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The NanoscaleThe Nanoscale��� ��� ���

Size effects, scaling laws, and surface areaSize 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 ?

What happens when we go from macro to nano

What material properties change ?

How do they change ?

And why ?

Size effects, scaling laws, and surface areaSize effects, scaling laws, and surface area

Macroscopic material properties

Mechanical (strength, hardness, elasticity…)

Electrical (conductivity)

Thermal (conductivity)

Colour

Chemical (reactivity, catalysis,…)

Macroscopic material properties

Mechanical (strength, hardness, elasticity…)

Electrical (conductivity)

Thermal (conductivity)

Colour

Chemical (reactivity, catalysis,…)

Properties are related to?Properties are related to?

structure, 

motion of electrons

surface area etc…..

structure, 

motion of electrons

surface area etc…..

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Look at structure first –Macro levelLook at structure first –Macro level

Example gold

Macro level:

Smooth (flat) surfaces

Continuous, uniform

Properties described by continuum equations

Its ‘classical’

Example gold

Macro level:

Smooth (flat) surfaces

Continuous, uniform

Properties described by continuum equations

Its ‘classical’

Relatively smooth

Composed of grains and boundaries, not uniform

Properties described by continuum equations

Its ‘classical’ but include grain boundaries

Relatively smooth

Composed of grains and boundaries, not uniform

Properties described by continuum equations

Its ‘classical’ but include grain boundaries

Look at structure first –Micro levelLook at structure first –Micro level

Not smooth (atomic or molecular surfaces)

Individual atoms and molecules, not uniform

Interactions of individual atoms and molecules determine properties

Quantum mechanical

Not smooth (atomic or molecular surfaces)

Individual atoms and molecules, not uniform

Interactions of individual atoms and molecules determine properties

Quantum mechanical

Look at structure first –Nano levelLook at structure first –Nano level

1. Imperfections1. Imperfections

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Perfect, infinite crystals don’t exist.Perfect, infinite crystals don’t exist.

Macroscopic crystals always contain defectsMacroscopic crystals always contain defects

Probability that an atom is substituted by an impurity:

Inspection would show that the smaller the nanomaterial the higher the probability of it being imperfection free

Assuming nanification does not introduce imperfections

Probability that an atom is substituted by an impurity:

Inspection would show that the smaller the nanomaterial the higher the probability of it being imperfection free

Assuming nanification does not introduce imperfections

Perfect, infinite crystals don’t exist.Perfect, infinite crystals don’t exist.

Imperfections

Point Line Surface

vacancy

interstitials

Schottky

Frenkel

vacancy

interstitials

Schottky

Frenkel

edge dislocations

Screw dislocations

edge dislocations

Screw dislocations

Surfaces

Grain boundaries

Surfaces

Grain boundaries

Effects?Effects?

We might expect these imperfections would have more of an effect at this small scale.

Example: Hall-Petch relationship

We might expect these imperfections would have more of an effect at this small scale.

Example: Hall-Petch relationship 2. Nanoparticle shape2. Nanoparticle shape

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A cluster?A cluster?

A collection of atoms in size range 1-100 nm

Atoms tend to close-pack but form relatively disordered structures

Magic numbers - icosahedral crystals

A collection of atoms in size range 1-100 nm

Atoms tend to close-pack but form relatively disordered structures

Magic numbers - icosahedral crystals

How many atoms are we talking about?How many atoms are we talking about?

Clusters can show quite different properties to bulk materialsClusters can show quite different properties to bulk materials

Chemical reactivityMelting point Interesting and useful

optical properties and applications

Biomedical applications ???

Chemical reactivityMelting point Interesting and useful

optical properties and applications

Biomedical applications ???

Bulk gold crystallises as face centred cubic (FCC)Cubes and octahedra

Bulk gold crystallises as face centred cubic (FCC)Cubes and octahedra

What crystal shape does gold have?What crystal shape does gold have?

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Shapes of gold crystalsShapes of gold crystals

Nano-particle shape

Nano-particle shape

Nanogold crystallises as icosahedra or Marks decahedra, or other shapesNanogold crystallises as icosahedra or Marks decahedra, or other shapes

Shape depends on rate at which different surfaces growShape depends on rate at which different surfaces grow

Certain crystallographic directions grow quicker

Certain crystallographic directions grow quicker

Truncated octahedral shapes are common for metallic nanoparticles as they have a large <111> surface area

Truncated octahedral shapes are common for metallic nanoparticles as they have a large <111> surface area

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Crystal shapes for different ratios, R, of <100> to <111>Crystal shapes for different ratios, R, of <100> to <111> 3. What 

about surface area?

3. What about 

surface area?

Why would surface be important?Why would surface be important?

