Effects of KI Encapsulation in Single-Walled Carbon Nanotubes by

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Effects of KI Encapsulation in Single-Walled Carbon Nanotubes by Raman and Optical Absorption Spectroscopy A. Ilie,*,† J. S. Bendall,† D. Roy,†,‡ E. Philp,§ and M. L. H. Green§ Nanoscience, UniVersity of Cambridge, 11 J. J. Thomson AVenue, Cambridge CB3 0FF, U.K., National Physical Laboratory, Hampton Road, Teddington TW11 0LW, U.K., and Inorganic Chemistry Laboratory, UniVersity of Oxford, South Parks Road, Oxford OX1 3QR, U.K. ReceiVed: October 22, 2005

The effect of KI encapsulation in narrow (HiPCO) single-walled carbon nanotubes is studied via Raman spectroscopy and optical absorption. The analysis of the data explores the interplay between strain and structural modifications, bond-length changes, charge transfer, and electronic density of states. KI encapsulation appears to be consistent with both charge transfer and strain that shrink both the C-C bonds and the overall nanotube along the axial direction. The charge transfer in larger semiconducting nanotubes is low and comparable with some cases of electrochemical doping, while optical transitions between pairs of singularities of the density of states are quenched for narrow metallic nanotubes. Stronger changes in the density of states occur in some energy ranges and are attributed to polarization van der Waals interactions caused by the ionic encapsulate. Unlike doping with other species, such as atoms and small molecules, encapsulation of inorganic compounds via the molten-phase route provides stable effects due to maximal occupation of the nanotube inner space.

1. Introduction Encapsulation of materials in the hollow interior of singlewalled carbon nanotubes (SWCNTs) is being explored as a way to modify the properties of nanotubes. Several types of materials with increasing complexity and occupation of the available space have been encapsulated, from chains of atoms1, to molecules,2-4 and to inorganic crystals.5 SWCNTs filled with inorganic compounds via the molten phase route5,6 are nanocomposites where controlled and environmentally stable properties can be obtained due to the maximal occupation of the inner space. Here, we study modifications occurring in KI encapsulated singlewalled carbon nanotubes (KI@SWCNTs) via Raman spectroscopy and optical absorption. This system is one of the first examples of inorganic compound filling of single-walled nanotubes that can be obtained in high yield,6 as well as being simple and readily prepared free of extraneous KI material.7 2. Experimental Details In this study, the host material was HiPCO SWCNTs, as opposed to arc discharge nanotubes used previously for KI encapsulation. These nanotubes were purchased purified from CNI. The purified empty nanotubes were subjected to established procedures for end opening, capillary filling with molten phase KI,6 and subsequent washing to remove extraneous KI.7 The resulting material had a KI filling yield of about 60%, as observed by high-resolution transmission electron microscopy (HRTEM). HRTEM imaging was performed on material in bundles, as well as dispersed in individual nanotubes, using a JEOL JEM-3000F field-emission gun transmission electron microscope (FEGTEM) at 300 kV and with a point resolution of 0.16 nm. * Corresponding author. E-mail: [email protected]. † University of Cambridge. ‡ National Physical Laboratory. § University of Oxford.

Raman spectroscopy was performed on a Renishaw spectrometer through a 50× objective and in the backscattering geometry. Several lasers were used for excitation, an air-cooled Ar+ laser at 488 and 514.5 nm (2.54 and 2.41 eV, respectively), a He-Ne laser at 632.8 nm (1.96 eV), and a near-IR diode laser at 785 nm (1.58 eV). The nanotube material was used in the form of thick bundles deposited on a silicon substrate, so the spectra acquired were characteristic of the overall nanotube distribution. Optical spectroscopy (OA) was performed on a Varian Cary4000 UV-vis-NIR spectrophotometer with a 175-900 nm wavelength range, at room temperature. Spectra were acquired from the nanotubes dispersed in a sodium dodecyl sulfate (SDS) solution, in two situations: with the nanotubes in the state of bundles and individually separated after sonication and thorough centrifugation. The corresponding spectra showed differences related to differences in the nanotube-nanotube interaction. Spectra from SDS were used for background correction. As the filling procedure involves elevated temperatures, up to 1000° C, that might affect the narrowest of the HiPCO nanotubes, it was necessary to prepare a reference HiPCO sample that underwent the same thermal history as the KI-filled nanotubes. Raman and optical spectroscopy were then used to confirm that the diameter distribution remained largely the same, an important consideration for subsequent comparisons. 3. Results and Discussion 3.1. Encapsulation Yield from HRTEM. HRTEM also revealed information about the type of KI filling in tubes of various diameters. HiPCO nanotubes are narrow, with a diameter (dt) distribution that peaks around 1 nm and is quite broad, with fwhm ≈ 0.2 nm. A larger, (10, 10) SWCNT (1.36 nm diameter) can easily accommodate 2 × 2 KI, the smallest KI nanocrystal configuration reported so far,5,6 while 3 × 3 KI has been found present in larger nanotubes (∼1.6 nm diameter).5,6 We found

10.1021/jp062937d CCC: $33.50 © 2006 American Chemical Society Published on Web 06/27/2006

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Figure 1. Radial breathing modes and assigned nanotubes for the HiPCO and KI@HiPCO materials at various excitation energies: (a) 2.54 eV, (b) 2.41 eV, (c) 1.96 eV, and (d) 1.58 eV. At 2.41 eV, the notch filter used precludes good sensitivity below about 180 cm-1. In (a) and (b), the spectra were normalized to the composite peak at 203 cm-1 and to the 248 cm-1 peak assigned to (7, 7), respectively. In (c) and (d), the displayed relationship between the spectra before and after encapsulation is approximate, and it follows the relative evolution of the peaks as detailed in Tables 2 and 3 for a scenario of negative axial strain.

