Guozhong Cao. Nanostructures & Nanomaterials: Synthesis, Properties & Applications
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76
Nanostructures and Nanomaterials
mode or conducting channel contributes
Go
=
2e2/h
=
12.9
kW
to the total
conductance. Another important aspect
of
ballistic transport is that no
energy is dissipated in the conduction,162 and there exist no elastic scatter-
ing. The latter requires the absence of impurity and defects. When elastic
scattering occurs, the transmission coefficients, and thus the electrical
conductance will be reduced,162p166 which is then no longer precisely quan-
tized.
167
Ballistic conduction of carbon nanotubes was first demonstrated by
Frank and his co-workers in Fig. 8.29.16* The conductance
of
arc-produced
7
.o
0.5
s
8
0.0
403 405 407
0
1000
2000
c
9u
Time
(s)
Intensity
(arb.
units)
g
0
0.5
l*O:7
I
-200
0
200 400
600
0
10
20
30
40
50
z-posltion
(nm)
Fig. 8.29.
(A)
Conductance of a nanotube contact that is moved at constant speed into and out
of the mercury contact as a function
of
time. The period
of
motion is
2
s
and the displacement
Az=
22.5
wm. The conductance “jumps” to
-1
Go
and then remains constant for -2 pm
of
its dipping depth. The direction
of
motion is then reversed and the contact is broken after
2
pm.
The cycle is repeated to show its reproducibility; cycles
201
through
203
are displayed
as an example.
(B)
Histogram of the conductance data
of
all
250
traces in the sequence. The
plateaus at
1
Go
and at
0
produce peaks in the histogram. The relative areas under the peaks
correspond to the relative plateau lengths. Because the total displacement is
known,
the
plateau lengths can be accurately determined; in this case, the
1
Go
plateau corresponds to a
displacement of 1880nm. Plateau lengths thus determined
are
insensitive
to
random oscilla-
tions
of
the liquid level and hence are more accurate than measurements from individual
traces. (C)
A
trace
of
a nanotube contact with
two
major plateaus, each with a minor pre-step.
This trace is interpreted
as
resulting
from
a nanotube that is bundled with a second one (as in
Fig.
(A),
inset). The second tube comes into contact with the metal -200nm after the first.
Shorter plateaus (from
-
10
to
50
nm
long) with noninteger conductance are often seen and
are interpreted
to
result from the nanotube tips.
A
clear example
of
this effect is
shown
in
(D).
[S.
Frank,
I?
Poncharal, Z.L. Wang, and
W.A.
de Heer,
Science
280,
1744
(1
998).]
Characterization and Properties
of
Nanomaterials
377
multi-wall carbon nanotubes is one unit of the conductance quantum
Go,
and no heat dissipation is observed. Extremely high stable current densities,
J>
lo7
Ncm2 have been attained.
Coulomb
blockade
or Coulomb charging occurs when the contact resist-
ance is larger than the resistance of nanostructures in question and when
the total capacitance
of
the object is
so
small that adding a single electron
requires significant charging energy.
169
Metal or semiconductor nanocrys-
tals of a few nanometers in diameter exhibit quantum effects that give rise
to discrete charging of the metal particles. Such a discrete electronic con-
figuration permits one to pick up the electric charge one electron at a time,
at specific voltage values. This Coulomb blockade behavior, also known
as "Coulombic staircase", has originated the proposal that nanoparticles
with diameters below
2-3
nm may become basic components of single
electron transistors (SETs).170
To
add a single charge to a semiconductor
or metal nanoparticle requires energy, since electrons can no longer be
dissolved into an effectively infinite bulk material. For a nanoparticle sur-
rounded by a dielectric with a dielectric constant of
cr,
the capacitance of
the nanoparticle is dependent on its size as:
C(r)
=
~T~E~E,
(8.29)
where
r
is the radius of the nanoparticle and
c0
is the permittivity of vac-
uum. The energy required to add a single charge to the particle is given by
the charging
en erg^'^','^^:
(8.30)
Tunneling
of
single charges onto metal or semiconductor nanoparticles
can be seen at temperatures of
kBT
<
E,,
in the
I-V
characteristics from
devices containing single nanoparti~les~~~,'~~ or fi-om
STM
measurements
of nanoparticles on conductive surfaces.'75 Such Coulomb staircase is
also observed in individual single-wall carbon nanotube~.'~~ It should be
noted that Eqs.
