Introduction to Nanotechnology and Nanomaterials
Chapter 2: Basics
1
Nanomaterials
Contents
q Introduction
q Basics
q Synthesis of Nano Materials
q Fabrication of Nano Structure
q Nano Characterization
q Properties and Applications
2
Nanomaterials
Basics
q Crystal structure
q Surface
q Kinetics
q Surface chemistry
q Consolidation
q Quantum confinement
3
Nanomaterials
qThin film agglomeration:
qPaper to read:
q“Comparison of the agglomeration behavior of Au and Cu films
sputter deposited on silicon dioxide, J.-Y. Kwon, T.-S. Yoon and
K.-B. Kim, J. Appl. Phys. 93(6), 3270 (2003)
qCan find out the paper in http://nfl.snu.ac.kr
Basics- Kinetics
q Homogeneous Nucleation
- supersaturation (DGv)
- surface
spherical nuclei
4 r 2
DG  43  r 3DGV  4 r 2
critical radius r *
2
 d (DG ) 
*

 * 0  r 
DGV
 dr r  r
barrier height DG*
5
4
Nanomaterials 3
 r 3DGV
3
16

r
DG* 
3DGV
W. D. Callister, Materials Science and Engineering
Basics- Kinetics
q Homogeneous Nucleation
ex) supersaturated solution
kT
kT
DGv  
ln( C / Co )  
ln( 1   )


  (C  Co ) / Co
6
Nanomaterials
 For nanoparticles
- DGv      T 
- 
TE >T1 >T2 >T3
Basics- Kinetics
q Nucleation Rate
.
N ~ n* (# of stable nuclei)  vd (collision frequency)
Qd
DG*
~K1 exp(
) K 2 exp( )
kT
kT
7
Nanomaterials
W. D. Callister, Materials Science and Engineering
Basics- Kinetics
q Nucleation Rate in Liquid
The rate of nucleation per unit volume and per unit time, RN, is proportional to
RN  nP  C0 P, where  : jump frequency
DG*
P  exp(
)
kT
a
1
2
y
1
number of atoms
J  (n1  n2 ) 
2
area  time
n: #of atoms/unit area
since, n1 / a  c1 , n2 / a  c2
c: #of atoms/unit volume
1
J  (c1  c2 )a
2
c
since, c1  c2  a
y
1
c
c
J   a 2   D
2
y
y
Thus,
1
D  a 2
2
8
Nanomaterials
Basics- Kinetics
Phase Transformation in Liquid:
From the Stokes-Einstein Relation,
Stokes law:
F  6 rv, where  (  )  6 r (drag coefficient by the friction)
Einstein relation:
D   kT
v
where,  
F
Thus,
kT
1
D
 a 2
6 r 2
Now, if we assume that a=r=l,
the diameter of the growth species

kT
3l 3
 DG* 
 C0 kT 
RN  nP  
exp  

3 
3
l

kT




Basics- Kinetics
q Mono-dispersed Particle
- Lamar diagram
10
How to achieve the uniformity in size?
1. High rate of nucleation
2. Quick down to the minimum concentration.
 prevent further nucleation
Nanomaterials
T. Sugimoto, Adv. Colloid Interface Sci., 28 (1987) 65
Basics- Kinetics
q Homogeneous Nucleation
- subsequent growth
(1) diffusion controlled
V
dr
 D (Cl  CS ) m
dt
r
where, Vm is the molar
volume of the nuclei
r 2  2 D (C  CS )Vmt  ro 2
r 2  k D t  ro 2
ro ( ro )
ro ( ro )
r 

r
k D t  ro 2
11
Nanomaterials
Basics- Kinetics
q Homogeneous Nucleation
Flux by diffusion,
x
c
x
1
4 D
dx

dc
x2
Jd
Jd
J d  4 x 2 D

r 
r
r
c ( r  ) 4 D
cb 4 D
1
dx  
dc  
dc
c(r )
ci
x2
Jd
Jd
Jd 
4 Dr (r   )

(Cb  Ci )
Since,
J
1 dV
1
dr

4 r 2
Vm dt Vm
dt
dr JVm
D (r   )