that in the HiPCO material 2 × 2 KI could also be encapsulated in narrower nanotubes, predominantly down to about 1.1-1.15 nm diameter. These observations are consistent with values of “optimum” and “threshold” nanotube diameters for 2 × 2 KI encapsulation we defined on the basis of the van der Waals interaction between filling and nanotube:8,9 doptimum ≈ 1.3 nm, and dthreshold ≈ 1.18 nm. For dt < dthreshold, encapsulation is only possible at the expense of compressing the KI crystal along the transverse direction, as shown by Wilson and Madden10 for the (8, 8) SWCNT (1.08 nm diameter). Moreover, it has been found that such narrow nanotubes also stabilize a twisted and puckered form of 2 × 2 KI.11,12 One would expect that the nanotubes also undergo stronger modifications when a strong repulsive interaction exists between the filling and the nanotube walls, as in narrow nanotubes,10 though all calculations published so far do not include nanotube relaxation. Single-row filling was also observed in nanotubes with diameter of e1 nm; however, to date, we have not been able to elucidate whether this is a new KI phase or just monoatomic filling, such as iodine.1 There is less HRTEM evidence of filling in nanotubes narrower than about 0.9 nm. There is therefore a cutoff diameter below which the nanotubes remain unfilled. 3.2. Radial Breathing Modes. Figure 1(a-d) shows the radial breathing modes (RBM) at the four excitation wavelengths for the HiPCO and KI-filled HIPCO. After filling, there are no significant RBM shifts but changes in their relative intensities. To understand these changes, we found it necessary to first assign the peaks of the unfilled material to the originating tube types. Two main criteria were used for the assignment. (i) Large RBM intensities result from nanotubes with diameters close to the peak of the diameter distribution and with Eii values of the transitions between pairs of van Hove singularities (vHS) that fall in the Raman resonance window (fwhm of about 120 meV for bundled nanotubes13) at a given excitation energy. However,

even inside the resonance window, the RBM intensity decreases nonuniformly with an increasing mismatch ∆E between Eii and Elaser. Such variations of ∆E at a given Elaser and for different types of nanotubes were able to explain their nonuniform Raman response when electrochemically doped.14 (ii) On the other hand, thermally induced deformation through annealing leads to specific intensity changes as the Eii transitions of a (n, m) nanotube shift relative to the undeformed case according to the rules:13 (1) for semiconducting (S) tubes with (2n + m)mod3 ) 1, E S22 V, E S33 v; (2) for S tubes with (2n + m)mod3 ) 2, E S22 v, E S33 V; (3) for armchair (n, n) metallic (M) tubes E M 11 ) ct; M2 V, E v (here, E M1,2 while (4) for the rest of the M tubes, E M1 11 11 11 designates the energy splitting due to the warping effect). The same rules have been found to govern the nanotube behavior under negative uniaxial strain (length contraction),15 while length contraction under annealing at moderate temperatures has also been obtained theoretically.16 Eii values for the HiPCO nanotube distribution are available as a complete library from a previous Raman multiwavelength study using tunable lasers,13 as well as from Kataura-type plots obtained from spectrofluorometric data.17 In this study, Raman spectroscopy was performed on bundled nanotubes, which have Eii resonances a few tens of millielectronvolts smaller than the nanotubes dispersed individually.13 For 2.41 and 1.96 eV excitation, we performed the RBM assignment (Tables 1 and 2, respectively) based on the two criteria outlined above. To anneal the nanotubes, the laser power was increased in a range where no permanent damage is induced in the tubes. Under such conditions, the RBM modes evolve as shown in Figure 2(a,c), and reversibly. Tables 1 and 2 summarize the nanotubes identified in this way, as well as the evolution of the corresponding RBM peaks in processes other than annealing, as discussed below. For 1.58 and 2.54 eV excitation, we used only criterion (i) to assign the nanotube types. At 1.58 eV, this single

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TABLE 1: 2.41 eV Excitationa ωRBM assigned (cm-1) SWCNT dt (2n + m) HiPCO type (nm) mod3 208

(14, 1) S 1.14

2

E S33 ) 2.485

248

(7, 7) M 0.95

0

1 EM 11 ) 2.35

264

(8, 5) M 0.89

0

1 EM 11 ) 2.32

0

2 EM 11 M1 E 11 2 EM 11

274

(9, 3) M 0.85

intensity ∆E changes (eV) laser bundles annealing

Eii (eV) bundles ref 13

≈

1 EM 11

≈

intensity changes “-“ axial strain

Eii (eV) intensity intensity SDS ∆E (eV) changes changes KI@ FeCl3 inter- dispersed SDS ref 13 dispersed HiPCO calation18

+ 0.075 not well E S v IV Iv (very E S33 V Iv 33 resolved strong) -0.06 ∼constant E M ) ct I ) ct E M ) ct I ) ct used for 11 11 normalization 1 1 -0.06 IV IV EM EM 11 v Iv 11 V IV +

0.16a

+

0.34a

-0.16

) 2.25 1 EM 11

intensity changes “+” axial strain

IV

2 EM 11 V M1 E 11 v 2 EM 11 V

Iv

2 EM 11 v M1 E 11 V 2 EM 11 v

IV

IV

Iv

2.55

+0.14

I ) ct.

2.43

+0.01

IV

2.43

+0.01

IV

2.35

-0.06

Nanotube types are assigned as described in the text. I is the generic intensity of the RBM mode, while ∆E ) Eii - Elaser with Eii of the bundled 1 M2 M1 unfilled material. E Sii and E M 11 values are from ref 13, while E 11 , marked by (a), are shifted relative to E 11 according to tight-binding estimations of the warping effect. The sense of changes of Eii and I is indicated for various phenomena, where v(V) denotes increase (decrease). All nanotubes are away from resonance, as indicated by the large ∆E values; therefore, their RBM modes have low sensitivity to annealing and charge transfer. Positive (+) uniaxial strain or bleaching by charge transfer only is not compatible with the peaks’ evolution after encapsulation, while negative (-) uniaxial strain is. Eii and ∆E values for the nanotubes individually dispersed are also shown in the last two columns; charge transfer alone is not compatible with the RBM evolution based on these values either. a

TABLE 2: 1.96 eV Excitationa

(2n + m)mod3

Eii (eV) bundles ref 13

intensity changes “-” axial strain

∆E (meV) bundles

Eii (eV) SDS dispersed ref 13

∆E (meV) SDS dispersed

1.22

0

1 EM 11 ) 2.0

I ) constant

+ 0.04

2.03

+0.07

(13, 4) M

1.2

0

1.93

-0.03

(10, 7) M

1.16

0

+ 0.07

2.07

(+0.11)

218

(12, 3) M

1.08

0

(11, 5) M

1.11

0

258

(11, 1) S

0.9

2

282

(8, 4) S

0.84

2

1 EM 11 V IV M1 E 11 V Iv 1 EM 11 V IV M1 E 11 V Iv E S22v IV E S22v IV

-0.11

205

1 EM 11 ) 1.85 M1 E 11 ) 2.03 1 EM 11 ) 1.95 M1 E 11 ) 2.03 E S22 ) 1.97 E S22 ) 2.05

(7, 5) S

0.82

1

ωRBM (cm-1) HiPCO

assigned SWCNT type

dt (nm)

