Nanostructures & Nanomaterials
by Synthesis, Properties and
Applications
Author : Guozhong Cao
Instructor : Prof. Chie Gau
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Chapter 2
Physical Chemistry of Solid
Surfaces
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Percentage of surface atoms
changes with cluster diameter
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For 1 g of Sodium Chloride, the original 1 g cube
is successively divided into smaller cubes.
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Due to the vast surface area, all
nanostructured materials possess a
huge surface energy and, thus are
thermodynamically unstable or
metastable.
Goal: to overcome the surface energy,
and to prevent the nanomaterials from
growth in size, driven by the reduction
of overall surface energy.
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Surface Energy
 Definition: energy required (or produced) to create a
unit area of a new surface, therefore,
γ= (∂G/ ∂A)ni, T, P
 G: Gibs free energy of the surface
 A: Surface area of the particles
 Surface area can be increased by cutting a particle
into two halves. The molecules of the newly created
surface possess fewer nearest neighbors or
coordination numbers, and thus have dangling or
unsatisfied bonds. Due to the dangling bonds on the
surface, surface atoms or molecules are under an
inwardly directed force and the bond distance
between molecules and the sub-surface molecules
becomes smaller. An extra force or energy is
required to pull the surface to its original positions.
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Surface Energy
This energy is defined as surface energy, γ
 γ = Nbερa /2
(1)
 Nb: number of broken bonds
 ε: bond strength
 ρa = number of atoms or molecules per unit
surface area density
 The above equation is very crude model and
does not account for interactions between
higher order neighbors.
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Surface Energy
For FCC structure with lattice constant
a, each atom will have a coordination
number 12, and each atom on the
surface {100} has 4 broken bonds, on
{110} 5 broken bonds and on {111} 3
broken bonds. Therefore,
γ{100} = 2/a2．4．ε．1/2
γ{110} = 2/20.5a2．5．ε．1/2
γ{111} = 2/30.5εa2
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According to Eqn (1), the lower Miller index facets have low surface
energy. System is stable only when it is in a state with the lowest
Gibbs free energy. Therefore, a crystal is often surrounded by low
index surfaces.
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Surface energy reduced by
 Surface relaxation: surface atoms or ions shift
inwardly.
 Surface restructuring through combining surface
dangling bonds into strained new chemical bonds
 Surface adsorption through chemical or physical
adsorption of terminal chemical species by forming
chemical bonds or weak attraction forces such as
electrostatic or van der Waals forces.
 Composition segregation or impurity enrichment on
the surface through solid-state diffusion.
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Surface energy reduction by
surface relaxation
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Surface energy reduction by
restructuring
The restructured {100} faces have the lowest
surface energy among {111}, {110} and {100}
faces.
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Surface energy reduction by
chemical or physical adsorption
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Reduction of surface energy for a
nanoparticle:
 One is to reduce the total surface area. That
is, surface tends to become spherical.
 For crystalline particle, facets forms because
they have smaller surface energy than a
spherical surface does. Since facets with a
lower Miller Index have a lower surface
energy than that with a higher Miller Index.
Therefore, crystal is often surrounded by low
index surfaces.
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Wulff plot: using γi =
Chi where C is the
constant and hi is the
perpendicular distance.
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Crystal Grown with Nonfacets
 At certain high temperature, the equilibrium
crystal surfaces may not be smooth, and
difference in surface energy of various
crystal facets may disappear. Such a
transition is called surface roughening or
roughening transition. Most nanoparticles
grown at elevated temperature are spherical
in shape (not facets).
 Kinetic factors (processing or crystal growth
conditions) may also prevent formation of
facets.
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Mechanisms for reduction of
overall surface energy
 Combining individual nanostructures together to form
large structures so as to reduce the overall surface
area, which includes:
 1. sintering: individual structures merge together
which occurs at 70% of Tm. Replacing solid-vapor
interface by solid-solid interface and becomes
polycrystalline.
 2. Ostwald ripening: A large one grows at the expense
of the smaller one until the latter disappears
completely, and becomes a single crystal. It occurs at
relatively low temperature.
 Agglomeration of individual nanostructures through
chemical bonds and physical attraction forces at
interfaces without altering the individual
nanostructures. The smaller the particles, the
greater the bonding forces are.
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Sintering and Ostwald ripening
process
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Chemical Potential as a Function
of Surface Curvature
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Note
From definition of chemicalμ and
surface energy γ:
G
i 
) n j ,T , P
ni
G
 
) ni ,T , P
A
Therefore,
G A
A

) ni ,T , P  
A ni
ni
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Conclusions
For a convex surface, the curvature is
positive, and thus the chemical potential
of an atom on such a surface is higher
than that on a flat surface.
An atom on a convex surface possesses
the highest chemical potential, whereas
an atom on a concave surface has the
lowest chemical potential.