Atoms on surface are in different ‘chemical environment’ to bulkNot completely bonded

So electron charge available to form bondssurface can be reactivecatalysis for example occurs at surface

Atoms on surface are in different ‘chemical environment’ to bulkNot completely bonded

So electron charge available to form bondssurface can be reactivecatalysis for example occurs at surface

Ratio of surface to bulk atomsRatio 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.

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.

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400

1500

3250

How much surface area?How much surface area?

1cm3

6cm2

1mm cubes

60cm2

1m cubes 6m2

1nm cubes 6000 m2

Large surface areas obtainedLarge surface areas obtained7 grams of nanoparticles (four nm) have a surface area

equivalent to a football field7 grams of nanoparticles (four nm) have a surface area

equivalent to a football field

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4. Associated surface energy?

4. Associated surface energy?

There is an energy associated with the surfaceThere is an energy associated with the surface

This is why water tries to form spherical drops.  

Sphere as smallest surface area for a given volume.

This is why water tries to form spherical drops.  

Sphere as smallest surface area for a given volume.

Surface energySurface energy

Origin

Atoms or molecules on a solid surface have unsatisfied bonds fewer nearest neighbors or coordination numbers

Origin

Atoms or molecules on a solid surface have unsatisfied bonds fewer nearest neighbors or coordination numbers

Bulk: atoms possess lower energy since they are more tightly bound.

Surface: atoms possess higher energy since they are less tightly bound.

E (surface

atoms)

- E (interioratoms)

= E (surface) ReacivityReacivity

This surface energy effect can make nanoclusters very reactiveThere are many examples of materials that are

relatively inert in the bulk but can explode as nanoscale powders.

This also makes nanoclusters unstable Many surface atoms to react with the environment

Likely to clump together at any possible opportunity !!

This surface energy effect can make nanoclusters very reactiveThere are many examples of materials that are

relatively inert in the bulk but can explode as nanoscale powders.

This also makes nanoclusters unstable Many surface atoms to react with the environment

Likely to clump together at any possible opportunity !!

AgglomerationDifficulty in processing

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SolubilitySolubility

Vapour pressure, and by extension solubility increases with decreasing particle size according to the Kelvin equation:

Terms from left to right are:

Boltzmann’s constant, vapour pressure, vapour pressure on an infinite plate, surface energy, molecular volume, radius

Note that may change with size (curvature dependent)

Vapour pressure, and by extension solubility increases with decreasing particle size according to the Kelvin equation:

Terms from left to right are:

Boltzmann’s constant, vapour pressure, vapour pressure on an infinite plate, surface energy, molecular volume, radius

Note that may change with size (curvature dependent) 33

So?So?

Greater surface areaGreater 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.

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.

Nanoscale vs MacroscaleNanoscale vs Macroscale

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Haven’t taken into account atomic nature of matterHaven’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 nanoscaleConfinement of electrons within a small volume has

dramatic effectsQuantum size effects

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 nanoscaleConfinement of electrons within a small volume has

dramatic effectsQuantum size effects

5. Quantum Confinement5. Quantum Confinement

mm m nmThickness of paper 0.1 100Human hair 0.02-0.2 20-200Talcum Powder 40Fiberglass fibers 10Carbon fibre 8Human red blood cell 4-6Wavelength of visible light 0.35-0.75 350-750Size of a modern transistor 0.35 250Size 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

Microscience ≠ NanoscienceMicroscience ≠ 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

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

The Science Changes! 

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Microscience ≠ NanoscienceMicroscience ≠ Nanoscience

Below that line: electrons –mushy clouds

The rules of Quantum Mechanics (Mushy electron waves) take over

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!

And our (Newtonian) instincts and assumptions are frequently dead wrong!

Quantum size effectQuantum size effect

Bohr radius of an electron moving in condensed matter is

∗

Typically a few to a few hundred nm

Therefore, practically possible to make nanoparticles smaller than the Bohr radius

In this case the energy of the electron increases

Band edge of optical absorption blue shifts for r < rB QUANTUM DOTS

Bohr radius of an electron moving in condensed matter is

∗

Typically a few to a few hundred nm

Therefore, practically possible to make nanoparticles smaller than the Bohr radius

In this case the energy of the electron increases

Band edge of optical absorption blue shifts for r < rB QUANTUM DOTS

Tunable band gaps –tunable opticsTunable band gaps –tunable optics

http://content.answers.com/main/content/wp/en/thumb/6/69/395px-Fluorescence_in_various_sized_CdSe_quantum_dots.png

• Shift to higher energy in smaller size• Discrete structure of spectra• Increased absorption intensity

Quantum ConfinementQuantum Confinement

average spacing that exists between consecutive energy levels

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Band gapBand gap

The band gap increases with reducing the size of the particles

The band gap increases with reducing the size of the particles

This relationship also holds true for absorption:This relationship also holds true for absorption:

Particle size smaller

Band gap increases

Emitted photon higher

energy & frequency

shorter wavelength

•DOI: 10.1007/s41061-016-0060-0

Bulk gold is yellowBulk gold is yellow

The Lycurgus Cup (4th

Century)Nanogold has many coloursNanogold has many colours

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Different properties – from band gaps?Different properties – from band gaps?