(Cb  Ci )Vm
dt 4 r 2
r
since, r    
12
Nanomaterials
dr JVm
D


(Cb  Ci )Vm (3.10)
dt 4 r 2 r

Basics- Kinetics
q Homogeneous Nucleation
(2) interface controlled
(2-1) monolayer growth
dr
 km r 2
dt
1 1
  kmt
r ro
ro 
r  r  2 
 ro 
(2-2) multilayer growth
dr
 kp
dt
r  k p t  ro
 r   ro
2
 The surface process is so fast that second
 The growth proceeds layer by layer;
layer growth proceeds before the first layer
the growth species are incorporated
growth is complete
into one layer and proceeds to another
layer
13
Nanomaterials
Basics- Kinetics
q Homogeneous Nucleation
- for the uniformity in size
 diffusion controlled process is desired
r
r
(2-1)
r (or t )
(2-2)
(1)
- how to achieve it
 extremely low concentration of growth species
high viscosity, diffusion barrier, controlled supply of growth species
14
Nanomaterials
Basics- Kinetics
q Homogeneous Nucleation
ex) ZnS
 diffusion of the HS- ion to the growing
particle is the rate-limiting process
15
Nanomaterials
R.Williams et al., J. Colloid Interface Sci. 106, 388 (1985).
Basics- Kinetics
q Heterogeneous Nucleation
sin 2  cos   2 cos   2
r r
2  3cos   cos 3 
*
*
DGheter
 DGhomo
f ( )
*
heter
*
homo
2  3cos   cos 3 
f ( ) 
4
16
Nanomaterials
W. D. Callister, Materials Science and Engineering
Basics- Surface chemistry
q Dispersion
- a highly homogeneous suspension of solids with a well-defined
rheological behavior
q Dispersion in liquid
- wetting - interparticle interaction
17
Nanomaterials
R. J. Pugh, Surface and Colloid Chemistry in Advanced Ceramic Processing
Basics- Surface chemistry
q Stabilization
18
Nanomaterials
R. J. Pugh, Surface and Colloid Chemistry in Advanced Ceramic Processing
Basics- Surface chemistry
q Electrostatic Stabilization
Surface charge density:
(1)
(2)
(3)
(4)
(5)
Preferential adsorption of ions
Dissociation of surface charged species
Isomorphic substitution of ions
Accumulation and depletion of electrons
Physical adsorption of charged species onto the surface
E  E0 
RT
ln ai
ni F
E0 : standard electrode potential
ni : valence state of ions
ai : activity of ions
F : Faraday's constant (=96500)
19
Nanomaterials
Basics- Surface chemistry
The concentration of charge determining ions corresponding to a neutral
or zero charged surface is defined as a point-of-zero charge (p.z.c).
At pH>p.z.c – the oxide surface is negatively charged due to the hydroxyl
groups, OHAt pH<p.z.c – the oxide surface is positively charged due to hydrogen ions,
H+
The surface charge density or surface potential, E in volt, is now simply
related to the pH and the Nernst equation.
2.303RT [( p.z.c)  pH ]
E
F
20
Nanomaterials
Basics- Surface chemistry
q Electric Potential at the Proximity of Solid Surface
The distributions of both ions are mainly
controlled by a combination of
(a) Coulombic force or electrostatic force
(b) entropic force or dispersion
(c) Brownian motion
21
Nanomaterials
Formation of double layer:
(a) Stern layer: electric potential drops linearly
through the tightly bound layer of solvent and
counter ions
(b) Gouy layer (diffuse double layer): beyond the
Helmholtz plane until the counter ions reach the
average concentration in the solution
(c) z(zeta) potential: potential at plane of shear
(slipping plane, Helmholtz plane)
Basics- Surface chemistry
 In the Gouy layer, the counter ions diffuse freely and the
electric potential does not reduce linearly.
E  e  ( h  H )
where,

