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5.4 Future Applications 213
5.2. Simulate the scattered light of the evanescent field generated by the at-
tenuated total reflection at the prism (refractive index 1.6) to air interface.
◦
A plane wave with a wavelength of 800 nm is incident at an angle of 45 and
the induced evanescent field is scattered by the sharpened metal probe of the
curvature of 20 nm, where the distance between the probe tip and the prism
surface is 15 nm.
5.3. The dragforce F drag actingon a metal sphere (diameter d) movingat
the constant speed of v in the medium can be expressed by Eq. (5.23) [5.11]

9d 1 1
F drag =3πµdv 1+ − , (5.23)
32 D H − D
where µ is the viscosity of the medium, H is the height of the sample chamber
and D is the distance between the sphere and the wall surface of the chamber.
The viscosity µ varies with the temperature T as shown by
262.37
log 10 µ = −1.64779 + . (5.24)
T + 273.15 − 133.98
How is the dragforce dependent on the trappingposition (particle-to-wall
distance) (a) and medium temperature (b)?
5.4. The van der Waals force F v between the particle and the wall is ex-
pressed as the Hamaker approximation shown by (5.25) [5.26], where H is the
Hamakar constant, a is the radius of the particle, δ is the shortest distance
between the particle and the wall.

H a a 1 1
F v = − + − + . (5.25)
6 δ 2 (δ +2a) 2 δ δ +2a
How is the van der Waals force dependenct on the distance between the
particle and the wall?

5.5. The electrostatic force actingon a particle is expressed as the Hoggap-
proximation shown by (5.26) [5.26], where (ψ 1 ,ψ 2 ) are the potentials of the
particle and the wall, 1/κ is the thickness of the electric double layer and ε is
the dielectric constant of the medium

1 + exp(−κδ) 2 2
F S = πεa 2ψ 1 ψ 2 ln +(ψ + ψ )ln{1 − exp(−2κδ)} .
1
1
1 − exp(−κδ)
(5.26)
How is the electrostatic force dependent on the distance between the par-
ticle and the wall?