02- 1

Nanoscale Phenomena

Physics at the Nanoscale • Electromagnetic force are

predominant

• Wave-particle duality of matter

• Quantum mechanical tunnelling – penetration of electron wavefunction into an energy barrier that is classically forbidden

• Quantum confinement > increased bandgap, leading to different electrical and optical properties

• Quantization of energy – discrete energy levels

• Internal magnetic field and coercive force – size dependent

• Random molecular motion – Brownian motion

02- 7

Chemistry at the Nanoscale • Intra-molecular bonding or chemical

interaction: ionic bonds, covalent bonds, metallic bonds – important to structure

• Inter-molecular bonding or physical interaction: ion-ion and ion-dipole, van-der Waals, hydrogen bond, plus hydrophobic interactions and repulsive forces (steric repulsions)

• Increase in surface-to-volume ratio > increased reactivity due to high surface energy of the surface atoms –important to catalysis and sensing

• Shape can also change surface area

• Increase in surface energy > decrease in melting point + increase in heat capacity

Spherical Fe Nanocrystals

How to calculate % of surface atoms in a nanocube? For a typical “bulk” object:

Volume density = 1023 atoms/cm3

Surface density = 1015 atoms/cm2

NB: 1 nm = 10-7 cm

For a nanocube of 1 nm side length:

Total # of atoms in a nanocube = 1023/cm3 × (10-7 cm)3 ~ 100

Total # of atoms on the surface of nanocube = 1015/cm2 × 6 × (10-7 cm)2 ~ 60

% of surface atoms = 60/100 = 60%

02- 8 Source: Klabunde et al., J. Phys. Chem. 100 (1996) 12142.

Reduction in M.P.

02- 9 Source: B. D. Fahlman, "Materials Chemistry", 2nd ed., Springer, New York (2011), Ch. 6.

• Atoms on the surface have higher energy (i.e. more like atoms in liquid).

• Surface energy increases as size decreases

• Lowering in MP ∝ 1/r

• Decrease ~ a few hundreds K for <10 nm

02- 10

Source: B. D. Fahlman, "Materials Chemistry", 2nd ed., Springer, New York (2011), Ch. 6.

Increase in Reactivity

02- 11

Side Length Number of Cubes in a 1 m3

Cube

Total Surface Area

1 m 1 6 m2

0.1 m 103 60 m2

0.01 m = 1 cm 106 600 m2

10-3 m = 1 mm 109 6000 m2 ~ 1 football

field (5390 m2)

10-9 m = 1 nm 1027 6x109 m2 = 6000 km2

1,500 x UW campus

Source: B. D. Fahlman, "Materials Chemistry", 2nd ed., Springer, New York (2011) ; Ch. 6

Increase in Heat Capacity

• Specific heat capacity: C = ∆Q/(m ∆T)

• For polycrystalline materials at high T: CV = 3 R /M ~ 26 J mol-1 K-1 , where M is mol wt, R is gas constant [ 1 J = 0.239 cal, 1 cal = heat needed to raise 1 g of H2O by 1 deg]

• For nanocrystalline material at high T: CV is higher than the bulk due to quantum confinement effects and higher surface energy.

• Examples: Pd 6 nm : +48% 25-37 J mol-1 K-1 at 250 K Cu 8 nm : +8% 24-26 J mol-1 K-1 at 250 K Ru 6 nm : +22% 23-28 J mol-1 K-1 at 250 K

02- 12

As the size of the object gets into the nanoscale…

In addition to changes in the mechanical property (related to physical structure), thermal property, and in reactivity (deteriorative property), changes in optical, electrical, and magnetic properties also occur.

Re mechanical property…

Surface and interfacial forces (e.g. adhesion forces, capillary forces, strain forces) dominate at the nanoscale. These forces could overcome forces at macro scale (e.g. gravity). E.g. superhydropho-bicity of lotus leaf; surface coating; NEMS.

02- 13

Source: http://spie.org/x33323.xml

The Lycurgus Cup 400 AD

The optical properties are due to light scattering effect resulting from surface plasmons of appropriate nanoparticle size and distribution – “Roman” Nano-plasmonics?

