Gogotsi Y. (Ed.) Nanotubes and Nanofibers

Подождите немного. Документ загружается.

fibers, cannot possibly be 1D. It is interesting to note that for both fiber series, one ends up with

about the same

(300 K) after annealing, whereas this value is approached from opposite directions

in the two different processes.

The qualitatively different

(T) behaviors in the two sets of fibers can be attributed to an MI

transition as a function of doping level [77]. On the metallic side for heavily doped tubes,

tends

22 Nanotubes and Nanofibers

1000

800

600

400

200

0 20 40 60 80

Stretch (%)

 (Ω cm)

FIGURE 1.18 Four-probe electrical resistivity at room temperature vs. stretch ratio for PVA composite

nanotube fibers. The experiments have been conducted on two series of samples (black squares, open circles).

Accurate cross-sectional areas were obtained from SEM image analysis. The resistivity decreases with stretch

ratio by a factor between three and four for the two sets of data. The absolute value is intermediate between

all-SWNT fibers and polymer composites. The dashed line is a guide to the eye. (From Badaire, S. et al.,

J. Appl. Phys. 96, 7509 (2004), with permission.)

–1

–3

1 10 100

Temperature (K)

Composite, 53% stretch

Annealed, 76% stretch

 (Ω cm)

FIGURE 1.19 Resistivity vs. temperature for composite (53% stretch) and annealed (76% stretch) nanotube

fibers (note log–log scale). Note that

(T) for the composite fiber is more strongly divergent as T → 0 as com-

pared to the annealed one. (From Badaire, S. et al., J. Appl. Phys. 96, 7509 (2004), with permission.)

to a finite value as T approaches zero, and the effective band gap, ⫺dln

/dT, vanishes as T

approaches zero; examples of this behavior are shown in

Figure 1.20. On the insulating side for

PVA-rich gel fibers or annealed oleum fibers,

diverges as T approaches zero, and the exponential

T dependence can be ascribed to strong localization and either 3D Mott or Coulomb gap variable-

range hopping [77]. The MI transition is revealed by systematic measurements of resistivity and

transverse magnetoresistance (MR) in the ranges 1.9 to 300 K and 0 to 9 T, as a function of p-type

redox doping. The observed changes in transport properties are explained by the effect of doping

on semiconducting SWNTs and tube–tube coupling.

How does the presence of endohedral C

affect the electronic properties of peapods? Despite

predictions based on work function differences between peas and pod, there is no evidence for

charge transfer redox doping by the endofullerenes.

Figure 1.21 shows

(T) data for a peapod sam-

ple and an unfilled control [70,71]. Near 300 K the resistivities are the same within experimental

error, and the peapod temperature dependence is steeper suggesting stronger disorder effects com-

pared with the empty tubes.

More fundamental than electron transport properties is the spectrum of allowed electron ener-

gies or density of states N(E). This can be measured on individual tubes using scanning tunneling

spectroscopy, which yields much important information. For bulk materials, one measures the

related quantities such as electron energy loss function, using electron energy loss spectroscopy

(EELS), absorption spectroscopy using thin films, or reflection spectroscopy if flat and reasonably

smooth surfaces are available. We close this section by giving a few examples.

Figure 1.22 shows the loss function of a 100-nm-thick film of ~60% SWNT deposited on a

TEM grid [78]. Both energy and momentum of the transmitted electrons can be determined, so the

observed transitions can be separated into dispersing and nondispersing, which correspond to “col-

lective” (plasmon) and “localized” interband processes, respectively. The inset shows the loss func-

tion over a wide energy range, in which the plasmons representing collective excitations of the

and

⫹

electrons can be clearly seen at 5.2 and 21.5 eV, respectively, in agreement with the

theory. Features in the loss function at 0.85, 1.45, 2.0, and 2.55 eV are independent of q and are

therefore assigned to interband transitions. Their nature is revealed by a Kramers–Kronig transform

Carbon Nanotubes: Structure and Properties 23

0.10

0.08

0.06

0.04

0.02

0.00

0 1 2 3 4 5 6 7 8

(11) PLV + Br

(12) PLV + HNO

T (K)

(13) PLV + H

= –d In /d In

FIGURE 1.20 Reduced activation energy W vs. T for the most conductive p-doped SWNT samples.

