Lecture February 4-6, 2012 Graphite, graphene, bucky balls, bucky tubes

Transcription

1 Lecture February 4-6, 2012 Graphite, graphene, bucky balls, bucky tubes Nature of the Chemical Bond with applications to catalysis, materials science, nanotechnology, surface science, bioinorganic chemistry, and energy Course number: Ch120a Hours: 2-3pm Monday, Wednesday, Friday William A. Goddard, III, 316 Beckman Institute, x3093 Charles and Mary Ferkel Professor of Chemistry, Materials Science, and Applied Physics, California Institute of Technology Teaching Assistants: Ross Fu Fan Liu Ch120a-1

2 Previous lectures 2

3 CH2 +CH2 ethene Starting with two methylene radicals (CH 2 ) in the ground state ( 3 B 1 ) we can form ethene (H2C=CH2) with both a σ bond and a π bond. 3 B 1 3 B 1 3 B 1 The HCH angle in CH2 was 132.3º, but Pauli Repulsion with the new σ bond, decreases this angle to 117.6º (cf with 120º for CH 3 ) 3

4 Twisted ethene Consider now the case where the plane of one CH 2 is rotated by 90º with respect to the other (about the CC axis) This leads only to a σ bond. The nonbonding π l and π r orbitals can be combined into singlet and triplet states Here the singlet state is referred to as N (for Normal) and the triplet state as T. Since these orbitals are orthogonal, Hund s rule suggests that T is lower than N (for 90º). The K lr ~ 0.7 kcal/mol so that the splitting should be ~1.4 kcal/mol. Voter, Goodgame, and Goddard [Chem. Phys. 98, 7 (1985)] showed that N is below T by 1.2 kcal/mol, due to Intraatomic Exchange (σ,π on same center) 4

5 Twisting potential surface for ethene The twisting potential surface for ethene is shown below. The N state prefers θ=0º to obtain the highest overlap while the T state prefers θ=90º to obtain the lowest overlap 5

6 CC double bond energies The bond energies for ethene are D e =180.0, D 0 = 169.9, D 298K = kcal/mol Breaking the double bond of ethene, the HCH bond angle changes from 117.6º to 132.xº, leading to an increase of 2.35 kcal/mol in the energy of each CH 2 so that D esnap = = kcal/mol Since the D esnap = kcal/mol, for H3C-CH3, The π bond adds 75.1 kcal/mol to the bonding. Indeed this is close to the 65kcal/mol rotational barrier. For the twisted ethylene, the CC bond is De = =115 Desnap = =120. This increase of 10 kcal/mol compared to ethane might indicate the effect of CH repulsions 6

7 bond energy of F 2 C=CF 2 The snap bond energy for the double bond of ethene of D esnap = = kcal/mol As an example of how to use this consider the bond energy of F 2 C=CF 2, Here the 3 B 1 state is 57 kcal/higher than 1 A 1 so that the fragment relaxation is 2*57 = 114 kcal/mol, suggesting that the F 2 C=CF 2 bond energy is D snap ~ = 70 kcal/mol. The experimental value is D298 ~ 75 kcal/mol, close to the prediction 57 kcal/mol 3 B 1 1 A 1 7

8 CC triple bonds Since the first CCσ bond is D e =95 kcal/mol and the first CCπ bond adds 85 to get a total of 180, one might wonder why the CC triple bond is only 236, just 55 stronger. The reason is that forming the triple bond requires promoting the CH from 2 Π to 4 Σ -, which costs 17 kcal each, weakening the bond by 34 kcal/mol. Adding this to the 55 would lead to a total 2 nd π bond of 89 kcal/mol comparable to the first 2 Π 4 Σ - 8

9 9

10 Cn What is the structure of C 3? 10

11 Cn 11

12 Energetics Cn Note extra stability of odd C n by 33 kcal/mol, this is because odd C n has an empty p x orbital at one terminus and an empty p y on the other, allowing stabilization of both π systems 12

