Lecture 5 January 11, 2012 CC Bonds

Transcription

1 Lecture 5 January 11, 2012 CC Bonds Nature of the Chemical Bond with applications to catalysis, materials science, nanotechnology, surface science, bioinorganic chemistry, and energy William A. Goddard, III, wag@wag.caltech.edu 316 Beckman Institute, x3093 Charles and Mary Ferkel Professor of Chemistry, Materials Science, and Applied Physics, California Institute of Technology Teaching Assistants: Caitlin Scott <cescott@caltech.edu> 1

2 Now combine Carbon fragments to form larger molecules (old chapter 7) Starting with the ground state of CH 3 (planar), we bring two together to form ethane, H 3 C-CH 3. As they come together to bond, the CH bonds bend back from the CC bond to reduce overlap (Pauli repulsion or steric interactions between the CH bonds on opposite C). At the same time the 2pp radical orbital on each C mixes with 2s character, pooching it toward the corresponding hybrid orbital on the other C 120.0º 1.086A 107.7º 1.095A 1.526A 111.2º 2

3 Bonding (GVB) orbitals of ethane (staggered) Note nodal planes from orthogonalization to CH bonds on right C 3

4 There are two extreme cases for the orientation about the CC axis of the two methyl groups Staggered vs. Eclipsed The salient difference between these is the overlap of the CH bonding orbitals on opposite carbons. To whatever extent they overlap, S CH-CH Pauli requires that they be orthogonalized, which leads to a repulsion that increases exponentially with decreasing distance R CH-CH. The result is that the staggered conformation is favored over eclipsed by 3.0 kcal/mol 4

5 Alternative interpretation The bonding electrons are distributed over the molecule, but it is useful to decompose the wavefunction to obtain the net charge on each atom. This leads to q H ~ and q C ~ q C ~ q H ~ These charges do NOT indicate the electrostatic energies within the molecule, but rather the electrostatic energy for interacting with an external field. Even so, one could expect that electrostatics would favor staggered. The counter example is CH 3 -C=C-CH 3, which has a rotational barrier of 0.03 kcal/mol (favoring eclipsed). Here the CH bonds are ~ 3 times that in CH3-CH3 so that electrostatic effects would decrease by only 1/3. However copyright 2011 overlap William A. Goddard decreases III, all rights reserved exponentially. 5

6 Propane Replacing an H of ethane with CH 3, leads to propane Keeping both CH 3 groups staggered leads to the unique structure Details are as shown. Thus the bond angles are HCH = and on the CH3 HCH =106.1 on the secondary C CCH=110.6 and CCC=112.4, Reflecting the steric effects 6

7 Trends: geometries of alkanes CH bond length = ± 0.001A CC bond length = ± 0.001A CCC bond angles HCH bond angles 7

8 Bond energies D e = E AB (R= ) - E AB (R e ) e for equilibrium) Get from QM calculations. Re is distance at minimum energy. 8

9 Bond energies D e = E AB (R= ) - E AB (R e ) Get from QM calculations. Re is distance at minimum energy D 0 = H 0AB (R= ) - H 0AB (R e ) H 0 =Ee + ZPE is enthalpy at T=0K ZPE = Σ(½Ћω) This is spectroscopic bond energy from ground vibrational state (0K) Including ZPE changes bond distance slightly to R 0 9

10 Bond energies D e = E AB (R= ) - E AB (R e ) Get from QM calculations. Re is distance at minimum energy D 0 = H 0AB (R= ) - H 0AB (R e ) H 0 =Ee + ZPE is enthalpy at T=0K ZPE = Σ(½Ћω) This is spectroscopic bond energy from ground vibrational state (0K) Including ZPE changes bond distance slightly to R 0 Experimental bond enthalpies at 298K and atmospheric pressure D 298 (A-B) = H 298 (A) H 298 (B) H 298 (A-B) D 298 D 0 = [C p (A) +C p (B) C p (A-B)] dt =2.4 kcal/mol if A and B are nonlinear molecules (C p (A) = 4R). {If A and B are atoms D 298 D 0 = 0.9 kcal/mol (C p (A) = 5R/2)}. (H = E + pv assuming an ideal gas) 10

