THORLABS EDU-OT3, User Manual

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Portable Optical Tweezers Kit Chapter 6: Experiments
Page 72
MTN024417-D02
Exercise
Determine the effective viscosity
𝜂𝜂
𝑔𝑔𝑒𝑒𝑒𝑒
of the sample with the 3 µm polystyrene spheres, by
solving the equation (33) according to viscosity and using the gradient
𝑚𝑚
of the measured
curve from the previous exercise.
Solution
The equation for the calculation of the effective viscosity
𝜂𝜂
𝑔𝑔𝑒𝑒𝑒𝑒
is:
𝜂𝜂
𝑔𝑔𝑒𝑒𝑒𝑒
=
2 𝑘𝑘
𝐵𝐵
𝑇𝑇
3 𝜋𝜋𝑅𝑅𝑚𝑚
(34)
Here, T is the room temperature, k
B
the Boltzmann constant,
𝑅𝑅
the radius, and m the
previously determined gradient of the PS-beads used.
The determined effective viscosity should be in the range of a few
10
−3 𝑁𝑁𝑠𝑠
𝑚𝑚
2
Exercise
After which speed can the PS-bead no longer be held? Determine the maximum holding
force of the optical tweezers.
Solution
If the PS-bead is in the optical trap, two forces act on it. First of all, the frictional force
𝐹𝐹
𝑅𝑅
,
which is caused by the suspension in which the PS-bead is located, and thus works against
the other force, the holding force
𝐹𝐹
𝐻𝐻
of the optical trap. The following equation describes
the frictional force
𝐹𝐹
𝑅𝑅
:
𝐹𝐹
𝑅𝑅
= 6 𝜋𝜋𝜂𝜂
𝑆𝑆𝑟𝑟𝑟𝑟
𝑅𝑅𝑣𝑣
(35)
Here,
𝜂𝜂
𝑆𝑆𝑟𝑟𝑟𝑟
is the effective viscosity of the suspension,
𝑅𝑅
is the radius of the bead, and
𝑣𝑣
is
the speed. The maximum holding force is said to have been reached precisely, when the
PS-bead at a certain speed
𝑣𝑣
𝑚𝑚𝐺𝐺𝑥𝑥
can just be held. This is the case when both forces are
in balance:
𝐹𝐹
𝑆𝑆𝑡𝑡𝑆𝑆𝑘𝑘𝑆𝑆𝑡𝑡
= 𝐹𝐹
𝐻𝐻 , 𝑚𝑚𝐺𝐺𝑥𝑥
= 6 𝜋𝜋𝜂𝜂
𝑆𝑆𝑟𝑟𝑟𝑟
𝑅𝑅𝑣𝑣
𝑚𝑚𝐺𝐺𝑥𝑥
(36)
The holding force is in the range of a few pN.
6.6. Other Samples
There is a wide range of samples that can be investigated with the optical tweezers.
•
Water from a pond or a hay infusion features microscopic organisms, some of
which can be trapped with the tweezers.