Effects of Scale

Effects of ScaleSIZE MATTERS

New properties enable new applications1. Chemical properties –

◦ reactivity, catalysis

2. Thermal properties –◦ melting temperature

3. Mechanical properties –◦ adhesion, capillary forces

4. Optical properties –◦ absorption and scattering of light

5. Electrical properties –◦ tunneling current

6. Magnetic properties –◦ superparamagnetic effect

At the nanometer scale, properties become size dependent

Many things change as we go “nano”

THE EFFECT OF FORCES

SURFACES. THE ATOMIC BEHAVIOUR.

Would we expect things to change as we change scale?Two diffuse limits

AREA

VOLUME MASS FORCE ACCELERATION

AREA SCALES WITH?

A � L2

FORCE SCALES WITH?

A � L2FORCE/MASS

ACCELERATION SCALES WITH?

A � L-1

VOLUME SCALES WITH?

V � L3

IMPLIES MASS SCALES WITH?

M � L3

Scaling laws –Consider elements with a linear dimension L

L

L

L

LL

F = ��X A

L2/L3 =L-1

Example: Weight Lifting

body mass, M, � ?

surface area � ?

Weight � surface area � (mass)?

L3

L2

mass 2/3

What’s the dependence of the maximum weight a human can lift on his/her body weight?

World weight-lifting record. The weight lifted (wT) is precisely proportional to the 0.67 power of body weight

Example from BioSensing & BioMEMS 530/580.672 Jeff Wang, Johns Hopkins University

Example: A beam bendingSay a cantilever beam

Deflection of a beam due to its own weight varies as L2

A beam 1000x (103)smaller

Bends 106 less!

01

MMass & (thus) Momentum

02

(106)3 = 1018 times smaller

03

Surface dependent things (area)

04


So what happens when we scale down?

From human scale, 1 metre to 1 �m (106 more important

WWhat's going on?

At human scales (and larger) we are VERY concerned with MOMENTUM

Momentum ��Mass ��VOLUME = L3

A little bothered with FRICTION

And almost ignore SURFACE TENSION, CHARGING, Van der Waals . . .

Area = L2

TUM

. .

Would we expect things to change as we change scale?Effects of gravity become negligible

compared to adhesive and friction effects

Surface tension dominates gravity

Don’t have to go that far, at the mm scale

30cm � 100X height of ant• Momentum tries to tear

them apart L-1

• Charge (H-bonds) & VDW help hold them together L2

• Ratio of cohesive to destructive forces is 1000 times more favorable

From even higher! 9m�3000X height of ant

Friction, surface tension, charging, VDW, are a million times more important!

The result at the �m scale

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 residual water trapped between beam and substrate

T. Abe and M.L. Reed, J. T. Abe and MMicromech

d Mhh &

. Reed, J.M.LM&&&& Microeng

. , J.gg 6, 213 Microme

(1996)

AAnother 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

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

Stiction ≡ Sticking + Friction

van der Waals bonding (plus maybe some

charging thrown in)

ns

ding e )

WWhat would that mean for things like nanobots withmmechanical moving parts

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

Nanogears - Possible?

01

MMass & (thus) Momentum

02

(109)3 = 1027times smaller

03

Surface dependent things (area)

04


So what happens when we scale down?

From human scale, 1 metre to 1 nm (109 more important

Friction, surface tension, charging, VDW, are now a billion times more important at the nanoscale!

The result now at the nm scale

Would we expect things to change as we change scale?

Surface effects dominate

Eventually quantum effects appear

Confinement

Confinement of electrons within a small volume has dramatic effects.

Important

Quantum mechanics is important at nanoscale

Thermal energy

Vibrations

QuantumMechanics

Quantumsize

effects

At the nanoscale

These vibrations are not seen at macro/micro level, but can at nanoscale

Thermal Energy

Atoms & molecules have thermal energy and they vibrate randomly

TThe atomic nature of matter

Quantum Confinement

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

Thicknessssssssss ooooofffff ppap

HHHHHuuumman hair

Talcum Powder

Wavelenggggtttthhhhh ooooofffff vv

Sizzzzzeee oooff a moder

Size of Smallpox

The Science Changes - Microscience ≠ Nanoscience� It is still the sensible world of Sir Isaac

Newton (and his physical laws)

� It is still the world WE commonly experience

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

3

222

0.77

0.7

0077

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

ss ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

02

03

04

05

01Bohr radius of an electron moving in condensed matter is

BOHR RADIUS

Typically a few to a few hundred nm

VERY SMALL

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

NANOPARTICLES

Band edge of optical absorption blue shifts for r < rBShorter wavelength

QUANTUM DOTS

In this case the energy of the electron increasesElectrons not as free to move about as in bulk material

THE ELECTRON ENERGY INCREASES

Quantum size effect

01

03

04

05

02Typically a few to a few hundred nm

VERY SMALL


NANOPARTICLES


QUANTUM DOTS



Quantum size effect

Bohr radius of an electron moving in condensed matter is

BOHR RADIUS

01

02

04

05

03Therefore, practically possible to make nanoparticles smaller than the Bohr radius

NANOPARTICLES


VERY SMALL


QUANTUM DOTS



Quantum size effect


BOHR RADIUS

01

02

03

05

04In this case the energy of the electron increasesElectrons not as free to move about as in bulk material



