Portable Optical Tweezers Kit
Chapter 6
:
Experiments
Rev B, February 15, 2022
Page 71
Mean Squared Displacement for Polystyrene Beads of Different Sizes
6.5.2. The Maximum Holding Force
In the following, we shall determine how well the optical tweezers can hold a polystyrene
bead. The goal is to determine the maximum holding force of the optical trap.
If one observes an individual polystyrene bead under the microscope which is moving
freely, frictional force acts on the particle. This inhibits the particle in its movement through
any liquid. This frictional force
𝐹𝐹
𝑅𝑅
is directly proportional to the speed
𝑣𝑣
, with which the
spheres move and can be described by the following equation:
𝐹𝐹
𝑅𝑅
= 6
𝜋𝜋𝜂𝜂
𝑆𝑆𝑟𝑟𝑟𝑟
𝑅𝑅𝑣𝑣
(32)
Here,
𝑅𝑅
describes the radius of the bead and
𝜂𝜂
𝑆𝑆𝑟𝑟𝑟𝑟
describes the effect of viscosity of the
suspension. The latter indicates how "thick" the combination of water and beads is and is
different for each sample. As the viscosity depends on various factors, it must be
determined through experimentation. It depends upon the mean squared displacement of
the particles, which was determined in the previous exercise. This resulted in a straight
line, whose gradient can be determined by means of the following equation:
𝑚𝑚
=
2
𝑘𝑘
𝐵𝐵
𝑇𝑇
3
𝜋𝜋𝜂𝜂
𝑔𝑔𝑒𝑒𝑒𝑒
𝑅𝑅
(33)
Here,
𝜂𝜂
𝑆𝑆𝑟𝑟𝑟𝑟
denotes the effective viscosity,
𝑅𝑅
is the radius of the PS-bead,
𝑇𝑇
is the
temperature of the sample in Kelvin (corresponds to room temperature), and
𝑘𝑘
𝐵𝐵
is the
Boltzmann constant, which is a natural constant and has a value of
1.38
⋅
10
−23 𝐽𝐽
𝐾𝐾
.
Summary of Contents for EDU-OT3
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