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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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So?

Nanoscale vs Macroscale

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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.

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Questions??