Chapter 4 Properties of nanomaterials

PROPERTIES OF NANOSTRUCTURES
1. Surface to Volume Ra;o
2. Cataly;c proper;es of nanomaterials
3. Size dependent Mel;ng temp of Nanomaterials
4. Op;cal Proper;es of nanomaterials (Metallic and semiconduc;ng)
5. Electrical proper;es of nanomaterials
6. Magne;c proper;es of nanomaterials
7. Bulk behavior of nanostructured materials,
8. Mechanical behavior: structural nanostructured materials, Elas;c
proper;es, Hardness and Strength, Duc;lity and Toughness

Size increases the surface
atoms and surface energy
Par;cle size, surface area and
surface energy of CaCO 3 .xi (the
surface energy of bulk CaCO 3
(calcite) is 0.23 Jm -2 .)

Surface to bulk atom ra;o

Catalysis
Catalysis is the change in rate of a chemical reac;on due to the par;cipa;on of a
substance called a catalyst.
Unlike other reagents that par;cipate in the chemical reac;on, a catalyst is not
consumed by the reac;on itself.
A catalyst may par;cipate in mul;ple chemical transforma;ons.
Catalysts that speed the reac;on are called posi;ve catalysts.
Substances that interact with catalysts to slow the reac;on are called inhibitors (or
nega;ve catalysts).
Substances that increase the ac;vity of catalysts are called promoters, and
substances that deac;vate catalysts are called cataly;c poisons.

Increasing the surface area of the solid increases the chances of collision taking
place. Imagine a reac;on between magnesium metal and a dilute acid like
hydrochloric acid. The reac;on involves collision between magnesium atoms and
hydrogen ions.

Size-dependent mel;ng of low-dimensional systems
Empirical rela;ons are established between the cohesive energy, surface tension,
and mel;ng temperature of different bulk solids. An expression for the sizedependent
mel;ng for low-dimensional systems is derived on the basis of an
analogy with the liquid-drop model and these empirical rela;ons, and compared
with other theore;cal models as well as the available experimental data in the
literature.

Size-dependent mel;ng of nanopar;cles
T mb = bulk mel;ng temperature
T m = mel;ng temperature of the nanopar;cles
ν 0 is the volume of an atom, and ϒ is the coefficient of surface energy of
the material
Β= Es;mated for different elements
Mel;ng temperature ( T m / T mb ) depends on the inverse of the par;cle diameter d.

Mel;ng of different-shaped nanopar;cles

Mel;ng of thin films
(ld)

General expression of Tm for low-dimensional systems

Size and shape dependent lajce parameters of metallic
nanopar;cles
It is predicted that the lajce parameters of nanopar;cles in several nanometers decrease
with decreasing of the par;cle size and the par;cle shape can lead to 10% of the total lajce
varia;on
= (a p -a)/a
Where a p and a are the lajce parameters of the nanopar;cle and the corresponding bulk
material.
where D (= 2R) is the diameter of the nanopar;cle, and K = α 1/2 G/ϒ .
α is a factor to modify the shape difference between the spherical and the non-spherical
nanopar;cles . For spherical nanopar;cle, α= 1, and for non-spherical nanopar;cle, α > 1.
ϒ is the surface energy per unit area at the temperature T (0 ≤ T < Tm, Tm is the mel;ng
temperature of metals) and G is the shear module .
Generally, both of the shear module and the surface energy are posi;ve; therefore, the lajce
parameter of the metallic nanopar;cles will decrease with decreasing of the par;cle size.
Equa;on is the basic rela;on for the size and shape dependent lajce parameters of metallic
nanopar;cles.

SHAPE DEPENDENCY
Apparently, the shape factor
approaches 1 with increasing the
quan;ty of planes. Therefore, the
values of regular polyhedral shapes
range from 1 to 1.49.
For disk-like nanopar;cles, the
value of shape factor depends on
the ra;o of height to radius.
Varia;on of the rela;ve
parameter of Pd
nanopar;cles as a func;on of
shape factor.