Extrapolating from the lowest data point 1.3 K to T ⫽ 0 shows that W, and any possible energy gap, vanishes,

signaling a true metallic state. (From Vavro, J. et al., Phys. Rev. B 71, 155410 (2005), with permission.)

to obtain real and imaginary parts of the dielectric function,

being directly proportional to the

optical absorption coefficient. The results are shown in

Figure 1.23, which reveals three interband

transitions at 0.65, 1.2, and 1.8 eV. These are the energy separations of the 1D van Hove singulari-

ties, slightly broadened by diameter dispersivity in bulk samples. We now understand the sequence

of transitions as E

, E

, and E

where n is the band index and Sand M denote semiconducting and

metallic tubes, respectively.

EELS also gives important information about the effects of redox doping on electronic proper-

ties [79].

Figure 1.24 shows how the loss function evolves with potassium concentration. The

upshift in the

plasmon near 6.5 eV is due to the gradual addition of an extra electron per n car-

bons to the previously empty

* conduction band. The extra delocalized electron is charge-com-

pensated by K

oxidizing to K

⫹

during intercalation. Figure 1.24(b) shows this relation explicitly,

with K/C determined from core-level spectroscopy. The disappearance of fine structure below 2 eV

signals the upshift in E

, which quenches the van Hove interband transitions since the final states

in the neutral material (Figure 1.23) are now occupied by doping.

Optical absorption and reflectance are complementary to EELS. The energy resolution is

higher, polarization and selection rule information is accessible, and the spectra extend to lower

energies which would otherwise be obscured in EELS by the tail of the ~100 kV incident electron

beam. The lower energy cutoff permits accurate measurements of the so-called Drude plasmon, a

collective excitation of the delocalized electrons, and how it evolves with doping.

Figure 1.25 shows the reflectance of an unoriented undoped film [80]. The solid curve is a model

fit, including a free carrier Drude term and several interband Lorentz oscillators. These results con-

firm that undoped material consists of a mixture of conducting and semiconducting nanotubes, typ-

ical for bulk samples. The interband transition energies are consistent with electronic structure

calculations for 1.4-nm-diameter tubes, and with EELS described above. The theory predicts that

because these transitions involve 1D van Hove singularities, they should be completely polarized

along the nanotube axis, i.e., they should vanish when the incident and transmitted beams are cross

polarized. This was proved in a clever experiment on magnetically aligned SWNT suspensions with

24 Nanotubes and Nanofibers

1 10 100

T (K)

 (mΩ cm)



/

10 100

Empty SWNTs

@SWNTs

FIGURE 1.21 Four-point resistivity vs. T for C

@SWNT (filled circles) and empty nanotubes (open

squares). The ratio empty/filled is shown in the inset. At ambient temperature the resistivities are indistin-

guishable. (From Vavro, J. et al., Appl. Phys. Lett. 80, 1450 (2002), with permission.)

the alignment locked in place by gelation [81]. Polarized Raman scattering was used to quantify the

degree of alignment. Combined with absorbance data from the partly aligned sample, the intrinsic

polarized absorbance is recovered. The fitted Drude plasma frequency

is 0.29 eV, characteristic

of a small concentration of conduction electrons or holes.

Chemical doping is revealed in absorption and reflectance spectroscopy by several mechanisms.

The higher concentration of free carriers shifts the Drude edge to higher energy. The Drude scatter-

ing time may be affected by doping-induced disorder or dimensional crossover. Low-energy inter-

band transitions may be quenched by the E

shift through valence or conduction band singularities.