02- 14

Chemical composition:

Silica (SiO2): 73%, Na2O: 14%, lime (CaO): 7% + 0.5% Mg

+ ~40 ppm Au + ~330 ppm Ag – These are present as colloidal nanoalloy (~70 nm) dispersed in the soda-lime-silica glass.

Reflected light = Appeared as green like jade Transmitted light = Appeared as red like ruby “The mythological scenes on the cup depict the death of Lycurgus, King of the Edoni in Thrace at the hands of Dionysus and his followers. A man of violent temper, Lycurgus attacked Dionysus and one of his maenads, Ambrosia. Ambrosia called out to Mother Earth, who transformed her into a vine. She then coiled herself about the king, and held him captive. The cup shows this moment when Lycurgus is enmeshed in vines by the metamorphosing nymph Ambrosia, while Dionysus with his thyrsos and panther (Fig 2), a Pan and a satyr torment him for his evil behaviour. It has been thought that the theme of this myth - the triumph of Dionysus over Lycurgus - might have been chosen to refer to a contemporary political event, the defeat of the emperor Licinius (reigned AD 308-24) by Constantine in AD 324.” Source: “The Lycurgus Cup – A Roman Nanotechnology” I. Freestone, N. Meeks, M. Sax, C. Higgitt, Gold Bulletin, 40 (2007) 270.

Size-dependent Properties of Gold

Surface plasmons (SPs) are natural collective oscillations of the electron gas in metals. The localized SP resonance frequency depends on the size and shape of the nanoparticle (and its dielectric function). Absorption peak broadens and shifts to longer wavelengths as size increases above 50 nm. Reflection (caused by scattering) is weaker at smaller sizes.

02- 15

Quantum Confinement

When an electron is promoted from valence to conduction bands, an electron-hole pair known as an exciton is created in the bulk lattice. The physical separation between e- and h+

is known as the exciton Bohr radius (rB). When the size (or diameter D) of an nano-object (quantum dot), i.e. D 2rB, this leads to quantum confinement of the exciton.

02- 16

Unlike bulk semiconductor crystal, the dimensions of a quantum dot (or an nano-object) could be quite small. Adding or removing an atom could change the dimension of the nanocrystal a lot, causing significant change in the bandgap of the bulk, Eg.

Exciton

Above: (A) Nanocrystal quantum dots are surrounded by a layer of organic molecules (surfactants) that allows precise size control, prevent conduction electrons from getting trapped at the surface, and make nanocrystals soluble. (B) The process of carrier multiplication—the freeing of two electrons (or creation of two excitons) with one high-energy photon—is depicted two ways: on the energy ladder and within the crystal lattice. In the latter, the valence electons orbit the atomic nuclei, and the conduction electrons move freely.

02- 17

Source: http://www.lanl.gov/science/1663/june2010/story2.shtml

Material m*e m*

h er Eex [meV]

rex [nm]

BN 0,752 0,38 5,1 131 1,1

GaN 0,20 0,80 9,3 25,2 3,1

InN 0,12 0,50 9,3 15,2 5,1

GaAs 0,063 0,50 13,2 4,4 12,5

InP 0,079 0,60 12,6 6,0 9,5

GaSb 0,041 0,28 15,7 2,0 23,2

GaP

InAs 0,024 0,41 15,2 1,3 35,5

InSb 0,014 0,42 17,3 0,6 67,5

ZnS 0,34 1,76 8,9 49,0 1,7

ZnO 0,28 0,59 7,8 42,5 2,2

ZnSe 0,16 0,78 7,1 35,9 2,8

CdS 0,21 0,68 9,4 24,7 3,1

ZnTe 0,12 0,6 8,7 18,0 4,6

CdSe 0,11 0,45 10,2 11,6 6,1

CdTe 0,096 0,63 10,2 10,9 6,5

HgTe 0,031 0,32 21,0 0,87 39,3

Si 7,5

To be useful for solar cell application, exciton binding energy must be greater than kT = 25 meV

02- 18

Other models include Coulombic interaction of excitons and the correlation energy

Source: B. D. Fahlman, "Materials Chemistry", 2nd ed., Springer, New York (2011) ; Ch. 6