echt 1997]. In this case, the unimolecular dissociation rate has an upper value of

kCi < Ke / 0.026 * 40k; . (3-4-4)

Under our experimental condition of low laser fluences, no fragmentation other than

unimolecular dissociation is observed. Therefore, equation (3-4-4) reflects the

competition between the unimolecular dissociation and electron emission.

3.5 Conclusions

This chapter described our experimental efforts in quantifying delayed electron

emission from multiphoton excited C6o molecules. A time-of-flight mass spectrometer

with single ion counting was employed to directly detect the electrons emitted from

excited C 60 molecules. At laser pulse energy of 8 mJ/per laser shot, electron emission

from excited C6o is observed as late as 300 ps after the excitation. The lower limit of the

probability of electron emission from the multiphoton excited C6o molecules is

determined to be about 2.6 %. This result indicates that the thermionic emission process

in the C6o molecule is less efficient than dissociation, however, it is not insignificant. An

onset of strong fragmentation was observed at the laser fluence of 100 mJ/cm , where

delayed electron emission reaches its maximum.

108

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 4

COLLISIONAL FORMATION OF ALKALI METALLOFULLERENES

4.1 Introduction

The large hollow cage structure of C 60 provides the possibility to house atoms

inside this molecule. One particular interest is to insert metal atoms, such as alkali metals

and alkaline earth metals, into the cage. The caged metal would modify the electronic

property of fullerenes and, thus, the new endohedral species could be used to construct

new materials. The research on endohedral fullerene formation and stability is needed to

explore opportunities for interesting applications.

This chapter presents a study of the formation of alkali metallofullerenes M@C6o

(M = Na and K). Two experimental approaches, ion implantation into films and gas phase

collisions, are discussed. This includes the development of the apparatus, the analysis of

the data, and the discussion of the evidence for the endohedral structure and the

energetics of M@C6o-

4.2 Endohedral Fullerene A@C6o in Collision Experiments

C$o is the most stable and possibly the smallest fullerene that can capture atoms to

form stable endohedral structures. Although experiments have been able to produce

milligram-quantities of endohedral fullerenes with larger cluster sizes such as La@Cs 2 ,

Y@C82, Ca@C 84 and Sc 2 @Cg4 [Shinohara 2000], there has been no report on the

109

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. existence of endohedral metallofullerenes M@Ceo that are stable in air. However,

endohedral fullerenes of this size do exist, and there have been efforts to study their

formation and structures. La@C6o was the first to be detected in a mass spectrometer; it

was formed by laser evaporation of a LaCh-impregnated graphite rod [Heath et al 1985].

r 60 +

H e@ C

640 680 720 Cluster Size

Figure 4-1. Ion products in the collision of C6o+ with He atoms at the collision energy of 44 eV. The spectrum is adopted from reference [Ross and Callahan 1991].

Another approach to form endohedral fullerenes is by low energy collisions. The

first experiment of this type involved collision of energetic fullerene ions with helium

atoms in a mass spectrometer at a collision energy of 44 eV [Weiske et al 1991]. Figure

4-1 shows a mass spectrum of the collision products [Ross and Callahan 1991],

Calculations indicate that this collision energy is sufficient to force a helium atom

through a six-member ring of the cage [Hrusak et al 1992, Kolb and Thiel 1993]. The

110

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. collision energy dependence of the capture cross section was measured by a few

experiments in collisions of neutral or ionic Ceo molecules with rare gas atoms or ions

such as He and Ne [Christian et al 1993, Wan et al 1992a, Campbell et al 1998a, Kleiser

et al 1993, Sprang et al 1994], In these experiments, it was possible to determine the

capture thresholds. The He capture threshold was experimentally found to be as low as 3

eV in a collision of He with laser desorption C6o' projectiles which have high internal

energy [Sprang et al 1994],

These experiments also revealed that the capture threshold depends on the internal

energy of the Qo molecules prior to the collisions. Cgo+ ions produced by laser desorption

have higher internal energy than C6o+ ions produced by electron impact ionization. The

internal energy difference between these two types of ions can be as large as 30 eV. Cold

Cgo cations from the laser desorption source have relatively high capture thresholds. With

the increase in internal energy of C6o, the capture threshold is decreased. The effective

size of the six- or five-member rings in the fullerene cage may increase when the internal

energy is higher. As a result, the potential barrier that the projectile needs to overcome to

form the endohedral complex is lowered. Molecular dynamics simulation has confirmed

the internal energy effect on the capture thresholds [Ehlich et al 1993].

Calculations using semi-empirical and ab initio methods show the formation of

thermodynamically stable windows on the potential energy surface of the triplet manifold

of Cgo corresponding to nine- and ten-membered rings in the excited C6o structure [Murry

and Scuseria 1994], The insertion barrier through this window to capture a He atom can

be lower than the insertion barrier through a six-member ring.

I ll

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. There may be more than one mechanism in the collisional capture of atoms. In

collisions of Ceo with He, the collision energy dependent capture cross-section showed

different behaviors in low and high-energy ranges [Campbell 1998a]. The measured

capture cross section can be fitted with a simple spherical model of

<% = « !-r„ IE ), (4-1-1)

where %Rq is a hard-sphere cross section, E is the collision energy, and F& is the

penetration barrier [Campbell and Rohmund 2000]. Two different barriers, 6 eV and 17

eV, were obtained from a fit to the data. In the low energy range, collisions have an

effective capture radius of Ro = 0.5 A which probably corresponds to a central collision

through a six-membered ring. At high energies, large impact collisions may contribute to

capture. An energetic projectile can collide with a C atom on the cage and break a C-C

bond to open a large window for the capture followed by the cage being re-closed. After

capture, fragmentation of C6o may or may not occur depending on the collision energy.

Collisions of Ceo with alkali metal ions Li+ and Na+ are supposed to have similar

dynamic behavior as collisions with He and Ne, respectively, because Li+/He, and

Na+/Ne are iso-electronic and close in sizes. The first experimental studies of gas phase

Cgo collision with alkali metal ions (Li+, Na+ and K+) were conducted in an ion guided

mass spectrometer [Wan et al 1992b, 1993]. Figure 4-2 shows the collision energy

dependence of the Li@Cn+ products.

The capture threshold increases with the size of the projectile metal ion. The

capture thresholds for Li@C6o+ and Na@Cgo+ were measured to be 6 eV and 18 eV,

respectively. K@C6o+ could not be detected; its capture threshold was estimated to be

about 40 eV [Wan et al 1992b, 1993]. The explanation is that for the smallest Li+,

112

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. penetration can occur through the six-membered ring whereas for larger metal ions,

penetration requires C-C bond breaking.

• - Li@Cg0

- a - Li@ C toX7 ® 150

p 100

D'" a - - - —C — • # —

60 80 100 120 Collision Energy (eV)

Figure 4-2. Relative capture cross-sections of Li@Cn+ in the collision of with Li+ ions at different collision energies. Data are from [Wan et al 1992].

Endohedral fullerenes have also been produced by implanting alkali metal ions

into fullerene films [Campbell et al 1997, Tellgmann et al 1996, Deng et al 1999], It is

expected that the yield of endohedral fullerenes in this method is higher than in the gas

phase collision approach. First, the C6o density in the target film is much higher than that

in the gas phase. Second, energetically excited collision complexes can quickly dissipate

their excess internal energy into the film so that the probability of fragmentation is

113

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. suppressed. Ion implantation into fullerene films may be developed as a technique to

produce macroscopic quantities of endohedral fullerenes.

4.3 Alkali Metal Ion Sources

In both of our experimental efforts, the ion implantation experiment and gas phase

collision experiment, the metal ion source is a key part of the apparatus. Well-defined

kinetic energy of the projectile ions is critical in the study of the dynamic behavior in low

energy collisions of Ceo with metal ions. Metal ions in our experiments are generated by

surface ionization. These ion sources provide ion beams with a very small kinetic energy

spread of 2 kgT ~ 0.3 eV [Alton 1995]. A disadvantage of these sources is their low

current. Our sources produce ion currents of less than 1 pA, but this is good enough for

the purposes of our experiments. We use cylindrical, resistively heated cartridges capped

with 0.25 ” diameter porous tungsten plugs that are coated with aluminasilicate glass

which is doped with sodium, potassium, or other alkali metals.

An ion gun was designed and built to extract, accelerate, focus and decelerate the

alkali metal ions. Figure 4-3 is the diagram of this ion gun. Ion currents of a few hundred

nano-amps are focused to a spot of about 5 mm in diameter for ion kinetic energies

exceeding 40 eV. At energies below 20 eV, the ion current from the ion gun decreases

dramatically. TOF-MS spectra of sodium and potassium sources, discussed further

below, indicate that the contribution from other ions does not exceed a few percent. Na+

ion output from the sodium ion source and K+ ion output from the potassium ion source

are shown in Figure 4-4. These ion sources are used in our experiments. The ion current

was measured with an electrode of diameter 0.8 cm and located at 2.0 cm from the exit of

114

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the ion gun. The ion gun operated in dc mode, and the ion beam was focused at the

detecting electrode. The metal ion current depends on the temperature of the tungsten

plug and the ion extraction field. Typically, the extraction fields are set to about 300 ~

800 V/cm depending on the ion energy.

"emitter

Figure 4-3. Diagram of metal ion gun. A, B, C - Einzel lens; D - Group of deflectors; E - Anode; F - Wehnelt; G - Bias; H - Radiation shield and ion gun support. Emitter - integrated heater cartridge and impregnated porous tungsten plug.

The alkali metal ion sources have also been characterized with mass spectrometric

analysis. Figure 4-5, 4-6, and 4-7 are mass spectra of sodium, potassium, and a

commercially obtained source claimed to be a Ca ion source. The mass spectrum of the

sodium ion source shows that the ion output is dominated by Na+, but K+ ions are also

detected in this source at the 1 % level. No other metal ions are detected. In the potassium

115

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. source, as shown in Figure 4-6, the K+ ions are the dominant ions but contributions from

other metal ions (Na+, Rb+, and Cs+), are about 10%. This ion source is a commercial

one. The purity of this potassium ion source has been greatly improved by re-coating the

emitter surface of an exhausted potassium ion cartridge with a mixture of K 2 CO3 , AI2 O3

and SiC>2 (STREM, purities 99+, 99+, and 99.8%, respectively) in the stoichiometric ratio

of 1:1:2. The emitter was then baked at temperatures above 1650 °C in flowing Ar

atmosphere for 10 minutes. A mass spectrum of this recoated potassium ion emitter is

shown in Figure 4-6(b); only K+ ions are observed. It is worth mentioning that the purity

of the ion source depends on the purity of the chemical coating on the emitter surface of

the tungsten plug.