Examples of these phenomena are evident in the reflectance spectra shown in

Figure 1.26 for potas-

sium-doped purified SWNT buckypaper [82]. These experiments were performed in sealed quartz

tubes to avoid air exposure; consequently, the results differ significantly from those quoted in an ear-

lier publication in which such precautions were not taken [83]. Data recorded in the range 0.07 to

4 eV show clearly that with increasing K concentration, the 1D van Hove transitions disappear and

the Drude edge shifts progressively to higher energies into the visible spectrum [84]. Colors from

purple to golden-brown, reminiscent of alkali graphite compounds, are observed as the K concen-

tration increases to saturation. The Drude edge blue-shifts strongly, signaling a large increase in con-

duction electron concentration after doping. Now the fitted value of

is 1.85 eV. In the

free-electron model for metals, the DC conductivity is proportional to

. This implies a ~40×

Carbon Nanotubes: Structure and Properties 25

Normalized intensity

0 10 20 30 40

0 1 2 3 4 5 6 7 8 9

Energy (eV)

q (Å

–1

)

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.5

0.6

FIGURE 1.22 The loss function of purified SWNT from EELS in transmission for the different q values is

shown. The contributions from the elastic peak have been subtracted. The inset contains the loss function over

an extended energy range, showing the

plasmon and the

⫹

plasmon at around 5 and 22 eV, respectively.

(From Pichler, T. et al., Phys. Rev. Lett. 80, 4729 (1998), with permission.)

enhancement in

by saturation doping, in excellent agreement with direct measurements.

Reference [83] reports a much smaller enhancement, underscoring the importance of avoiding air

exposure. Similar experiments with electron acceptor doping show a maximum upshift to only

1.2 eV. The weaker effect on

with acceptors is again familiar from graphite intercalation com-

pounds, in which the fraction of a free hole per intercalated molecule is considerably less than the

fraction of a free electron per alkali ion.

A key parameter in characterizing doped bulk SWNT samples is the position of the Fermi

energy, above or below the neutrality point for donors and acceptors, respectively. This is straight-

forward in electrochemical experiments, in which temperatures are limited to near ambient and the

sample is not optically accessible at all wavelengths. An alternative is provided by the phonon drag,

or electron–phonon scattering contribution to the thermopower. The basic idea is quite simple [85],

and is shown schematically in

Figure 1.27(a). The Fermi surface of a 1D metal consists of two points

separated in k by a wave vector of amplitude |Q|. Momentum-conserving (inelastic) electron–

phonon scattering thus requires participation of acoustic phonons with wave vector Q, which are

absorbed or emitted as electrons scatter from the left- to right-moving branch of E(k). Thus, the tem-

perature dependence will reflect the temperature dependence of the heat capacity, and phonon drag

is quenched below a characteristic temperature T

given approximately by 0.2

(cf. Figure

1.27(a)). |Q| is set by the chemical potential

, which in turn is controlled by the doping level; h and

are the Planck and Boltzmann constants, respectively. Operationally (Figure 1.27(b)), one records

thermopower vs. temperature, locates T

from the peak in the derivative, and backs out E

from the

26 Nanotubes and Nanofibers

3210





(Ω cm)

–1

/10

0.0

0.3

0.6

201510

Energy (eV)

–2

FIGURE 1.23 Real and imaginary parts of the dielectric function (upper panels) and the real part of the opti-

cal conductivity for SWNT (solid curves), C

(dot–dash curves) and graphite (dotted curves). (From Pichler,

T. et al., Phys. Rev. Lett. 80, 4729 (1998), with permission.)

Carbon Nanotubes: Structure and Properties 27

Relative intensity

q = 0.1 Å

–1

1 2 3 4 5 6 7 8 9

Energy loss (eV) K/C

6.5

7.2

Pristine

2.0

1.5

1.0

0.5

0.0

0.00 0.05 0.10 0.15

Square of drude plasmon position (eV

)

(a) (b)

FIGURE 1.24 (a) The loss function of pristine and potassium-intercalated SWNT; the potassium concentra-

tion increases from bottom to top. The dashed line indicates the shift of the position of the charge carrier plas-

mons with increasing concentration. (b) The quantitative relation between the square of the energy position of

the charge carrier plasmon and the relative potassium concentration. (From Liu, X. et al., Phys. Rev. B 67,

125403 (2003), with permission.)