1

: Debye-Huckel screening length
F 2 i Ci Z i2
 r  0 RT
 Double layer thickness is typically of about 10 nm.
 An electrostatic repulsion between two equally sized spherical particles
of radius r, and separated by s
 R  2 r  0 rE 2 e  S
22
Nanomaterials
D.J.Shaw, Introduction to colloid and surface chemistry, 1992
Chapter 1:
Water
Dielectric constant: 78
Viscosity: 1 cp
N s
kg

m2
ms
1P( poise)  0.1Pa  s
Pa  s 
1cP(centipoise)  1mPa  s  0.001Pa  s
Chapter 1:
Water
For hydrogen model
The potential ,V, is taken as the Coulombic
potential V  e2 / 4 0 r , and solve Schrodinger
equation by setting the polar coordinates.
4 0 2
rn  (
)  n 2  a0  n 2 , where, a0  0.53 A(Bohr radius)
4
me
me 4
1
1
Wave function is designated by four quantum numbers.
En  


13.6

(eV).
2
2
2
2(4 0 ) n
n

n ,l , ml , ms
4 0 r 2
rn  (
)  n 2  a0  n 2 , where, a0  0.53  80  42.4 A(Bohr radius)
4
me
me 4
1
1
1
En  


13.6

(
e
V)


0.00213

(eV )
2(4 0 r ) 2 n 2
n2
n2
Models for Double-Layer Structure
(from Electrochemical Methods; Fundamentals and Applications)
Since the metallic electode is a good conductor, it supports no electric field within itself at
equilibrium.
Any excess charge on a metallic phase resides strictly at the surface.
Helmholtz proposed that the counter-charge in solution also resides at the surface – two
sheets of charge, having opposite polarity, separated by a distance of molecular order.
Such a structure is equivalent to a parallel capacitor,

 0
(1)
V
d
 : stored surface charge density
V: volatge drop between the plates


 Cd  0
V
d
(2)
The Gouy-Chapman Theory
Even though the charge on the electrode is confined to the surface, the same is not
necessarily true of the solution.
A finite thickness would arise due to an interplay between the tendency of the charge on the
metallic phase to attract or repel the carriers according to polarity
And the tendency of thermal process to randomize them.
ni  n0 exp(
 zi e
)
kT
(3)
The total charge per unit volume in nay lamellar is then,
 ( x)   ni zi e   ni0 zi e exp(
i
From Poisson equation,
i
 zi e
)
kT
d 2
 ( x)   0 2
dx
(4)
(5)
Poisson-Boltzmann equation
d 2
e


dx 2
 0
 ni0 zi exp(
i
 zi e
)
kT
(6)
Since,
d 2 1 d d 2

( )
2
dx
2 d dx
 zi e
d
2e
0
d ( )2  
n
z
exp(
) d

i i
dx
 0 i
kT
(7)
(8)
By integration,
(
d 2 2kT
) 
dx
 0
0
n
 i exp(
i
 zi e
)  const
kT
At distance far from the electrode,   0 and (
(
d 2 2kT
) 
dx
 0
0
n
 i [exp(
i
 zi e
)  1]
kT
(9)
d
)0
dx
(10)
For symmetrical electrolyte z:z solution (electrolyte having only one cationic
species and one anionic species, both with charge z,
2kTn 0
 ze
ze
 d 
[exp(
)  exp(
)  2]

 
 0
kT
kT
 dx 
2
since,
e x  e x
sinh x 
2
e 2 x  2  e 2 x
2
(sinh x) 
4
0
ze 2
 d  8kTn
[sinh(
)]

 
 0
2kT
 dx 
2
d
8kTn 0 1/2
ze
 (
) sinh(
)
dx
 0
2kT
(
d
parameters  and
differ in sign)
dx
(11)
The potential Profile in the Diffuse Layer:
Equation (11) can be rearranged and integrated in the following manner,