11 Bond energies, temperature corrections Experimental measurements of bond energies, say at 298K, require an additional correction from QM or from spectroscopy. The experiments measure the energy changes at constant pressure and hence they measure the enthalpy, H = E + pv (assuming an ideal gas) Thus at 298K, the bond energy is D 298 (A-B) = H 298 (A) H 298 (B) H 298 (A-B) D 298 D 0 = [C p (A) +C p (B) C p (A-B)] dt =2.4 kcal/mol if A and B are nonlinear molecules (C p (A) = 4R). {If A and B are atoms D 298 D 0 = 0.9 kcal/mol (C p (A) = 5R/2)}. 11

12 Snap Bond Energy: Break bond without relaxing the fragments Snap E relax = 2*7.3 kcal/mol Adiabatic D snap De snap (109.6 kcal/mol) D e (95.0kcal/mol) 12

13 Bond energies for ethane D 0 = 87.5 kcal/mol ZPE (CH 3 ) = 18.2 kcal/mol, ZPE (C 2 H 6 ) = 43.9 kcal/mol, D e = D = 95.0 kcal/mol (this is calculated from QM) D 298 = = 89.9 kcal/mol This is the quantity we will quote in discussing bond breaking processes 13

14 The snap Bond energy In breaking the CC bond of ethane the geometry changes from CC=1.526A, HCH=107.7º, CH=1.095A To CC=, HCH=120º, CH=1.079A Thus the net bond energy involves both breaking the CC bond and relaxing the CH 3 fragments. We find it useful to separate the bond energy into The snap bond energy (only the CC bond changes, all other bonds and angles of the fragments are kept fixed) The fragment relaxation energy. This is useful in considering systems with differing substituents. For CH3 this relation energy is 7.3 kcal/mol so that D e,snap (CH 3 -CH 3 ) = *7.3 = kcal/mol 14

15 Substituent effects on Bond energies The strength of a CC bond changes from 89.9 to 70 kcal/mol as the various H are replace with methyls.explanations given include: Ligand CC pair-pair repulsions Fragment relaxation Inductive effects 15

16 Ligand CC pair-pair repulsions: Each H to Me substitution leads to 2 new CH bonds gauche to the original CC bond, which would weaken the CC bond. Thus C 2 H 6 has 6 CH-CH interactions lost upon breaking the bond, But breaking a CC bond of propane loses also two addition CC-CH interactions. This would lead to linear changes in the bond energies in the table, which is approximately true. However it would suggest that the snap bond energies would decrease, which is not correct. 16

17 Fragment relaxation Because of the larger size of Me compared to H, there will be larger ligand-ligand interaction energies and hence a bigger relaxation energy in the fragment upon relaxing form tetrahedral to planar geometries. In this model the snap bond enegies are all the same. All the differences lie in the relaxation of the fragments. This is observed to be approximately correct Inductive effect A change in the character of the CC bond orbital due to replacement of an H by the Me. Goddard believes that fragment relaxation is the correct explanation PUT IN ACTUAL RELAXATION ENERGIES 17

18 Bond energies: Compare to CF 3 -CF 3 For CH 3 -CH 3 we found a snap bond energy of D e = *7.3 = kcal/mol Because the relaxation of tetrahedral CH 3 to planar gains 7.3 kcal/mol For CF 3 -CF 3, there is no such relaxation since CF3 wants to be pyramidal, FCF~111º Thus we might estimate that for CF 3 -CF 3 the bond energy would be D e = kcal/mol, hence D 298 ~ 110-5=105 Indeed the experimental value is D 298 =98.7±2.5 kcal/mol suggesting that the main effect in substituent effects is relaxation (the remaining effects might be induction and steric) 18

19 Stopped L4, January 11,

20 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. 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 ) 20