SIZE
DEPENDENCY
Discussion:
(1) The lajce parameter varia;on depends on the par;cle size and the par;cle shape, and the
varia;on decreases with increasing the shape factor;
(2) The smaller the par;cle size is, the stronger the dependence of lajce parameter to the
par;cle shape is;
(3) Both the par;cle shape and the par;cle size can affect the lajce parameter of
nanopar;cles, but the par;cle size is the main factor, and the par;cle shape is secondary
factor. In generally, the par;cle shape will contribute about 10% to the total lajce varia;on.
In other words, if we ignore the par;cle shape effect when we calculate the lajce parameters
of metallic nanopar;cles, the rela;ve error in the final value resul;ng from the par;cle shape
effect may reach 10%.

OPTICAL PROPERTIES OF METAL NANOPARTICLES

The light absorp;on in metal nanopar;cles originates from an interes;ng
phenomenon called localized surface plasmon resonance. According to the Drude–
Lorentz model, the atoms in metals exist in a plasma state, having a core of
posi;vely charged nuclei surrounded by a pool of nega;vely charged electrons and
hence named as ‘plasma electrons’.
In the presence of an electromagne;c radia;on, the electric vector displaces the free
electrons and the columbic electrosta;c atrac;on of the nuclei will restore the
electrons to the original posi;on.
As a result of the oscilla;ng nature of the electric field of light, the electron cloud
coherently oscillates over the surface with a resonance frequency ‘ωp’. When the
frequency of this oscilla;on matches with that of incident radia;on, a resonance
condi;on is established which results in the intense absorp;on, oven termed as
‘surface plasmon (SP) absorp;on’.

Op;cal absorp;on proper;es of metal nanopar;cles :
The surface Plasmon Resonance
The Mie theory

Op;cal proper;es of metal nanopar;cles
par;cle size,
shape,
composi;on,
and the local dielectric environment.

1- Size
The op;cal proper;es of large and small nanopar;cles are markedly different.
Kreibig and Vollmer define two types of size effects: extrinsic and intrinsic . The
threshold for the two regimes occurs for diameters of around 10 nm in the case of
Au nanopar;cles.
The op;cal proper;es of nanopar;cles with diameters above the threshold are
dominated by extrinsic effects, which are related to the diameter and the bulk
dielectric func;on of the metal. A red-shiving and broadening of the resonance peak
is seen for increasing radius, due to retarda;on effects.
For nanopar;cles with diameters below the threshold several special considera;ons
must be made due to intrinsic effects. This size range is clearly within the quasi-sta;c
regime, and so electrodynamics effects such as retarda;on do not play a role in the
op;cal proper;es. However, surface scatering of electrons occurs due to the
par;cle dimensions being smaller than the mean free path, leading to damping of
the plasmon oscilla;on and a resul;ng atenua;on and broadening of the resonance
peak.

2- Shape
Haes et al. elegantly demonstrated the importance of par;cle shape by
simula;ng the op;cal spectra of various Ag nanopar;cle types with constant
volume. The largest difference occurs between the sphere and pyramid, with a ~200
nm shiv in peak wavelength posi;on. The peak posi;on shiv correlates well with an
increase in the number of sharp ;ps or edges as the shape is changed from sphere to
pyramid. Plots of |E|2 intensity in the same paper show that the near-field intensity
is strongly confined at sharp features, which results in the red-shiving of the far-field
response.

