Fahlman B.D. Materials Chemistry

Подождите немного. Документ загружается.

the range 1–30 nm, based on its composition (see below). Quantum dots currently

ﬁnd applications as sensors, lasers, LEDs, nanophotonic devices,

[74]

and ﬂuorescent

biomarkers. In fact, new high-density disks (e.g., Blu-ray high-deﬁnition DVD

format) may only be read via blue lasers, which are fabricated from quantum dots.

Long-term applications for these structures will likely include optical computing

and high-efﬁciency solar cells.

As you may recall from Chapter 4, when an electron is promoted from the valence

to conduction bands, an electron–hole pair known as an exciton is created in the bulk

lattice. The physical separation between the electron and hole is referred to as the

exciton Bohr radius (r

) that varies depending on the semiconductor composition.

In a bulk semiconductor crystal, r

is signiﬁcantly smaller than the overall size of the

crystal; hence, the exciton is free to migrate throughout the lattice. However, in a

quantum dot, r

is of the same order of magnitude as the diameter (D) of the

nanocrystal, giving rise to quantum conﬁnement of the exciton. Empirically, this

translates to the strongest exciton conﬁnement when D  2r

Analogous to the “par ticle-in-a-box” model from introductory physical chemis-

try, exciton quantum conﬁnement results in discrete energy levels rather than the

continuous bands of a bulk semiconductor crystal (Figure 6.14). Since the gap

between adjacent ener gy levels is inﬁnitesimally small for a bulk semiconductor,

the bandgap is considered as a ﬁxed value. In contrast, since the dimensions of a

quantum dot are extremely small, the addition/subtraction of a single atom will

signiﬁcantly change the nanocrystal dimensions and bandgap. Table 6.5 lists the r

values for common semiconductor crystals whose bandgap may be easily ﬁne-tuned

by simply changing the diameter of the quantum dot, as long as the dimensions are

smaller than r

In the early 1980s, Efros described the size-dependent electronic properties of

quantum dots, ﬁrst delineating that the bandgap, E

, will increase from the bulk

1E+21

9E+20

8E+20

7E+20

6E+20

5E+20

4E+20

3E+20

2E+20

1E+20

0 1020304050

Energy (meV)

Density of states

60 70 80 90 100 110

120

Quantum Well (2D)

Quantum Wire (1D)

Quantum Dot (0D)

Bulk (3D)

Figure 6.14. Density of states (DOS) for electrons in bulk semiconductors (3-D, blue), quantum wells

(2-D, red), quantum wires (1-D, green), and quantum dots (0-D, black).

478 6 Nanomaterials

value based on a 1/R

conﬁnement energy term (Eq. 2). According to quantum

conﬁnement theory, electrons in the conduction band and holes in the valence band

are spatially conﬁned by the potential barrier of the surface. Due to conﬁnement of

both electrons and holes, the lowest energy optical transition from the valence to

conduction band will increase in energy, effectively increasing the bandgap.

¼ E

2mR

;ð2Þ

where E

is the bandgap of the bulk semiconductor; h, Planck’s constant; R, the

radius of the quantum dot; and m is the reduced mass of the exciton given by m

+ m

). Here m

and m

are masses of the electron and hole, respectively.

This model was expanded by Brus and coworkers to include Coulombic interac-

tion of excitons and the correlation energy (Eq. 3).

¼ E

2mR



1:786e

þ 0:284E

;ð3Þ

where E

is the Rydberg (spatial correlation) energy of bulk semiconductor:

¼ 13:56



;

where e

is the permittivity of free space; e, the dielectric constant of the bulk

semiconductor; and m

is the mass of the electron.

Hence, the absorption energy of quantum dots will shift to higher frequenc y with

decreasing radius of the dots, with a dependence of 1/R

. For exampl e, CdSe QDs

with a diameter of 1.2–1.5 nm have a bandgap of 3.0 eV; in contrast, 3.0–3.5 nm

CdSe QDs have a bandgap of 2.3 eV, which is closer to its bulk value (1.8 eV). This

is readily determined from the observed colors of quantum dots with varying radii,

shifting from blue to red with increasing size (Fig ure 6.15).

[75]

For anyone who has admired the bright red colors of stained glass windows, it

may be surprising to note that this too is a nanoparticle phenomenon. In fact, the reds

and yellows observed in antiquated stained glass as far back as the early seventeenth

Table 6.5. Calculated Exciton Bohr Radii for Various Semiconductors

Material r

)

Si 55

CdS 28

CdSe 61

CdTe 100

ZnO 18

ZnS 50

PbS 204

PbSe 460

InAs 340

InSb 540

6.3. Nanoscale Building Blocks and Applications 479

century are caused by the presence of gold and silver nanoparticles, respectively.