20 30 40 50 60 70 80 90 Ion Energy (eV)

Figure 4-4. Na+ and K+ ion output as a function of ion kinetic energy. The ion gun operated in dc mode. The ion output was measured with an electrode of diameter 0 . 8 cm and located at 2 . 0 cm from the outlet of the ion gun. The ion emitter cartridges are heated by (2.0 A, 8.0 V) and (2.0 A, 8 . 8 Y) for the sodium and potassium sources, respectively.

116

Ion intensity (relative) 10 101 Figure 4-5. Mass spectrum of a commercial sodium ion source. The The source. ion sodium commercial a of spectrum Mass 4-5. Figure ° source is contaminated by about 1 % of K+. 1of % about by contaminated is source fern 0 0 0 0 0 10 4 160 140 120 100 80 60 40 20 Na' o Ms (amu) Mass Ion 117 llIKli IonEnergy = 60 eV SodiumIon Source

COO (a) Potassium Ion Source Ion Energy = 60 eV Na

Rb Cs

CO C o (b) UNH Potassium Ion Source Ion E nergy = 5 0 eV

o o

20 40 60 80 100 120 140 160

Ion Mass (amu)

Figure 4-6. Mass spectra of potassium ion sources, (a) Ions detected in the output of a commercial potassium ion source. The impurity metal ions reach some 10% of the total ion output, (b) Re-coating the ion emitter enhanced the purity of the potassium ion source.

118

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 105 Comercial ion source - Ca Ion energy = 60 eV

Cs Na

Rb'

10° 20 40 60 80 100 120 140 160 Ion M ass (amu)

Figure 4-7. Mass spectrum of a commercial ion source claimed to be doped with calcium. This ion source does not emit any Ca+ (mass 40 amu), but K+ (mass 39 and 41 amu), and other alkalis.

119

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. We had planned to also form alkaline earth metallofullerene by collision of Qo

with ions. However, efforts were hampered by the unavailability of commercial alkaline

earth ion sources of sufficient purity and intensity. Figure 4-7 shows the mass

spectrometric analysis of a commercial alkaline earth ion source which was claimed to be

a Ca source by the supplier. In the spectrum, K+ ions and Cs+ ions have the highest

intensity. No Ca+ ions are observed.

4.4 Metallofullerene Formation by Ion Implantation into Ceo Films

Our first effort in making alkali metallofullerene is to use ion implantation into

C6o films. Higher efficiency in the metallofullerene production is expected since the ion

beam is focused on the C6o film. Homogeneous films are grown by rotating the target C6o

films and continuously growing the C6o film during ion implantation.

4.4.1 LDI-MS Experiment

Figure 4-8 shows the experimental setup for the ion implantation experiments. An

effusive beam of Cgo, as described in section 3.2.2, is directed to a stainless steel disc to

deposit a C6o film. At the same time the metal ion beam is focused onto the disc at the

same radial distance from the center of the disc. The rotation of the disc is driven by a

stepping motor. The motion of the disc can be operated in two different modes,

continuous rotation and single step motion. In most of our experiment, a film is grown by

continuously rotating the disc. Bores on the disc are used to monitor the flux of both, the

two Cgo beam and metal ion beam. A quartz microbalance and an electrode are placed

behind the disc to measure the deposition rate of the C6o film and the intensity of the

120

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. metal ion beam respectively. The C6o deposition rate is controlled by the flux of the Ceo

molecular beam. The flux is determined by the source temperature. Films are grown for a

few hours at rates of about 1 nm/s. During the film growth, the metal ion beam is injected

to the C6o film. The molar ratio between the metal ions and C 60 molecules can be

controlled by adjusting C6o deposition rate or metal ion current.

Once the film deposition is completed, the metal ion and C6o molecular sources

are switched off, and in situ mass spectrometric analysis of the metal ion implanted C6o

film is performed by laser desorption. The advantage of this in situ analysis in our system

is that contamination and chemical reaction with ambient gases is avoided. This provides

a more accurate analysis since C6o-based alkali metallofullerenes may be unstable in air

[Tellgmann et al 1996, Campbell et al 1997]. The film is analyzed by laser desorption

and ionization mass spectrometry (LDI-MS) using a Nd:YAG laser operating at the 3rd

harmonic mode (laser wavelength 355 nm and pulse duration about 7 ns). The laser beam

is mildly focused at the disc with energy of 1 mJ per laser pulse.

The ion optics for the LDI mass spectrometer, shown in Figure 4-9, contain a set

of three metal rings to provide a static ion extraction field, a set of three cylinders of an

Einzel lens for ion focusing, and four electrodes for ion deflection. The total length of

this system is 112 mm with a diameter of 56 mm. The spacing between the deposition

disc and the first extraction ring is 0.6 mm. This small spacing provides a homogeneous

extraction field so as to secure a good resolution of the mass spectrometer. The field-free

ion flight tube is 190 cm long. The high ion extraction field of about 1.5 kV/cm is applied

to achieve the best ion collection and extraction efficiency.

121

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Rotating stainless steel disc

C«, oven Metal ion gun

Ion deflector MCP detector

Ion extraction Ion focus lens static

Nd:YAG laser, 355 nm, 1 mJ/shot, mildly focused

Figure 4-8. Laser Desorption and Ionization Mass Spectrometer (LDI-MS).

122

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4-9. The rotating disc (left) onto which the C6o film is grown, the ion optics for laser desorption ionization mass spectrometry.

123

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The incoming laser beam is close to the axis of the mass spectrometer. The shape

and orientation of the plasma plume generated by the laser depends on the incident angle

of the laser beam. A nearly normal incidence on the target guarantees optimum ion

collection and extraction efficiency. In our apparatus, the incident angle is estimated to be

5° off the surface normal.

wou CO ■ ------F 2 5 2 2 OS o 3500 - C60 film: u.CM Thickness 600 nm A ^ ' 3000 deposition rate 200 A/min 0 6 0 > source temperature 550 °C CT3 2500 _ Laser: 355 nm / 51 mW 2 ' 2000 > ,

1500 - 0 . o o o Ini -

— 500 -

L ...... 0 I ______i______1______r______L______a______J______ii 1______ii...... 1...... i ...... 660 680 700 720 740 760 780 Ion Mass (amu)

Figure 4-10. LDI-MS spectrum of a C6o film. No fragment from Cgo is observed. The asymmetric tail of the C6o peak is due to fullerenes that contain 13C isotopes.

High intensity of the laser used for desorption and ionization causes significant

fragmentation of the C6o molecules and background ions, which should be avoided in our

study. At normal operation condition, our Nd:YAG laser generates a beam with pulse

power of a few MW at the wavelength of 355 nm. The intensity of this laser is too high

124

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. for our purposes so that we use a set of quartz plates to attenuate the laser beam to obtain

the desired laser intensity. The flat thin quartz plates do not change the beam profile so

that a rather homogeneous laser beam is obtained for the desorption and ionization.

The stainless steel disc substrate was irradiated with high laser intensity, pulse

power about 2 MW, for several hours to remove any contaminants from the disc. Figure

4-10 shows the LDI-MS spectrum of a pure C 6o film. The film was grown with pure C 6 o

powder (99.5% purity) at an oven temperature of 550 °C and a deposition rate of about 3

A per second. During the deposition, the vacuum system was maintained at about 6.5 x

10' 7 torr. The spectrum was recorded with a laser wavelength of 355 nm and pulse power

of about 0.36 MW. No fragmentation of C 6o is observed in this mass spectrum. These

experimental conditions were also used to study the yield of metallofullerenes.

4.4.2 Metallofullerene Products

Figure 4-11 shows laser desorption mass spectra of C 6 o + Na+ films. C 6o Films

were deposited at a rate of about 1 nm/s and sodium ions were co-implanted into the

films. C6o+ ions and NaC 6o+ ions are observed in these spectra. The multiplet structure of

the peaks reflects the natural abundance (about 1.11%) of 13C isotopes. This multiplet

structure demonstrates that the resolving power of our LDI-MS exceeds m/Am = 720.

No fragment ions such as Csg+ and NaCsg+ are observed in the spectra. The laser

energy is relatively low in order to avoid fragmentation in the desorption and ionization

process. Fragmentation into C 58 and NaCss could possibly be produced during the Na+

ion implantation due to the energy transfer at implantation energies exceeding some 50

eV. Fullerenes of size of n < 60 are not IPR structures; they are much more reactive than

125

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Cgo- Even if C 58 and NaCss were generated in the ion implantation, they would probably

not survive over the time duration between implantation and desorption. This time

duration is typically a few hours.

The spectra in Figure 4-11 demonstrate a threshold energy of 20 < Ethresh < 40 eV

for the formation of sodium metallofullerenes which are sufficiently stable to yield long-

lived, observable complex ions upon laser desorption. Our experiments do not provide

direct information about the geometries of the NaCeo complex. However, the existence of

a threshold of about 30 eV indicates that the Na must be strongly bound to the C 60 cage.

These complexes most likely have the structure of endohedral fullerene, Na@C6o- An

exohedral complex would form without such threshold energy. No NaC6o+ ions are

observed at 20 eV implantation energy. Either they cannot be desorbed and ionized by

the laser, or they dissociate within a few microseconds, or they do not exist at all.

The intensity ratio of Na@C6o+-‘C6o+ reaches about 37% at the implantation energy

of 100 eV. Varying the laser fluence within a reasonable range but without causing

fragmentation into Css+ does not change this ratio. However, this ratio is not a direct

measure of the endohedral fraction in the films. At a wavelength of 355 nm, ionization of

C60 and NaQo is the result of thermionic emission [Deng and Echt 1998]. The efficiency

of this type of ionization depends on the cluster’s ionization energy (IP). Na@C6o is

expected to have lower ionization energy than due to the low ionization energy of Na

atom (5.14 eV). Thus, Na@C6o will probably have higher ionization efficiency than Ceo-

Implantation of alkali metals into Ceo films has also been investigated by

Campbell and coworkers [Tellgmann et al 1996, Campbell et al 1997]. In their

experiments, different deposition methods were used. They grow the film with alternating

126

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. layers of C6o and metal ions. The observed maximum yield of Na@C6o+ relative to C6o+

was 5% in their report, a magnitude lower than in our method. Presumably, co-depositing

Cfio and Na+ to grow homogeneous sodium-fullerene films is a better method than

growing layered films.

