Hamaker constants are characteristic material properties that determine the magnitude of the nonlinear van der Waals force between atoms, molecules and nanoscale aggregates of atoms. This paper explores the novel possibility of using Harmonic Balance based nonlinear system identification methods to extract from the nonlinear vibration spectrum of resonant atomic force silicon microcantilevers, the Hamaker constants between a few atoms at the tip of the microcantilever and graphite, gold and silicon carbide samples. First, the nonlinear dynamics of a diving board microcantilever coupled to the samples through van der Waals force potentials are investigated through a discretized model of the system. Next, the feasibility of using Harmonic Balance based nonlinear system identification techniques are demonstrated using simulations of the discretized model. Finally the method is implemented on an AFM system. The results indicate that the proposed method provides a novel alternative way to measure Hamaker constants and the measured results are within the range of known experimental data.

1.
Israelachvili, J. N., 1992, Intermolecular and Surface Forces, 2nd edition, Academic Press, San Diego.
2.
Cappella
,
B.
, and
Dietler
,
G.
,
1999
, “
Force-distance Curves by Atomic Force Microscopy
,”
Surf. Sci. Rep.
,
34
, pp.
1
104
.
3.
Visser
,
J.
,
1972
, “
On Hamaker Constants: A Comparison between Hamaker Constants and Lifshitz- van der Waals Constants
,”
Adv. Colloid Interface Sci.
,
3
, pp.
331
363
.
4.
Bergstrom
,
L.
,
1997
, “
Hamaker Constants of Inorganic Materials
,”
Adv. Colloid Interface Sci.
,
70
, pp.
125
169
.
5.
Argento
,
C.
, and
French
,
R. H.
,
1996
, “
Parametric Tip Model and Force-distance Relation for Hamaker Constant Determination from Atomic Force Microscopy
,”
J. Appl. Phys.
,
80
(
11
), pp.
6081
6090
.
6.
Hutter
,
J. L.
, and
Bechhoefer
,
J.
,
1994
, “
Measurement and Manipulation of van der Waals Force in Atomic-force Microscopy
,”
J. Vac. Sci. Technol. B
,
B12
(
3
), pp.
2251
2253
.
7.
Biggs
,
S.
, and
Mulvaney
,
P.
,
1994
, “
Measurement of the Forces between Gold Surfaces in Water by Atomic Force Microscopy
,”
J. Chem. Phys.
,
100
(
11
), pp.
8501
8505
.
8.
Gady
,
B.
, et al.
,
1996
, “
Identification of Electrostatic and van der Waals Interaction Forces Between a Micrometer-size Sphere and a Flat Substrate
,”
Phys. Rev. B
,
53
, pp.
8065
8070
.
9.
Gady
,
B.
,
Reifenberger
,
R.
, and
Rimai
,
D. S.
,
1997
, “
Contact Electrification and the Interaction Force between a Micrometer-size Polystyrene Sphere and a Graphite Surface
,”
Langmuir
,
13
, pp.
2533
2537
.
10.
Gady
,
B.
, et al.
,
1998
, “
The Interaction between Micrometer-size Particles and Flat Substrates: A Quantitative Study of Jump-to-contact
,”
J. Adhes.
,
67
, pp.
291
305
.
11.
de Pablo
,
P. J.
, et al.
,
1999
, “
Adhesion Maps Using Scanning Force Microscopy Techniques
,”
J. Adhes.
,
71
, pp.
339
356
.
12.
Garcı´a
,
R.
, and
Perez
,
R.
,
2002
, “
Dynamic Atomic Force Microscopy Methods
,”
Surf. Sci. Rep.
,
47
, pp.
197
301
.
13.
Magonov
,
S. N.
,
Elings
,
V.
, and
Whangbo
,
M. H.
,
1996
, “
Phase Imaging and Stiffness in Tapping-mode Atomic Force Microscopy
,”
Surf. Sci.
,
375
, pp.
385
391
.
14.
Ho¨lscher
,
H.
, et al.
,
1999
, “
Determination of Tip-sample Interaction Potentials by Dynamic Force Spectroscopy
,”
Phys. Rev. Lett.
,
83
(
23
), pp.
4780
4783
.
15.
Du¨rig
,
U.
,
2000
, “
Interaction Sensing in Dynamic Force Microscopy
,”
New J. of Phys.
,
2
, pp.
1
5
.
16.
Du¨rig
,
U.
,
1999
, “
Conservative and Dissipative Interactions in Dynamic Force Microscopy
,”
Surf. Interface Anal.
,
27
, pp.
467
473
.
17.
Yasuda
,
K.
, and
Kamiya
,
K.
,
1997
, “
Experimental Identification Technique of Vibrating Structures with Geometrical Nonlinearity
,”
ASME J. Appl. Mech.
,
64
, pp.
275
280
.
18.
Krauss
,
R. W.
, and
Nayfeh
,
A. H.
,
1999
, “
Experimental Nonlinear Identification of a Single Mode of a Transversely Excited Beam
,”
ASME J. Appl. Mech.
,
18
, pp.
69
87
.
19.
Doughty
,
T. A.
,
Davies
,
P.
, and
Bajaj
,
A. K.
,
2000
, “
A Comparison of Three Techniques Using Steady State Data to Identify Nonlinear Modal Behavior of an Externally Excited Cantilever Beam
,”
J. Sound Vib.
,
249
(
4
), pp.
785
813
.
20.
de Pablo
,
P. J.
, et al.
,
1998
, “
Jumping Mode Scanning Force Microscopy
,”
Appl. Phys. Lett.
,
73
, pp.
3300
3302
.
21.
Moreno-Herrero
,
F.
, et al.
,
2000
, “
The Role of Shear Forces in Scanning Force Microscopy: a Comparison Between the Jumping Mode and Tapping mode
,”
Surf. Sci.
,
453
, pp.
152
158
.
22.
Gil
,
A. J.
, et al.
,
2001
, “
Different Stages of Water Adsorption on Au by Dynamic SFM and Jumping Mode
,”
Appl. Phys. A: Solids Surf.
,
A72
, pp.
137
140
.
23.
Lee
,
S. I.
, et al.
,
2002
, “
Nonlinear Dynamics of Microcantilevers in Tapping Mode Atomic Force Microscopy: A Comparison Between Theory and Experiment
,”
Phys. Rev. B
,
66
(
11
), Art. No.
115409
115409
.
24.
Ruetzel
,
S.
,
Lee
,
S. I.
, and
Raman
,
A.
,
2003
, “
Nonlinear Dynamics of Atomic Force Microscope Probes Driven in Lennard-Jones Potentials
,”
Proc. R. Soc. London, Ser. A
,
459
(
2036
), pp.
1925
1948
.
25.
Meirovitch, L., 1997, Principles and Techniques of Vibrations, Prentice Hall, Upper Saddle River, New Jersey.
You do not currently have access to this content.