VERY SMALL


NANOPARTICLES


QUANTUM DOTS

Quantum size effect


BOHR RADIUS

Quantum size effect

01

02

03

04

05Band edge of optical absorption blue shifts for r < rBShorter wavelength

QUANTUM DOTS


VERY SMALL


NANOPARTICLES



Quantum size effect


BOHR RADIUS


BOHR RADIUS01

02

03

04

05


VERY SMALL


NANOPARTICLES




QUANTUM DOTS

Quantum size effect

Quantum ConfinementEquate to band gap

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“blue shift”

Tunable 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

Nanogold has many colours

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

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

Electronic propertiesone 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

Tunneling effect - a nanoscopic phenomenon

Electron tunneling is attained when a particle with lower energy is able to exist on the other side of an energy barrier with higher potential energy

https://physicsopenlab.org/2017/05/30/tunnel-effect/

Not enough energy to go over barrier, so must “tunnel”

Classical World

Quantum World


Example 1.

Quantum Tunnel Composite (QTC)◦ Metal nano-particles immersed in a non-conductive elastomer (flexible), they are used as pressure sensors

◦ In their normal state they are perfect insulators but when compressed they become good conductors and allow for high currents to pass


– “classical” electrical resistance varies linearly (proportional to distance), while quantum tunneling varies exponentially to decreasing distance, by activating a resistance change of a factor up to 1012 between


Example 2.Basis of the operation of the Floating Gate MOSFET, component used in computer memories.

This structure is a capacitor, and is capable of holding electric charge for very long time, which has allowed it to be used as memory cell in many electronic applications.


Nanomaterials

What about surfaces & interfaces as we go nano?

How much surface area?

1cm3

6cm2

1mm cubes

60cm2

1�m cubes 6m2

1nm cubes

6000 m2

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

Surface area

400

1500

3250

Associated surface energy

There 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.

Surface energy

◦ Atoms or molecules on a solid surface are in a different chemical environment

◦ They have unsatisfied bonds◦ electron charge available to form 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.

Esurface atoms > Einterface atoms > Ebulk atoms

So surfaces can be reactive

?

Ratio of surface to bulk atoms as particles get smaller

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.

Nanoscale vs Macroscale – Melting Point

Surface atoms require lessenergy to move because they are in contact with fewer atoms of the substance

Reactivity

◦ This surface energy effect can make nanoclusters very reactive◦ There are many examples of materials that are relatively inert in the bulk but can explode as nanoscale powders.

Aluminium Dust Explosion

Reactivity

This surface energy effect also makes nanoclusters unstable ◦ Likely to clump together at any possible opportunity !!

Agglomeration leads to difficulty in processing

Solubility

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, temperature, vapour pressure, vapour pressure on an infinite plate, surface energy, molecular volume, radius

Why does solubility increase?54

�

Note that �may change with size (curvature dependent)

help create better catalysts.

01 Improved reactivity

Impacts about one-third of the huge global catalyst markets, in the oil and chemical industries.

02 Improved reactivity

Makes nanostructured membranes and materials ideal candidates for

water treatment

03 Large surface area

Adding particles for specific purposes, for applications ranging from drug delivery to clothing insulation.

04 Functionalisation

Other Changes

Nanoparticle shape

What crystal shape does gold have?Bulk gold crystallises as face centred cubic (FCC)

◦ Cubes and octahedra

SShapes of gold crystals

ImperfectionsIMPORTANT CONSEQUENCES FOR ALL THERMO-

MECHANICAL PROPERTIES AND PROCESSES

Perfect, infinite crystals don’t exist.

Imperfections

Point Line Surface

� vacancy

� interstitials

� Schottky

� Frenkel

� edge dislocations

� Screw dislocations

� Surfaces

� Grain boundaries

Macroscopic crystals always contain defects

Substitutional

� The smaller the nanomaterial the higher the probability of it being substitutionally free

� Nanocrystals are predicted to be essentially vacancy-free; their small size precludes any significant vacancy concentration

For nano-crystalline materials

Assuming nanification does not introduce imperfections

Interfaces?ANOTHER STORY

Interfaces?

For crystalline materials we are really talking about grain boundaries

Atoms here have higher energies

We would expect some effect, as grain size approaches nanoscale

•DOI: 10.1007/s11661-006-0032-z

Example: Resistivity

Computer simulations of grain boundaries have shown that the band gap can be reduced by up to 45%.

In the case of metals grain boundaries increase the resistivity as the size of the grains relative to the mean free path of other scatters becomes significant.

These atoms behave differently to bulk atoms (

our discussion on surfaces)

Grain boundaries – play a significant role in materials properties

For nanostructured materials with grain size of 5 nm, nearly 50% of atoms will reside in or near the GB

Grain Boundary Effects on Microstructural Stability of Nanocrystalline Metallic Materials Zhu et al.,

The contribution of different microstructural elements to the volume fraction as a function of grain size (d), assuming a grain-boundary thickness (δ) of 1 nm.

Grain Boundaries

Implies properties in ultra-finegrained materials which will be principally controlled by interfacial properties rather than those of the bulk.

We shall see this later

0102

0304

Scaling laws making surface things much more important

More surface areaMore associated surface energyReactivity & solubility

Quantum confinementBand gaps, tunnelling

Crystal shapeInterfaces, grain boundaries, imperfections

Summary

Effects of Scale

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