An attempt to form potassium metallofullerenes by K+ ion implantation into C^o

films was also made. No potassium metallofullerene ions were observed in our LDI-MS

spectra for K+ ions implanted below 200 eV. Figure 4-12 shows a spectrum recorded

after implantation at 100 eV. The Ceo deposition and implantation conditions are similar

to those described earlier for Na+ implantation. The absence of KC6o+ suggests that

K@C60 cannot be formed by collision. Potassium ions are about 70% heavier than

sodium ions; they are also larger in size (ionic radii are 0.98 A for Na+ and 1.33 A for

K+). Insertion of a potassium ion into the C6o cage requires higher energy and massive

bond breaking. On the other hand, the energy transfer to C(,o is more efficient with the

increase in the atomic mass. Therefore, even if K+ can be forced into the C^o cage, the

high excitation energy in the complex will probably cause its immediate dissociation.

4.5 Metallofullerenes in Gas Phase Collisions

A second approach in our study of metallofullerenes is the gas phase collision-

induced formation of metallofullerene. One of the advantages of this approach is that the

intermolecular interaction is avoided so that dynamic processes can be investigated.

Another advantage is that the product ions in the collision can be detected in a very short

time, a few microseconds, so that relatively unstable product ions can be observed. A

more accurate value for the insertion threshold energy is expected.

127

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. : ------20 eV + o C 60 5 z (0

1 -2

: ------40 eV c + 0 60 > 03 CO Na@C60+ j l| W c 0 : — 60 eV C 60+ c o 1 Na@C60+

■ \

: _ _ oo eV c <» Na@C60+

| |

, . , , i , , , , i . , . ■ ...... 1 ... .

Ion Mass (amu)

Figure 4-11. LDI-MS spectra of Na+ ion implanted C6o films. The intensity of the sodium metallofullerene ion depends on the implantation energy. This figure shows spectra for implantation energies from 20 to 100 eV. The implanted C^o films are prepared with the ratio between Na+ and C6o of roughly 1:1.

128

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced Figure 4-12. LDI-MS spectrum of K+ implanted C6o film. No potassium potassium No C6o film. implanted K+ of spectrum LDI-MS 4-12. Figure ealfleeein eeosre.Teipatto nryi 100eV. is energy implantation The observed. were ions metallofullerene Ion Intensity (relative) 400 600 800 200 300 500 700 100 film thickness 237nm filmthickness 100eV energy implantation laser at 355nm, 43mW 355nm, at laser ~200nA intensity K+ion K+C60film implanted 680 700

Ion M ass (amu) ass M Ion 720 129 740 Expected KC( Expected 760 J1315 780 4.5.1 Ion-Molecular Collision TOF Mass Spectrometer

The ion-Ciso collision mass spectrometer is shown in Figure 4-13. The C6o beam

and the metal ion beam intersect at an angle of 90° between two parallel metal plates with

central holes covered by wire mesh. The plates are part of the two-stage extraction optics,

the Wiley-McLaren lens [Wiley and McLaren 1955] of a TOF mass spectrometer. Figure

4-14 and Figure 4-15 are photographs of the ion collision and extraction components.

The ion-molecule collision time-of-flight mass spectrometry requires pulsed ions.

The whole collision-extraction process consists of two phases, the collision phase and the

extraction phase. In the collision phase, C6o molecules collide with metal ions in field free

space. Ions produced in the collision include metallofullerene ions, fullerene ions, and

metal ions. These ions are extracted toward the detector that is located in the direction

perpendicular to the plane defined by the Cm beam and metal ion beam.

The metal ion beam emitted from the ion gun is pulsed by an ion gate which is

made of three parallel grids, shown in Figure 4-13. The outer grids are permanently

grounded while the potential at the middle grid can be switched rapidly between 0 and

120 V (the kinetic energy of the metal ions is below 120 eV). A complete pulse sequence

is as follows: While the metal ions are blocked by the ion gate, the potentials at the two

ion product extraction plates are switched from about 3000 V and 2480 V, respectively,

to ground. A few microseconds later, the metal ion gate is opened for about 2 ps. After

another few ps, the ion extraction voltages are raised back to 3000 V and 2480 V,

respectively. Some 100 ps later the ion extraction potentials are switched back to ground

and another cycle begins.

130

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Micro-balance

C60 Flux Monitor

Ion Extraction MCP Detector

Ion Deflector

C60 O ven Temperature control

E xtraction D eflection Preamplifier C ontrol •Control £ Discriminator DO Ion G ate E x tractio n TDC D elay

C60 O ven Metal Ic S o u rc e — \qan G u G M etal ion D ata Energy Control P ro c e s s in g G ate P u lse G ate Delay Pulse Generator ' n □ g

Figure 4-13. Ion-molecule collision TOF mass spectrometer.

131

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4-14. Axial view of the ion collision and extraction components. A is the ion extraction plate; B is the Ceo oven; C is the molecular flux monitor (microbalance); and D is the metal ion gun.

132

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4-15. Top view of the ion collision and extraction components. The Cgo source is on the right; the microbalance is on the left. The ion optics consists of a Wiley-McLaren lens and a set of ion deflector (shown near top of the photograph).

133

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The metal ion gate is an essential part in controlling the kinetic energy of the

metal ions. Metal ions cannot enter the product ion extraction region once the extraction

voltages are applied. However, when the ion extraction electrodes return back to zero

voltages, metal ions from a non-gated ion gun would move to the collision region with

ill-defmed kinetic energies. In our early experiments, without the metal ion gate, we

found that a small fraction of the product ions did not depend on the nominal metal ion

energy. These product ions were formed by collisions of C^o with metal ions which were

present in the ion source when the extraction field was turned on. These metal ions did

not have a defined kinetic energy.

A critical consideration is the time delay between the metal ion gate and the ion

extraction. The optimum delay depends on the speed of the metal ions. For example,

sodium ions at an energy of 40 eV will travel at a speed of 1.8 cm/ps; thus the time these

metal ions need to traverse the ion gate, and move from the gate into the extraction region

located about 3.0 cm away from the metal ion gate, cannot be ignored.

Another concern is the energy and speed of product ions that are formed in

collisions. For large delays between product ion formation and the extraction pulse, the

ions will move too far off the axis of the mass spectrometer and, hence, miss the detector.

For a fully inelastic collision between Na+ ions at 40 eV and C6o from a source at 580 °C,

the product ion will travel at 0.06 cm/ps at an angle of about 20° with respect to the metal

ion beam. In an early version of the experiment, the metal ion beam was directed

collinearly with the axis of the mass spectrometer. This geometry avoids the loss of

product ions, but it made mass assignments difficult because the time-of-flight of product

ions depends on their kinetic energy immediately after formation. Therefore, the

134

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. perpendicular geometry was chosen in later experiments. The time delay between the end

of the metal ion pulse and the onset of product ion extraction needs to take the above

considerations into account. In our experiments, this delay was typically 2 to 4 ps.

4.5.2 Ion Optics

Ion extraction is critical for the ion collection efficiency and also for the

resolution of the TOF mass spectrometer. The mass analysis in the TOF mass

spectrometer is based on the mass-to-charge ratio m/q of the ions. When a singly charged

ion is accelerated to certain energy, its time of flight from the extraction region to the

detector depends only on the mass of the ion. In a gas phase collision TOF mass

spectrometer, there are two factors that can significantly affect the resolution of the

instrument. One of these factors is the initial velocity of the ion along the flight axis. The

other factor is the initial position of the ion in space. In general, the time of flight t(U, Uo,

S) of an ion is a function of the extraction energy U, its initial energy Uo and its initial

position, S, in the extraction region. Figure 4-16 is a diagram of the geometry of the two-

field Wiley-McLaren ion optics. Using the parameters assigned in the figure, the energy

of an ion at position S is

U = U0 + SqEx + S2qE2 (4-5-1)

The total time-of-flight of an ion from the extraction region to the detector is

t{U0,S) = t{+12+13, (4-5-2)

where, tj, t2, and tj are the time-of-flight in the fields Ej, E2 and the field free tube,

respectively. They can be expressed as

135

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4-16. Geometry of the two-field Wiley-McLaren ion optics.

In equation (4-5-3), the signs of + and - correspond to the initial velocity of the

ion being away from and toward the detector, respectively. In our apparatus, the direction

of the ion extraction is perpendicular to the plane of metal ion beam and the C6o

molecular beam. Therefore, the initial speed of the ion products along the direction of the

extraction is minimized, and the initial speed of all the product ions along the direction of

the extraction can be ignored. Thus, equation (4-5-3) and equation (4-5-4) can be

simplified to

(4-5-6)

136

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (-Ju-Jsjs;)- (4-5-7) qhx

In our apparatus, the center of the C6o molecular beam is in the plane between the

back plate and the plate next to it in the extraction plates. The center of the molecular

beam is represented by the dash line in Figure 4-16 and its position is marked as Sm. The

initial position of product ions formed in the collision has a spatial spread of

S = Sm±AS. (4-5-8)

This spatial spread decreases the resolution of the mass spectrometer. Ions starting at

different positions have different time of flight. The effect of the spatial broadening on

the TOF resolution can be minimized. Let us define a dimensionless parameter

IS Ex + S2E2 ,. c « = , * ...L. L } (4 . 5 .9 ) V »mh\

and note that

S2qE2 = U2, (4-5-10a)

S^Et=^-(U,-U2), (4-5-10b)

the parameter a can be written as

a = ^ l + S1/[Sm{Ul/U2~l)\, (4-5-11)

then, the total of time-of-flight of an ion starting at Sm can be written as

>(Sj = , h \ l laS. + ^ 4 + S3). (4-5-12) ^[S.C/,+«.((/,- i/J l a + l V

The best resolution will be reached at the minimum or maximum of t(S), such that

{dt/dS\ = 0.

137

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 400 Ion optics geometry: 360 S m = 2.54 cm S2 = 0.76 cm 320 S„ = 75.0 cm

280

a 240

a=2.482 200

160

120

2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 Parameter a

Figure 4-17. The a parameter for the best resolution of the ion-collision TOF mass spectrometer.

This yields the following equation

2 a 3(l + a)Sm - 2a 2S2 - (l + a)S3 = 0. (4-5-13)

The above equation provides a criterion to optimize the geometry and the extraction field

of the ion-collision TOF mass spectrometer with the two-field extraction optics.