1/2 x
 8kTn 0 
d
 sinh( ze / 2kT )     0 
0
ze
where, if we let
 a,
2kT


 dx
0

d
d
2


 sinh( ze / 2kT )  sinh a  ea  e a d
0
0
0
1
1
du, and e  a  ,
u
u
2
1
2
1
2
1
du

du

du
 (u  1/ u) au
a  u 2 1
a  (u  1)(u  1)
2 1 1
1
1
  [

]du  [ln(u  1)  ln(u  1)]0
a 2 u 1 u 1
a
1 u  1  1 e a  1  1
e a /2  e  a /2 
 [ln
]0  [ln a ]0  [ln[ a /2  a /2 ]]0
a u 1
a e 1
a
e e
1
2kT
tanh( ze / 4kT )
 [ln[tanh( a / 2)]]0 
ln
a
ze
tanh( ze0 / 4kT )
let, e a  u , then a  ln u, ad 
Thus,
2kT
tanh( ze / 4kT )
8kTn 0 1/2
ln[
]  (
) x
ze
tanh( ze0 / 4kT )
 0
(13)
tanh( ze / 4kT )
2n 0 z 2 e 2 1/2
ln[
]  (
) x
tanh( ze0 / 4kT )
 0 kT
or ,
tanh( ze / 4kT )
2n 0 z 2 e 2 1/2
 x
 e , where,  =(
)
tanh( ze0 / 4kT )
 0 kT
(14)
ze0
If 0 is sufficiently low that (
)  0.5
4kT
ze
ze
tanh(
)
4kT
4kT
Then,
  0 e  x
The reciprocal of k has units of distance and characterizes the spatial decay of
potential: Electric double layer thickness
The Relation between sM and f0:
Since,
 0 A
d
) x 0
d
dx
(19)
recognizing that q/A is the solution phase charge density  S
q  CV 
V   0 A(
 M   S  (8kT  0 n 0 )1/2 sinh(
ze0
)
2kT
ze
d
8kTn 0 1/2
(
 (
) sinh( 0 ))
dx
 0
2kT
(20)
 M  11.7C *1/2 sinh(19.5 z0 )
where, C * is mol/L for  M in  C/cm 2 .
Differential Capacitance:
2 z 2e 2 0 n0 1/2
ze
d M
Cd 
(
) cosh( 0 )
d0
kT
2kT
For dilute aqueous solution at 25 C,
Cd  228 zC *1/2 cosh(19.5 z0 )
where, Cd is in  F/cm 2
(21)
Stern’s Modification:
In the Gouy-Chapman Model,
- The ions are not restricted with respect to location in the solution phase
- They are considered as point charges that can approach the surface arbitrary
closely
- Therefore, at high polarization, the effective separation distance between the
metallic and solution phase charge zones decreases continuously toward zero.
- This is not realistic. The ions have a finite size and cannot approach the
surface any closer than the ionic radius.
- If they remain solvated, the thickness of the primary solution sheath would
have to be added to that radius.
- In other word, we can envision a “plane of closest approach” for the centers
of the ions at some distance x2
The interfacial model, first suggested by Stern, can be treated by extending the
considerations of the last section,

d
8kTn 0 1/2
 sinh( ze / 2kT )  (  0 ) x dx
2
2
x
(22)
or ,
tanh( ze / 4kT )
 e  ( x  x2 ) , where 2 is the potential at x2
tanh( ze2 / 4kT )
ze2
8kTn 0 1/2
 d 


(
)
sinh(
)


 0
2kT
 dx  x  x2
(23)
(24)
Since the charge density at any point from the electrode surface to the OHP is zero
(?), the potential profile in the compact layer is linear,
d 2
From Poisson equation,    0 ( 2 )
dx
d
0  2  ( ) x  x2  x (the potential profile is linear)
dx
(25)
Note also that all of the charges on the solution side resides in the diffuse layer, and
its magnitude can be related to 2,
ze
d
) x  x2  (8kT  0 n 0 )1/2 sinh( 2 )
2kT
dx
By substitution for 2 ,
 M   S   0 (

M
 M x2
ze
)]
(0 
 (8kT  0 n ) sinh[
 0
2kT
(26)
0 1/2
(27)
Differentiation and rearrangement gives,
(2 0 z 2 e 2 n 0 / kT )1/2 cosh( ze2 / 2kT )
d M

Cd 
2 0 z 2 e 2 n0
ze
d0 1  ( x2
)
)1/2 cosh( 2
)(
2kT
kT
 0
(28)
1
x2
1


Cd  0 (2 0 z 2 e 2 n 0 / kT )1/2 cosh( ze2 / 2kT )
1
1
1


Cd C H C D
(29)
(30)
Basics- Surface chemistry
q Van der Waals attraction
induced dipole- induced dipole (London) ~ x-6
permanent dipole- induced dipole (Debye) ~ x-6
permanent dipole- permanent dipole (Keesom) ~ x-6
q Attraction between two spheres

