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The Nanoscale
Effects of scale:Size effects, scaling laws, and surface area
Size effects, scaling laws, and surface area
What happens when we go from macro to nano
What material properties change ?
How do they change ?
And why ?
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Size effects, scaling laws, and surface area
Macroscopic material properties
Mechanical (strength, hardness, elasticity…)
Electrical (conductivity)
Thermal (conductivity)
Colour
Chemical (reactivity, catalysis,…)
Properties are related to ?????
structure,
motion of electrons
surface area etc…..
Size effects, scaling laws, and surface area
Look at structure first and how it scales with size - example gold metal.
Macro level:
Smooth (flat) surfaces
Continuous, uniform
Properties described by continuum equations
Its ‘classical’
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Size effects, scaling laws, and surface area
Micro level:
Relatively smooth
Composed of grains and boundaries, not uniform
Properties described by continuum equations
Its ‘classical’ but include grain boundaries
Size effects, scaling laws, and surface area
Nano level:
Not smooth (atomic or molecular surfaces)
Individual atoms and molecules, not uniform
Interactions of individual atoms and molecules determine properties
Quantum mechanical
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1. Imperfections
Size effects, scaling laws, and surface area
Perfect, infinite crystals don’t exist.
Macroscopic crystals always contain defects
What imperfections (defects) can there be?
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Size effects, scaling laws, and surface area
Perfect, infinite crystals don’t exist.
Macroscopic crystals always contain defects
Point defects
Such as?
e.g. vacancy, or institials
Schottky - equal number of + and - ion vacancies
Frenkel - equal number of vacancies and interstitials
Present even at thermal equilibrium
Important in electrical conductivity and colour centresof ionic crystals
Size effects, scaling laws, and surface area
Dislocations
Line defects, nearly always present in real crystals
Very important to mechanical properties
Plastic slip can occur along dislocations
Give rise to regions of regular structure -grains or crystallites, separated by dislocations or grain boundaries.
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Effects?
We might expect these imperfections would have more of an effect at this small scale.
Example: Hall-Petch relationship
2. Nanoparticle shape
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Nano particle structure
bulk gold crystallizes as FCC cubes and octahedra
Size effects, scaling laws, and surface area
Cluster - Collection of
atoms in size range 1-100 nm
Atoms tend to close-pack but form relatively disordered structures
Magic numbers -icosahedral crystals
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Size effects, scaling laws, and surface area
Clusters can show quite different properties
Chemical reactivity
Melting point
Interesting and useful optical properties and applications
Biomedical applications ???
These are size effects. How many atoms in 10 nm gold cluster ???
How many atoms are we talking about?
30,000 atoms
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How many atoms are there in a nanoparticle?
What is its mass?
What is its surface area?
Total Atoms - Surface Atoms
Some equations For n layers, # of atoms N
in an FCC nanoparticle is
# of atoms on the surface, Nsurf
Diameter
where d = distance between nearest neighbour centres
# FCC nanoparticle atoms
Shell #, n
Diameter
Total, N On surfaceNsurf
% surface
� = 1
310�� − 15�� + 11� − 3
����� = 10�� − 20� + 12
dia = 2� − 1 �
1 234
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1. If the diameter of a gold atom is 0.288 nm, how big would a cluster containing 50 shells or 4.04 x 105 Au atoms be (in nm)?
2. How many aluminium atoms in an Al nanoparticle 10nm in diameter? (Diameter of Al atom is 0.286nm)
3. For question 2, what percent of atoms are on the surface?
# FCC nanoparticle atoms
Shell #, n
Diameter
Total, N On surfaceNsurf
% surface
1 1d 1 1 100
2 3d 13 12 92.3
3 5d 55 42 76.4
4 7d 147 92 62.6
5 9d 309 162 52.4
10 19d 2869 812 28.3
25 49d 4.90x 104
5.76 x 103 11.7
50 99d 4.04 x 105
2.4 x 104 5.9
100 199d 3.28 x 106
9.8 x 104 3.0
Shapes of gold crystals
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Nano-particle shape
Nanogold crystallises as icosahedra or Marks decahedra, or other shapes
Properties of nanocrystals
Shape depends on rate at which different surfaces grow
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Properties of nanocrystals
Shape depends on rate at which different surfaces grow
And by energy considerations
Truncated octahedral shapes are common for metallic nanoparticles as they have a large <111> surface area
Pictures on next slide show crystal shapes for different ratios, R, of <100> to <111>
Shapes of nanocrystals
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(GPa)
Anisotropy
Properties of crystals may be different in different directions
Measured values: Al: 69, Cu: 117, Fe: 200
Metal Modulus of Elasticity (GPa)
[100] [110] [111]
Al 63.7 72.6 76.1
Cu 66.7 130.3 191.1
Fe 125.0 210.5 272.7
3. What about surface area?
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Surface area
Why is surface important ?
