7.7 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Bimodal atomic force microscopy | 2/2 | https://en.wikipedia.org/wiki/Bimodal_atomic_force_microscopy | reference | science, encyclopedia | 2026-05-05T10:03:52.382038+00:00 | kb-cron |
where
T
=
T
1
T
2
{\displaystyle T=T_{1}T_{2}}
is a time where the oscillation of both modes are periodic;
Q
i
{\displaystyle Q_{i}}
the quality factor of mode i. Bimodal AFM operation might be involve any pair of eigenmodes. However, experiments are commonly performed by exciting the first two eigenmodes. The theory of bimodal AFM provides analytical expressions to link material properties with microscope observables. For example, for a paraboloid probe (radius
R
{\displaystyle R}
) and a tip-sample force given by the linear viscoelastic Kelvin-Voigt model, the effective elastic modulus
E
e
f
f
{\displaystyle E_{eff}}
of the sample, viscous coefficient of compressibility
η
c
o
m
{\displaystyle \eta _{com}}
, loss tangent
tan
ρ
{\displaystyle \tan \rho }
or retardation time
τ
{\displaystyle \tau }
are expressed by
E
e
f
f
=
4
2
Q
1
R
k
2
2
k
1
Δ
f
2
2
f
02
2
A
1
3
/
2
A
01
2
−
A
1
2
{\displaystyle E_{eff}=4{\sqrt {2}}{\frac {Q_{1}}{\sqrt {R}}}{\frac {k_{2}^{2}}{k_{1}}}{\frac {\Delta f_{2}^{2}}{f_{02}^{2}}}{\frac {A_{1}^{3/2}}{A_{01}^{2}-A_{1}^{2}}}\,}
η
c
o
m
=
E
e
f
f
ω
1
[
A
01
sin
ϕ
1
−
A
1
A
01
cos
ϕ
1
]
{\displaystyle \eta _{com}={\frac {E_{eff}}{\omega _{1}}}\left[{\frac {A_{01}\sin {\phi _{1}}-A_{1}}{A_{01}\cos {\phi _{1}}}}\right]\,}
tan
ρ
=
2
π
ω
1
η
c
o
m
E
e
f
f
=
2
π
ω
1
τ
{\displaystyle \tan \rho =2\pi \omega _{1}{\frac {\eta _{com}}{E_{eff}}}=2\pi \omega _{1}\tau \,}
For an elastic material, the second term of equation to calculate
η
{\displaystyle \eta }
disappears because
A
1
=
A
01
sin
ϕ
1
{\displaystyle A_{1}=A_{01}\sin {\phi _{1}}}
which gives
η
=
0
{\displaystyle \eta =0}
. The elastic modulus is obtained from the equation above. Other analytical expressions were proposed for the determination of the Hamaker constant and the magnetic parameters of a ferromagnetic sample.
== Applications == Bimodal AFM is applied to characterize a large variety of surfaces and interfaces. Some applications exploit the sensitivity of bimodal observables to enhance spatial resolution. However, the full capabilities of bimodal AFM are shown in the generation of quantitative maps of material properties. The section is divided in terms of the achieved spatial resolution, atomic-scale or nanoscale.
=== Atomic and molecular-scale resolution === Atomic-scale imaging of graphene, semiconductor surfaces and adsorbed organic molecules were obtained in ultra high-vacuum. Angstrom-resolution images of hydration layers formed on proteins and Young's modulus map of a metal-organic frame work, purple membrane and a lipid bilayer were reported in aqueous solutions.
=== Material property applications === Bimodal AFM is widely used to provide high-spatial resolution maps of material properties, in particular, mechanical properties. Elastic and/or viscoelastic property maps of polymers, DNA, proteins, protein fibers, lipids or 2D materials were generated. Non-mechanical properties and interactions including crystal magnetic garnets, electrostatic strain, superparamagnetic particles and high-density disks were also mapped. Quantitative property mapping requires the calibration of the force constants of the excited modes.
== References ==