3- Dielectric environment
The op;cal proper;es of metal nanopar;cles are strongly sensi;ve to the surrounding dielectric environment,
which is useful for tuning their op;cal proper;es or for biosensing.
In general, an increase of refrac;ve index of medium surrounding a nanopar;cle results in a red-shiv of the LSP
peak.
McFarland and VanDuyne studied the scatering spectra of single Ag nanopar;cles as a func;on of the
surrounding refrac;ve index . A linear fit between peak posi4on and refrac4ve index of a surrounding solvent
was demonstrated (Fig. 2.22).
A thin oxide layer forms on the surfaces of Ag, Cu and Al form when these metals are exposed to air.
Langhammer et al. considered the case of the self-limi4ng oxide that forms on Al, which was es4mated to be 3
nm thick [136]. This oxide growth has two effects on Al nanopar4cles: (1) the core Al par4cle is reduced in size
during the oxide growth, (2) the local dielectric environment is changed by the outer alumina shell. SVM
simula4ons showed that the change in dielectric environment has the strongest effect on the op4cal proper4es of
the nanopar4cle, and gives rise to a moderate red-shiQ for large par4cles, and a strong red-shiQ for small
par4cles.

4- Intrapar;cle coupling
In the core-shell nanopar;cle, the inner and outer surfaces of the shell support different
resonances. Coupling between the two surfaces leads to an altera;on of the overall op;cal
response of the nanopar;cle. Prodan et al. developed a hybridiza4on model that can explain
the interac4on between elementary plasmons supported by complex nanopar4cles . For
example, the op4cal response of a core-shell nanopar4cle can be considered as the
hybridiza4on of a shell plasmon and a cavity plasmon. The strength of the interac4on is
controlled by the shell thickness. The op4cal proper4es of core-shell nanopar4cles can be
tuned by modifying the core material, core diameter, shell material and shell thickness.
Increasing the refrac4ve index or diameter of the core leads to a red-shiQ of the resonance.
Decreasing the shell thickness also results in a resonance red-shiQ, which is par4cularly
drama4c for very thin shells.
Standard Mie theory models for core-shell par4cles do not include the effect of surface
scaTering, which can be important for thin shells.
Moroz developed an extension to Mie theory to model the effects of surface scaTering in coreshell
nanopar4cles. The effect is the same as for very small solid spheres, i.e. damping that
leads to aTenua4on and broadening of the peak.

5- Interpar;cle coupling
Systems composed of mul;ple par;cles may exhibit op;cal proper;es different than that of an isolated
par;cle, even if each par;cle in the group is iden;cal. In the near-field, evanescent fields of proximate
nanopar;cles can interact. At larger distances nanopar;cles interact in the far-field through their
scatered fields, which is par;cularly relevant for periodic arrays. Jensen et al. inves;gated near-field
coupling between two iden;cal Ag nanospheres using DDA simula;ons (Fig 2.23). For a par;cle radius of
30 nm, an interpar;cle spacing of 30 nm results in a 10 nm red-shiv of the resonance peak. For much
smaller spacing the effect is much more drama;c, resul;ng in 100 nm and 125 nm red-shivs for a spacing
of 4 nm and 2 nm respec;vely.
Closely-spaced nanopar;cle pairs exhibit strong polariza;on sensi;vity, as coupling effects are much
weaker for incident light polarized perpendicular to the par;cle pair axis. Complete transfer of energy
from one nanopar;cle can occur via dipole-dipole interac;on, leading to the idea of sub-wavelength
waveguides based on linear chains of metal nanopar;cles. The principle interest in coupled metal
nanopar;cle dimers is the intense electric field enhancement observed in the gap between the par;cles,
which is far larger than those obtained around isolated par;cles. These are found to be strongly related to
the interpar;cle separa;on, with smaller distances producing larger field enhancement.
Par;cles arranged in a periodic patern will scater photons coherently, leading to a change in the
observed far-field scatering spectrum due to interac;on between scatered photons. Periodic
arrangements of nanopar;cles form a diffrac;on gra;ng, and coupling of LSPs to evanescent or radia;ng
gra;ng modes alters the ex;nc;on spectrum from that of isolated nanopar;cles. Essen;ally the
diffrac;on gra;ng imposes restric;ons on the angular distribu;on of scatering, and so inhibits or
strengthens scatering at given wavelength. Therefore the op;cal proper;es of a periodic array of
nanopar;cles depend on the gra;ng period in addi;on to the proper;es of the individual nanopar;cles.