However, the use of gold nanoparticles may date back even further, as reports of

“soluble” gold extractions date back to the ﬁfth century B.C. in Egypt and China.

[76]

However, for metallic nanoclusters/nanoparticles with diameters ca. > 2 nm, the

observed color has a different origin than semiconductor quantum dots, since there is

no bandgap between valence and conduction bands, and the energy states form a

continuum analogous to bulk metal.

For these metallic nanostructures, another phenomenon known as surface plas-

mon resonance (often denoted as localized surface plasmon resonance, LSPR) is

active for these structures, involving speciﬁc scattering interactions between the

impinging light and the nanostructures. In particular, the oscillating electric ﬁeld of

the incoming light causes the coherent oscillation of the conduction electrons,

resulting in a concomitant oscillation of the electron cloud surrounding the metal

nuclei (Figure 6.16).

[77]

The leading theory that describes the scattering behavior of small spherical

particles with light dates back to the work of Mie in the early 1900s (Eq. 4):

[78]

EðlÞ¼

24pN

3=2

l ln(10)

ðlÞ

ðe

ðlÞþ2e

þ e

ðlÞ

ð4Þ

where E(l) is the extinction (sum of absorption and scattering); N

, the density of

the nanostructures; r, the radius of the nanostructure; e

, the dielectric constant

Figure 6.15. The size-dependency on the optical properties of CdSe nanocrystals. With decreasing size,

the ﬂuorescence peak is shifted to shorter wavelengths. Also shown is the reduced photobleaching

exhibited by CdSe nanocrystals – (top-bottom photos): suspension of nanocrystals in solution, before

and after irradiation with UV light, respectively. Reproduced with permission from Pellegrino, T.; Kudera,

480 6 Nanomaterials

of the metallic nanostructure; l, the wavelength of absorbing radiation; and e

, e

are

the imaginary and real (respectively) portions of the l-dependent dielectric function

of the nanostructure.

This theory is still relevant today, alongside Raleigh scattering theory, to describe

the colors of our sky as well as the appearance of suspensions such as milk and latex

paints. It should be noted that for non-spherical nanostructures, the denominator of

the bracketed term above is replaced with:

ðlÞþwe

ðÞ

;

where w may range from a value of 2 (perfect sphere) to 17 (e.g., for a 5:1 aspect

ratio nanostructure) and beyond.

[79]

Based on Eq. 4, the factors that govern the oscillation frequency (and the observed

color) are: electron density (size/shape of the nanostructures, Figures 6.17 and 6.18),

the effective nuclear charge of the nuclei, and the size/shape of the charge distribu-

tion (polarization effects, strongly affected by the dielectric constant of the metal).

As you might expect, further effects toward the resonance frequency/intensity are

E-field

Metal

sphere

−

cloud

Figure 6.16. Schematic of LSPR for a nanosphere, showing the induced oscillation of the electron cloud

relative to the nuclei. Reproduced with permission from Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz,

Figure 6.17. The inﬂuence of size and shape on the light-scattering, and resultant colors, of silver

6.3. Nanoscale Building Blocks and Applications 481

482 6 Nanomaterials

observed from the nanostru ctural composition

[80]

and its surrounding solvent.

As such, noble metal nanoparticles have been used as tunable platforms

for biological sensing (Figure 6.19). It should be noted that LSPR contributes

most strongly to the observed colors of the coinage metals (Cu, Au, Ag). Many

other metals such as Pb, In, Hg, Sn, etc. also exhibit this phenomenon, but appear

colorless since either the plasmon resonance frequency lies in the UV region, or the

nanoparticles are readily oxidized under ambient conditions.

For the smallest of metal lic nanoclusters with dimensions ca. <2 nm, the surface

plasmon absorption disappears. Since so few atoms comprise discrete nanoclusters

of this size, the spacings between adjacent energy levels (referred to as the Kubo

gap, d, Eq. 5) become comparable to the thermal energy, kT

[81]

– especially at lower

temperatures and smaller nanocluster diameters. This results in a shift in conductive

properties of the nanocluster, from metallic to insulating, with decreasing size

(Figure 6.20).

[82]

For instance, photoelectron measurements of Hg

clusters have

shown that a signiﬁcant HOMO-LUMO gap of ca. 3.5 eV is present for Hg

clusters,

relative to only ca. 0.2 eV for Hg

250

; it is estimated that gap closure occurs for Hg

clusters with n  400 atoms.