Generally, the geometry of a system is pre-designed. Thus, the practical way to obtain the

best resolution of the system is through tuning the extraction potentials Uj/q and l/2/q. In

one of our mass spectrometers, the geometry is (Sm, S2 , S3) = (2.54 cm, 0.76 cm, 75.0

cm). The numerical calculation, as shown in Figure 4-17, gives a = 2.482. In the

experiment, we use Uj/q = 3000 V. According to the above analysis, this requires that

138

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. U^q should be set at 2434 V in order to reach the best resolution of our mass

spectrometer. An experimental test on our instmment gave the optimum resolution for U2

= 2480 V in good agreement with the analysis above. In fact, the extraction plates have a

thickness of 0.6 mm and a set of deflector plates is mounted after the extraction lens, as

shown in Figure 4-13 and Figure 4-15. These factors may cause some deviation between

the calculation and the test result.

4.5.3 Collision of C 60 with Potassium Ions

Formation of product ions by gas-phase collisions of C 60 with potassium ions is

discussed in this section. A set of TOF mass spectra in Figure 4-18 shows the collision

product ions for different collision energies. In the experiment, Ceo molecules effuse from

the Knudsen cell at a temperature of 570 °C. The K+ ion source is described in section

3.2. Both fullerene ions and potassium metallofullerene ions were observed in these

spectra. A threshold was observed for the formation of metallofullerenes. Only C6o+ was

observed for collision energies below 48 eV. The formation of C6o+ is most likely a

statistical process, which will be discussed in section 5.4. The largest metallofullerene,

KC58+, requires a collision energy exceeding 48 eV. Smaller fullerene C„+ ions and KCn+

ions appear at higher collision energies.

Fullerene and metallofullerene product ions are internally hot due to the energy

transfer during the collision. Once the internal excitation energy exceeds a threshold,

decay processes may take place. Figure 4-19 shows the collision energy dependence of

fullerene product ions. C6o+ ions are observed above a collision energy of 36 eV. They

reach a peak intensity at the energy of about 60 eV. Above this energy, the first fragment

139

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ions, C 58 +, show up. The Cs8+ ion reaches its peak intensity at the energy at which the

C6o+ ion intensity has a steep drop. This behavior indicates that C 58 + ions are produced

from Cfio+ in a unimolecular dissociation process.

The intensity of the potassium metallofullerene ion products is shown in Figure 4-

20. These data indicate a correlation between the depletion of KCs8+ and the formation of

KC56+. The same correlation is observed between smaller KCn+ and their fragment KCn.

2 . The KC„+ ions have steep breakdown behaviors. The breakdown behavior reflects the

internal energy of the excited complexes; it is determined by a few quantities: the initial

internal energy of C6o molecules emerging from the Knudsen cell, the collision energy in

the center-of-mass frame, the binding energy of K+ to Ceo, the energy for the loss of C2

from KC60+, and the kinetic energy of the fragments. The breakdown energy provides a

way to study the dynamic properties of the metallofullerenes; this will be discussed in

chapter 5.

In our experiments, no KC6o+ was observed within the investigated range of

collision energies. The absence of KC6o+ in our experiment agrees with results reported

by another research group [Wan et al 1993]. One possible explanation is that the K@Ceo+

is highly excited because of a high insertion threshold. Therefore, it will undergo

unimolecular dissociation within less than 10 ps before it can be detected in the mass

spectrometer. This process can be expressed as

I? + C60-> (K@C60+)* — K@C58+ + c2. (4-5-14)

Another possibility is that the size of the potassium ion is too large so that the insertion

causes prompt dissociation. The insertion of large atoms into the C 60 cage requires C-C

bond breaking which may lead to direct C2 loss so that the product ion is K@Css+ instead

140

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 300 250 ai0930 200 36 eV 150 100

250 ai0929 200 40 eV 150 100

■4—» CD 250 ai0928 0 200 44 eV 150 100

c u C 250 ai0927 48 eV £ 200 150 100

250 ai0926 200 52 eV 150 100

7000 7200 7400 7600 7800 8000 8200 8400 8600 8800 9000 Channel Number

Figure 4-18(a). Mass spectra of ions formed by collision of Cgo with potassium ions. At collision energies below 48 eV, no potassium metallofullerene is observed.

141

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 400 ai0925 300 56 eV 200 100 KC

ai923 300 60 eV 200

100 0) > ai0921 300 £ 62 eV 200

100

£ ai0919 O 300 64 eV 200

100

ai0917 300 66 eV 200 KC k c ; 100 k c ;

7000 7200 7400 7600 7800 8000 8200 8400 8600 8800 9000 Channel Number

Figure 4-18(b). Mass spectra of ions formed by collision of C6o with potassium ions. Fragment ions, smaller than KCs8+, are observed at collision energies above 56 eV.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 350 300 ai0915 250 6 8 eV 200 150 k c ; 100 k c ;

300 ai0911 250 74 eV 200 150 100

CD > ■ * -> 300 CD ai0907 0 250 82 eV 200 & 150 0 100 c 0 c u c 300 ai0904 O 250 91 eV 200 150 100

300 ai0902 250 101 eV 200 KC k c ; KC 150 100

7000 7200 7400 7600 7800 8000 8200 8400 8600 8800 9000 Channel Number

Figure 4-18(c). Mass spectra of ions formed by collision of C6o with potassium ions. At collision energies higher than 70 eV, and KC 58 + do not survive.

Figure 4-19. The energy dependence of the fullerene ion intensities in the in intensities ion ions. C6oof fullerene potassium collision with the of dependence energy The 4-19. Figure relative intensity -1 8 6 7 4 0 2 3 5 1

0 0 0 0 0 0 0 10 120 110 100 90 80 70 60 50 40 olso e r (V lab.) (eV, y erg en collision 3.5 kc ; 3.0 o - kc ; • a - kc ; 2.5 - v - kc ; & « 2.0 -o- kc ; 0 1 1.5 0 > 03 0 0.5 ST ra— □— □— 0.0

-0.5 50 60 70 80 9040 100 110 120 collision energy (eV, lab.)

Figure 4-20. The energy dependence of the potassium metallofullerene ion products in the collision of C6o with potassium ions.

145

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of K@C6o+. This alternative possibility can be expressed as

f + C60-> K@C58+ + C2. (4-5-15)

The threshold energy for the formation of the metallofullerene KCs8+ is found to

be about 48 eV (lab). The existence of this threshold energy is considered as evidence of

the endohedral nature of the structure. In general, the threshold energy will depend on

several factors, such as the size of the inserting atom, the internal energy of the fullerene

molecule before collision, and the charge states of both the target and projectile. Insertion

thresholds increase with the size of the projectile atom, and they increase with decreasing

internal energy of C6o [Ehlich et al 1993]. Experimentally determined insertion threshold

may have large, unspecified errors. There was a study of collision of potassium ions with

Cgo, which reported that the threshold energy for the formation of KCs8+ is about 40 eV

[Wan et al 1993]. In that experiment, there was a large uncertainty in the kinetic energy

of K+ ions because the metal ion beam was guided in an octapole trap. The energy spread

was estimated to be 3 eV, much larger than that in our experiment. Another major

difference between that report and our experiment is the time window for the ion

detection. In their experiment, product ions had to survive for 0.5 to 5 ms. This time

could be too long for short lived metallofullerenes. Only the less excited molecules,

corresponding to ions generated at low collision energy, can survive over that time and be

detected. In our experiment, the time scale is shorter by two to three orders of magnitude.

More product ions and ions with larger excitation energies can be detected in our system.

146

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.5.4 Collision of C6o with Sodium Ions

Sodium is a smaller alkali metal element next to potassium. The ionic radius of a

sodium ion (0.98 A) is smaller than that of a potassium ion (1.33 A). The insertion of a

sodium ion into the cage of the C<$ molecule is expected to be easier. Observing a lower

energy threshold for the sodium metallofullerene formation would be evidence of the

existence of its endohedral structure. The formation of sodium metallofullerenes was

studied in our ion-molecular collision experiment.

Figure 4-21 shows mass spectra of the collision of C6o with sodium ions at low

collision energies. In the experiments, C6o molecules effuse from the Knudsen cell at a

temperature of 570 °C. In these spectra, NaC6o+ ions are observed at collision energies

above 30 eV. No other product ions are observed at collision energies below 35 eV.

The mass of sodium is 23 amu, only 1 amu less than the mass of a carbon dimer

C2 . Our mass spectrometer does not have high enough resolution to distinguish between a

Cn+ ion and a NaCn- 2 + ion. Nevertheless, Figure 4-21 clearly shows that, with increasing

collision energy, successive loss of C 2 occurs.

Figure 4-22 shows the energy dependence of the intensity of the three highest

mass groups, NaC6o+, NaCss+ + C6o+, and NaCs6+ + Css+, respectively. An energy

threshold at about 30 eV can be observed in Figure 4-22. This energy threshold is much

lower than the value of about 48 eV for the collisional formation of potassium

metallofullerene, shown in Figure 4-20. NaC6o+ ion intensity reaches its maximum at the

collision energy of about 42 eV (lab system). As noticed before for collisions of C 60 with

K+ ions, once the intensity of a cluster ion of given size reaches a maximum, the next

smaller cluster ion starts to appear. This behavior is also observed in Figure 4-22. It is

147

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. explained as the unimolecular dissociation of the excited cluster. No C6o+ ion is observed

at the collision energy below 35 eY. This indicates that collisions below 35 eV do not

transfer enough energy to the C6o molecule to cause thermionic emission. The collision-

induced unimolecular dissociation and thermionic emission will be discussed in Chapter

4.6 Summary

This chapter described an experimental study of metallofullerene formation. The

instrument development includes the laser desorption-ionization mass spectrometer, ion-

molecule collision mass spectrometer, and the surface ionization alkali metal ion source.

Ions from the ion source have well-defined kinetic energy, which is essential in the

determination of the energy dependence of metallofullerene formation in the ion-

molecule collisions. Threshold energies were found in formation of potassium

metallofullerenes and sodium metallofullerenes. Threshold energies of potassium

metallofullerenes are higher than those of sodium metallofullerenes. This correlates with

the size of ionic radii of Na+ and K+. It indicates that the alkali metallofullerene products

have the endohedral structures. Sodium ion implantation into a C6o film produces stable

sodium metallofullerene. It could be a method of producing metallofullerenes in

macroscopic quantity.

The ion-molecule collision experiments provide information on the maximum

internal energy that a Cn+ and MCn+ may have before it undergoes unimolecular

dissociation or thermionic emission on a time scale of about 10 microseconds. This

information reflects the dynamic processes in the excited clusters; it will be used in the

148

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. following chapter to determine, by quantitative modeling, some physical and chemical

properties of fullerenes and metallofullerenes.