(8.29)
and
(8.30)
clearly indicate that the charging energy
is independent of materials. Figure
8.30
shows a characteristic
I-V
curve
for such a device with a single gold nanoparticle, where the charging
energy gives rise to a barrier
to
a current flow known as Coulomb block-
ade.177 When a gate electrode is added to the structure, the chemical
potential of the nanoparticle as well as the voltage of current flow can be
modulated. Such a three-terminal device known as a single-electron tran-
sistor has received great attention as an exploratory device ~tructure.'~~J'*
Tunneling conduction
is another charge transport mechanism important
in the nanometer range and has been briefly discussed in Chapter
7.
378
Nanostructures and Nanomaterials
Fig.
8.30.
(A) Au STM tip addressing a single cluster adsorbed on an Au-on-mica sub-
strate (inset) and Coulomb staircase I-V curve at
83
K; potential
is
tip-substrate bias;
equivalent circuit
of
the double tunnel junction gives capacitances
Cupper=
0.59 aF and
C,,,,=
0.48 aF. (B) voltammetry (CV
-,
100
mV/s; DPV
-,
*
are current peaks, 20mV/s,
25
mV pulse, top and bottom are negative and positive scans, respectively)
of
a
0.1
mM
28 kDa cluster solution in 2
:
1
toluene: acetonitrile/0.05 M Hx4NC104 at a 7.9
X
10-3cm2
Pt electrode, 298
K,
Ag wire pseudoreference electrode.
[R.S.
Ingram, M.J. Hostetler,
R.W.
Murray, T.G. Schaaff, J.T. Khoury,
R.L.
Whetten, T.P. Bigioni, D.K. Guthrie, and
P.N. First,
J.
Am.
Chem.
SOC.
119,
9279
(1
997).]
Tunneling involves charge transport through an insulating medium sepa-
rating two conductors that are extremely closely spaced. It is because the
electron wave functions from two conductors overlap inside the insulating
material, when its thickness is extremely thin. Figure
8.3
1
gives the tun-
neling conductivity as a function of
C,,
to
C,,
fatty acid monolayers and
is demonstrated that the electrical conductivity decreases exponentially
with increasing thickness of insulating layer.
*79
Under such conditions,
electrons are able to tunnel through the dielectric material when an elec-
tric field is applied.
It
should be noted that Coulomb charging and tun-
neling conduction, strictly speaking, are not material properties. They are
system properties. More specifically, they are system properties depend-
ent on the characteristic dimension.
Characterization
and
Properties
of
Nanomaterials
379
25
30
35
dlA
4
Fig.
8.31.
The tunneling conductivity
of
a self-assembled monolayer as a function of
molecular length or film thickness, when changing from
CI4
to
C23
fatty acid monolayers,
demonstrating that the electrical conductivity decreases exponentially with increasing
thickness
of
insulating layer.
[H.
Kuhn,
J. Photochem.
10,
11
1
(1979).]
8.4.4.4.
Effect of microstructure
Electrical conductivity may change due to the formation of ordered
microstructure, when the size is reduced to a nanometer scale. For exam-
ple, polymer fibers demonstrated an enhanced electrical conductivity.'80
The enhancement was explained by the ordered arrangement of the poly-
mer chains. Within nanometer fibris, polymers are aligned parallel to the
axis of the fibris, which results in increased contribution of intramolecu-
lar conduction and reduced contribution of intermolecular conduction.
Since intermolecular conduction
is
far smaller than intramolecular con-
duction, ordered arrangement of polymers with polymer chains aligned
parallel to the conduction direction would result in an increased electrical
conduction. Figure
8.32
shows the electrical conductivity of polyhetero-
cyclic fibris as a function of diameter.ls2
A
drastic increase in electrical
conductivity with a decreasing diameter was found at diameters less than
500
nm. Smaller the diameter, the better alignment
of
polymer
is
expected.
A
lower synthesis temperature also favors a better alignment and thus a
higher electrical conductivity.
380
Nanostructures
and
Nanomaterials
0
1
000
2
Fibril Diameter (nm)
Fig.
8.32. The electrical conductivity
of
polyheterocyclic fibris as a function
of
diameter.
[Z.
Cai,
J.
Lei,
W.
Liang,
V.
Menon,
and
C.R. Martin,
Chem.
Muter:
3,960 (1991).]
8.4.5.
Ferroelectrics and dielectrics
Ferroelectric materials are polar compound crystals with reversible spon-
taneous polarization,I8' and are now candidate dielectrics for integration
in the microelectronic systems.
