The document discusses several size-dependent properties of nanomaterials. As particle size decreases: - Surface area to volume ratio increases, increasing surface and quantum effects - Electronic structure changes from continuous bands to discrete energy levels - Optical properties like absorption spectra and color are altered - Reactivity and melting point decrease due to higher surface energy - Magnetic and wetting properties change, with contact angle decreasing - Density may increase or decrease depending on changes in cohesion and lattice constants

1. SUBMITTED BY
N.MUGILAN
M.TECH 1ST YEAR
NANO SCIENCE AND TECHNOLOGY
Size Effect of Nanomaterials
NAST-613 Elements of Materials Science and Physical
Properties of Nanomaterials

2. 1. Introduction
2. Size dependent effect
3. Geometric structure
4. Electronic Structure
5. Optical properties
6. Surface to volume ratio
7. Reactivity
8. Melting point
9. Magnetic properties
10. Density
11.Wettability and surface tension
12.References

3. simplest Nanoparticles
structure with
are the
size in the nm range
form of
or of
larger molecule
structural radius <100nm.
 E.g.-Fullerens,metal cluster
such as protein
SIZE DOES MATTER-SMALL IS
VERY DIFFERENT

4.  Earlier the bulk materials were characterized
by the properties such as
Composition
Melting Point
Vapour Pressure
Solubility
Boiling Point
pH
 But as size decreases the criteria for
characterizing the nanoparticles also changes
.They are characterized by
Size,shape of interacting surface
Melting Point
Wettability
Band gap
Surface area
Surface Tension
Pore Size

5. There are basically 2 types of size dependent effects
1.Surface effect 2.Quantum confinement effect
The dispersion F of a sample is defined as the fraction or
percentage of atom at a surface relative to the total number of
atoms in the sample.
Dispersion,F=Surface area/Volume
Surface area of a sphere ,A=4πr2
Volume ,V=4πr3/3
Dispersion F=A/V= 3/r or 6/d
If the diameter of a specimen reaches the diameter of two atoms,
every atom is directly exposed to the surface ,and
F=1

6. Fig shows the eg of a cubic crystal with n atoms along an edge and total no of
N=n3 atoms.n=no of atom in the cluster
The smallest cube has 8 atoms and each of them is at the surface ,while the
next larger cube has 27 atoms with 1 at the center.For larger cube the
dispersion scales 1/N1/3 ,which is proportional to 1/d.

7. Quantum confinement effect in materials with delocalized electrons
Atoms have there well known atomic orbitals.The core of the orbitals are confined to
a relatively small volume and remain localised.Each of the N atoms contributes with
its atomic state to a band so that although the width of the band increases slightly
.when more atom is added,the density of the state within the band is basically
proportional to the no of atom with an ensemble with extended band structure.
Thus the density of state is very large for a bulk amount of matter but low for
smallclusters

8. Usually the crystal structure of a large nanocluster is
the same as the bulk structure of the material, with
somewhat different lattice parameters .
e.g. 80nm Al particles have FCC which is the
same as the unit cell of bulkAluminium.
But some exception do however occur for particles
having diameter <5nm
e.g. 3-5nm gold particle have icosahedral
structure rather than the bulk FCC structure

9. When atoms form a lattice the discrete energy of atoms
are smudged out into energy bands ,the term density
of states refers to no of energy levels in a given interval
of energy.
• For metals,the top band is not totally filled .
• For semiconductor the top occupied bandis the valence
band is filled and there is a small energy separation
between it and the next higher unfilled band.
When metal particles of bulk size is reduced to a few
100 atoms the density of states in the CB the top band
containing electron changes automatically .
The continious density of state in the band is replaced
by a set of discrete energy levels which may have
energy level spacing > energy kBT .

10. The small cluster is analogous to the molecule having discrete energy
levels with bonding and anti bonding orbitals .Eventually a size is
reached where the surface of the particles are separated by the distances
which of the order of the wavelength of electrons .here the energy level
can be modelled by the quantum mechanical treatment reffered as
Quantum size effect.
The emergence of new electronic properties can be understood in terms
of Hiesenberg uncertainity principle.