149

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 300 250 ak1601 35 eV 200 NaC' 150 100

0 > 250 - ak1602 03 40 eV 200 150 100

- 0 c ak1603 250 2 45 eV 200 150 100

250 ak1604 50 eV 200 150 Cl+NaC; 100 NaC'

7000 7200 7400 7600 7800 8000 8200 8400 8600 8800 9000 Channel Number

Figure 4-21(a). Mass spectra of product ions from collisions of C6o with sodium ions. NaC< 5o+ is the largest ion observed. It is the only product observed at collision energy below 35 eV. The masses of C6o+ and NaCs8+ differ by only 1 amu; they cannot be resolved separately.

150

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 250 ak1605 55 eV 200 150

100 C l+ N a C l 56 54

0 > 250 ak1606 60 eV 200 d 150 •H w 100 0 50 C C ak1607 9 l 250 65 eV 200 150 100

250 ak1609 75 eV 200 Cl+Nacl Ct+NaCl Cl+NaC 150 100 50

7000 7200 7400 7600 7800 8000 8200 8400 8600 8800 9000 Channel Number

Figure 4-21(b). Mass spectra of product ions from collisions of C6o with sodium ions. No NaC6o+ is observed at and above 55 eV. Cn+ and NaCn_ 2 + peaks coincide within our mass resolution.

151

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced Figure 4-22. The energy dependence of product ion intensities in collisions collisions in intensities ion product of dependence energy The 4-22. Figure of C6oof ions. sodium with Ion Intensity (relative) 10 9 7 4 8 6 2 3 5 0 0 2 4 6 8 0 8 0 2 54 52 50 48 6 4 4 4 2 4 40 38 36 34 32 30 Product of (Na+, C60) collision. olso Eeg e, lab) (eV, Energy Collision 152 CHAPTER 5

THEORETICAL ANALYSIS

5.1 Introduction

The study of fullerene collision reactions, either collision of neutral C6o molecules

with atomic ions or collision of C6o ions with atoms, is one of the possible approaches to

determine the physical properties of fullerenes. Some of the experimental phenomena

observed for collision energies ranging from a few eV to GeV have been reviewed in

Chapter 1. Particular interest in these studies is for gas phase collisions with collision

energy below 200 eV. In this energy range, several processes can be observed. They

include charge transfer, thermionic ionization, fragmentation, fission, and formation of

endohedral complexes. The collision experiments provide an opportunity to study the

structural, physical and chemical properties of fullerenes.

Fragmentation of fullerenes with excess energies below ~ 100 eV proceeds by

consecutive loss of C 2 dimers [Wan et al 1993]. This can be explained as evaporation

from the clusters. The collision energy is transferred into the internal energy of the C 60

molecules. The internal energy is equilibrated among degrees of freedom of the molecule

before unimolecular dissociation occurs.

The collisional formation of alkali metallofullerenes was described in chapter 4.

One of the key features is the observation of energy thresholds for the appearance of

potassium and sodium metallofullerenes. These thresholds reflect the endohedral

153

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. structure of the metallofullerene products. Based on the experimental evidence, we

conclude that endohedral potassium fullerenes K@Cn+ (n = 58, 56, 54, ...) and

endohedral sodium fullerenes Na@Cn+ (n = 60, 58, 56, 5 4 ,...) have been observed in our

experiments. The energy dependent intensities of the product ions reflect their physical

properties, such as their internal energy, Cz binding energy, heat capacity of the cluster,

etc. In this chapter, we will deduce these properties from our experimental data. One of

our focuses will be on the formation and dissociation of Na@C6o+.

Another focus will be on the formation of bare C6o+ ions in collisions of C6o with

K+. There are two basic mechanisms for the C6o+ ion formation, charge transfer and

thermal ionization. In collisions of C6o with rare gas ions below 200 eV, the charge

transfer cross section was found to be relatively large [Christian et al 1993, Wan et al

1992], Since the ionization potentials of rare gases (e.g. 21.56 eV for Ne) are much larger

than that of Ciso (7.6 eV), charge transfer from Ceo to rare gas ions is a highly exothermic

and efficient reaction. However, in collisions of C6o with alkali metal ions, charge

transfer is expected to be inefficient or even impossible, because the ionization potentials

of alkali metal atoms (5.14 eV for Na and 4.34 eV for K, respectively) are smaller than

that of Cgo- Therefore, Cgo+ ion products most likely originate from the thermal ionization

of highly excited C6o- This will be discussed in more detail in Section 5.4.

5.2 Formation and Dissociation of Fullerenes with Encapsulated Na

5.2.1 Experimental Breakdown Curve

In a completely inelastic, “sticking” collision of a C^o molecule with an ion, the

internal energy of the collision product is the sum of the initial internal energy of C6o, the

154

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. collision energy (in the center-of-mass), and the complexation energy, i.e. the adiabatic

binding energy of the newly formed complex. The higher the collision energy is, the

higher the internal energy of the endohedral complex will be which, in turn, will increase

the rate of its fragmentation. This behavior can be observed in the experimental data if

the intensity of the endohedral complex is presented as a function of the collision energy.

This type of graph is called the breakdown curve of the complex. The curve reflects the

value of the breakdown energy. The breakdown energy of a product ion is defined as the

energy at which the collision complex is so highly excited that it has 50% probability to

undergo fragmentation before it can be identified in the mass spectrometer. The

breakdown energy may be expressed in terms of the actual excitation energy of the

complex at the 50 % fragmentation probability, or in terms of a more accessible

parameter, like the collision energy. The breakdown energy reflects the stability of the

complex; its value will depend on the structure of the complex formed in the collision.

Endohedral structure, exohedral structure and hetero-structure have different breakdown

energies.

Either the caged atom or a carbon dimer may fragment from an excited

endohedral complex. Release of a caged atom would feature an activation energy roughly

equal to the insertion threshold for the formation of the endohedral complex (about 30 eV

for NaC6o+). Loss of C 2 would cost about 10 eV, as determined for bare C6o+- However, a

caged atom may change the strength of the C-C bonding, depending on the nature of the

caged atom and its charge state. C 60 is a good electron acceptor and a caged metal atom

can transfer electrons to the C 60 host. The Coulomb interaction may strengthen the cage

and make the C-C bonding stronger. Similarly, the dissociation energy of C 60 is higher

155

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. than that of C6o+ by 0.54 eV [Lifshitz 2000], and for Cm it may even be higher. Other

effects such as the motion of the inner atom and its size may also determine the stability

of an endohedral complex. All these effects would change the energy of binding a C 2 to

fullerenes, and therefore, the breakdown energy.

In our experiment, the dynamic behavior of Na@C6o+ ion is measured in the

collision energy range from 20 eV to 60 eV. Mass spectra are recorded for energy steps

as small as 0.5 eV. The experiment was described in chapter 4. All our TOF mass spectra

reflect the product ion distribution about 9-11 ps after the collision. Important features of

our experiments are accurate knowledge of the initial internal energy of the target C 6 0 ,

and the collision energy. The collision energy is well defined due to the pulsed ion gate

and the small kinetic energy spread (about 0.3 eV) of the metal ion beam from the surface

ionization source, as discussed in Chapter 4. The C 60 beam effuses from a Knudsen cell

that is kept at a temperature of 500 - 570 °C. The number density of C$o in the collision

region is of the order of 106 cm'3; multiple collisions of metal ions with C 60 are

negligible. The current of the alkali metal ion beam is measured in a dc mode for each

collision energy before recording the mass spectrum. A typical Na+ ion current is a few

hundred nA with a spot of 5 mm in diameter for energies exceeding Eiab = 30 eV, as

shown in Figure 4-4. The metal ion current does not remain constant at different ion

energy. The yield of product ions in collisions is corrected for changes in the ion current.

The measured breakdown curve of Na@C6o+ was shown in Figure 4-22. Starting

from a threshold energy of about 30 eV, the intensity of the Na@C6o+ ion product

increases approximately linearly. As the collision energy increases, the energy transfer to

the product ions increases and thus the product ions have higher internal energy. At the

156

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. collision energy of about 42 eV (in the lab system), the Na@Ceo+ intensity drops due to

an increase in the rate of C 2 loss.

5.2.2 Modeling the Breakdown Curve

According to the theory discussed in chapter 2, the dynamic behavior of an

excited Na@C6o+ is determined by the activation energy of its unimolecular dissociation,

loss of C 2 . This activation energy can be derived if the breakdown curve of Na@C6o+ is

properly modeled. In particular, the relation between the collision energy and the internal

energy of the product complex, Na@C6o+, has to be known.

The experimental breakdown curves are simulated as a product of the cross-

section o(Ecm) for collisional formation of Na@C6o+, and the probability that this ion will

not undergo unimolecular dissociation within the time window t < tmax■ Our experiments

indicate that the reaction cross-section a(Ecm) increases linearly above some threshold

energy Ethresh, which is in agreement with the results of molecular dynamics simulations

for Li+ + C 60 collisions [Bemshtein and Oref 1998], Fitting the linear relation to several

data sets, such as shown in Figure 4-22, consistently gave us a threshold of Ethresh - 29.6

eV in the center-of-mass system for the formation of Na@C6o+- Hence, the following

relation is used to model the observed yield of Na@Cgo+,

INa@C6o+ = o'o' {Ecm - Ethresh )■ exp(- Ktwx), (5-2-1)

where k is the canonical rate constant of the C 2 dissociation of the parent ion Na@Cgo+.

In our apparatus, the time window tmax is determined by the mass of the metal ions. For

sodium ions the time window has a range from 9 to 11 ps.

This rate constant k is expressed in the Arrhenius form as discussed in chapter 2,

157

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. k = v0 exp (5-2-2) V kKTh j

where Vo is a pre-exponential frequency factor, Ea is the activation energy for C 2 loss, and

Tb is the fictitious heat bath temperature of the complex; it is determined by the excitation

energy E* ofNa@C

F F^ E* =E(Th) - k BTb +-e- + ------2------, (5-2-3) V b) Bb 2 12( C - k B)Tb

where E(Tb) is the caloric curve of a canonical ensemble. We assume

E(Tb)=0.01486 Tb - 7.631 eV, (5-2-4)

with E in unit of eV and Tb in unit of kelvin. Equation (5-2-4) agrees with the caloric

curve suggested for C6o+ at similar excitation energies [Matt et al 1999] except that for

our endohedral complex we add a value of 3 ksT to the heat capacity to account for the

contribution from the encapsulated Na+ ion. The excitation energy E* is the sum of

collision energy Ecm, the average internal energy, or vibrational energy, Eov of a canonical

ensemble of C 60 emerging from the Knudsen cell at temperature Tov, and the adiabatic

complexation energy Eenci0 of Na++ C6o- That is,

E =Ecm+Eov+Een

The center-of-mass collision energy Ecm for Na+ + Cgo is about 3% less than the

kinetic energy Eiab of the Na+ ion in the lab system. The kinetic energy in the center-of-

mass Eon has a certain distribution. In our system with the cross beam geometry, the

kinetic energy distribution J{Ecm) is mainly given by the energy distribution of metal ions

emerging from the surface ionization source at Ts, which has a width of about 2 ksTs~ 0.3

eV [Alton 1995],

158

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Eov is derived by nonlinear interpolation from the caloric curve that was

calculated for a variety of different temperatures by Wurz et al [Wurz and Lykke 1992].