13 Stability of odd Cn 13

14 14

15 Bond energies and thermochemical calculations 15

16 Bond energies and thermochemical calculations 16

17 Heats of Formation 17

18 Heats of Formation 18

19 Heats of Formation 19

20 Heats of Formation 20

21 Bond energies 21

22 Bond energies 22

23 Bond energies Both secondary 23

24 24

25 Average bond energies 25

26 Average bond energies 26

27 Real bond energies Average bond energies of little use in predicting mechanism 27

28 Group values 28

29 Group functions of propane 29

30 Examples of using group values 30

31 Group values 31

32 Strain 32

33 Strain energy cyclopropane from Group values 33

34 Strain energy c-c3h6 using real bond energies 34

35 Stained GVB orbitals of cyclopropane 35

36 Benson Strain energies 36

37 Allyl radical 37

38 Allyl Radical 38

39 Allyl wavefunctions It is about 12 kcal/mol 39

40 Resonance in thermochemical Calculations 40

41 Resonance in thermochemical Calculations 41

42 Resonance energy butadiene 42

43 Benzene resonance 43

44 Benzene resonance 44

45 Benzene resonance 45

46 Benzene resonance 46

47 Benzene resonance 47

48 Benzene and Resonance referred to as Kekule or VB structures 48

49 Resonance 49

50 Benzene wavefunction is a superposition of the VB structures in (2) benzene as + 50

51 More on resonance That benzene would have a regular 6-fold symmetry is not obvious. Each VB spin coupling would prefer to have the double bonds at ~1.34A and the single bond at ~1.47 A (as the central bond in butadiene) Thus there is a cost to distorting the structure to have equal bond distances of 1.40A. However for the equal bond distances, there is a resonance stabilization that exceeds the cost of distorting the structure, leading to D 6h symmetry. 51

52 Cyclobutadiene For cyclobutadiene, we have the same situation, but here the rectangular structure is more stable than the square. That is, the resonance energy does not balance the cost of making the bond distances equal A 1.5x A The reason is that the pi bonds must be orthogonalized, forcing a nodal plane through the adjacent C atoms, causing the energy to increase dramatically as the 1.54 distance is reduced to 1.40A. For benzene only one nodal plane makes the pi bond orthogonal to both other bonds, leading to lower cost 52

53 graphene Graphene: CC=1.4210A Bond order = 4/3 Benzene: CC=1.40 BO=3/2 Ethylene: CC=1.34 BO = 2 CCC=120 Unit cell has 2 carbon atoms 1x1 Unit cell This is referred to as graphene 53

54 Graphene band structure 1x1 Unit cell Unit cell has 2 carbon atoms Bands: 2pπ orbitals per cell 2 bands of states each with N states where N is the number of unit cells 2 π electrons per cell 2N electrons for N unit cells The lowest N MOs are doubly occupied, leaving N empty orbitals. The filled 1 st band touches the empty 2 nd band at the Fermi energy Get semi metal 2 nd band 1 st band 54

55 Graphite Stack graphene layers as ABABAB Can also get ABCABC Rhombohedral AAAA stacking much higher in energy Distance between layers = A CC bond = Only weak London dispersion attraction between layers D e = 1.0 kcal/mol C Easy to slide layers, good lubricant Graphite: D 0K =169.6 kcal/mol, in plane bond = Thus average in-plane bond = (2/3)168.6 = kcal/mol = sp 2 σ + 1/3 π Diamond: average CCs = 85 kcal/mol π = 3*27=81 kcal/mol 55

56 energetics 56

57 Stopped Feb. 4,

58 Graphene: generalize benzene in all directions 58

59 Have to terminate graphene: two simple cases Armchair edge For each edge atom break two sp2 sigma bonds but form bent pi bond in plane = 92 kcal/mol Length = 3*1.4=4.2A 22 kcal/mola Thus both graphene ribbon surfaces (edges) have similar energies Zig-zag edge For each edge atom break sp2 sigma bond, maybe not break pi bond? 111.7/2 = 56 kcal/mol per dangling bond Length = 1.4*sqrt(3)= 2.42A 23 kcal/mol/a 59

60 C 60 flat sheet Cut from graphene 6 arm chair 5 zig-zag Total cost 832 kcal/mol! 60

61 C 60 fullerene No broken bonds Just ~11.3 kcal/mol strain at each atom 678 kcal/mol Compare with 832 kcal/mol for flat sheet Lower in energy than flat sheet by 154 kcal/mol! 61