A  2r 2
2r 2
S 2  4rS
A    2
 2

ln(
)

6  S  4rS S  4rS  4r 2
S 2  4rS  4r 2 
where, A is a positive const. termed the Hamaker const.
when
35
S
 Ar
is much less than 1,  A 
r
12S
Nanomaterials
G. CaO, Nanostructures & Nanomaterials (2004)
Basics- Surface chemistry
q Example- CdTe nanowire
dipole-dipole interaction between nano-particles produce nanowires with self assembling modes
intermediate stage
36
nano-wire
Nanomaterials
Z. Tang, Science, 297 (2002)237
Basics- Surface chemistry
q DLVO theory
  R   A
kinetic barrier
secondary
minima
primary
minima
37
Nanomaterials
http://www.zeta-meter.com/
P. C. Hiemenz, Principles of colloid and surface chemistry (1986)
Basics- Surface chemistry
q DLVO theory
- effect of
Hamaker constant
surface potential
electrolyte conc.
Larger – smaller
thickness of double
layer- more attraction
Larger – more attraction
Larger – more repulsion
10-3 M
10-2 M
P. C. Hiemenz, Principles of colloid and surface chemistry (1986)
Basics- Surface chemistry
q Steric Stabilization
Steric stabilizer : amphipathic block
or graft copolymer
D. H. Napper, Polymeric Stabilization of Colloidal Dispersions (1983)
Basics- Stability of Nanoparticle
q Metal oxide nanoparticles in aqueous suspensions
- kinetic stability- energy barrier (DLVO theory)
- dispersion, aggregation, flocculation
- thermodyamic stability- surface energy minimization
- Ostwald ripening (dissolution-reprecipitation)
* Is it possible to avoid the ripening of nanoparticles in suspension and to control their
dimension by monitoring the precipitation conditions?
ex) thermodynamically stable dispersed system- microemulsion
answer) possible
When the pH of precipitation is sufficiently far from the point of zero charge and
the ionic strength sufficiently high, the ripening of nanoparticles is avoided. The
stability condition, defined by a 'zero' interfacial tension, corresponds to the
chemical and electrostatic saturation of the water-oxide interface. In such a
condition, the density of charged surface groups reaches its maximum, the
interfacial tension its minimum and further adsorption forces the surface area to
expand and consequently, the size of nanoparticles to decrease.
L. Vayssieres, Int. J. Nanotech. 2, 411 (2005)
Basics- Stability of Nanoparticle
q
Microemulsion
- clear, stable, isotropic liquid mixtures of oil, water, and surfactant, frequently
in combination with a co-surfactant.
- aqueous phase may contain salt(s) and/or other ingredients, and the “oil”
may actually be a complex mixture of different hydrocarbons and olefins.
- thermodynamically stable
- interfacial tension is very low (10-2~10-3 mN/m)
E. Ruckenstein, Chem. Phys. Lett. 57, 517 (1978)
B.K. Paul, Current Science 80, 990 (2001)
Basics- Stability of Nanoparticle
q Metal oxide nanoparticles in aqueous suspensions
point of zero
interfacial tension
 decreases
as pH increases
S.M.Ahmed, J. Phys. Chem. 73, 3546 (1969)
unstable
-ripening
stable
- no growth
L. Vayssieres, Int. J. Nanotech. 2, 411 (2005)
Basics- Consolidation
q Consolidation (sintering)
processes involved in the heat treatment of powder compacts
at elevated temperatures, usually at T > 0.5Tm [K], in the
temperature range where diffusional mass transport is
appreciable resulting in a dense polycrystalline solid.
- pore removal
densification
43
Nanomaterials
MgO-doped Al2O3
J. P. Schaffer et al, The Science and Design of Engineering Materials
Basics- Consolidation
q Solid state sintering
final
intermediate
initial
44
Nanomaterials
Basics- Consolidation
q Densification vs. Grain Growth
500m
TiO2 & SiO2-doped Al2O3
45
Nanomaterials
O. S. Kwon, Acta Mater., 50 (2002) 4865-4872