[83]

Figure 6.18. Top: calculated UV-visible extinction (black), absorption (red), and scattering spectra (blue)

of Ag nanocrystals, illustrating the effect of shape on spectral characteristics: (a) sphere, (b) cube,

images of individual Ag nanobars and the corresponding normalized LSPR spectra. The longitudinal

plasmon peak red-shifts with increasing aspect ratio for the nanobars; (b) calculated LSPR (scattering)

spectra for Ag nanobars 100, 150, and 200 nm in length, keeping width ¼ 55 nm and height ¼ 50 nm;

longitudinal plasmon peak location versus aspect ratio. The peaks of both nanobars and nanorice red-shift

with increasing length, but on average the peaks of nanobars are 80 nm red-shifted from nanorice.

1200

800

400

Intensity

Wavelen

th (nm)

450 500 550 600

Figure 6.19. Biological sensing using Ag nanoparticles. Shown is (a) a dark-ﬁeld optical image of

surface-functionalized (biotinylated) Ag nanoparticles, and (b) the shift in wavelength before (1) and

after (2) exposure to 10 nM streptavidin. Reproduced with permission from Haes, A. J.; Stuart, D. A.;

6.3. Nanoscale Building Blocks and Applications 483

In band theory, the breadth of a band is directly related to the strength of interactions

among nearest neighbors. For atoms/molecules (Figure 6.20, far right) this interaction is

weak, which corresponds to a narrow band. However, as additional atoms are added to

the solid, stronger interactions will ensue, resulting in a greater density of states near the

Fermi level – additional states near the band edges develop last. Hence, the insulating

properties of very small nanoclusters are due to the small number of neighboring atoms,

which are held together primarily by nonmetallic interactions (e.g., van der Waal

forces).

[84]

As nanocluster size increases, the atomic s/p and d orbitals from a larger

number of constituent atoms will broaden into bands, forming an energy continuum.

Quantum conﬁnement effects also cause a change in the optical properties of

metallic nanoclusters. For instance, since the spacing between interband energy

levels increases with decreasing nanocluster size, the 5d

! 6(sp)

band absorp-

tion for gold (Figure 6.21) will become increas ingly blue-shifted with decreasing

dimensions (i.e., the observed color will be red-shifted).

[85]

dðe

Þ/

;ð5Þ

where d is the Kubo gap, energy spacing between adjacent E levels; N

, the number

of atoms in the nanocluster; z, their valence; and e

, the energy of the Fermi level

(e.g., 8 eV for Au).

Metal

Metal cluster /nanoparticle Atoms & Molecules

Size- Induced Metal-Insulator Transition

Insulator

Diameter : D >>10

Nuclearity : N >>10

Kubo Gap : d <<10

−6

D ~ 10

−10

N ~ 10

−10

d ~10

−6

−1K

D ~ 10

−10Å

N ~ 10

−10

d ~1−10

D < 10Å

N < 10

d > 10

Bulk Metal

Energy

Density-of-States

Figure 6.20. Schematic of the density of states exhibited by bulk metal relative to increasingly smaller

nanoclusters. The approximate diameter, nuclearity, and Kubo gap for each size regime are indicated.

As the nanocluster size decreases, the energy continuum of the bulk metal is transformed into discrete

energy levels, especially at band edges. Reproduced with permission from Rao, C. N. R.; Kulkarni, G. U.;

484 6 Nanomaterials

As you might expect, magnetism is also affected by decreasing particle size.

In particular , bulk ferromagn e tic mater ia ls such as a-Fe, Fe

, a-Fe

,and

Ni will become paramagnetic and display a zero magnetization once their dia-

meters reach critical sizes of 5, 16, 20, and 15 nm, respectively.

[86]

Whereas bulk

ferri-/ferromagnetic materials undergo a transition to the paramagnetic state

above their Curie temperature, such superparamagnetic nanomaterials undergo

this transition at a temperature below its Curie temperature. Though super-

paramagnetism poses a current limitation to increasing t he bit ar eal dens ity of

magnetic hard drives, heat-assisted magnetic recording (HAMR) devices are being

developed t o continue further progress in this ﬁeld.

[87]

Some other applications

that may exploit the tunable magnetism of nanostructures include tunably-viscous

liquids (ferroﬂuids

[88]

) and biomedicine (e.g., drug-delivery, diagnostics, magne-

tofection, et c.).

The ﬁrst 0-D nanoarchitecture: the fullerenes

Without question, our modern “nanotechnology revolution” was catalyzed by the

mid-1980s discovery of carbon nanoclusters known as fullerenes (e.g., C

etc.).

