Page 203 - Science at the nanoscale

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June 5, 2009
8.4. Optical Tweezers
(a)
(b)
Laser Beam
Fluid Flow
Objective Lens
Trapped
Microsphere
Force calibration of optical trapping force by fluid drag
Figure 8.31.
force.
microsphere as shown in Figure 8.31. The sphere in the fluid flow
will experience a viscous drag force F, given by:
(8.5)
Drag Force F = 6πRηv
where R = radius of sphere, η = viscosity of water = 0.001002
2
Ns/m , v = velocity of the flowing fluid. Initially at low flow
velocity, the sphere remains trapped because the optical trap-
ping force is stronger than the drag force. As the flow velocity
increases, the drag force increases and causes a slight deviation of
the bead from its equilibrium position. At flow velocity greater
than a critical velocity, known as the terminal velocity, the drag
force becomes greater than the maximum optical trapping force
and the sphere becomes detached from the optical tweezers. Thus
the maximum optical trapping force achievable at a fixed laser
power corresponds to the viscous drag force at terminal velocity.
Typically, the force exerted by the focused laser beam falls in the
range from a few pN up to a few hundred pN depending on the 193 ch08
power of the laser beam employed.
Another force calibration technique makes use of a video-
tracking method or a position sensitive detector to accurately
determine the position of a trapped microsphere. The fluctuation
in the position of the trapped microsphere due to thermal
fluctuation can be captured, and the extent of fluctuation gives
a measure of the stiffness of the optical trap. In order to mea-
sure the trap stiffness α, the position of the beads within the trap
must be measured to nanometre or better resolution. Once the
positions of the beads are accurately determined, one can make
use of equipartition theory to determine the trapping strength of