Summary of the op;cal proper;es of metal nanopar;cles
The op;cal proper;es of metal nanopar;cles are a strong func;on of the par;cle composi;on, size,
shape, dielectric environment and the orienta;on and proximity of par;cles with respect to each other.
Increasing the size of a par;cle results in a red-shiv and broadening of the peak posi;on, and an
increase in the ra;o of scatering to absorp;on. Large par;cles also support higher- order modes, which
occur at progressively shorter wavelengths, and have a larger absorp;on to scatering ra;o than the
corresponding dipolar peak.
Near-field coupling between nanopar;cles results in a red-shiv, but is only relevant for interpar;cle
spacing of the order of the par;cle diameter or less. Waveguide-mediated interpar;cle coupling is only
relevant for periodic arrangements of par;cles situated on slab waveguides, and results in the
appearance of fringes in the ex;nc;on spectrum.
Increasing the refrac;ve index of a homogenous medium surrounding a par;cle results in a linear redshiv
of ex;nc;on peak posi;on. Inhomogeneous mediums such as substrates and mul;layers can result
in the excita;on of higher-order modes or drama;cally change the ex;nc;on spectrum due to
interference effects.
The strongest field enhancement occurs for par;cles with sharp ;ps (e.g. triangular prisms) or par;cle
dimers with extremely small gaps. Interes;ngly, there appears a loose correla;on between field
enhancement and red-shiving of the LSP peak posi;on.

OPTICAL PROPERTIES OF SEMICONDUCTING NANOPARTICLES

Exciton (Yakov Frenkel in 1931)
bound state of an electron and hole
atracted to each other by the electrosta;c Coulomb force.
It is an electrically neutral quasipar;cle
exists in insulators, semiconductors and some liquids.
An exciton forms when a photon is absorbed by a semiconductor. This excites an electron from the
valence band into the conduc;on band. In turn, this leaves behind a localized posi;vely-charged hole. The
electron in the conduc;on band is then atracted to this localized hole by the Coulomb force. This
atrac;on provides a stabilizing energy balance. Consequently, the exciton has slightly less energy than
the unbound electron and hole. The wave func;on of the bound state is said to be hydrogenic, an exo;c
atom state akin to that of a hydrogen atom. However, the binding energy is much smaller and the
par;cle's size much larger than a hydrogen atom.

Frenkel excitons
In materials with a small dielectric constant, the Coulomb interac;on between electron and
hole may be strong and the excitons thus tend to be small, of the same order as the size of the
unit cell. Molecular excitons may even be en;rely located on the same molecule, as in
fullerenes. In these cases, the electron and hole lie within the same unit cell. This Frenkel
exciton, named aver Yakov Frenkel, has a typical binding energy on the order of 0.1 to 1 eV.
Frenkel excitons are realized in alkalihalide crystals and in organic molecular crystals
composed of aroma;c molecules. Anthracene, Tetracene, Pentacene, Phenanthrene,
Porphyrin, Phenazine, PTCDA,etc
Wannier-Mot excitons
In semiconductors, the dielectric constant is generally large. Consequently, electric field
screening tends to reduce the Coulomb interac;on between electrons and holes. The result is
a Wannier exciton, which has a radius larger than the lajce spacing. As a result, the effect of
the lajce poten;al can be incorporated into the effec;ve masses of the electron and hole.
Likewise, because of the lower masses and the screened Coulomb interac;on, the binding
energy is usually much less than a hydrogen atom, typically on the order of 0.01eV. This type
of excitons are typically found in semiconductor crystals with small energy gaps and high
dielectric constant, but have also been iden;fied in liquids, such as liquid xenon. In single-wall
carbon nanotubes, excitons have both Wannier-Mot and Frenkel character.