196

(9, 9) M

-0.01

1.92

-0.04

+ 0.07

2.06

(+0.1)

+ 0.01

2.03

+0.07

+ 0.09

2.11

(+0.17)

1.92

-0.04

a

Nanotube types are assigned as described in the text. Symbols and comments are similar to those for Table 1. When considering individually (SDS) dispersed nanotubes, a different peak assignment is valid, while some of the nanotubes assigned for the bundled material have ∆E values (as shown in parentheses in the last column) that are too large to be in the resonance window.

criterion is enough for unique assignment (see Table 3). This is because at this energy there is no overlap of several Eii branches in the Kataura plot, as noted also by Kavan et al.14 At 2.54 eV, the main peak around 203 cm-1 has shoulders at 189 and 197 cm-1, and it allowed unique assignment based on the fact that these nanotubes are precisely in resonance at 2.54 eV. For some peaks at both 1.58 and 1.96 eV, two nanotubes were marked on the respective figures and tables as contributing: this is to show that after encapsulation there can be structural changes as described below that can modify the balance between the contributions of the respective tubes. Before encapsulation, the tube with the smallest ∆E is the dominant one. After KI filling, the relative intensities of the RBM modes changed nonuniformly (Table 1), with some peaks increasing while the others decreased without a monotonic dependence on nanotube diameter. There are two basic phenomena that can lead to such change of the relative RBM intensities. On one hand, there can be a simple electronic effect of charge transfer, when one adds electrons to an empty vHS or removes electrons from a filled vHS, resulting in bleaching of the Eii transitions and quenching of the corresponding Raman modes. As discussed by Kavan et al.,14 the way each type of nanotube responds in Raman to such doping depends on the size of ∆E: the intensity of the RBM mode of a nanotube closer to resonance, and thus with smaller ∆E, decreases more sensitively than that of a nanotube far away from resonance, and thus with large ∆E. On the other hand, a true enhancement of a RBM mode, i.e., that

is not just relative to the others in the group, is a clear sign of changes in the resonance conditions, and thus of the corresponding Eii. In the case of encapsulation of materials, one expects both charge transfer and changes of Eii positions of other origin to occur. Therefore, in general, to distinguish between changes in resonance conditions or nonuniform bleaching, the resonance profile of the RBM modes should be traced. In the absence of this, only the appearance of new peaks, absent or of very low intensity before encapsulation, qualifies with certainty as a phenomenon of tuning into resonance. The evolution of our data is reminiscent of that encountered in previous work on HiPCO SWCNTs modified continuously through molecule filling/intercalation18 (summarized in Table 1). There, the 248 cm-1 peak at 2.41 eV excitation remained unchanged and was used for comparing the changes in the other RBM modes. In Table 1, we attributed this peak to the (7, 7) metallic armchair nanotube, whose resonances Eii are indeed expected to remain unchanged under any type of uniaxial mechanical strain.15 Moreover, changes of the longitudinal dimension of this class of nanotubes are also minimal under charge injection.19,20 Relative to this peak with its minimal intensity change, the 208 cm-1 peak attributed to a (14, 1) semiconducting nanotube increased strongly after KI filling, while the peaks at 264 and 274 cm-1 decreased to a lesser degree. This indicates that the laser energy is out of resonance with the empty (14, 1) tube but then is brought into resonance due to KI filling, while the other nanotube types still remained

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Figure 2. Evolution of the radial breathing modes under laser annealing by increasing the laser power: (a) HiPCO at 2.41 eV; (b) KI@HiPCO at 2.41 eV; (c) HIPCO at 1.96 eV; (d) KI@HiPCO at 1.96 eV. In each case, the highest laser intensity was limited to such a value that a reversible evolution of the spectra was maintained. In each figure, n × P denotes how the power has been increased from one spectrum to the other. P, the initial power used, is different in each of the four cases.

TABLE 3: 1.58 eV Excitationa ωRBM (cm-1) assigned Eii (eV) ref 13 HiPCO SWCNT type dt (nm) (2n + m)mod3 bundles 206

∆E (meV) Eii (eV) ∆E (meV) bundles ref 13 SDS separated SDS separated

intensity changes “-“ axial strain

(14, 1) S

1.153

2

E S22 ) 1.58

IV

0.0

1.64

+0.06

(13, 3) S

1.17

2

E S22 ∼ 1.55

Iv

0.03

1.62

+0.04

I ≈ constant IV

0.05

1.58

+0.0

) 1.54

IV

0.04

1.58

+0.0

) 1.525

IV

0.055

1.57

+0.01

) 1.51

IV

0.07

1.55

-0.03

) 1.59

IV

0.01

1.665

+0.085

) 1.59

IV (already at resonance)

0.01

1.683

+0.103

216

(9, 7) S

1.103

1

E S22 ) 1.53

226

(10, 5) S

1.04

1

234

(11, 3) S

1.014

1

(12, 1) S

0.98

1

267

(10, 2) S

0.87

1

(11, 0) S

0.86

1

E S22 E S22 E S22 E S22 E S22

a Nanotube types are assigned as described in the text. Negative (-) uniaxial strain (where increases for (2n + m)mod3 ) 2 and decreases for (2n + m)mod3 ) 1) is compatible with I changes after encapsulation, while positive (+) uniaxial strain reverses these tendencies and therefore is not. For bundled nanotubes, ∆E is smallest for the 206 cm-1 peak which changes the least compared with the others; this peak’s intensity should thus decrease the most should charge transfer be the dominant phenomenon after encapsulation. Charge transfer alone is not compatible either when considering values for the SDS dispersed nanotubes: in this case, the 216 and 226 cm-1 peaks should be the most sensitive.

