Page 63 - Mechanics of Asphalt Microstructure and Micromechanics

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56 Ch a p t e r w o

bending, this is constant. There are two operating modes for the AFM: contact-mode
and intermittent-contact mode. Contact-mode cantilevers work well with reasonably
hard materials such as metals, ceramics, and most polymers and the surface topography
should not have abrupt edges or tall, steep features. Intermittent-contact cantilevers
generally work well on all surfaces. They are more expensive and a bit more difficult to
use, but they can accurately image surfaces that are very soft (e.g., organics, polymer
coatings) and surfaces with steep features. Both types of cantilevers have the ability to
detect the elastic and adhesive properties of surface materials.
When using the vibrational characteristics of the cantilever (classical 1-D, fixed-free
beam) its mechanical resonant frequency can be determined using the dimensions of
the structure and material properties from which it is made. Thus, this frequency is re-
lated to the cantilever spring constant (k) and material density (ρ) according to the fol-
lowing equation:
t E k
ω (2-26)
0 2 ρ
l m
eff
where m, t, and l are cantilever parameters, and E is the elastic modulus
2.5.2 Scanning Tunneling Microscope (STM)
A scanning tunneling microscope (STM) is a powerful instrument for imaging surfaces
at the atomic level based on electron tunneling (Bonnell, 2001). Electron tunneling is a
phenomenon that relies on quantum mechanics which allows a finite number of elec-
trons to cross a very thin barrier between two closely spaced metals or semiconductors.
Images are obtained by “rastering” a tip over the surface of a sample. For an STM, good
resolution is considered to be 0.1 nanometer lateral resolution and 0.01 nanometer
depth resolution. With this resolution, individual atoms within materials are routinely
imaged and manipulated. The STM can be used not only in ultra high vacuum, but also
in air, water, and various other liquid or gas ambients, and at temperatures ranging
from near zero Kelvin to a few hundred degrees Celsius. During scanning, when a con-
ducting tip is brought very near to the surface to be examined, a bias (voltage differ-
ence) applied between the two allows electrons to tunnel through the vacuum between
them. The resulting “tunneling current” is a function of tip position, applied voltage,
and the local density of states (LDOS) of the sample. Images are acquired by monitoring
the current as the tip’s position scans across the surface.
STM can be operated in two modes: constant current mode where a constant bias is
applied between the sample and the tip, and constant height operation mode where a
constant height and bias are simultaneously maintained. The tip motion for the three
directions (x, y, and z) is controlled by piezoelectric elements. STM requires extremely
clean and stable surfaces, sharp tips, very good vibration control, and sophisticated
electronics.
For a metal tip brought very close to a flat sample surface, the resulting current (I)
is given by the following equation:
I = Cr t r s e z*k0.5 (2-27)
where r t and r s are the sample and tip electronic structures
z = the tip-sample separation
k = the wave number, and
C = a constant