11. The color of the material is determined by the
wavelength of the light that is absorbed by it .The
absorption occur because electrons are induced by the
incident light to make transition between the lower lying
occupied levels and the higher unoccupied energy levels.
In semiconductors the band gap will be increased as
the cluster size is decreased –a blue shift in the
absorption spectrum of the semiconductor .
Individual energy level separation are also dependent on
the clusters which affect the energy needed for the
transitions of electron to excited states.

12. Cluster of different sizes will therefore have different
absorption spectra & hence different color
e
V
B6 B8 B12

13. NOT ALL THAT’S
GOLD DOES
GLITTERS
ALL THAT’S GLITTERSIS
NOTGOLD

14. 2inches
2inches
1inch
1inch
Volume=8 cubic inches
Surface area=24 sq. inches
Surface :Volume =24:8=3
Volume=1cubic inch
Surface area=6 sq. inches
Surface :Volume =6:1=6
Surface to volume ratio increases with reducing
the size

15. Since electronic structure of nanostructures depends on
their size their ability to react with other species also
depends on size .This has important application for design
of catalytic agent .
As with decrease in size the surface area increases ,so
nanostructure have more surface area for reaction .
Hence reactivity increases with decrease in particle size.

16. As the particle
size decrease the
melting point
decrease ,since
the surface
energy increases
with increase in
surface area
•Melting Point ofGold
(Tm=1064oC)

17. With the decrease in
particle size the
hysteresis loopbecomes
smaller.
Coercivity and
Remenance decreases
with the particle size

18. Density can be generally varied by changing the pressure or the
temp. But it has been observed that density changes with the change
in the thickness of the layer in nm range .
 Mass density of Cu,Cr,TiN film on MgO was found to be
lower than the corresponding bulk value.
 SiO2,SiC on stainless steel showed increase in density .
 Cu,Ag,Au showed no significant change .
The size-dependent density of nanoparticles or nanostructured
materials is expected to be governed by two issues:
(i) cohesion of atoms and (ii) the volume of the unit cells
It has been shown that the cohesive energy per atom decreases
with the size of the nanoparticles while lattice constant of
nanoparticles may increase or decrease . It has been shown that
the lattice contraction takes place for nanoparticles because of
the surface bond contraction.
Lattice expansion takes place for nanostructured materials
because of the bond elongation at the grain boundaries.

19. In nanostructured materials, the lattice constant increases with
decreasing size. It is shown that variation of lattice parameter and
cohesive energy of nanostructured materials are given by
a 3d 2dv,d v
a
 
h
&a  a (1
3h
)
where h is the atomic diameter.
Both for nanoparticles and nanostructured materials, the cohesive
energy decreases with decreasing particle size though the decrease
is weaker in the latter case .
On the other hand,the lattice parameter decreases for
nanoparticles but increases for nanostructured materials as
the size is reduced.
Density is estimated as
 
ma

av,d
v c2
v

20. Size dependent density
of Au nanostructured
materials

21.  lg cos sg sl
Wettability is the phenomenon of ability of liquid to maintain
contact with the solid surface , resulting in intermolecular
interaction when the two phases are brought in contact.
It is quantitatively measured in terms of contact angle .
.
YOUNG’S EQUATION-

22. Contact angle
Contact angle is the angle at which the liquid-vapour
interface meets the solid –surface interface
WETTING  1
ContactAngle

23. Effect of nanoparticles
Liquid containing nanoparticles exibit different
spreading or thinning behaviour on solids than liquids
without nanoparticles.
The contact angle of the surfaces decreases with
increasing surface coverage
For smaller sized nanoparticles the surface to volume
ratio increases ,so the surface energy increases, this
leads to the decrease in the contact angle.
Contact angle α particle size
ParticleSize
1
WETTING

24. 1. Effect of nanoparticles on Wetting of different solid surface-
Savitri Hansda
2. Size dependent density of nanoparticles and nanostructered
materials-Karuna Kar Nanda
3. Physics and Chemistry of nanostructures : Why nano is
different-Emil Roduner,Institute of Physicsl
Chemistry,University of Stuttgart
4. Nanoparticles(Lecture)-Do Kyung Kim
5. Properties of individual nanoparticles
6. Size matters :Why nano is different?-Emil Roduner