E S22

in the resonance window. We believe that this is a phenomenon of true tuning into resonance. For the RBM modes, tuning from outside to maximum resonance requires Eii shifts of about at least 60 meV, corresponding to half of the fwhm of the Raman resonance window for bundled nanotubes.13 The further temperature rise at increased laser power continued this trend and, additionally, downshifted all the RBM modes by about 1.5 cm-1 (see Figure 2b). Such behavior suggests that the mechanism affecting the RBM modes’ intensities may be common for both filling and annealing and therefore could involve negative axial strain. This is supported by the trends in Figure 2 and Tables 1 and 2 for both 2.41 and 1.96 eV, respectively. ∆E ) Eii - Elaser (with Eii of the bundled unfilled HiPCO material) is also shown in these tables, giving an indication about the sensitivity of each nanotube to changes such as charge transfer.14 At 2.41 eV, all the nanotubes assigned are quite away from resonance in the unfilled material, possibly explaining also why their RBM

modes do not change that much under annealing. Similar low sensitivity is expected at charge transfer. On the basis of the ∆E sensitivity criterium, charge transfer alone cannot explain the changes of the RBM relative intensities in Figure 1a,b (Table 1). Similarly to the strong increase in intensity of the (14, 1) RBM mode, peaks absent in the unfilled HiPCO material at 2.41 eV excitation became visible after KI encapsulation, such as 220 and 231 cm-1. So far, we were not able to assign these peaks with a high degree of confidence, as the nanotubes that have such RBM frequencies21 have their Eii values when unfilled significantly far away from resonance. This would suggest that stronger DOS modifications took place in order to bring these nanotubes in resonance at 2.41 eV excitation. At 1.58 eV excitation, we assigned the nanotube types the same as in ref 14. With this assignment, the RBM evolution after encapsulation is compatible with Eii shifting as under

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TABLE 4: 2.54 eV Excitationa ωRBM (cm-1) HiPCO

assigned SWCNT type

d (nm)

(2n + m)mod3

Eii (eV) ref 13 bundles

intensity changes “-“ axial strain

∆E (meV) bundles

189

(11, 7) S

1.23

2

E S22 ) 2.55

IV (already at resonance)

+ 0.01

197

(12, 5) S

1.18

2

E S22 ) 2.54

0.0 -0.01

) 2.53

203

(13, 3) S

1.15

2

E S22

227

(12, 2) S

1.03

2

E S22 ) 2.69*

IV

Eii (eV) ref 13 SDS dispersed 2.61 (11, 7) S 2.47 (15, 2) S 2.6 (12, 5) S ∼2.57 (13, 3) S 2.55 (14, 1) S 2.69

∆E (meV) SDS dispersed +0.07 -0.07 +0.06 +0.03 +0.01 (+0.15)

a

Nanotubes types are assigned as described in the text. The asterisk denotes an Eii value corresponding to individually separated nanotubes; the value for bundled tubes is several tens of millielectronvolts lower. When values for the individually dispersed nanotubes are used, the peak at 203 cm-1 should be the most sensitive to charge transfer relative to the shoulders at 189 and 197 cm-1; charge transfer is therefore not the dominant phenomenon, as in this case, the composite peak at 203 cm-1 should alter its shape. ∆E values in parentheses denote values that are outside the resonance window.

Figure 3. G-band modes for the HiPCO and KI@HiPCO materials at various excitation energies: (a) 2.54 eV, (b) 2.41 eV, (c) 1.96 eV, and (d) 1.58 eV. The shifts of the G+/-, as well as those of the D and D* modes (shown in Figure 5), are tabulated as insets. The normalization to the G+ line is only as a guide to the eye and does not reflect the real relationship between the G-bands before and after encapsulation; deduced relationships between the full spectra before and after encapsulation are shown in Figure 5.

negative uniaxial strain. In such a scenario, the peak at 206 cm-1 changes the least, due to balancing of opposite tendencies of (14, 1) and (13, 3) semiconducting nanotubes, while the intensities for the other nanotubes decrease (see Table 3). Table 3 also shows that bleaching by charge transfer only is not consistent with the relative evolutions of these peaks, as in this case, the peak at 206 cm-1 should decrease the most, since the corresponding nanotubes are the closest to resonance (have the smallest ∆E) compared to the other ones. At 2.54 eV excitation, the composite peak around 203 cm-1 can only decrease in intensity after encapsulation, whatever the modifications introduced, as the contributing nanotubes are already in perfect resonance (Table 4). This implies that relative to this peak the peak around 227 cm-1 decreases more. Moreover, because 227 cm-1 is tentatively attributed to the (12, 2) semiconducting nanotube, that is, below the diameter threshold values given in section 3.1, this would support the idea that narrower encapsulated nanotubes are affected more than the larger ones. As further argued in the next sections, this seems to be a more general conclusion of this work. Tables 1-4 also show as an additional test that even when considering the Eii values for the nanotubes individually

separated13 the scenario involving charge transfer only is not consistent with the RBM evolution. 3.3. High-Energy Vibrational Modes. The changes in the high-energy modes (HEM) of the Raman spectra, D, G, and D* (the second-order D mode) peaks are more directly related than the RBM modes to changes in the C-C bond stiffness (effective spring constant),22,23 and thus bond length,23 while charge transfer is a well-documented way to produce changes in the bond lengths.19,20 Both first- and second-order high-energy vibrational modes are affected by the KI filling, as shown in Figures 3 (a-d) and 5 (a-d). 2.54, 2.41, and 1.96 eV excitation wavelengths probe tangential G+/- modes of both metallic and semiconducting nanotubes of the HiPCO distribution, while 1.58 eV reveals semiconducting nanotube modes only (Table 5, Supporting Information). The extended G - metallic bands between about 1450 and 1560 cm-1 at 2.54 and 2.41 eV excitations (corresponding to diameters in the ranges 0.850.95 and 0.85-1.1 nm, respectively) are strongly quenched after KI filling. Additionally, as seen in Figures 3 (insets) and 5, there are small upshifts of the G+/- peaks, while the D and D* peaks upshift more substantially with stronger dependence on the excitation energy than the tangential modes, as noted previ-