Excitonic effects:
The photons of energy larger than the semiconductor gap can create electron – hole pairs.
Due to the Coulomb interac;on between them, the electron and hole can remain together
forming a new neutral par;cle called exciton.
Since excitons have no charge, they cannot contribute to electrical conduc;on.
Exciton forma;on is very much facilitated in quantum well structures, because of the
confinement effects which enlarge the overlapping of the electron and hole wave func;ons.

EXCITONIC EFFECTS IN QUANTUM WELLS
(a), In which the Bohr radius of the exciton is
much smaller than the quantum well width,
and the one in (b), for which the width of the
well is smaller than aB.
Exciton binding energy as a func;on of the
quantum well width.
(a) Exciton orbits in a very bulk crystal;
(b) the spherical form of the exciton
becomes elongated when the width of
the QW is smaller than the exciton
radius.
Binding energies for holes in a GaAs–AlGaAs
quantum well as a func;on of well width.
Aver [5].

Elas;c Proper;es
The elas;c constants of nanocrystalline (nc) materials prepared by the inert gas condensa;on
method gave values, for example for Young’s Modulus, E, that were significantly lower than
values for conven4onal grain size materials.
Krs4c and coworkers (1993) suggested that the presence of extrinsic defects—pores and
cracks, for example—was responsible for the low values of E in nc materials compacted from
powders.
This conclusion was based on the observa4on that nc NiP produced by electropla4ng with
negligible porosity levels had an E value comparable to fully dense conven4onal grain size Ni.
it is now believed that the intrinsic elas4c moduli of nanostructured materials are essen4ally
the same as those for conven4onal grain size materials un4l the grain size becomes very
small, e.g., < 5 nm, such that the number of atoms associated with the grain boundaries and
triple junc4ons becomes very large.

Hardness and Strength
Hardness and strength of conven;onal grain size materials (grain diameter, d > 1 μm) is a func;on of grain
size. For duc;le polycrystalline materials the empirical Hall-Petch equa;on In terms of yield stress, is
σο = σi + kd -1/2 , where σο = yield stress, σi = fric;on stress opposing disloca;on mo;on, k = constant, and
d = grain diameter . And for hardness, is Hο = Hi + kd -1/2 .
To explain these empirical observa;ons, several models have been proposed, which involve either
disloca;on pileups at grain boundaries or grain boundary disloca;on networks as disloca;on sources. In
all cases the Hall-Petch effect is due to disloca;on mo;on/genera;on in materials that exhibit plas;c
deforma;on.
It is clear that as grain size is reduced through the nanoscale regime ( 1 μm) metals. The experimental results of hardness measurements,
show different behavior for dependence on grain size at the smallest nc grains (

Duc;lity and Toughness
Grain size has a strong effect on the duc;lity and toughness of conven;onal grain
size (> 1 μm) materials. For example, the duc;le/britle transi;on temperature in
mild steel can be lowered about 40°C by reducing the grain size by a factor of 5.
On a very basic level, mechanical failure, which limits duc;lity, is an interplay or
compe;;on between disloca;ons and cracks. Nuclea;on and propaga;on of cracks
can be used as the explana;on for the fracture stress dependence on grain size.
Grain size refinement can make crack propaga;on more difficult and therefore, in
conven;onal grain size materials, increase the apparent fracture toughness.
However, the large increases in yield stress (hardness) observed in nc materials
suggest that fracture stress can be lower than yield stress and therefore result in
reduced duc;lity.
An intriguing sugges;on based on early observa;ons of duc;le behavior of britle nc
ceramics at low temperatures is that britle ceramics or intermetallics might exhibit
duc;lity with nc grain structures.

Superplas;c Behavior
Superplas;city is the capability of some polycrystalline materials to exhibit very
large tensile deforma;ons without necking or fracture. Typically, elonga;ons of
100% to > 1000% are considered the defining features of this phenomenon.
As grain size is decreased it is found that the temperature is lowered at which
superplas;city occurs, and the strain rate for its occurrence is increased. The creep
rates might be enhanced by many orders of magnitude and superplas;c behavior
might be observed in nc materials at temperatures much lower than 0.5 TM.