SWNT

Obad

FiI

0.1

0 5000 10000 15000 20000 25000

Frequency (cm

–1

)

Reflectance

Photon energy (eV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

FIGURE 1.25 Reflectance of an unaligned SWNT mat measured from 25 to 25,000 cm

⫺1

(lower scale), cor-

responding to the energy interval 0.003–3 eV (upper scale). R approaches 1 at E ⫽ 0, characteristic of a metal.

Four interband transitions involving 1D van Hove singularities are identified by the downward arrows. (From

Hwang, J. et al., Phys. Rev. B 62, R13310 (2000), with permission.)

relevant dispersion relations. In the example shown, we see the sharp contrast between undoped and

sulfuric acid-doped data from which a Fermi level depression of 0.5 eV is obtained.

The phonon drag method for locating E

suffers one major drawback — it relies on a model for

the energy band dispersion E(k). The original one-electron tight-binding models have been

extremely useful [86], while the importance of higher order effects is becoming evident [87]. For

studies of the metallic state of doped nanotube materials, it would be helpful to have a characteri-

zation technique which directly measures the free carrier concentration (Hall effect), or at least the

density of states at the Fermi energy N(E

). The Pauli paramagnetism of conduction electrons pro-

vides one option. This is difficult to observe directly in magnetization measurements due to strong

diamagnetic corrections, which are not well quantified. This limitation is overcome by conduction

electron spin resonance (CESR), which in essence is the Zeeman effect of delocalized electrons.

Evidence for Pauli spins in raw SWNT soot was reported 10 years ago [88]. This was controversial

because (1) it was believed that the random orientation combined with anisotropic metallic proper-

ties would broaden the CESR beyond recognition, and (2) assuming stochastic growth such that

only approximately one third of the tubes is metallic, and given the theoretical result that N(E

) per

mole is only approximately one fourth that of 3D graphite, these few intrinsic metallic spins might

be undetectable. The original interpretation was supported by subsequent measurements of the tem-

perature dependence of integrated CESR linewidth [89]. While the more typical paramagnetic res-

onance associated with localized spins obeys a Curie law temperature dependence, susceptibility

χ~1/T, the nanotube χ was independent of T in the range 70 to 300 K. The same sample exhibited

the aforementioned shallow minimum in resistivity vs. T at about 200 K, so the T independence of

Pauli

ruled out an MI transition in the undoped material.

CESR was extended to alkali-doped buckypaper using in situ electrochemical doping to follow

the resonance vs. K concentration [90].

Figure 1.28(a) shows the evolution of the full profile, which

consists of a narrow Pauli contribution, magnified in Figure 1.28(b), superposed on a broad anti-

ferromagnetic resonance (AFMR) associated with residual transition metal catalyst. The Pauli

28 Nanotubes and Nanofibers

0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

Reflectivity

Increasing

Rb concentration

E (eV)

Rubidium-doped SWNT in situ

FIGURE 1.26 Reflectance vs. photon energy for four SWNT buckypaper samples with increasing carrier

concentration from alkali doping. Leftmost curve is for undoped SWNT. Doping causes a strong blueshift of

the free carrier Drude edge, and quenches the interband transitions as E

increases through the first two-con-

duction band van Hove singularities. (From Zhou, W. et al., Phys. Rev. B 71, 205423 (2005), with permission.)

CESR grows in intensity with increasing K concentration, while the position and width are constant.

The AFMR intensity diminishes as the sample becomes more conducting and the microwave skin

depth decreases.