KI Encapsulation in SWCNTs ously.23 The G+/- shifts obtained here are less than those reported for SWCNTs intercalated with CrO3 or Ag.24,25 These upshifts are consistent with hardening (shrinking) of the C-C bonds, if a monotonic relationship between the G-band vibrational frequency and the bond length26 is assumed to be valid in nanotubes,23,28,29 as for graphite intercalated compounds.30-32 Depending on the type of the contributing nanotubes, these upshifts can indicate electron depletion from (i.e., hole injection to) the nanotube19 (see also section 3.6). The G- shift at 1.96 eV appears to have a different origin, as discussed in section 3.5. For the metallic nanotubes at 2.54 and 2.41 eV, a weakened Breit-Wigner-Fano profile and quenching of their G- band is observed in Figure 3 (a,b). This translates to decreased electron-phonon coupling33 due to electron depletion of the nanotubes. Further, electron depletion in metallic nanotubes is always related to longitudinal contraction.19 Density functional theory calculations of KI encapsulation in a larger (dt > dtoptimum), (10, 10) nanotube have shown that the electronic density of the nanotube wall can indeed decrease after filling,34 consistent with our findings. Note that ref 34 found the chargetransfer process in this system to be quite complex, as on the other hand, the electronic density in the nanotube-filling interspace was found to increase. This has been attributed to electron-transfer contributions to the interspace from both the nanotube wall and the KI filling. 3.4. Optical Absorption and Changes in JDOS. Optical absorption (OA) measurements in the spectral region covered by the Raman measurements give insight into the joint densityof-states (JDOS) changes. In single-walled nanotubes, JDOS exhibits singularities corresponding to interband optically allowed transitions between Eii,35 while the optical absorption spectrum is a convolution of the JDOS of all the nanotube types present in the diameter distribution. Figure 4 compares the absorbance of the unfilled nanotubes with the KI-filled material in the UV-vis-NIR range. Figure 4a,b shows the spectra as acquired and after π background extraction, respectively. Both spectra were acquired for nanotubes suspended in surfactant (SDS) solution and individually separated after thorough dispersion and separation by centrifugation. Spectra were acquired also from the unfilled and KI-filled materials suspended in surfactant (SDS) solution but still in the state of bundles (Figure 4c). The spectrum for the unfilled nanotubes from Figure 4b was consistent with that shown in ref 36 and corresponded to a majority of individually SDS-separated nanotubes. The presence of a large number of peaks in the absorption spectra from Figure 4 is the result of the polydisperse nature of the HiPCO material. For comparison with the Raman data, the spectrum from the nanotube bundles (Figure 4c) is more appropriate. Bundling shifts the OA peaks to lower energies, by a few tens of millielectronvolts, compared to the peaks from individually separated nanotubes. This is similar to the bundling effects obtained in the Raman experiments.13 The broad OA features from Figure 4b,c are the same. As seen in Figure 4c, there are several broad regions where the OA of the nanotubes is affected by encapsulation. However, a clear delineation between them is made difficult by the lack of reference features relative to which a normalization could be made. There are two broad regions where OA decreases after KI encapsulation: (2) between about 1.55 and 1.98 eV, and (4) between about 2.1 and 2.5 eV. These regions alternate with regions where the OA increases or remains constant after KI filling: (1) between 1.35 and 1.55 eV, (3) between 1.98 and 2.1 eV, and (5) above 2.5 eV. Simple charge transfer would lead to progressive quenching of the Eii transitions closest to

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Figure 4. Absorbance expressed as a function of excitation energy HiPCO and KI@HiPCO materials: (a) and (b) for individually separated nantubes, before and after π background extraction, respectively. (c) Both types of nanotubes are in the bundled state, after π background extraction. Positions of the peaks in (b) are the same as in ref 36, and upshifted nonuniformly relative to (c), where nanotubenanotube interactions are operational.

the Fermi level, and thus of the lowest OA peaks, as noted in various types of doping processes.37,38 However, the alternating enhancement and quenching in the OA is rather suggestive of displacement of the corresponding Eii resonances after filling and also in opposite directions in the energy spectrum. As mentioned in section 3.2, different (2n + m)mod3 classes of nanotubes can modify their Eii transitions in opposite directions when subjected to the same type of structural deformation. A further, stronger reason for these OA modifications is that the regions delineated above correspond to different diameters of nanotubes, which can be affected by encapsulation in very different ways. Nanotubes in regions (2) and (4), with the strongest OA bleaching, correspond to diameters d mainly in the range 0.9-1.15 nm. These nanotubes did encapsulate KI, but their diameter is below dthreshold at which there is the onset of a strong, repulsive interaction between the nanotube cage and the filling. On the other hand, the nanotubes in region (1) correspond to the largest diameters, between 1.1 and 1.3 nm, with those larger than 1.18 nm making up the majority. Similarly, those in region (5) correspond to diameters larger than 1.17 nm. The nanotubes from regions (1) and (5) encapsulate KI, but we suggest that due to their larger diameters encapsulation induces lesser changes (see below). Region (3) corresponds to nanotubes with diameters predominantly smaller than 0.8 nm, which are thus proven to still be present in the sample after the chemical processes associated with the encapsulation, but too narrow to allow encapsulation (see section 3.1).

13854 J. Phys. Chem. B, Vol. 110, No. 28, 2006

Ilie et al.

Figure 5. Full spectra showing the RBM, D, and D* modes, as well as the G-bands for the HiPCO and KI@HiPCO materials, at four excitation energies: (a) 2.54 eV, (b) 2.41 eV, (c) 1.96 eV, and (d) 1.58 eV. The spectra before and after encapsulation were normalized according to the discussion in the text: to the composite peak at 203 cm-1 in (a), to the (7, 7) peak at 248 cm-1 in (b), to the 196 cm-1 peak in (c), and to the 206 cm-1 peak in (d). These peaks are indicated by arrows.

In summary, such an alternating OA spectrum appears to be mainly the result of nonuniform encapsulation and different effects that can occur in nanotubes of various diameters. The fine structure of the OA spectrum shows nonuniform shifts of several tens of millielectronvolts. These values are affected by the nanotube-nanotube interaction in bundles, as shown by the differences between Figure 4b and c. The region between 2.4 and 2.6 eV is different, as here there is a stronger mismatch between the peaks and valleys of the filled and the unfilled nanotubes; together with the regions of increased absorption, they might indicate DOS modifications of different nature than those corresponding to the other zones of the spectrum. 3.5. Relationship between RBM and G-Band Modes after Encapsulation. If the assignment of the nanotubes contributing to the RBM modes is correct, the G-band modes should evolve in ways compatible with the RBM evolution after encapsulation. This is because, in samples with low density of defects, as is the case here (this is shown by the low intensity of the D-bands), the G-bands originate mainly from first-order processes,39 while the RBM modes are also first-order processes. Thus, for an individual SWCNT, enhancement (decrease) of its RBM intensity should be reflected in an enhancement (decrease) of its G-band modes, though the sensitivity of various vibrational modes can be quite different.40 For a distribution of nanotubes, there is a balance between different tendencies for various groups of nanotubes, which can lead to a more complex behavior. Table 5 lists all the nanotubes contributing to the G-band, separating those resonant with the incoming photon (for which Eii ) Elaser) from those resonant with the outgoing photon, of lower energy (since now Eii ) Elaser - Ephonon, with Ephonon ≈ 0.2 eV). These relations are valid for Stokes processes, as encountered here. Changes in the G-band contributions of the listed tubes are inferred from the RBM behavior in the case of the incoming resonance and from changes in the JDOS in the case of the outgoing resonance. Modifications of JDOS affect