But we multiply their values by a factor of 1.15 to bring them into agreement with the

more recently published data that pertain to higher temperatures [Matt et al 1999,

Kolodney et al 1995b, Vostrikov et al 2000, Andersen and Bondemp 2000]. At the

temperature of Tov= 843 K, we use Eov = 5.22 eV. The internal energy distribution f(E 0V)

of the Cgo target molecules that effuse from the Knudsen cell has a width of

TovJk~C = 0.86 eV [Schroeder 2000],

Eendo of Na@C6o+ has been calculated using ab initio methods in a few

publications [Proft et al 1996, Hira and Ray 1995, Liu et al 1994, Cioslowski 1995]. The

calculated values vary considerably partly because the off-center relaxation of the caged

ion and the structural relaxation of the cage itself are difficult to determine. We use a

value of Eendo = 1 eV which agrees with all published values within about ± 0.5 eV.

Radiative cooling causes the energy loss in the excited product parent ions [Matt

et al 1999, Vostrikov et al 2000, Andersen and Bonderup 2000, Tomita 2001, Laskin and

Lifshitz 1997, Hansen and Campbell 1996], so that E* and k[T(E*)] become time

dependent. The radiative cooling will broaden the breakdown curve, and shift it to higher

collision energy. The energy loss by radiative cooling is expressed as [Tomita 2001]

Krad = 4.5 X 10~17r 6 eV/s, (5-2-6)

where T is the temperature of the excited fullerene, in unit of kelvin. This expression may

not be a good estimation for Na@C6o+ ions at low temperature, but it is proper for the

highly excited Na@C6o+ ions formed in collisions [Andersen and Bonderup 2000]. At an

internal energy of about E* = 50 eV, the expression (5-2-6) closely agrees with an

159

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. expression suggested by Matt et al [Matt et al 1999] for a microcanonical ensemble of

C6o- In considering the radiative cooling, the excitation energy E* follows the relation

E'=(Ec„+K. + E„d,h ^ I . (5-2-7)

The actual ion yield as observed in the experiment is the sum over the time interval 9-11

ps during the ion extraction in the mass spectrometer.

Due to the energy distributions in Ecm and Eov, the yield of the Na@C6o+ ion

intensity should be a summation over the excitation energy distribution j[E *). The width

of this energy distribution, a E>, is of the order of 1 eV as determined by the width of the

kinetic energy distribution of the Na+ ions and the width of the initial internal energy of

C<5o. This width only presents a lower limit because other factors may give rise to further

broadening. In the modeling, cr . is treated as a fit parameter, subject to this lower limit.

In the calculation, we choose a set of parameters (ao, Ethresh, Vo, Ea and ) to

compute breakdown curves based on equation (5-2-1). The parameters are adjusted to

achieve a best fit to the experimental data. The parameters ao and Ethresh correlate little

with the other parameters, ao is just a normalization factor. Ea and cr . correlate little with

each other, but both of them strongly correlate with the pre-exponential frequency vo. For

a given vq, the other four parameters are optimized by minimizing the sum of squared

deviations from the experimental data. The best parameter values are obtained to a

precision of better than 10'5 after two or three iterations.

A few assumptions are implied in our modeling. The first assumption is that the

dissociation rate can be expressed by the Arrhenius relation, and that the finite heat bath

temperature Tb can be obtained by the internal energy E* as expressed in equations (5-2-

2) and (5-2-3).

160

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Total excitation energy in Na@C60+ (eV) 35 40 45 50 55 60

JQ L.

■O Na@C 0) 1 c o

Figure 5-1. Energy dependence of the collisional formation of Na@C6o+ (solid symbols). The solid line is obtained by modeling the ion yield. The open dots represent the sum of the yields of Na@C58 + and C6o+- The dashed line represents the predicted yield of Na@C 58 + fragments obtained from the modeling for Na@C6o+.

161

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The second assumption is that the nonradiative decay of Na@C 60+ is by

unimolecular dissociation, i.e. C2 loss from the excited Na@Cgo+ is considered to be the

only nonradiative decay channel. The escape of Na+ from Na@C6o+ is practically

impossible since this type of dissociation costs an energy of about 30 eV. Based on the

investigated excitation energies, C 2 loss is the only effective fragmentation channel.

Na@C6o2+ ions are not observed.

The third assumption is that the pre-exponential frequency factor of C 2 loss from

Na@C6o+ agrees with that for C6o+. We use a value of vo= 5><1019 s"1 [Matt et al 2001],

5.2.3 Results and Discussions

The breakdown curve of Na@C6o+, measured with the fullerene source

maintained at constant 570 °C, is shown in Figure 5-1. The full dots in the figure are

Na@C6o+ ions (mass 743 amu with its higher isotopomers) extracted from the TOF mass

spectra by Gaussian fits. The bottom axis represents the kinetic energy of Na+ in the lab

system. The top axis represents the total excitation energy of the collision product

Na@Ceo+ immediately after its formation, calculated using equation (5-2-7).

An excellent fit to the experimental Na@Cgo+ ion yield curve is shown as the

solid line in Figure 5-1, which gives the activation energy for C 2 fragment from the

excited Na@C6o+ with a value of Ea - 10.17 ± 0.02 eV and a width of a £, =2.49 eV.

This activation energy for C 2 loss is very close to that of C6o+, 10.0 ± 0.2 eV,

according to a recent analysis of all published theoretical and experimental values [Matt

et al 2001]. Our result is reasonable in that the caged Na does not make significant

change to the binding of C 2 . The interaction between the caged Na+ and the cage is most

162

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. likely Coulombic. The sizes of alkali metal ions, such as Na+ and K+, are small compared

with the inner space of a Ceo molecule. The encapsulated alkali metal would not much

change the strain on the Ceo cage. Another important effect would be the electron transfer

from the caged elementto the C6o- C

affinity 2.7 eV and ionization potential 7.6 eV). However, the second ionization

potentials of alkali elements are high (31.6 eV for K+ and 47.3 eV for Na+, respectively).

Charge transfer from the Na+ ion to the Ceo cage is not likely. Therefore, the effect of the

encapsulated Na+ on the C-C bond is expected to be small. As a result, the activation

energy for C 2 loss from Na@C6o+ is expected to be close to that of the C< 5o molecule. The

latter has the value of 10.54 ± 0.2 eV [Lifshitz 2000, Matt et al 2001].

There was a recent report on the dissociation energy of Rg@Ceo+, with Rg = Ne,

Ar and Kr [Laskin et al 2001], which found the dissociation energy of Kr@C6o+ to be

23% larger than that of C6o+. This result is not well understood and needs further

investigation. In that study, the kinetic energy release in unimolecular decay of

collisionally excited, pre-existing endohedral ions was analyzed. That approach is not

as direct as our method of measuring the rate constant of a microcanonical ensemble.

The insertion threshold for the formation of Na@C6o is observed to be 29.6 eV in

our experiment. The accuracy of the measurement depends on how well the kinetic

energy of the projectile ions is defined. As the kinetic energy of the metal ions in our

surface ionization source has a narrow distribution, 0.3 eV rms width, this threshold

energy can be counted as an accurate measurement.

The insertion threshold for the formation of Na@C6o+ has also been measured by

Wan and co-workers [Wan et al 1993]. Their reported insertion threshold is only 18 eV.

163

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Poor ion energy definition may account for this discrepancy. In their instrument, the ion

energy distribution is estimated to be 3 eV, about 10 times larger than ours. A wider

energy distribution causes a less steep breakdown curve. Figure 5-2 compares their

Na@C6o+ breakdown curves with ours. Their breakdown curve is much broader. This

shifts the insertion threshold to lower values. Also, Wan et al made no attempt to

quantitatively model their data.

It is worth to examine our assumption that Na@C6o+ has the same pre-exponential

frequency factor of Vo - 5x 1019 s'1 as C6o+ has. The accuracy of the derived dissociation

energy depends on this frequency factor. The frequency factor can be expressed as

[Lifshitz 2000]

v„=<7(4,?; / /.fe4a»,e„* /eL} J l+r!l , . <5-2-8) tub +/,+/2

For C 60 molecules, a is the reaction path degeneracy with a value of 30, (/„& is the final

vibrational partition function of the C 5 8 -C2 pair, Q vib is the initial vibrational partition

function of C 6 0 , Qmt is the rotational partition function of C 2 , QSUrf is the C 58 -C2 stick

surface partition function, Ij and I2 are the moments of inertia of C 58 and C 2 respectively,

fib 2 is the moment of inertia of the C 58 -C2 pair where fi is the reduced mass and b is the

impact parameter. The C-C bonding on the C 60 cage is not changed significantly by the

encapsulated Na+, as discussed earlier. The loss of vibrational frequencies for Na@C6o+,

due to the dissociation process

Na@C60+-+Na@ C58+ + C2, (5-2-9)

164

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Total excitation energy in Na@C60+ (eV) 35 40 45 50 55 60

-Fitto Na@C60 Na@C ----- NafgC^ [Wan et al 1993] • Measured Na@C60

•O

30 35 45 5040 55 Collision energy in lab (eV)

Figure 5-2. Comparison of breakdown curves. The dotted line is the breakdown curve reported by Wan et al [Wan et al 1993], measured with a kinetic energy spread of about 3 eV, an order of magnitude larger than in our experiment (full dots and solid line).

165

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Total excitation energy in Na@C60+ (eV) 40 45 50 55

o initial after 10 ps

dissociation

w c CD radiation c o -t—» CD T3 CD O'

o 35 40 45 50 55 Collision energy in lab (eV)

Figure 5-3. Effect of radiation on the dissociation rate. Solid lines show the excitation energy dependence of the dissociation rate of Na@C6o+ and of the radiative loss [Tomita et al 2001]. The dashed lines are rates 10 ps after excitation, computed by taking radiative cooling into account (equation 5-2-7).