Atoms on surface are in different ‘chemical environment’ to bulk
Not completely bonded
So electron charge available to form bonds
surface can be reactive
catalysis for example occurs at surface
Surface area
There is energy associated with the surface
This is why water tries to form spherical drops. Sphere as smallest surface area for a given volume.
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Surface area
This can make nanoclusters very reactive
There are many examples of materials that are relatively inert in the bulk but can explode as nanoscale powders.
This also makes nanoclusters unstable and likely to clump together at any possible opportunity !!
AgglomerationDifficulty in processing
Surface area
A bar of gold
How many atoms in total ??
How many atoms on the surface ??
What percentage of atoms on the surface ??
What happens as the piece of gold approaches the nanoscale?
# FCC nanoparticle atoms
Shell #, n
Diameter
Total, N On surfaceNsurf
% surface
1 1d 1 1 100
2 3d 13 12 92.3
3 5d 55 42 76.4
4 7d 147 92 62.6
5 9d 309 162 52.4
10 19d 2869 812 28.3
25 49d 4.90x 104
5.76 x 103 11.7
50 99d 4.04 x 105
2.4 x 104 5.9
100 199d 3.28 x 106
9.8 x 104 3.0
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Ratio of surface to bulk atoms
Consider surface area to volume ratio as a function of entity size
The increased importance of interfaces provides opportunities but may also present problems during operation.
How much surface area?
1cm3
6cm2
1mm cubes
60cm2
1mm cubes 6m2
1nm cubes 6000
m2
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Large surface areas obtained
7 grams of nanoparticles (four nm) have a surface area
equivalent to a football field
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Surface area
Assume a spherical piece of gold.
Ratio of surface area to volume for sphere ?
Volume 4
3R3 Surface area 4R2
Surface Area
Volume
3
R
• Percentage of atoms on surface scales as L-1
Let’s calculate a surface area!
20 g of 10nm gold particles, what is the surface area?
How should we do this?
Volume of a 10nm sphere:
If Au density is 19.3 g/cm3, weight of one sphere:
Particles in 20g:
Total surface area:
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Surfaces
� =4
3���
0.14nm
nm3
0.66
=8���
9�����
1 Atoms weighs?
Surface area of
nanocluster?
Volume of a spherical nanoparticle:
Radius of a gold atom =
Volume of a gold atom:
Assume Packing density
# atoms in a cluster :
1 mole of Au atoms weighs 197g (6.022
x 1023 atoms)
Surface area of a sphere = 4r2
Greater surface area
Improved reactivity
help create better catalysts.
already impacts about one-third of the huge U.S.—and global—catalyst markets, affecting billions of dollars of revenue in the oil and chemical industries.
Large surface area also makes nanostructured membranes and materials ideal candidates for water treatment and
It also helps support “functionalization” of nanoscalematerial surfaces (adding particles for specific purposes), for applications ranging from drug delivery to clothing insulation.
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4. Associated surface energy?
Surface energy40
E (surface
atoms)
- E (interior
atoms)
Surface Energy!
= E (surface)
Higher energy!
Surface atoms have
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Surface energy
Origin
Atoms or molecules on a solid surface posses fewer nearest neighbors or coordination numbers, thus have unsatisfied bonds exposed to the surface
Surface: atoms possess higher energy since they are less tightly bound.
Bulk: atoms possess lower energy since they are more tightly bound.
Surface energy
A simple model of this surface energy:
Assume interaction between atoms is simple pair-wise potential WAA
Potential is short ranged and acts only between nearest neighbours
Energy of an atom in bulk is sum of interactions with zb nearest neighbours
2 ,
AAbbulkA
WzE
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Energy of an atom in surface is sum of interactions with zs nearest neighbours
2 ,
AAssA
WzE
• Atom must have more nearest neighbours in bulk, that is zb > zs
EA ,s EA ,bulk
• Moving an atom from the bulk to the surface increases the internal energy• The properties of nanoclusters can be very different
Since WAA is negative
Surface energyHaven’t taken into account atomic nature of
matter
Atoms and molecules have thermal energy and they vibrate randomly
These vibrations cannot be seen at macro or micro level, but can at nanoscale
Quantum mechanics is important at nanoscale
Neglected effect of surface on properties
Confinement of electrons within a small volume has dramatic effects
Quantum size effects
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mm mm nm
Thickness of paper 0.1 100
Human hair 0.02-0.2 20-200
Talcum Powder 40
Fiberglass fibers 10
Carbon fibre 8
Human red blood cell 4-6
Wavelength of visible light 0.35-0.75 350-750
Size of a modern transistor 0.35 250
Size of Smallpox virus
Electron wavelength: Upper limit ~ 10 nm
Diameter of Carbon Nanotube
3
Diameter of DNA spiral 2
Diameter of C60 Buckyball 0.7
Diameter of Benzene ring 0.7
Size of 1 atom 0.1
The Science Changes!