the cross section of all the first-order Raman processes.35,40 A direct correspondence between the features of JDOS and the G-band intensity is not straightforward though, due to the averaging effect of the nanotube distribution, and because the G-band modes, unlike the RBM modes, are very closely grouped for all the nanotube types. However, when the JDOS exhibits strong perturbations, such as around 1.76 eV (see Figure 4), these perturbations should be clearly reflected in the G-band intensity. Changes in JDOS can be qualitatively evaluated from Figure 4. Table 5 (as Supporting Information) helps to extract some trends due to encapsulation for various groups of nanotubes. Accordingly, one can summarize as follows: (1) At 2.41 eV, the G-band intensity for the semiconducting nanotubes is expected to increase overall, mainly due to the (14, 1) nanotube and several unidentified others at 220 and 231 cm-1 that become strongly resonant after encapsulation, while that for the metallic nanotubes is expected to decrease (based on the overall decrease of the RBM modes and on the decrease in the OA around 2.21 eV), despite the constant RBM contribution of (7, 7). This behavior is retrieved in Figure 5b showing the two Raman spectra before and after encapsulation over a large range and after normalization to the (7, 7) RBM mode (peak at 248 cm-1) that is expected to change the least. (2) At 1.96 eV excitation, the intensity of the semiconducting tubes is expected to decrease, since for the outgoing resonance (at 1.76 eV), there is strong bleaching of the JDOS, while the intensity of (11, 1) and (8, 4) nanotubes, resonant with the incoming photon, also decreases. All these nanotubes are below dthreshold. On the other hand, the metallic contribution in the RBM relative to that of the semiconducting tubes increases after encapsulation (see Figure 1c). Therefore, one expects strong quenching of the overall G-band relative to the metallic RBM modes, with the G-band gaining a stronger metallic profile. Moreover, the shift of the G- line is artificially amplified by the new balance between the metallic and semiconducting modes. Figure 5c, in which the spectra before and after encapsulation were normal-

KI Encapsulation in SWCNTs ized to the RBM intensity of the metallic (9, 9) nanotube (peak at 196 cm-1), confirms this overall behavior. (3) At 1.58 eV excitation, only the semiconducting nanotubes are responsive. Additionally, we have the relationships I206/IHEM ≈ ct., though IRBM/IHEM decreases after encapsulation. As the decrease of the overall intensity IRBM is mirrored by a decrease of the G-band contribution for the incoming resonance, it follows that the G-band contribution for the outgoing resonance (at 1.38 eV) increases after filling. This seems plausible on the basis of the increased optical absorption around 1.38 eV after encapsulation. (4) At 2.54 eV excitation (Figure 5a), IRBM decreases overall, mainly because several nanotubes making the composite peak around 203 cm-1 are in perfect resonance with the incoming photon. This is mirrored by the G-band evolution, as semiconducting contributions due to the outgoing resonance are much less important (bad resonance condition with the outgoing photon). Thus, the semiconducting G-band would roughly scale with the main RBM peak. Additionally, the metallic G-band, in resonance with the outgoing photon, is found to decrease, and this correlates with the decrease in the optical absorption at 2.34 eV. 3.6. Effects of Encapsulation: Charge Transfer, Strain, and DOS Modifications. The Raman and optical measurements described above revealed (i) changes in the relative intensities of various RBM peaks (with the large majority decreasing, while only a few increasing), as well as changes in the RBM and G-band relative intensities; (ii) quenching of the metallic G-bands; (iii) G-band shifts consistent with C-C bond hardening (shrinking); (iv) indications of potential uniaxial negative strain (length contraction); and (v) changes in the JDOS, not consistent with gradual bleaching as seen in other doping processes. These effects can be due to several phenomena involving the SWCNT template that can be associated with encapsulation. There can be charge transfer between the nanotube and the encapsulated material that can fill or deplete states otherwise available for electronic transitions,37 such as in nanotubes doped with atomic and molecular species,1-4,37 or electrochemical charging.14 The ionic nature of the KI filling can introduce further specific perturbation of the delocalized charge distribution on the nanotube wall through polarization van der Waals interactions induced by KI dipoles. Charge transfer of any sign is conducive to quenching of the optical transitions and Raman modes. Strain of the nanotube wall can also occur, mainly for dt < doptimum when the nanotube wall interacts repulsively with the filling. In general, the origin of strain can be complex,41-43 both of structural and electronic nature. For example, it is welldocumented that charge transfer is accompanied by changes in bond length, usually anisotropic.19,20 HRTEM observations showed that structural changes of the nanotubes can occur due to filling with ionic systems: slight nanotube “polygonization” as in the case of RbI@SWCNT,44 or changes of the nanotube’s cross section from circular to oval, as in the case of [email protected] Changes in the cross section could result in nanotube length contraction, a fact that was found to be compatible with the Raman modes evolution after encapsulation. There are several scenarios that could lead to this. In one, there can be a pinch-type deformation of the nanotube, where the C-C bond length and the nanotube surface area are preserved, but the bond angles change. This has been shown to be possible for pinch, bend, and twist phonon modes associated with annealing.16 Alternatively, length contraction can be the result of changes in the C-C bond length: (i) when bonds either expand but, at the same time, bend outward,22 or (ii) on the