62 First observation Heath, Smalley, Krotos Laser evaporation of carbon + supersonic nozzle Observe various sized clusters in mass spect Change various conditions found peak at C60! Smalley and Krotos each independently postulated futball (soccer ball structure) ~1986 ^ H. W. Kroto, J. R. Heath, S. C. O'Brien, R. F. Curl and R. E. Smalley (1985). "C60: Buckminsterfullerene". Nature 318: doi: /318162a0. 62

63 Nature 1985: discovery of C 60 63

64 10 torr He Evidence for C60, Nature 1985 maximize clustercluster reactions in integration cup 760 torr He 64

65 Many papers on C60, no definitive proof that it had fullerene structure, lots of skepticism 65

66 Many papers on C60, no definitive proof that it had fullerene structure, lots of skepticism In 1990 physicists W. Krätschmer and D.R. Huffman for the first time produced isolable quantities of C60 by causing an arc between two graphite rods to burn in a helium atmosphere and extracting the carbon condensate so formed using an organic solvent. Then, Nature 347, (27 September 1990) W. Krätschmer, Lowell D. Lamb, K. Fostiropoulos & Donald R. Huffman; Solid C60: a new form of carbon A new form of pure, solid carbon has been synthesized consisting of a somewhat disordered hexagonal close packing of soccer-ball-shaped C60 molecules. Infrared spectra and X-ray diffraction studies of the molecular packing confirm that the molecules have the anticipated 'fullerene' structure. Mass spectroscopy shows that the C70 molecule is present 66 at levels of a few per cent.

67 Nature 1990, Krätschmer, Lamb, Fostiropoulos, Huffman Sears arc welder with flowing He, get soot of C60. grams per hour 68

68 Carbon 13 NMR spectrum of C60 1 peak NMR the key experiment Definitive proof that C60 is fullerene Carbon 13 NMR spectrum of C70 5 peaks, definitive proof of fullerene structure 69

69 C 540 All fullerens have 12 pentagonal rings 70

70 Polyyne chain precursors fullerenes, all even 71

71 72

72 Mechanism for formation of fullerenes Heath 1991: Fullerene road. Smaller fullerenes and C3 etc add on to pentagonal sites to grow C60 Contradicted by He chromatography and high yield of endohedrals Smalley 1992: Pentagonal road. Graphtic sheets grow and curl into fullerenes by incorporating pentagonal C3 etc add on to pentagonal sites to grow C60 Contradicted by He chromatography Arc environment: mechanism goes through atomic species (isotope scrambling) He chromatography Go through carbon rings and form fullerenes Has high temperature gradients Ring growth road. Jarrold based on He chromatography 73

73 He chromatography (Jarrold) Relative abundance of the isomers and fragments as a function of injection energy in ion drifting experiments Conversion of bicyclic ring to fullerene when heated 74

74 Energies from QM 75

75 Force Field for sp1 and sp2 carbon clusters 76

76 4n vs 4n+2 for Cn Rings 77

77 Population of various ring and fullerene species with Temperature Based on free energies from QM and FF 78

78 Bring two C30 rings together 79

79 Energetics (ev) for isomerizations converting bicyclic ring to monocyclic or Jarrold intermediates for n = 30, 40, 50 2 rings TS to form tricyclic E tricyclic TS convert E tricyclic C 34 C 60 C 40 TS to Bergman cyclization singlet (leads to Jarrold ring mechanism) 80

80 Energetics (ev) for initial steps of Jarrold Jarrold pathway If get here, then get fullerene Modified Jarrold Number pi bonds 81

81 Downhill race from tricyclic to bucky ball energetics (ev) 30 ev of energy gain as form Fullerene Number sp2 bonded centers 82

82 Structures in Downhill race from tricyclic to bucky ball 83

83 energetics (ev) Energy contributions to downhill race to fullerene Number sp2 bonded centers 84

84 C60 dimer Prefers packing of 6 fold face De = 7.2 kcal/mol Face-face=3.38A 85

85 Crystal structure C60 Expect closest packing: 6 neighbors in plane 3 neighbors above the plane and 3 below But two ways ABCABC face centered cubic ABABAB hexagonal closet packed Predicted crystal structure 3 months before experiment Prediction of Fullerene Packing in C60 and C70 Crystals Y. Guo, N. Karasawa, and W. A. Goddard III Nature 351, 464 (1991) 86

