W. Richard Bowen and Nidal Hilal 4

(a)
4 µm
0
(b)
4 µm
0
6.2 THE AfM AS A fORCE MEASUREMENT TOOL IN PHARMACEUTICALS 181
Force (nN)
(e)
8
7
6
5
4
3
2
1
0
�1
Retracting
0 20 40 60
Log E (Pa)
Force (nN)
The value of indentation can then be related to the combined elastic
modulus of the tip and the sample (K) by:
L
K �
( � R)
10
9
8
7
6
5
4
3
2
1
3 2
0 50 100 150
Relative z (nm)
200 250 300
1
1. Si Reference
2. Crystalline
3. Amorphous
1.0 � 10 8
1.0 � 10 7
1.0 � 10 6
1.0 � 10 5
1.0 � 10 4
2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
Load (nN)
Extending
80 100 120 140 160 180
Relative z (nm)
3 1/ 2
8
Crystalline
Amorphous
FIgure 6.4 (a) AFM images of unmodified sorbitol (topographic height and phase
images), insert highlights banding pattern; (b) AFM images within a quench-cooled
domain of sorbitol, which would be expected to have a more amorphous nature;
(c) nanoindentation curves for the crystalline and amorphous domains; (d) load dependence
on Young’s modulus and (e) force curve from the amorphous domain. Reproduced
with permission [37].
(6.1)
where L is the load and R is the radius of the probe. Since the combined
elastic modulus contains the elastic moduli for the tip and the sample,
(c)
(d)