21 Comparison of The GVB bonding orbitals of ethene and methylene 21

22 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) 22

23 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 23

24 geometries For the N state (planar) the CC bond distance is 1.339A, but this increases to 1.47A for the twisted form with just a single σ bond. This compares with for the CC bond of ethane. Probably the main effect is that twisted ethene has very little CH Pauli Repulsion between CH bonds on opposite C, whereas ethane has substantial interactions. This suggests that the intrinsic CC single bond may be closer to 1.47A For the T state the CC bond for twisted is also 1.47A, but increases to 1.57 for planar due to Orthogonalization of the triple coupled pπ orbitals. 24

25 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 25

26 bond energy of F 2 C=CF 2 The snap bond energy for the double bond of ethene od 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 26

27 Bond energies double bonds Although the ground state of CH2 is 3 B 1 by 9.3 kcal/mol, substitution of one or both H with CH3 leads to singlet ground states. Thus the CC bonds of these systems are weakened because of this promotion energy. 27

28 C=C bond energies 28

29 CC triple bonds Starting with two CH radicals in the 4 Σ - state we can form ethyne (acetylene) with two π bonds and a σ bond. This leads to a CC bond length of 1.208A compared to for ethene and for ethane. The bond energy is D e = 235.7, D 0 = 227.7, D 298K = kcal/mol Which can be compared to De of for H2C=CH2 and 95.0 for H3C-CH3. 29

30 GVB orbitals of HCCH 30

31 GVB orbitals of CH 2Π and 4Σ- state 31

32 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 - 32

33 Bond energies 33

34 34

35 Diamond Replacing all H atoms of ethane and with methyls, leads to with a staggered conformation Continuing to replace H with methyl groups forever, leads to the diamond crystal structure, where all C are bonded tetrahedrally to four C and all bonds on adjacent C are staggered A side view is This leads to the diamond crystal structure. An expanded view is on the next slide 35

36 Infinite structure from tetrahedral bonding plus staggered bonds on adjacent centers 2 nd layer st layer nd layer c 1 1st layer nd layer Chair configuration 1st layer of cylcohexane Not shown: zero layer just like 2 nd layer but above layer 1 3 rd layer just like the 1 st layer but below layer 2 36

37 The unit cell of diamond crystal An alternative view of the diamond structure is in terms of cubes of side a, that can be translated in the x, y, and z directions to fill all space. Note the zig-zag chains c-i-f-i-c and cyclohexane rings (f-i-f)-(i-f-i) There are atoms at all 8 corners (but only 1/8 inside the cube): (0,0,0) all 6 faces (each with ½ in the cube): (a/2,a/2,0), (a/2,0,a/2), (0,a/2,a/2) plus 4 internal to the cube: (a/4,a/4,a/4), (3a/4,3a/4,a/4), (a/4,3a/4,3a/4), (3a/4,a/4,3a/4), Thus each cube represents 8 atoms. All other atoms of the infinite crystal are obtained by translating this cube by multiples of copyright a in 2011 the William x,y,z A. Goddard directions III, all rights reserved c c f i c f c i f f i c f c i f c c 37

38 4 b 2 b Diamond Structure 5 a 3 a 1 a b 4 a 2 a 5 b 3 b 1 c 7 Start with C1 and make 4 bonds to form a tetrahedron. Now bond one of these atoms, C2, to 3 new C so that the bond are staggered with respect to those of C1. Continue this process. Get unique structure: diamond Note: Zig-zag chain 1 b Chair cyclohexane ring: b -7-1 c 38

39 Properties of diamond crystals 39

40 Properties of group IV molecules (IUPAC group 14) There are 4 bonds to each atom, but each bond connects two atoms. Thus to obtain the energy per bond we take the total heat of vaporization and divide by two. 40 Note for Si, that the average bond is much different than for Si H

