86
3 Potential- or Adsorbate-Induced Changes in Surface Stress …
Equation (3.9) means that the value of ζ g,q can be obtained from the values of Y s and
Z e . The phase angle of ζ g,q is equal to the argument
ψ s − ψ e +
π
2
in Eq. (3.9).
The frequency response of an elastic cantilever to an external driving force depends
strongly on the cantilever geometry (length: L, width:b, and thickness:h) and on the
fluid in which it is immersed. Provided that the cantilever is an isotropic elastic solid
with negligible internal friction and its cross section is uniform over whole length
under the geometrical restriction of L b h, the resonant frequency at flexural
mode in vacuum and in fluid can be theoretically predicted [41]. For a rectangular
glass cantilever (L = 25 mm, b = 3 mm, and h = 0.1 mm) used as a substrate, the
predicted resonant frequencies at the first mode in vacuum and in solution are 139
and 43 Hz, respectively [39].
Figure 3.11 shows (a) the absolute value
ζ g,q
of surface stress–surface charge
density coefficient and (b) the phase angle ψ g,q of surface stress relative to surface
Fig. 3.11 a Absolute value
ζ g,q
of surface stress–surface charge density coefficient and b the
phase angle ψ g,q of surface stress relative to surface charge density for the (111)-textured Au (111)
thin-film (cantilever) electrode (L = 24.2 mm, b = 3 mm, and h = 0.1 mm) in 0.1 M HClO 4
solution, responding to a sinusoidal potential input of ± 50 mV at a steady-state potential of 0.2 V
(SSE) where no faradaic process takes place [39]. Reproduced from [39] with permission from The
Electrochemical Society
3 Potential- or Adsorbate-Induced Changes in Surface Stress …
Equation (3.9) means that the value of ζ g,q can be obtained from the values of Y s and
Z e . The phase angle of ζ g,q is equal to the argument
ψ s − ψ e +
π
2
in Eq. (3.9).
The frequency response of an elastic cantilever to an external driving force depends
strongly on the cantilever geometry (length: L, width:b, and thickness:h) and on the
fluid in which it is immersed. Provided that the cantilever is an isotropic elastic solid
with negligible internal friction and its cross section is uniform over whole length
under the geometrical restriction of L b h, the resonant frequency at flexural
mode in vacuum and in fluid can be theoretically predicted [41]. For a rectangular
glass cantilever (L = 25 mm, b = 3 mm, and h = 0.1 mm) used as a substrate, the
predicted resonant frequencies at the first mode in vacuum and in solution are 139
and 43 Hz, respectively [39].
Figure 3.11 shows (a) the absolute value
ζ g,q
of surface stress–surface charge
density coefficient and (b) the phase angle ψ g,q of surface stress relative to surface
Fig. 3.11 a Absolute value
ζ g,q
of surface stress–surface charge density coefficient and b the
phase angle ψ g,q of surface stress relative to surface charge density for the (111)-textured Au (111)
thin-film (cantilever) electrode (L = 24.2 mm, b = 3 mm, and h = 0.1 mm) in 0.1 M HClO 4
solution, responding to a sinusoidal potential input of ± 50 mV at a steady-state potential of 0.2 V
(SSE) where no faradaic process takes place [39]. Reproduced from [39] with permission from The
Electrochemical Society