J. Phys. Chem. B, Vol. 110, No. 28, 2006 13855 contrary, when C-C bonds predominantly contract. As a result of both structural and electronic effects, the electronic DOS can change: through mere shifts of the van Hove singularities as in a strained nanotube,38,42,43 or in a more substantial and complex way due to polarization van der Waals and/or chemical interactions.25 “Polygonization” of nanotubes has been shown theoretically to change their band structure in a substantial way by inducing σ*-π* hybridization.46 To gain more insight into the phenomena consistent with the Raman observations, one needs to quantify the magnitude of the various effects observed. The RBM frequencies depend less on the overall volume change of the nanotube but instead primarily on changes of the C-C bond stiffness, through related bond-stretching and bond-bending force constants.22 Nevertheless, one cannot take the lack of shifting of the RBM modes seen here as evidence of no changes in the C-C bond length. As shown in an experiment involving controlled, strong tensile uniaxial stress (extension) on individual SWCNTs, RBM frequencies can remain unchanged, while high-frequency vibrational modes upshift in energy significantly.47 The tangential modes’ shifts can be used to estimate the C-C bond length changes  and the level of charge transfer fc, as in refs 23 and 30. Considering the bond changes as isotropic, according to ref 23 ∆ω/ω0 ) -2γ and  ≈ 0.08fc, with γ ) 1.1 being the phonon deformation potential. These relationships contain two serious approximations: (i) Bond changes for single-walled nanotubes can be significantly anisotropic in a variety of phenomena, such as surface charging (transfer), and the more complex phenomena described in this study. However, such an isotropic approximation is reasonably good at describing the aVerage behavior of the overall nanotube sample.23 Averaging comes from the fact that, for the same level and sign of transferred charge, nanotubes can contract or extend longitudinally and in different amounts, depending on their type:19 i.e., under hole injection, metallic nanotubes always contract, while semiconducting nanotubes either contract if of the (2n + m)mod3 ) 2 type or extend if of the (2n + m)mod3 ) 1 type. (ii) As discussed above, both structural and electronic (charge transfer) effects can contribute to ; therefore, the relationships above give an upper estimation of the average value for fc by not considering the structural contribution to . The different G+ and G- shifts can be due to different shifts of the TO and LO phonon branches after filling.23 For the semiconducting nanotubes,  of about 0.06% and 0.03% are obtained from the G+ peaks at 2.54 and 2.41 eV excitation, while a value of about 0.04% is obtained from the G- shift at 1.58 eV. These  values correspond to fc values of 0.0075, 0.0037, and 0.005 holes/C atom, respectively. Though these values reflect the sample average response, inspection of the various contributing nanotubes show that at 2.54 and 2.41 eV only semiconducting tubes with (2n + m)mod3 ) 2 contribute (Table 5, Supporting Information). These nanotubes all contract longitudinally under electron depletion (hole injection) from their wall. Thus, the small average values of  and fc obtained from the G-band upshifts do not come from compensating large positive and negative individual contributions, but indeed reflect low levels of bond contraction and electron depletion in the individual nanotubes. Such fc values are too small to cause the bleaching of the allowed optical transitions: values about 10 times higher, or more, are necessary for this.37,48 The  values estimated above translate to an overall length (unit cell) compression on the order of 0.1-0.2%,20 depending on the type of nanotube. This in turn is consistent with Eii shifts of about 20-30 meV.15 These energy shifts are about one-half too small

13856 J. Phys. Chem. B, Vol. 110, No. 28, 2006 to cause a complete tuning in or out of resonance of the RBM and HEM modes in the semiconducting nanotubes. However, since these estimations are averaged over groups of nanotubes, values in specific individual nanotubes could be larger. Table 5 also shows, on the other hand, that the  value corresponding to 1.58 eV comes from averaging values of strain of opposite sign, as both classes of (2n + m)mod3 nanotubes contribute to it; therefore, in this case, one can expect larger effects for the individual nanotubes. We do not have an estimation of strain and charge transfer in the metallic nanotubes due to the strong quenching of their G-bands. From this discussion, as well as from section 3.1, it appears thus that charge transfer alone does not explain well the data evolution after encapsulation and that strain of different origin is involved. The overall strain estimated from the G-band mode shifts for larger semiconducting nanotubes is borderline to explain the phenomena of tuning into resonance recorded at 2.41 eV excitation. Stronger effects seem to occur in narrower nanotubes, reflected through quenching of the optical absorption and both the Raman G-band and RBM modes. The increase in the optical absorption in some energy ranges, as opposed to bleaching, as well as modifications in the 2.4-2.6 eV region, that are further apart from the original spectrum before encapsulation, indicate that DOS might also be affected in a more substantial way than merely through strain-induced shifts. The nature of the interaction between the nanotube and the encapsulated KI is not clear though at the moment, and it may well be that this interaction and its strength change with decreasing nanotube diameter. There are several arguments why encapsulation should more strongly affect the narrower of the nanotubes: (i) the interatomic potential between the filling and the nanotube wall is in general repulsive9,10 and can reach stronger values than in the case of larger nanotubes, where the interaction is attractive;10 (ii) tubes of smaller diameter are more reactive,49 and (iii) there are increasingly stronger deviations of the work function of the nanotubes from that of graphite when decreasing the diameter.50 Work on encapsulation of organic molecules inside single-walled nanotubes4 demonstrated that ionization energy and electron affinity of the guest species can indeed be a major factor controlling the achievable doping level. However, with respect to our results, it is difficult to predict trends because of unknown changes in the properties of KI itself when decreasing diameter and increasing pressure inside narrower nanotubes.51 Finally, it is interesting to compare the levels of strain that occur in the encapsulated nanocrystal and the nanotube template. While the C-C bond lengths are modified in the range of 0.1% as a result of encapsulation, the ionic crystal’s bonds transverse to the nanotube axis can change by the order of 2-10% depending on the type of nanotube, larger (such as (10, 10)) or narrower (such as (8, 8)), respectively.6,10 This emphasizes the ability of the atoms of the ionic compound in the molten phase to rearrange under attractive/repulsive interactions with the nanotube wall, as opposed to the nanotube cage that acts as a rigid template, with strong bonds. 4. Conclusions In conclusion, KI filling in narrow SWCNTs with a diameter distribution that peaks around 0.9-1 nm appears to involve both charge transfer and strain that shrink both the C-C bonds and the overall nanotube along the axial direction. Values of strain and charge transfer were estimated for the larger semiconducting nanotubes, showing a low level of electron depletion from the nanotube wall. This is on the order obtained in some cases of