182~183
Ferroelectrics are also pyroelectrics
and piezoelectrics and, thus, can be used in infrared imaging systems184
and microelectromechanical systems.185 The causes of size effects on
ferroelectrics are numerous, and it is difficult
to
separate true size effects
from other factors such as defect chemistry and mechanical strain, which
makes the discussion on size effects difficult.
Ferroelectricity differs from other cooperative phenomena in that a sur-
face requires termination of electrical polarization, which forms a depolar-
izing field. The strength of such a depolarization field
is
obviously
dependent on the size and can influence the
ferroelectric-paraelectric
tran-
sition.186 Such a size effect has been explained as follows
by
Mehta
et
al.
lg7
Assuming the ferroelectric is a perfect insulator and
is
homogeneously
poled, and the polarization charge is localized at the surface, the depolar-
ization electric field,
EFE,
in the ferroelectric is constant and given by:
E
P(
1-6)
FE-
&,&,
(8.3
1)
where
E,
is the permittivity of vacuum,
E,
is the ferroelectric's dielectric
constant,
P
is the saturation polarization of the ferroelectric, and
6
is
dependent on the ferroelectric size:
r
L
O=
2&,C
+
L
(8.32)
Characterization and Properties
of
Nanomaterials
381
where
L
is the characteristic size of the ferroelectric, i.e. the distance sep-
arating oppositely charged surfaces of the ferroelectric as a result of spon-
taneous polarization, and
C
is a constant dependent only on the material
that is in contact with the charged ferroelectric surfaces.
It
is clear that the
depolarization field is strongly size dependent, i.e. a decreasing size would
result in an increasing depolarization field. Size effects
on
the ferroelec-
tric phase transition have been investigated both the~retically'~~-'~~ and
e~perimentally'~~-'~~. Batra
et
al.
have pointed out that the ferroelectric
phase in ferroelectric films, for example, cm or lOOnm thick, becomes
unstable by the presence
of
strong depolarization fields if the surface
charges due to the polarization are not fully compensated and that below
"transition length", the polarizations are not
table.'^^$'^^
In a polycrystalline ferroelectric, the ferroelectric properties may dis-
appear when the particles are smaller than a certain size. Such a relation
could be understood considering the phase transition temperature reduces
with the particle size.
A
reduction in particle size results in a high tem-
perature crystal structure stable at low temperatures. Consequently, the
Curie temperature, or the
ferroelectric-paraelectric
transition temperature
decreases with a reduced particle size. When the Curie temperature drops
below room temperature, ferroelectrics lose its ferroelectricity at room
temperature. Size effects on ferroelectric and dielectric properties of bulk
and thin film ferroelectrics have been summarized in excellent review
articles.
'
979198
Ishikawa and coworkers'99 studied the size effect on the ferroelectric
phase transition in PbTi03 nanoparticles that were synthesized by wet
chemical routes from alkoxide precursors, and with the particle size con-
trolled by firing temperature. They found when the particle size is less
than 50 nm, the transition temperature determined by Raman scattering,
decreases from its bulk value of 500°C as the size decreases. They further
derived the size dependence of the Curie temperature by an empirical
expression for PbTiO, nanoparticles:
500
-
588.5
D-
12.6
T,
("C)
=
(8.33)
where
D
is the average size of PbTi03 nanoparticles (nm) and their experi-
mental results are plotted in Fig.
8.14
with the solid line from Eq.
(8.33).*01
In polycrystalline ferroelectrics, there are other factors that may influ-
ence the ferroelectric properties. For example, residual strains may actu-
ally stabilize the ferroelectric state to smaller sizes.200,201 Dielectric
constant or relative permittivity of ferroelectrics would increase with a
decreasing grain size, and such a decrease becomes much more profound
when the size is smaller than
1
micrometer as predicted by simulation?02
3
82
A''
p.
..
A
.
Nunostructures and Nanomateriuls
A
Thin
Fllm
Hoffman
&
Wasel
(47)
6oM)
.......
,
........
,
........
,
...
fr
3000
4
01
1
io
100
Grain
Size
(pm)
Fig.
8.33.
Dielectric constant
or
relative permittivity
of
ferroelectrics would increase with
a decreasing grain size to
1
pm
in diameter and then decrease with further decrease in
grain size
or
film thickness.
[T.M.
Shaw,
S.
Trolier-McKinstry, and
RC.
McIntyre,
Ann.
Rev.
Muter:
Sci.
30,
263
(2000).]
however, the experimental results show that the dielectric constant would
increase with a decreasing particle size and reach a maximum at
-
1
pm
in diameter and then decrease as the particle size or film thickness reduces
further as shown in
Fig.