Figure 1.28(b) shows that χ

Pauli

, proportional to the double integral of the CESR

line, increases monotonically with K/C. Now that an absolute scale is established, the absence of

CESR in this undoped material is surprising since there is ample sensitivity.

It also calls into question the origin of the T-independent signal observed previously in unpuri-

fied soot [89].

Figure 1.29 shows that χ

Pauli

is independent of T for two saturation-doped samples,

from 30 to 290 K. This proves beyond doubt that alkali-doped SWNTs are true metals. The absolute

value 5 × 10

⫺8

emu/g translates to N(E

) ⫽ 0.015 states/eV per carbon per spin, approximately five

times smaller than a theoretical estimate [91]. The anomalously small value in doped material, and

the absence of a true ESR signal in clean undoped material, remain to be resolved.

The independence of the CESR linewidth on temperature is unusual. The inverse of the width

is proportional to the spin relaxation rate, which is usually dominated by spin–orbit interaction with

Carbon Nanotubes: Structure and Properties 29

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

2Kg T/h

0 50 100 150 200 250 300

T (K)

(µV/K)

(

0 100 200 300

0.1

0.3

(a)

(b)

(a)

(b)



Q Q

∆S/∆T

T (K)

FIGURE 1.27 Phonon drag in SWNT. Top: calculated phonon heat capacity vs. T for a p-type doped nan-

otubes with chemical potential

applicable to semiconducting or metallic tubes is shown in the inset. The cut-

off in occupied phonon energies leads to a weak threshold in thermopower S. Bottom: S (T) and its derivative

for SWNT fibers extruded from sulfuric acid (b) and after annealing to remove the acid and return

toward

zero. The peak in the derivative (b) is a measure of the doping-induced downshift in E

. (From Vavro, J. et al.,

Phys. Rev. Lett. 90, 065503 (2003), with permission.)

the dopants. The only explanation is inhomogeneous doping; small saturation-doped regions are

created at the outset, and their number density increases with global K/C without affecting their

size. This model is supported by accompanying x-ray diffraction data [90].

1.3.4 MAGNETIC AND SUPERCONDUCTING PROPERTIES

We close with a brief mention of these collective phenomena in bulk nanotube materials. An excel-

lent entrée to the magnetism controversy is the recent paper by Cesvedes et al. and references

therein [92]. The authors prove convincingly that there is no bulk magnetism in a clean multiwall

nanotube sample. On the other hand, when placed on a flat ferromagnetic substrate, fringing fields

can be observed by magnetic force microscopy. Thus, the prospect for “contact-induced magnet-

ism” and the application of carbon nanotubes to nanoscale spintronic devices remain open.

Magnetic contrast is observed for carbon nanotubes placed on cobalt or magnetite substrates, but is

absent on silicon, copper, or gold. Spin transfer of about 0.1 µB per contact carbon atom is obtained.

The dialog about nanotube superconductivity began with a very simple argument [93]: if one could

tune the chemical potential to the peak of a van Hove singularity, either chemically or electrostatically,

30 Nanotubes and Nanofibers

2000 4000 6000 3300 3400 3500

Magnetic field (G) Magnetic field (G)

Undoped

0.04

0.029

0.019

0.012

0.004

Undoped

K-K fit of

undoped

(a) (b)

FIGURE 1.28 Conduction electron spin resonance in K-doped SWNT. (a) Ferromagnetic resonance of Ni

catalyst particles in undoped and fully doped SWNT (light and heavy curves, respectively). The narrow CESR

peak is not seen in the undoped sample, and the Ni resonance changes line shape as the sample becomes more

conducting and the skin depth decreases. (b) The CESR line grows continuously with increasing K concentra-

tion, while the spin relaxation rate (linewidth) and g factor (position) remain constant. (From Claye, A. S.

et al., Phys. Rev. B 62, R4845 (2000), with permission.)