Microscience ≠ Nanoscience
Above that line: electrons – hard spheres
It is still the sensible world of Sir Isaac Newton (and his physical laws)
It is still the world WE commonly experience
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The Science Changes!
Microscience ≠ Nanoscience
Below that line: electrons –mushy clouds
The rules of Quantum Mechanics => Mushy electron waves take over
and our (Newtonian) instincts and assumptions are frequently dead wrong!
5. Quantum Confinement
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Quantum Confinement In Nano Crystals, the Electronic energy levels
are not continuous as in the bulk but are discrete (finite density of states), because of the confinement of the electronic wave function to the physical dimensions of the particles.
As size decreases(<de Broglie wavelength*)
electrons (and holes) are confined
“particle in a box”
The minimum potential energy of an electron confined in a nanoparticle is higher than expected in classical physics and energy levels of different electronic states are discrete.
Thus, particle size has a drastic effect on the density of electronic states and thus on the optical response.
Quantum Confinement
Nanomaterials S2008 Greg Heness
average spacing that exists between consecutive energy levels
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Band gap
The band gap increases with reducing the size of the particles
Why is this important?
band gap is small -the emitted photon will have less energy (longer wavelength)
This relationship also holds true for absorption: To be absorbed, a photon must have at least the band gap energy.
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Bulk gold is yellow
The Lycurgus Cup (glass; British Museum; 4th century A. D.)
When illuminated from outside, it appears green. However, whenIlluminated from within the cup, it glows red. Red color is due to very small amounts of gold powder (about 40 parts per million)
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Lycurgus Cup illuminated from within
When illuminated from within, the Lycurgus cup glows red. The red color is due to tiny gold particles embedded in the glass, which have an absorption peak at around 520 nm
Nanogold has many colours
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Tunable band gaps – tunable optics
http://content.answers.com/main/content/wp/en/thumb/6/69/395px
Size Effect: Optical Spectra
A.P.Alivisatos, J. Phys. Chem. 100, 13227 (1996)
• Shift to higher energy in smaller size• Discrete structure of spectra• Increased absorption intensity
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Different properties – from band gaps?
consider this graph showing the catalytic activity of a gold nanoparticle as a function of size:
the activity is negligible for particles greater than
6 nm in diameter but
peaks for sizes of about 3nm
Why is this? The answer is not yet known with any certainty but
Electronic properties
one clue is that the gold changes from a metal (no band gap) to a semi-conductor (has a band gap) at about this size.
Somehow, being a semiconductor in this case is good for being a catalyst
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6. Scaling Laws
Scaling laws
Force = stress x area
Force scales with L2
Mass = density x volume
Mass scales with L3
Acceleration = force / mass
Accel. Scales with L-1
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Can derive many other scaling laws using a similar approach
e.g. characteristic vibration frequency
Relevant when scaling objects into the nano region – nanomachines
Scaling laws
What's going on?
At human scales (and larger) we are VERY concerned with MOMENTUM
A little bothered with FRICTION
And almost ignore SURFACE TENSION, CHARGING, Van derWaals . . .
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What's going on?
But the balance of forces changes as things get smaller:
Momentum a Mass a VOLUME = L3
But ALL of the other above forces depend on contact
Area = L2
So what happens when we scale down?
From human scale, 1 metre to 1 micron
Mass & Momentum
(106)3 = 1018
times smaller
Surface dependent
things
(106)2 = 1012
times smaller
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Making friction, surface tension, charging, VDW, a million times more important!
Becoming a billion times more important at the nanoscale!
Mass & Momentum
(106)3 = 1018
times smaller
Surface dependent things
(106)2 = 1012
times smaller
Example of how the familiar can begin to act very unfamiliar:
The cantilever beams that produce today's DLP projection TV's:
That's the goal, but early cantilever beams ended up looking like this:
← Longer cantilevers drooped down and "welded" themselves to substrate
More specifically: Surface tension of minute amount of residual water trapped between beam and substrate
T. Abe and M.L. Reed, J. Micromech & Microeng 6, 213 (1996)
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another example
Sandia's micro-transmission DID work:
Small (30 mm) gear
spun at 300,000 RPM!!
BUT seized up after 477,000 rotations
Psst! Do the math:
477,000 / 300,000 → 95 second lifetime
Stiction ≡ Sticking + Friction
Where "Sticking" = van der Waals bonding
(plus maybe some charging thrown in)
"Courtesy of Sandia National Laboratories,SUMMiTTM Technologies, www.mems.sandia.gov"
General nanoparticle properties
1. Imperfections
perfect crystalline
2. Shape
Small number of atoms
3. Surface Area
Large fraction of surface atoms
symmetry breaking at surface
changes in bond structure, atom coordination and lattice constant
4. Associated Surface Energy
large surface energy
5. Quantum Confinement
quantum confinement (size) effect
“particle-in-a box”
discrete electron energy levels
6. Scaling Laws
Friction, momentum etc.