86 C60 is face centered cubic 87

87 C70 is hexagonal closest packed 88

88 Vapor phase grown Carbon fiber, R. T. K. Baker and P. S. Harris, in Chemistry and Physics of Carbon, edited by P. L. Walker, Jr. and A. Thrower (Marcel Dekker, New York, 1978), Vol. 14, pp ; G. G. Tibbetts, Carbon 27, (1989); R. T. K.Baker, Carbon 27, (1989). M. Endo, Chemtech 18, (1988). Formed carbon fiber from 0.1 micron up Xray showed that graphene planes are oriented along axis but perpendicular to the cylindrical normal 89

89 Multiwall nanotubes "Helical microtubules of graphitic carbon". S. Iijima, Nature (London) 354, (1991). Ebbesen, T. W.; Ajayan, P. M. (1992). "Large-scale synthesis of carbon nanotubes". Nature 358: Outer diameter of MW NT inner diameter of MW NT 90

90 Single wall carbon nanotubes, grown catalytically S. Iijima and T. Ichihashi, "Single-shell carbon nanotubes of 1-nm diameter".nature (London) 363, (1993) used Ni D. S. Bethune, C.-H. Kiang, M. S. de Vries, G. Gorman, R. Savoy, J. Vazquez, and R. Beyers, "Cobalt-catalyzed growth of carbon nanotubes with singleatomic-layer walls".nature (London) 363, (1993). used Co Ching-Hwa Kiang grad student with wag on leave at IBM san Jose 91

91 Single wall carbon nanotubes, grown catalytically S. Iijima and T. Ichihashi, "Single-shell carbon nanotubes of 1-nm diameter".nature (London) 363, (1993) used Ni D. S. Bethune, C.-H. Kiang, M. S. de Vries, G. Gorman, R. Savoy, J. Vazquez, and R. Beyers, "Cobalt-catalyzed growth of carbon nanotubes with singleatomic-layer walls".nature (London) 363, (1993). used Co Ching-Hwa Kiang grad student with wag on leave at IBM san Jose Catalytic Synthesis of Single-Layer Carbon Nanotubes with a Wide Range of Diameters C.- H. Kiang, W. A. Goddard III, R. Beyers, J. R. Salem, D. S. Bethune, J. Phys. Chem. 98, (1994). Catalytic Effects on Heavy Metals on the Growth of Carbon Nanotubes and Nanoparticles C.-H. Kiang, W. A. Goddard III, R. Beyers, J. R. Salem, and D. S. Bethune, J. Phys. Chem. Solids 57, 35 (1995). Effects of Catalyst Promoters on the Growth of Single-Layer Carbon Nanotubes; C.-H. Kiang, W. A. Goddard III, R. Beyers, J. R. Salem, and D. S. Bethune, Mat. Res. Soc. Symp. Proc. 359, 69 (1995) Carbon Nanotubes With Single-Layer Walls," Ching-Hwa Kiang, William A. Goddard III, Robert Beyers and Donald S. Bethune, " Carbon 33, (1995). "Novel structures from arc-vaporized carbon and metals: Single-layer carbon nanotubes and metallofullerenes," Kiang, C-H, van Loosdrecht, P.H.M., Beyers, R., Salem, J.R., and Bethune, D.S., Goddard, W.A. III, Dorn, H.C., Burbank, P., and Stevenson, S., Surf. Rev. Lett. 3, (1996). 92

92 Kiang CNT form

93 Kiang CNT form

94 Distribution of diameters for carbon SWNT, Kiang

95 96

96 Examples Single wall carbon nanotubes 97

97 Some bucky tubes (8,8) armchair (14,0) zig-zag (6,10) chiral 98

98 Contsruction for (6,10) edge

99 13.46A diameter (10,10) armchair carbon SWNT 40 atoms/repeat distance 100

100 (14,0) zig-zag Bucky tube 101

101 13.5A Crystal packing of (10,10) carbon SWNT Density SWNT: 1.33 g/cc Graphite 2.27 g/cc Heat formation Graphite 0 C (10,10) CNT ,7A Ec Young s modulus SWNT 640 GPa Graphite 1093 GPa Ea Young s modulus SWNT 5.2 GPa Graphite 4.1 GPa 102