166

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. would be approximately the same as the vibrational frequency loss in the dissociation

process

C6o+ —> Cs8+ + C 2 . (5-2-10)

In this case, the change in (/„* / Q'vib is insignificant [Lifshitz 2000]. The changes in

other parameters in the expression are negligible. Therefore, the pre-exponential

frequency factor of Na@C6o+ should be close to that of Ceo-

Another quantity that we can deduce from the data is the breakdown energy,

defined as the energy E* where the survival probability of the Na@C6o+ is 50%. It is

directly reflected by the experimental data and shows little dependence on the

assumptions made in the modeling process; a value of E*break - 49.10 eV is obtained.

Given the time constraints for the detection of Na@C6o+, we can specify the unimolecular

rate constant for loss of C 2 from Na@C6o+ to be 94000 s'1 at the internal energy of 49.10

eV.

Finally, we examine how important radiative cooling is in our study. Figure 5-3 shows

the initial dissociation rate (in s'1) and radiative rate (in eV/s) as a function of the energy

computed from equations (5-2-2) - (5-2-7). Within 10 ps, Na@Cgo+ at the breakdown

energy (49.10 eV) looses about 1.3 eV energy by radiation, and the dissociation rate

drops by a factor of two. Completely neglecting the radiative cooling in the modeling

would increase the derived value of Ea by only about 1.3%.

167

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.3 Heat Capacity of Ceo

5.3.1 Calculation of Caloric Curve

The heat capacity of a cluster is normally determined from its caloric curve E(T),

the relation between the internal energy and the temperature. The internal energy,

predominantly vibrational energy, of a cluster is determined by the temperature of the

cluster and its vibrational modes. The size of clusters is between small molecules and

bulk materials. The heat capacity of a cluster is difficult to determine both in theory and

experiment. In particular, the temperature of an isolated cluster is difficult to measure.

Likewise, in most experiments, the internal energy of a free cluster is difficult to

determine. For example, in multiphoton absorption experiments, the number of absorbed

photons is not distinct, but follows some distribution. If a cluster fragments or is ionized

as a result of the excitation, its excitation energy will be reduced by the activation energy

for the fragmentation or ionization and the poorly known kinetic energy of the emitted

fragments or electrons. Because of these difficulties, very few experiments have been

reported that address the heat capacity of an atomic cluster. Sometimes the heat capacity

of the corresponding bulk material is used to estimate the heat capacities of atomic

clusters. However, clusters have finite number of atoms. Clusters generally have higher

symmetry than bulk material. This results in a cut-off towards low vibrational

frequencies, and the Debye model cannot be applied to a cluster.

C§o is more accessible and stable; it can be synthesized in large quantities and

grown into crystals. Efforts have been made to measure the vibrational modes in C6o

solids. Several active IR and Raman vibrational frequencies have been observed [Bethune

et al 1991, Kratschmer et al 1990]. The Ceo molecule has a highly symmetric (/*)

168

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. structure; its 60 atoms are located at the 60 identical vertices of a regular truncated

icosahedron. Due to this high symmetry, infrared absorption experiments have identified

only four infrared-active vibrational modes; this is confirmed by calculations using group

theory. Calculations have determined all 46 vibrational normal modes in this molecule

[Jishi et al 1992, Stanton and Newton 1988, Negri et al 1991]. With this information, it is

possible to calculate the caloric curve for the Ceo molecule. The calculation is based on

the Boltzmann energy distribution expressed in equation (2-1-19). The C«) molecule has

174 degrees of freedom. Similar to the Einstein model of lattice vibrations [Kittel 1953],

the molecule can be thought of as a system with 174 independent oscillators. The internal

energy of the molecule is the sum of the average canonical energy of all these oscillators,

which is

5 oo £jy/iv,g, exp(- nhv,lk,T) £(T) = -L-^±.------, (5-3-1) g(. exp(- nh \i / kBT) i n =0

where v,- is the vibrational frequency and g, is the degeneracy of the corresponding

vibrational mode. Using the calculated frequencies for all 46 vibrational modes and their

degeneracies [Jishi et al 1992], as listed in Table 5-1, we calculate the caloric curve from

equation (5-3-1). The result of our calculation is presented in Figure 5-4 as the solid line.

It can be fitted by a second order polynomial in a temperature range from 200 K to 4000

E(T) = 4.9234x 10“7 T 2 + 0.01227 - 3.6668 eV. (5-3-2)

This gives the heat capacity of the C6o molecule as

C (r)= 0.0122 + 9.8468 x 10"7T eV/K. (5-3-3)

169

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 5-1. The 46 vibrational frequencies (v) and their degeneracies ( g) of Cgo- These parameters are used with equation (5-3-1) to calculate the caloric curve E(T) of the C6o molecule. These frequencies and degeneracies are adopted from reference [Jishi et al 1992].

c . Degeneracy Frequency „ . Degeneracy Frequency Symmetiy fe)______(cm'1) Symmetry fe) Ag 1 4 9 2 A u 1 1 1 4 2 1 4 6 8

F,g 3 5 0 1 Fju 3 5 0 5 9 8 1 5 8 9 1 3 4 6 1 2 0 8 1 4 5 0

F2g 3 5 4 1 F2u 3 3 6 7 8 4 7 6 7 7 93 1 1 0 25 1351 1 2 1 2 1575

Gg 4 4 9 8 Gu 4 3 8 5 6 2 6 7 8 9 8 0 5 9 2 9 1 0 5 6 961 13 75 1 3 2 7 1521 1413

Hg 5 2 6 9 Hu 5 361 4 3 9 5 43 7 0 8 7 0 0 7 8 8 801 1 1 0 2 1 1 2 9 1 2 1 7 1385 1401 1 5 5 2 15 75

170

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 90 Caloric curve E(T) of C(

< 1 5 - • • Kolodney et al (JCP 1995) c

0.1 100 1000 6000 Temperature (K)

Figure 5-4. Caloric curve of Ceo- The dashed line is from the equipartition theorem; the solid line and the dotted line are calculated from statistical mechanics with the 46 vibrational modes and their degeneracies.

171

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The caloric curve of C6o has been calculated before by Kolodney and co-worker

[Kolodney et al 1995] using the same method but with a combination of experimentally

and theoretically determined vibrational frequencies. Their result is close to our

calculation, as shown in Figure 5-4. They gave heat capacities of 0.0138 and 0.0143

eV/K at 1000 K and 2000 K, respectively. Our values are 0.0132 and 0.0142 eV/K at

1000 K and 2000 K, respectively. Classically, the equipartition theorem predicts a heat

capacity that is constant with a value of ( 3N-6)kB. For Ceo, it is 0.015 eV/K. This is

considerably higher than results from statistical calculations, equation (5-3-1).

5.3.2 Ceo Heat Capacity Measurement

As discussed in section 5.2, significant fragmentation of the endohedral complex

takes place at the breakdown energy. Since the endohedral complex Na@Ceo+ is the

product of a completely inelastic collision, its internal energy E* is the sum of the initial

internal energy of C6o before the collision Eov, the complexation energy Ee„d0, and the

collision energy Ecm (in CM system) as expressed in equation (5-2-5). Eov is determined

by the temperature of the Knudsen cell from which the C 60 molecular beam is emitted,

and the caloric curve of C6o- When the temperature of the Knudsen cell is increased from

Ti to T2, a shift AEcm in the breakdown curve to lower collision energies should be

observed in the experiment. This shift AEcm equals the change in the initial internal

energy of the C 60 molecules, E0V(T2) - E0V(Tj). Thus, the heat capacity can be measured

directly.

172

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Total Excitation Energy in Na@Cg0 (eV) 35 40 45 50 55 60

C60 source: Na@C a 500 °C v 535 °C o 5 7 0 °C w 1 c 3 n u.

0 >- oC

30 35 40 45 50 55 Collision Energy (eV, lab)

Figure 5-5. The breakdown curves of Na@C6o+ ions measured for different C

173

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Heat capacity of C

> 0 slope = 12.6 ±1.4 meV/ °C

L_D) 0 C 0 0 E 0 x-t—» :

500 520 540 560 580 Cg0 temperature (°C)

Figure 5-6. Heat capacity of molecules. The heat capacity is measured by the change in the breakdown energy of Na@C6o+ ions as the C6o source temperature changes.

174

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 5-5 shows the breakdown curves of the Na@C6o+ product ions measured

for Cgo source temperatures of 500, 535 and 570 °C, respectively. Figure 5-6 shows the

shift AEcm for these temperatures. From these data, we obtain the heat capacity of C&) as

AE C = cm = 12.611.4 meV/K at 500 °C < T< 570 °C. (5-3-4) AT

According to the calculated heat capacity, the average heat capacity in this temperature

range is 13.0 meV/K. This result is in excellent agreement with our measurement.

The method discussed above may be applied to some other large molecules that

can be vaporized. One of the advantages of the method is that the presence of competing

cooling channels for the excited complex, such as radiative cooling, does not affect the

results. For all source temperatures, the total excitation energy E* at the breakdown point

is the same. Another advantage of our method is that only the relative change in the

collision energy is needed to determine the heat capacity. Any systematic error in the

absolute value of the collision energy will be canceled. An error would occur if the

radiative energy loss from the molecule were significant, but equation (5-2-6) shows that

this can be safely ruled out, at least for C6o at temperature below 1000 °C.

A disadvantage of the method is that it requires a C(,o molecular beam with well-

defined temperature. The number density of Cgo in the molecular beam has to be large

enough, which sets a lower temperature limit of some 400 °C. At very high temperature,

> 800 °C, Cgo will thermally decompose in the source [Kolodney et al 1994, Stetzer et al

1997],

175

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.4 Collision Induced Thermionic Emission

5.4.1 Collision Induced Ionization and Efficiency of Energy Transfer

Thermionic emission from hot Ceo molecules has been studied by exciting the

molecule via multiphoton absorption [Campbell and Levine 2000], electron impact

collisions [Bekkerman et al 1998, Gallogly et al 1994], and surface collisions [Yeretzian

and Whetten 1992], Thermionic emission can also be initiated by inelastic collision with

ion projectiles. In collisions of C6o with ions, there are two basic ionization mechanisms,

thermionic emission and charge transfer. In collisions of C6o with Ne+ at energy below

200 eV, charge transfer was found to be the dominant mechanism, since the ionization

energy of the Ne atom is almost 14 eV larger than that of Cgo [Christian et al 1993, Wan

et al 1992a]. The ionization energies of Mg and Cgo are much closer, but charge transfer

still dominates the formation of Cgo+ ions in low energy collisions of Mg+ with Cgo in the

gas phase [Thompson et al 2002]. Etowever, the ionization energies of alkali metal atoms

are a few eV lower than that of Cgo, and charge transfer in these collisions would become

inefficient. No effort has been made to study the details of thermionic emission from

collisionally excited Cgo, and the energy transfer efficiency in the collisions. Such an

analysis will be presented for data obtained from the collisions of Cgowith K+ ions.

