Biomedical Engineering Reference
In-Depth Information
The adhesion sequence may now be considered in terms of the two
experimental variables: For indenter-imposed positions far from the
surface,
z has two real solutions, one describing the stable
equilibrium separated state and another describing an un-physical
unstable equilibrium state. The stable state is characterized by
ss , and
Δ
0
;
the tip is barely perturbed from its imposed position. The unstable state is
characterized by
Δ
zs
/
1
; the tip is very close to the surface (but for
an adhesion sequence in which the indenter moves the probe to approach
the surface, this state is not physically accessible). Far from the surface,
the stiffness field of the tip is dominated by that of the restoring
influence of the spring and for unforced thermal motion the tip vibrates
with a frequency and amplitude determined by the spring stiffness and
temperature.
For indenter-imposed positions closer to the surface, but still greater
than the critical value, s > s 0 , Δ z again has two real solutions. However,
although the stable state is characterized by
1
−Δ
zs
/
1
1 , the tip is
significantly perturbed from its imposed position. The stiffness field
experienced by the tip is considerably reduced as the attractive influence
of the surface competes with the restoring influence of the spring. As a
consequence, the frequency of vibration of the tip decreases and the
amplitude of vibration increases. The unstable state is now characterized
by 1 −Δ z / s < 1 and although closer to the surface than the stable state,
is now much closer to the stable state.
For indenter-imposed positions approaching the critical value,
s s 0 , Δ z still has two real solutions but they are both converging on
the critical value,
Δ
z / s
<
s 0 / 2 . In this position, the tip experiences near
to vanishing stiffness (as the surface field almost cancels the spring
field), the frequency of vibration of the tip about the larger, stable
equilibrium position is very small, and the amplitude of vibration is very
large. As a consequence, the tip may move close enough to the surface so
as to reach beyond the smaller, unstable equilibrium position. If it does
so, the net force on the tip becomes negative and the tip is irreversibly
attracted to the surface in a non-equilibrium manner with greater and
greater (negative) force. This is the adhesive “snap-on” phenomenon. In
Δ
z
 
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