41 Comparisons of successive bond energies SiH n and CH n p lobe lobe p lobe lobe p p 41

42 Redo the next sections Talk about heats formation first Then group additivity Then resonance etc 42

43 Benzene and Resonance referred to as Kekule or VB structures 43

44 Resonance 44

45 Benzene wavefunction is a superposition of the VB structures in (2) benzene as + 45

46 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. 46

47 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 47

48 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 48

49 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 49

50 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 50

51 energetics 51

52 Allyl Radical 52

53 Allyl wavefunctions It is about 12 kcal/mol 53

54 Cn What is the structure of C 3? 54

55 Cn 55

56 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 56

57 Stability of odd Cn 57

58 58

59 Bond energies and thermochemical calculations 59

60 Bond energies and thermochemical calculations 60

61 Heats of Formation 61

62 Heats of Formation 62

63 Heats of Formation 63

64 Heats of Formation 64

65 Bond energies 65

66 Bond energies 66

67 Bond energies Both secondary 67

68 68

69 Average bond energies 69

70 Average bond energies 70

71 Real bond energies Average bond energies of little use in predicting mechanism 71

72 Group values 72

73 Group functions of propane 73

74 Examples of using group values 74

75 Group values 75

76 Strain 76

77 Strain energy cyclopropane from Group values 77

78 Strain energy c-c3h6 using real bond energies 78

79 Stained GVB orbitals of cyclopropane 79

80 Benson Strain energies 80

81 Resonance in thermochemical Calculations 81

82 Resonance in thermochemical Calculations 82

83 Resonance energy butadiene 83

84 Allyl radical 84

85 Benzene resonance 85

86 Benzene resonance 86

87 Benzene resonance 87

88 Benzene resonance 88

89 Benzene resonance 89

90 Graphene: generalize benzene in all directions 90

91 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 91

92 C 60 flat sheet Cut from graphene 6 arm chair 5 zig-zag Total cost 832 kcal/mol! 92

93 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! 93

94 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. 94

95 Nature 1985: discovery of C 60 95

96 10 torr He Evidence for C60, Nature 1985 maximize clustercluster reactions in integration cup 760 torr He 96

97 Many papers on C60, no definitive proof that it had fullerene structure, lots of skepticism 97

98 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 98 at levels of a few per cent.

99 Nature 1990, Krätschmer, Lamb, Fostiropoulos, Huffman Sears arc welder with flowing He, get soot of C60. grams per hour 100

100 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 101

101 C 540 All fullerens have 12 pentagonal rings 102

102 Polyyne chain precursors fullerenes, all even 103

103 104

104 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 105

105 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 106

106 Energies from QM 107

107 Force Field for sp1 and sp2 carbon clusters 108

108 4n vs 4n+2 for Cn Rings 109

109 Population of various ring and fullerene species with Temperature Based on free energies from QM and FF 110

110 Bring two C30 rings together 111

111 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) 112

112 Energetics (ev) for initial steps of Jarrold Jarrold pathway If get here, then get fullerene Modified Jarrold Number pi bonds 113

113 Downhill race from tricyclic to bucky ball energetics (ev) 30 ev of energy gain as form Fullerene Number sp2 bonded centers 114

114 Structures in Downhill race from tricyclic to bucky ball 115

115 energetics (ev) Energy contributions to downhill race to fullerene Number sp2 bonded centers 116

116 C60 dimer Prefers packing of 6 fold face De = 7.2 kcal/mol Face-face=3.38A 117

117 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) 118

118 C60 is face centered cubic 119

119 C70 is hexagonal closest packed 120

120 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 121

121 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 122

122 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 123

123 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). 124

124 Kiang CNT form

125 Kiang CNT form

126 Distribution of diameters for carbon SWNT, Kiang

127 128

128 Examples Single wall carbon nanotubes 129

129 Some bucky tubes (8,8) armchair (14,0) zig-zag (6,10) chiral 130

130 Contsruction for (6,10) edge

131 13.46A diameter (10,10) armchair carbon SWNT 40 atoms/repeat distance 132

132 (14,0) zig-zag Bucky tube 133

133 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 134

134 Vibrations in (10,10) armchair CNT 135

135 Carbon fibers and tubes 136

136 Vibrations in (10,10) armchair CNT 137

137 Vibrations in (10,10) armchair CNT 138

138 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) 139

139 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) 140

140 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 141

141 Mechanisms Proposed for Nanotube Growth Stepwise Process Adsorption Dehydrogenation Saturation Diffusion Nucleation Growth 142

142 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,

143 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. 144

144 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,

145 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,

146 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. 147

147 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,