8.33.'99
The mechanical boundary conditions can also affect the stability
of
the
ferroelectric phase and impact the equilibrium domain structures, since
many ferroelectrics are also ferroelastic. This makes the size dependence
of
ferroelectricity very complicated, since the elastic boundary conditions
of
isolated particles, grains within a ceramic, and thin films are different.
It should be noted that no direct observation of superparaelectric behavior
in ferroelectrics has been documented yet.
8.4.6. Superparamagnetism
Ferromagnetic particles become unstable when the particle size reduces
below a certain size, since the surface energy provides a sufficient energy
for domains to spontaneously switch polarization directions.
As
a result,
ferromagnetics become paramagnetics. However, nanometer sized ferro-
magnetic turned to paramagnetic behaves differently from the conventional
paramagnetic and is referred to as superparamagnetics.
Nanometer sized ferromagnetic particles
of
up to
N
=
1
O5
atoms ferro-
magnetically coupled by exchange forces, form a single domain,203 with a
large single magnetic moment
p
with up to
lo5
Bohr magnetons,
pB.
Bean
and Livingston demonstrated that these clusters or particles at elevated
Characterization and Properties
of
Nanornaterials
383
temperatures can be analogously described as paramagnetic atoms or mol-
ecules, however with much larger magnetic moments.204 The magnetiza-
tion behavior of single domain particles in thermodynamic equilibrium at
all fields is identical with that of atomic paramagnetism, except that an
extremely large moment is involved, and thus large susceptibilities are
involved. An operational definition of superparamagnetism would include
at least two requirements. First, the magnetization curve must show no
hysteresis, since that is not a thermal equilibrium property. Second, the
magnetization curve for an isotropic sample must be temperature depend-
ent to the extent that curves taken at different temperatures must approxi-
mately superimpose when plotted against
H/T
after correction for the
temperature dependence of the spontaneous magnetization.
Superparamagnetism was first predicted to exist in small ferromagnetic
particles below a critical size by Frankel and D~rfman.~~~ This critical size
was estimated to be
15
nm in radius for a spherical sample of the common
ferromagnetic materials.206 The first example of superparamagnetic prop-
erty was reported in the literature as early as
1954
on nickel particles
dispersed in silica matrix?07 Figure
8.34
shows the typical magnetization
H-KILO-OERSTEDS
Fig.
8.34.
Typical magnetization curves
of
2.2nm iron particles suspended in mercury at
various temperatures and the approximate
H/T
superposition observed for their
77
K
and
200K
data.
[C.P.
Bean and
I.S.
Jacobs,
J.
Appl.
Phys.
27,
1448
(1956).]
3
84
Nanostructures and Nanomaterials
curves of
2.2
nm iron particles suspended in mercury at various tempera-
tures and the approximate
H/T
superposition observed for their 77
K
and
200K
data.208 For low temperatures, the coupling of the spin to the
magnetic anisotropy axis
of
the system becomes important.*@ The spin
tends to align to a certain crystal axis. For example, bulk HCP cobalt has
a uniaxial crystal anisotropy.
8.5.
Summary
Many characterization and analytical techniques have been applied for the
study of nanomaterials and nanostructures; only a few widely used methods
are reviewed in this chapter. Both bulk and surface characterization tech-
niques find applications in the study of nanomaterials. However, bulk meth-
ods
are used to characterize the collective information of nanomaterials such
as
XRD
and gas sorption isotherms. They do not provide information of
individual nanoparticles or mesopores. Since most nanomaterials have uni-
form chemical composition and structures, bulk characterization methods
are extensively used. Surface characterization methods such as SPM and
TEM offer the possibilities to study individual nanostructures. For example,
the surface and inner crystallinity and chemical compositions
of
nanocrys-
tals
can be studied using high resolution TEM. Bulk and surface character-
ization techniques are complementary in the study of nanomaterials.
Physical properties
of
nanomaterials can be substantially different from
that of their bulk encounters. The peculiar physical properties of nanoma-
terials arise from many different fundamentals. For example, the huge sur-
face energy is responsible for the reduction of thermal stability and the
superparamagnetism. Increased surface scattering is responsible for the
reduced electrical conductivities. Size confinement results in a change
of
both electronic and optical properties of nanomaterials. The reduction
of
size favors an increase in perfection and, thus, enhanced mechanical
properties of individual nanosized materials; however, the size effects on
mechanical properties of bulk nanostructured materials is far more com-
plicated, since there are other mechanisms involved, such as grain bound-
ary phase and stresses.
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