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 3 nm

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 3 nm

Why is this? The answer is not yet known with any certainty 

Electronic propertiesElectronic 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

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

6. Scaling Laws6. Scaling Laws

Scaling lawsScaling 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

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

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? What's going on? 

At human scales (and larger) we are VERY concerned with MOMENTUMMomentum Mass VOLUME = L3

A little bothered with FRICTIONAnd almost ignore SURFACE TENSION,

CHARGING, Van der Waals . . .

Area = L2

At human scales (and larger) we are VERY concerned with MOMENTUMMomentum Mass VOLUME = L3

A little bothered with FRICTIONAnd almost ignore SURFACE TENSION,

CHARGING, Van der Waals . . .

Area = L2

So what happens when we scale down? 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

Making friction, surface tension, charging, VDW, a million times more important!

Becoming a billion times more important at the nanoscale!

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

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Forces between objectsForces between objects

At nanoscale gravitational forces and nuclear forces are very weak

Van der Waals not and we shall see their importance when we look at self assembly

At nanoscale gravitational forces and nuclear forces are very weak

Van der Waals not and we shall see their importance when we look at self assembly

Magnitude of forces (gravitational, electrostatic, etc.)

Distance between them Their size

Forces (cont.)Forces (cont.)

Casimir forces between two mirrors or sheets of metal

Force fall off rapidly with distance d-4

At microscale – negligible

At nanoscale 105N/m (atmospheric pressure)

May be expected to affect the operation of nanoscale devices

Casimir forces between two mirrors or sheets of metal

Force fall off rapidly with distance d-4

At microscale – negligible

At nanoscale 105N/m (atmospheric pressure)

May be expected to affect the operation of nanoscale devices

e.g. Stiffnesse.g. Stiffness

Spring constant, k, of a cantilever varies with 1/l3

As does resonant frequency

Ensures a fast response

In fact nanomechanical devices are extremely stiff

, =

In a vacuum, no problems

In a normal environment:

Spring constant, k, of a cantilever varies with 1/l3

As does resonant frequency

Ensures a fast response

In fact nanomechanical devices are extremely stiff

, =

In a vacuum, no problems

In a normal environment:

The cantilever beams that produce 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 residualwatertrapped between beam and substrate

The cantilever beams that produce 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 residualwatertrapped between beam and substrate

T. Abe and M.L. Reed, J. Micromech & Microeng 6, 213 (1996)

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Another exampleSandia's micro‐transmission Another exampleSandia's micro‐transmission 

Small (30 m) gear spun at 300,000 RPM!!

DID work BUT seized up after 477,000 rotations

Do the math:

477,000 / 300,000 → 95 second lifetime

Small (30 m) gear spun at 300,000 RPM!!

DID work BUT seized up after 477,000 rotations

Do the math:

477,000 / 300,000 → 95 second lifetime

"Courtesy of Sandia National Laboratories,SUMMiTTM Technologies, www.mems.sandia.gov"

Stiction ≡ Sticking + FrictionStiction ≡ Sticking + Friction

van der Waals bonding (plus maybe some

charging thrown in)

FerromagnetismFerromagnetism

Nanoparticles of normally ferromagnetic materials Still have large magnetic susceptibility in presence of a

large external magnetic field

But lacks the remnant ferromagnetism characteristic

“Superparamagnetism” (domain sizes)

And? Lower limit (about 20nm) for magnetic storage

appications of nanoparticles At room temperature thermal energy overcomes the

magnetostatic energy resulting in zero hysteresis

Nanoparticles of normally ferromagnetic materials Still have large magnetic susceptibility in presence of a

large external magnetic field

But lacks the remnant ferromagnetism characteristic

“Superparamagnetism” (domain sizes)

And? Lower limit (about 20nm) for magnetic storage

appications of nanoparticles At room temperature thermal energy overcomes the

magnetostatic energy resulting in zero hysteresis

Summary - General nanoparticle propertiesSummary - General nanoparticle properties

1. Imperfectionsperfect crystalline

2.ShapeSmall number of atoms

3.Surface AreaLarge fraction of surface atomssymmetry breaking at surfacechanges in bond structure, atom

coordination and lattice constant

1. Imperfectionsperfect crystalline

2.ShapeSmall number of atoms

3.Surface AreaLarge fraction of surface atomssymmetry breaking at surfacechanges in bond structure, atom

coordination and lattice constant

Summary - General nanoparticle propertiesSummary - General nanoparticle properties

4. Associated Surface Energy

large surface energy5. Quantum Confinement

quantum confinement (size) effect“particle-in-a box”discrete electron energy levels

6. Scaling Laws

Friction, momentum etc.

4. Associated Surface Energy

large surface energy5. 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??Questions??

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