[89]

The 1996 Nobel Prize in Chemistry was awarded to Richard Smalley,

Robert Curl, and Sir Harold Kroto for this discovery, which focused the worldwide

spotlight on unique nanoscale materials and their possible applications. To date, the

Figure 6.21. Schematic illustration of the band structure (orbital energy vs density of states) of fcc-Au,

indicating the approximately correct bulk bandwidths and displacements, and density of states (solid

curve). The discrete levels are indicated by solid (broken) lines below (above) the Fermi level eF, with a

(mean) level spacing appropriate to a clusters of 50 Au atoms. The vertical arrows designate optical

transitions in the 1.7–2.5 eV range, originating at the top of the 5d band (ed) and terminating at each of the

ﬁrst few unoccupied levels. Adapted from the calculations and interpretation of ref 43. Schaaff, T. G.;

Saﬁgullin, M. N.; Khoury, J. T.; Vezmar, I.; Whetten, R. L.; Cullen, W. G.; First, P. N.; Gutierrez-Wing,

C.; Ascensio, J.; Jose-Yacaman, M. J. J. Phys. Chem. B 1997, 101, 7885.

6.3. Nanoscale Building Blocks and Applications 485

most common applications for fullerenes include MRI contrast agents (exploiting

its container properties), drug-delivery agents (through surface functionalization),

fulleride-based superconductors, and light-activated antimicrobial agents

[90]

(Figure 6.22). It should be noted that the term fullerene does not simply mean

the C

carbon allotrope termed Buckminsterfullerene (or “Buckyballs”),

[91]

but

rather the entire class of closed-cage carbon clusters that are comprised of exactly

12 pentagons, and a varying number of hexago ns (e.g., 20 hexagons for C

A recent application for fullerenes that would rank high in the “cool” category is

the development of surface-rolling molecules that are aptly termed nanocars/nano-

trucks.

[95]

Rather than stabilized nanoparticles, these nanovehicles are organic

molecules that contain fullerenes as wheels (Figure 6.23). The placement of the

nanocars onto a gold surface is as easy as spin-casting from a toluene suspension.

Due to strong adhesion forces between fullerenes and metal surfaces, the nanocars

spontaneously deposit with all four “nanowheels” on the substrate. The axles

consist of triple-bonded alkyne groups that allow rotation of the fullerene

wheels, transporting the nanocar across a gold surface in response to changes in

temperature.

[96]

Though only pivoting and translational motion are currently

AcO O

OAc

OCOPh

Figure 6.22. Examples of fullerene applications. Shown are (a) Gd

—[OH]

(x  27) and Gd

—[C(COOH)

]

used as MRI contrast agents,

[92]

(b) the ionic unit cell for the superconductive

alkali metal fulleride Cs

[93]

and (c) the conjugate structure of C

covalently bound to the lung

cancer drug Paclitaxel.

[94]

486 6 Nanomaterials

possible, this work sets an important step toward the realization of nanomachines for

an endless number of possible applications.

As with other major discoveries such as Teﬂon and nylon, the synthesis of C

was serendipitous (Figure 6.24).

[97]

In fact, the experiments that led to the discov-

ery of fullerenes were aimed at simulating the environment of a carbon-rich red

giant star. As such, the discovery of C

has been dubbed “the celestial sphere that

fell to earth.”

[98]

The experimental system featured the laser vaporization of a

graphite target into a heli um carrier gas w herein the atoms nucleated into c lusters.

The gas was then cooled using supersonic expansion, and injected into a time-of-

ﬂight mass spectrometer for analysis (Figure 6.25 a). Reactive gases such as

hydrogen or nitrogen could also be added to the carrier gas, for the synthesis of

other reaction products. It should be noted that this technique is now used to

generate nanoclusters of a wide variety of metals, s emic onduct ors (e.g., Si), and

insulators (e.g., Al

) depending on the nature of the target and co-reactant gases

employed.

[99]

The ﬁrst large-scale synthesis of fullerenes was discovered in 1989 by Huffm an

and Kratschmer; this provided a macroscopic quantity of C

in order to conﬁrm the

proposed icosohedral structure. Their technique consisted of the arc-evaporation of

graphite electrodes via resistive heating within an atmosphere of ca. 100 atm. helium

(Figure 6.25b).

[101]

Other more rece nt techniques such as high- temperature combus-

tion of benzene and a benchtop graphite arc process (Fig ure 6.26) were developed in

order to reduce the cost and complexity associa ted with fullerene synthesis. Not only

will such improvements allow for more widespread fabrication of fullerenes for

research/applications (i.e., synthesis no longer limited to groups with supersonic

Figure 6.23. Images and dimensions of a nanocar on a Au(111) surface. The bright features are the

Chemical Society.

6.3. Nanoscale Building Blocks and Applications 487