102 Vibrations in (10,10) armchair CNT 103

103 Carbon fibers and tubes 104

104 Vibrations in (10,10) armchair CNT 105

105 Vibrations in (10,10) armchair CNT 106

106 Mechanism for gas phase CNT formation Polyyne Ring Nucleus Growth Model for Single-Layer Carbon Nanotubes C-H. Kiang and W. A. Goddard III Phys. Rev. Lett. 76, 2515 (1996) 107

107 Mechanism for gas phase CNT formation A two-stage mechanism of bimetallic catalyzed growth of singlewalled carbon nanotubes Deng WQ, Xu X, Goddard WA Nano Letters 4 (12): (2004) 108

108 But mechanism of gas phase C SWNT, no longer important The formation of Carbon SWNT by CVD growth on a metal nanodot on a support is now the preferred mechanism for forming SWNT 109

109 Mechanisms Proposed for Nanotube Growth Stepwise Process Adsorption Dehydrogenation Saturation Diffusion Nucleation Growth 110

110 Vapor-Liquid-Solid (Carbon Filament) Mechanism Vapor carbon feed stock adsorbs unto liquid catalyst particle and dissolves. Dissolved carbon diffuses to a region of lower solubility resulting in supersaturation and precipitation of the solid product. Originally developed to explain the growth of carbon whiskers/filaments. Temperature, concentration or free energy gradient is implicated as the driving force responsible for diffusion. Wagner, R. S.; Ellis, W. C. Appl. Phys. Lett. 1964, 4, 89. Bolton, et al. J. Nanosci. Nanotechnol. 2006, 6,

111 Yarmulke Mechanism Dai, et al. Chem. Phys. Lett. 1996, 260, 471. Raty, et al. Phys. Rev. Lett , Carbon-carbon bonds form on the surface (either before or as a result of super-saturation). Diffusion of carbon to graphene coating can be an important rate limiting step. Coating of more than a complete hemisphere results in poisoning of catalyst. New layers can start beneath the original layer after/as it lifts off the surface resulting in MWNT. 112

112 Experimental Confirmation of a Yarmulke Mechanism Atomic-scale, video-rate environmental transmission microscopy has been used to monitor the nucleation and growth of single walled nanotubes. Hofmann, S. et al. Nano Lett. 2007, 7,

113 Role of the Catalyst Particle in Nanotube Formation Size of catalyst particles is related to the diameter of the nanotubes formed. Catalyst nanoparticles are known to deform (elongate) during nanotube growth. Structural properties of select catalyst surfaces (Ni111, Co111, Fe1-10) exhibit appropriate symmetry and distances to overlap with graphene and allow thermally forbidden C 2 addition reaction. Graphene is believed to stabilize the high energy nanoparticle surface. MWNT have been observed growing out of steps, which they stabilize. Hong, S.; et al. Jpn J. Appl. Phys. 2002, 41, Vinciguerra, V.; et al. Nanotechnol. 2003, 14, 655. Hofmann, S. et al. Nano Lett. 2007, 7,

114 Tip vs. Base Growth Mechanisms Huang, S.; et al. Nano Lett , Kong, J.; et al. Chem. Phys. Lett. 1998, 292, 567. Same initial reaction step: absorbtion, diffusion and precipitation of carbon species. Strength of interaction between catalyst particle and catalyst support determines whether particles remains on surface or is lifted with growing nanotube. Images of nanotubes show catalyst particles trapped at the ends of nanotubes in the case of tip growth, or nanotubes bound to catalysts on support in the case of base growth. Alternatively capped nanotube tops show base growth. A kite (tip) growth mechanism has been used to explain the growth of long (order of mm), well ordered SWNTs. 115

115 Limiting Steps for Growth Rates Diffusion of reactive species either through the catalyst particle bulk or across its surface can play an important role in determining the rate of nanotube growth. In the case of carbon species which dissociate less readily the rate of carbon supply to the particle can act as the rate limiting step. The rate of growth must also take into account a force balance between the friction of the nanotube moving through the surrounding feedstock gas and the driving force for/from the reaction. Vinciguerra, V.; et al. Nanotechnol. 2003, 14, 655. Hofmann, S. et al. Nano Lett. 2007, 7, 602. Hafner, J. H.; et al. Chem. Phys. Lett. 1998, 296,