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Definition of Chemical Potential
The difference of chemical potential
may be regarded as the cause of a
chemical reaction or of the tendency of
a substance to diffuse from one phase
into another. The chemical potential is
thus a kind of chemical pressure and is
an intensive property of system.
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For the case of ideal gas, integrate Eqn
(2.111), one obtains
μ = μo + RT ln p/po
Similarly, one obtains solubility Sc
μ = μo + RT ln Sc/Sco
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Ostwald Ripening Process
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Ostwald Ripening Process
Results in
1. abnormal grain growth (in the sintering
of polycrystalline materials) which leads
to inhomogeneous microstructure and
inferior mechanical properties of the
products.
2. Eliminating smaller particles and the
size distribution becomes narrower
during growth of nanoparticles.
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Triggering and Stopping of
Ostwald Ripening Process
 Ostwald ripening process can be triggered after
initial nucleation and subsequent growth by raising
the temperature. That is, the concentration of solid
in solvent falls below the equilibrium solubility of
small nanoparticles, and the small ones dissolve into
the solvent. Once a nanoparticle starts to dissolve
into the solvent, the dissolution process never stops
until the nanoparticle is dissolved completely. The
large particles will grow until the concentration of
solid in the solvent equals the equilibrium solubility of
these large nanoparticles.
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Stabilization of Nanoparticles
Electrostatic stabilization: kinetically
stable
Steric stabilization: thermodynamically
stable
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Electrostatic Stabilizationsurface charge density
 When a solid emerges in a polar solvent or an
electrolyte solution, a surface charge will be
developed due to:
 1. preferential adsorption of ions due to
dissolution.
 2. dissociation of surface charged species.
 3. Isomorphic substitution
 4. Accumulation or depletion of electrons at
the surface.
 5. Physical adsorption of charged species onto
the surface.
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Surface charge density
 Therefore, a electrode potential is
established as Nernst eqn
E = Eo + RgT．lnai/niF
where Eo is the standard electrode potential
when the concentration of the ions is unity,
ni is the valence state of ions,
ai is the activity of ions
Rg is the gas constant
F is the Faraday’s constant
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For oxide in water
 Typical charge determining ions are
protons or hydroxyl groups, their
concentrations are described by
pH (pH = -log [H+])
When pH<pzc (corresponds to a neutral
surface), H+ is the charge determining ions
and the surface is positively charged.
When pH>pzc (neutral), OH- is the charge
determining ions and the surface is negatively
charged.
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Surface charge
determining
ions
Counter ions
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A is Hamaker
constant
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For S/r <<1, ΦA = -Ar/12S
For van der Waals attraction between two
molecules, ΦA ～ -S-6
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Interaction between two particles
Φ = ΦA + ΦB
Repulsion
attraction
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repulsion
Occurance of
2ndary min
leads to
flocculation.
attraction
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Limitations of the electrostatic
stabilization
Electrostatic stabilization is a kinetic
stabilization method.
It is only applicable to dilute system.
It is almost not possible to redisperse
the agglomerated particles
It is difficult to apply to multiple phase
systems, since in a given condition,
different solids develop different
surface charge and electric potential.
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Steric Stabilization or Polymeric
Stabilization
It is thermodynamic stabilization
method, so that particles are always
redispersible.
A very high concentration can be
accommodated, and the dispersion
medium can be completely depleted.
It is not electrolyte sensitive.
It is suitable to multiple phase system.
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Polymeric Stabilization Leads to
Monosized nanoparticles
Polymeric stabilization leads to narrow
size distribution. Polymer layer
absorbed on the surface of
nanoparticles serves as a diffusion
barrier to the growth species, resulting
in a diffusion limited growth. Diffusion
limited growth would reduce the size
distribution of the initial nuclei, leading
to monosized nanoparticles.
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Good or Poor Solvent
When polymer dissolved in a solvent
tends to expand to reduce the overall
Gibbs free energy of the system, such a
solvent is called good solvent.
When polymer in solvent tends to coil up
or collapse to reduce the Gibbs free
energy, such a solvent is called poor
solvent.
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Different Kinds of Polymer
Interacting with Solid Wall
or diblock polymer
or (c) non-absorbing polymer
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Interaction between Polymer Layers,
Coverage of polymer on the solid surface less than
50%, -- interpenetration of polymer layer -freedom reduction of polymer -- reduction of
entropy -- increase of Gibbs free energy
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Interaction between Polymer Layers
Coverage of polymer on the solid surface approaching
100%, -- compressed of two polymer layers -- coil up
of polymer in both layers -- increase of ΔG.
Poor solvent and low
coverage, interpenetration leads to further coil
up of polymer, decrease
in ΔG.
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Absorbing Polymer
For full coverage, the situation for
absorbing polymer is the same as the
anchored polymer.
For a partial coverage, situation for
absorbing polymer in good solvent can
lead to increase in ΔG, while in poor
solvent it can lead to decrease in ΔG
for L<H<2L, and lead to increase in ΔG
for H<L.
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Mixed Steric and Electric
Interactions
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