JPK instruments nanowizard afm - Youngs Modulus of Materials

JPK Instruments NanoWizard
®
Handbook Version 2.2a
45
8.3 Young’s Modulus of materials
The Young's Modulus is an elastic property of a material, and is defined as the
stress of a material divided by the strain. This is a normalized
measure of the
compressibility - the higher the value the stiffer is the sample.
F
L
ΔL
A
The Young’s Modulus, E is given by:
strain tensile
stress tensile
E =
(1)
A
F
area sectional-cross
force tensile
stress tensile ==
(2)
L
L
length original
extension
strain tensile
∆
==
(3)
Substituting (2) and (3) into (1) gives:
L.A
F.L
E
∆
=
Typical E-values for some materials
living cells
1 - 10 kPa
0.001 – 0.01 ּ 10
9
Pa
0.01 – 0.1 bar
very soft rubber
1 MPa
0.001ּ 10
9
Pa
10 bar
DNA
0.3 GPa
0.3 ּ 10
9
Pa
3,000 bar
*
proteins
0.5 GPa
0.5 ּ 10
9
Pa
5,000 bar
wood
1 GPa
1 ּ 10
9
Pa
10,000 bar
water
2.2 GPa
2.2 ּ 10
9
Pa
22,000 bar
PMMA
3 GPa
3 ּ 10
9
Pa
30,000 bar
silicon <110>
170 GPa
170 ּ 10
9
Pa
1,700,000 bar
steel
200 GPa
200 ּ 10
9
Pa
2,000,000 bar
Carbon nanotubes
Single-walled (SWNT)
multi-walled (MWNT)
~ 1000 GPa
1280 GPa
~ 1000 ּ 10
9
Pa
1280 ּ 10
9
Pa
~ 10,000,000 bar
12,800,000 bar
diamond
1150 GPa
1150 ּ 10
9
Pa
11,500,000 bar
*Cluzel, P., et al., Science (1996)
271, 792
If a piece of material is compressed
homogeneously, the calculation of the Young’s
Modulus is straightforward. For AFM measurements, however, the indentation
geometry is m
ore complicated, because the surface is locally indented with a
specific tip shape and fitting is required. The Hertz model
is the standard model
used to analyze AFM force-distance curves to extract the elasticity.
However, the
Hertz model makes serious assumptions about the sample, for example that it is