Ilie et al. electrochemical doping23,52 and less than for strong dopants such as alkali atoms.41,53 Stronger effects occurred in the narrower tubes, manifested through bleached regions in the optical absorption spectrum and the quenching of the BWF metallic feature of the Raman G-band. DOS modifications of a more complex nature are apparent in some energy regions, around 2.4-2.6 eV and 1.3 eV. Changes in the C-C bond length are orders of magnitude smaller than changes expected to occur in the KI filling on the direction transverse to the tube’s axis. As the filling is tightly packed, one expects doping effects and changes in the electronic density of states to be environmentally stable. Acknowledgment. The authors wish to thank J. Sloan and S. Friedrichs for supporting HRTEM information. This work is part of an exploratory project within the Interdisciplinary Research Collaboration (IRC) in Nanotechnology, United Kingdom. A.I. and J.S.B. acknowledge funding from the IRC in the form of a research grant, and a studentship, respectively. Supporting Information Available: Table 5 containing additional data. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Fan, X.; Dickey, E. C.; Eklund, P. C.; Williams, K. A.; Grigorian, L.; Buczko, R.; Pantelides, S. T.; Pennycook, S. J. Phys. ReV. Lett. 2000, 84, 4621. (2) Smith, B. W.; Monthioux, M.; Luzzi, D. E. Nature (London) 1998, 396, 323. Smith, B. W.; Luzzi, D. E.; Achiba, Y. Chem. Phys. Lett. 2001, 331, 137. (3) Suenaga, K.; Tence, M.; Mory, C.; Colliex, C.; Kato, H.; Okazaki, T.; Shinohara, H.; Hirahara, K.; Bandow, S.; Iijima, S. Science 2000, 290, 2280. (4) Takenobu, T.; Takano, T.; Shiraishi, M.; Murakami, Y.; Ata, M.; Kataura, H.; Achiba, Y.; Iwasa, Y. Nat. Mater. 2003, 2, 683. (5) Sloan, J.; Kirkland, A. I.; Hutchinson, J. L.; Green, M. L. H. Chem. Commun. 2002, 13, 1319. (6) Meyer, R.; Sloan, J.; Dunin-Borkowski, R. E.; Kirkland, A. I.; Novotny, M. C.; Bailey, S. R.; Hutchinson, J. L.; Green, M. L. H. Science 2000, 289, 1324. (7) Brown, G.; Bailey, G. S. R.; Novotny, M.; Carter, R.; Flahaut, E.; Coleman, K. S.; Hutchison, J. L.; Green, M. L. H.; Sloan, J. Appl. Phys. A 2003, 76, 457. (8) doptimum ) dKI + dC ≈ 1.3 nm, with dC ) 0.34 nm, the van der Waals diameter of C, and dKI ≈ 0.965 nm, the diagonal of the KI crystal, taken along the I- ions, with center-to-center spacing 0.56 nm and ionic radii rI- ≈ 0.2 nm.5 This corresponds to the minimum of the filling-nanotube van der Waals interaction energy. Other possible diameters with a lower bound are obtained in the case when the van der Waals energy is merely zero (as opposed to a minimum); in this case, some repulsion exists between the filling and the nanotube. This allows for a decrease in the vdW separation of about 0.05-0.06 nm,9 i.e., dthreshold ) doptimum - 2 × 0.06 ≈ 1.18 nm. The existence of such a threshold based on repulsive interactions between the filling and the nanotubes walls is suggested also in ref 10. (9) Hodak, M.; Girifalco, L. A. Chem. Phys. Lett. 2001, 350, 405. (10) Wilson, M.; Madden, P. A. J. Am. Chem. Soc. 2001, 123, 2101. (11) According to ref 12, the calculated diameters at which the puckered form of 2 × 2 KI stabilizes preferentially and rests in the minimum of the total energy range from about 1.05 to 1.18 nm, depending on the type of SWCNT. (12) Wilson, M. Chem. Phys. Lett. 2002, 366, 504. (13) Fantini, C.; Jorio, A.; Souza, M.; Strano, M. S.; Dresselhaus, M. S.; Pimenta, M. A. Phys. ReV. Lett. 2004, 93, 147406. (14) Kavan, L.; Kalbac, M.; Zukalova, M.; Dunsch, L. J. Phys. Chem. B 2005, 109, 19613. (15) Lucas, M.; Young, R. J. Phys. ReV. B 2004, 69, 085405. (16) Kwon, Y.-K.; Berber, S.; Tomanek, D. Phys. ReV. Lett. 2004, 92, 015901. (17) Weisman, R. B.; Bachilo, S. M. Nano Lett. 2003, 3, 1235. (18) Kukovecz, A.; Pichler, T.; Pfeiffer, R.; Kramberger, C.; Kuzmany, H. Phys. Chem. Chem. Phys. 2003, 5, 582. (19) Gartstein, Y. N.; Zakhidov, A. A.; Baughman, R. H. Phys. ReV. B 2003, 68, 115415. (20) Sun, G.; Kurti, J.; Kertesz, M.; Baughman, R. H. J. Phys. Chem. B 2003, 107, 6924.

KI Encapsulation in SWCNTs (21) That the RBM modes are not expected to change significantly after encapsulation is supported by the behavior of the (14, 1) nanotube at 2.41 eV, as well as by the unfilled nanotube’s behavior under strong uniaxial stress, such as in ref 34. (22) Raravikar, N. R.; Keblinski, P.; Rao, A. M.; Dresselhaus, M. S.; Schadler, L. S.; Ajayan, P. M. Phys. ReV. B 2002, 66, 235424. (23) Rafailov, P. M.; Stoll, M.; Thomsen, C. J. Phys. Chem. B 2004, 108, 19241. (24) Corio, P.; Santos, A. P.; Santos, P. S.; Temperini, M. L. A.; Brar, V. W.; Pimenta, M. A.; Dresselhaus, M. S. Chem. Phys. Lett. 2004, 383, 475. (25) Fagan, S. B.; Souza Filho, A. G.; Mendes Filho, J.; Corio, P.; Dresselhaus, M. S. Chem. Phys. Lett. 2005, 406, 54. (26) The majority of the experimental studies so far support such an interpretation, with a few exceptions, such as ref 27, that raised the possibility of a non-monotonic relationship. (27) Chen, G.; Furtado, C. A.; Bandow, S.; Iijima, S.; Eklund, P. C. Phys. ReV. B 2005, 71, 045408. (28) Corio, P.; Santos, P. S.; Brar, V. W.; Samsonidze, Ge. G.; Chou, S. G.; Dresselhaus, M. S. Chem. Phys. Lett. 2003, 370, 675. (29) Corio, P.; Jorio, A.; Demir, N.; Dresselhaus, M. S. Chem. Phys. Lett. 2004, 392, 396. (30) Pietronero, L.; Strassler, S. Phys. ReV. Lett. 1981, 47, 593. (31) Chieu, T. C.; Timp, G.; Dresselhaus, M. S.; Endo, M.; Moore, A. W. Phys. ReV. B 1983, 27, 3686. (32) Kamitakahara, W. A.; Zaretsky, J. L.; Eklund, P. C. Synth. Met. 1985, 12, 301. (33) Brown, S. D. M.; Jorio, A.; Dresselhaus, M. S.; Dresselhaus, G. Phys. ReV. B 2001, 64, 073403. (34) Yam, C.; Ma, C.; Wang, X.; Chen, G. Appl. Phys. Lett. 2004, 85, 4484. (35) Dresselhaus, M. S.; Dresselhaus, G.; Saito, R.; Jorio, A. Phys. Rep. 2005, 409, 47. (36) O’Connell, M. J.; Bachilo, S. M.; Huffman, C. B.; Moore, V. C.; Strano, M. S.; Haroz, E. H.; Rialon, K. L.; Boul, P. J.; Noon, W. H.; Kittrell, C.; Ma, J.; Hauge, R. H.; Weisman, R. B.; Smalley, R. E. Science 2002, 297, 593.

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