In a collision, a portion of the kinetic energy is transferred to the internal energy

of the Cgomolecule; this may lead to thermionic emission. The rate of electron emission

is determined by the total excitation energy E *, and the amount of energy absorbed by the

Cgo molecule during the collision. The experimental observation of thermionic emission

requires that the temperature of the Cgomolecule be at about 3000 K or higher. To reach

176

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. this temperature, the Cm molecule needs to absorb energy of about 30 eV or more in the

collision.

Due to the covalent C-C bonding, the structure of C6o is strong and resilient. High

efficiency of energy transfer can be accomplished when C6o collides with small atoms,

such as alkali metals, and at low energy. The collision can be described by a two-stage

model [Wan et al 1993], In the first stage, the projectile ion elastically collides with a

group of carbon atoms in the cage leading to a deformation of the cage. In the second

stage of the collision, the transferred energy is redistributed over all degrees of freedom

of the molecule. The hot molecule may then undergo thermionic emission, unimolecular

dissociation, and black-body-like radiation.

In a particular collision event, the amount of energy transferred is determined by a

few factors, such as the impact parameter, the orientation of the Ceo molecule, and the

collision energy. The impact parameter and the orientation determine the size of the

carbon atom group involved in the first stage of the collision. In an elastic central

collision of C6o a small atom, the efficiency of energy transfer is given by [Wan et al

1993]

AE Am.m, (mF+mA)(mF-m c) (5-4-1)

where tha and me are masses of projectile ion and the colliding carbon atom group,

respectively. Ecou is the collision energy in the center-of-mass (CM) system and A E is the

amount of energy transferred to the carbon atoms. For example, if four carbon atoms are

involved in collision with a potassium ion, the energy transfer efficiency is about 97%

according to equation (5-4-1). When a sodium ion collides with a group of two carbon

177

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. atoms, nearly all the kinetic energy will be transferred to the group. High efficiency of

energy transfer is possible.

5.4.2 Modeling the C6o+ Ion Product in Collision

Experiments of measuring the C6o+ ion product in collisions of C«) with K+ have

been discussed in chapter 4. The yield of C6o+ for various collision energies is shown in

Figure 4-16. By modeling our experimental data, we will show the high efficiency of

energy transfer supporting the above two-stage collision model. Thermionic emission

turns out to be a reasonable explanation for the C6o+ ion products in this collision

experiment.

The internal energy E* of the excited Ceo molecule is the sum of the energy

absorbed in the collision A E and the initial internal energy Einit,

(5-4-2)

E init is the average internal energy of a canonical ensemble of that emerges from the

Knudsen cell at temperature of Tov. For a temperature of Tov = 843 K, Einit = 5.22 eV

[Deng and Echt 2002]. A E is the transferred energy that is going to be determined in this

study.

The ionization energy of C6o is known as IP = 7.6 eV. The rate constant of

thermionic emission is expressed in Arrhenius form,

Ke = ve exp -( I P \ (5-4-3)

The pre-exponential frequency factor ve has a value of 2><1016 s’1 [Klots 1991], and the

rate of the competing C 2 loss is

178

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ' (5-4-4) K a = Va e X P k T V KB1b J

where an activation energy Ea = 10 eY [Lifshitz 2000], and a pre-exponential frequency

factor of va = 5x l0 19 s'1 [Matt et al 2001] are used in the following analysis.

The energy loss via radiation is expressed as

K rad =4.5xl0~17r 6 eV/s (5-4-5)

with T in kelvin [Tomita et al 2001]. The time window in our TOF mass spectrometer is

about 10 ps. The energy loss due to the radiation is small. However, we include it in our

data analysis. Hence, the internal energy of the excited C6o is time dependent,

E* = A.E + Einit - K ra d t. (5-4-6)

The isokinetic bath temperature, as described in Section 2.2.4, is determined by

the internal energy of Ceo,

K = E(Tt)-k,Tt^ + ■ E , (5-4-7) 2 12(C-^)rA

where Ea is the activation energy with the values of 10 eV and 7.6 eV for C 2 loss and

electron emission, respectively. E(T) is the caloric curve of a canonical ensemble. We use

our previous results, equation (5-3-2),

E(T) = 4.9234xl0"7r 2 + 0.01222"-3.6668 eV, (5-4-8)

with E in eV and T in kelvin.

The Cgo+ ion yield at time t in the experiment is expressed as

/ + (/) = I oKX E { t)y [KM,)yKMt))]t. (5-4-9) ^-60

In the above expression, Iq is a normalization factor.

179

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The internal energy of the collisionally excited Ceo has a distribution arising from

the kinetic energy spread of the metal ions from the surface ionization source, and from

the distribution of the initial internal energy of Ceo, Einu- As discussed in Section 5.2.2,

the combined energy spread due to the kinetic energy spread of the K+ ion and the

distribution of the initial internal energy of Ceo is estimated (rms) to be a £. « 0.94 eV.

Another major contribution to the final internal energy distribution, E*, may come from

the energy transfer in the collision. The efficiency of energy transfer will depend on the

orientation of C6o and the impact parameter. Experimentally, we average over all

orientations and impact parameters, and only an average efficiency of energy transfer is

measured.

5.4.3 Results and Discussions

In the K+ + Ceo collision experiment, C6o+ is the most prominent product ion for

collision energies below 70 eV (lab system). We model the C6o+ ion yield and obtain an

expression for the efficiency of energy transfer in the collision process. Figure 5-7 shows

experimental data (open square dots) for C6o+ ion yield. The modeling curve (solid line)

is in very good agreement with the experimental data. Above 36 eV, the energy transfer

is expressed analytically as

&E = aEcoll+P (eV), (5-4-10)

where a = 0.35 ± 0.02 and /? - 21.84 ± 2 eV. The energy transfer efficiency rje = AE/Ecou

is also shown in Figure 5-7 as a dashed line.

The efficiency of energy transfer in this energy range is high. At 60 eV (in lab

system, or 57 eV in CM system) the efficiency of energy transfer is about 78%. Using

180

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. equation (5-4-1), we see that a group of 7 ~ 8 carbon atoms is involved in the first stage

of collision. With increasing collision energy, more carbon atoms are involved in the

collision and the energy transfer efficiency decreases.

Figure 5-8 shows the efficiency of energy transfer as a function of the number of

carbon atoms derived from equation (5-4-1). It should be mentioned that the elastic

central collision model is a simplified model and some discrepancy between this model

and experimental results is expected, which can be seen in the figure.

The efficiency of energy transfer derived from our analysis is an effective

efficiency averaged over all possible impact parameters and molecular orientations. The

average energy transferred per collision in the (Li+, Cgo) system has been calculated by a

classical trajectory calculation [Bemshtein and Oref 1998]. An analytical expression for

the energy transfer was also derived from the calculation. The direct comparison of our

experimental analysis for (K+, Cgo) collision with that calculation is not possible because

the mass of potassium is over five times larger than that of a lithium ion and, thus, the

collision mechanisms at the same collision energy are quite different. As a trend,

however, the energy transfer in (K+, Cgo) collision is more efficient than that in (Li+, Cgo).

In the modeling, we assumed that the internal energy distribution in collisionally

excited Cgo has a width of about 1 eV as a lower limit. The efficiency of energy transfer,

expressed in equation (5-4-10), does not have a steep slope. Therefore, the width of the

energy distribution is not a critical parameter in the modeling. Figure 5-9 shows that the

modeled Cgcf yield does not change much if the width cr£. is increased from 1 eV to 3

eV.

181

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Excitation energy (eV) 35 40 45 50 55 1 10 □ ai20 — modeling 9 — efficiency 0.9 8

7 'tra n sf = a * Ecoll (CM)+ b =3 a = 0.35 ± 0.02 -Qu 6 b = 21.84 ± 2 -£• 5 '55 c 0.7 03 4 t o c 3 o 2 0.6 O 1 0 0.5

1 30 40 50 60 70 80 90 100 110 Collision energy (CM, eV)

Figure 5-7. Thermal ionization of C6o after collision of Cm with K+ ions. The square symbols show the experimental C6o+ ion intensity. The data are modeled assuming thermionic emission (solid line). The efficiency of energy transfer, derived from the model, is shown as the dashed line.

182

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Collision energy (CM, eV)

20 40 60 80 100 120 140 1.1

1.0 exprmnt X'X — a — model 0.9

0.3

0.2

Number of carbon atoms

Figure 5-8. Efficiency of energy transfer in the collision of C6o with potassium ions. This figure shows the efficiency of energy transfer obtained from our analysis (solid dots), and the dependence of rje on the number of carbon atoms involved, according to the two-stage model, equation (5-4-1).

183

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Excitation energy (eV) 35 40 45 50 55 60

10 9

8 □ experiment — modeling, width 3.0 eV 7 — modeling, width 1.0 eV 6 5 4 3 2 CO 1 0

■1 30 40 70 80 905060 100 110 Collision energy (CM. eV)

Figure 5-9. Effect of energy broadening a £. on the intensity of C6o+ ion. Increase in the width from 1 eV to 3 eV does not cause a significant change since the efficiency of energy transfer has a weak energy dependence.

184

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.5 Conclusions

The dissociation energy of Na@C6o+ and the heat capacity of Ciso have been

determined through a study of product ions formed in collisions of Cgo with sodium ions.

Modeling the breakdown curve of Na@C6o+ enabled us to extract the activation energy of

C2 loss from Na@C

to the activation energy of C 2 loss from C6o+ which is 10 eV. The result indicates that the

encaged sodium ion does not significantly change the C-C bonds of the fullerene shell.

Changing the internal energy of the target C 60 molecules causes a shift in the

breakdown curve of Na@C6o+- The shift is used to measure the heat capacity of C 60

molecules. The heat capacity is determined to be 0.0126 ± 0.0014 eV/K at temperatures

of 500 °C < T< 570 °C. The value agrees with the result of a statistical calculation using

all 46 vibrational modes of the C 6 0 molecule.

The third topic in this work is the collision-induced ionization of Ceo- C6o+

formation in the collision of C 60 with K+ is modeled as thermionic emission. This

mechanism explains the C6o+ yield in our experiment. The C^q+ intensity reaches its

maximum at a collision energy of 57 eV (in CM system). At this collision energy the

efficiency of energy transfer is 78 %. The high efficiency can be explained using the two-

stage collision model.

185

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. BIBLIOGRAPHY

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