0 100 200 300

Grade I

Grade II

Susceptibility

(10

–6

emu/mol C)

Temperature (K)

FIGURE 1.29 The Pauli spin susceptibility vs. T for saturation-doped SWNT is independent of T above 30 K,

characteristic of a metallic state. (From Claye, A. S. et al., Phys. Rev. B 62, R4845 (2000), with permission.)

one should have a high N(E

) value, a prerequisite for BCS superconductivity. The obvious problem in

applying this to bulk material is the diameter dispersivity. Even in single tubes, higher order interactions

will broaden the square-root energy divergences. This has not prevented some from conjecturing T

above 400 K for nanotube superconductors. Super-current flow through an SWNT with low-resistance

contacts was reported in 1999 [94]; analogous to contact-induced magnetism, no claims were made for

bulk nanotube superconductivity. Evidence for a bulk anisotropic Meissner effect below 20 K in aligned

0.4-nm-diameter SWNT was claimed and justified by the argument that small-diameter tubes will be the

stiffest, and thus, the average phonon energy in the BCS equation will be favorable [95]. This dramatic

result has not been reproduced by other researchers since it appeared 4 years ago. As with bulk mag-

netism, it would appear that the jury is still out concerning bulk superconductivity in carbon nanotubes

and other nanostructures.

1.4 SUMMARY AND PROSPECTS

It is difficult to counter the argument that carbon is the most amazing element in the Periodic Table.

In the space of a mere 30 years, we have experienced the discovery of (or renaissance in) three mate-

rial families: graphite intercalation compounds (GICs), fullerene solids, and nanotubes. GICs pro-

vided a wealth of detailed chemical and physical information, while immediate applications were

frustrated by cost, lack of air stability, and most importantly, the lack of new or greatly improved

applications and properties. Though the foundations of physics and chemistry remain unshaken, the

Li ion battery industry has certainly benefited greatly from this store of knowledge. Fullerene solids

fared better, and may yet surprise us in the practical world; while no large volume application has

yet emerged, the elucidation of electronic properties in this highly correlated system has made

invaluable contributions to fundamental science. Nanotubes may offer the best prospects yet; money

is already being made on some small-scale applications. The combination of enhanced properties

encourages the drive to multifunctional materials, and also affords an excellent laboratory for study-

ing 1D phenomena. Extensions to other tubular and nanowire-like materials provide ample scope

for new discoveries.

ACKNOWLEDGMENTS

The nanotube phase of my research life has been enriched by delightful interactions with numerous

students, postdocs, colleagues, and collaborators. This chapter draws heavily from the work of

recently awarded theses of Roland Lee, Zdenek Benes, Agnes Claye, Norbert Nemes, Juraj Vavro,

and Marc Llaguno, and soon to be awarded theses of Wei Zhou and Csaba Guthy. Funding from the

National Science Foundation, the Office of Naval Research, and especially the Department of

Energy are gratefully acknowledged. I am grateful as well to Linda Fischer for a most thorough

proofreading.

REFERENCES

1. S. Iijima, Helical microtubules of graphitic carbon, Nature 354, 56–58 (1991).

2. R. C. Haddon and S.-Y. Chow, Hybridization as a metric for the reaction coordinate of the chemical

reaction: concert in chemical reactions, Pure Appl. Chem. 71, 289–294 (1999).

3. F. Du and K. I. Winey, this volume.

4. N. Wang, G. D. Li and Z. K. Tang, Mono-sized and single-walled 4 Å carbon nanotubes, Chem. Phys.

Lett. 339, 47 (2001).

5. G. Eres, A. A. Puretzky, D. B. Geohegan and H. Cui, In situ control of the catalyst efficiency in chem-

ical vapor deposition of vertically aligned carbon nanotubes on predeposited metal catalyst films,

Appl. Phys. Lett. 84, 1759–1761 (2004).

6. R. Tenne, this volume.

Carbon Nanotubes: Structure and Properties 31