Difference between revisions of "Procedure: Particle tracking"

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Characterizing instrument stability

To verify that your system is sufficiently stable for accurate particle tracking, measure a dry specimen containing 1μ beads in bright field contrast. Chose a field of view in which you can see at least 3-4 beads. Using a 40x objective, track the beads for about 3 min. Use the bead tracking processing algorithm on two beads to calculate two trajectories. To further reduce common-mode motion from vibrations, calculate the differential trajectory from the individual trajectories of these two beads. Calculate the MSD from the differential trajectory. Your MSD should start out less than 10 nm² at t = 1 sec. and still be less than 100 nm2 for t = 180 sec.

Estimating the diffusion coefficient by tracking suspended microspheres

According to theory,^[1][2][3][4] the mean squared displacement of a suspended particle is proportional to the time interval as: $ \left \langle {\left | \vec r(t+\tau)-\vec r(t) \right \vert}^2 \right \rangle=2Dd\tau $, where r(t) = position, d = number of dimensions, D = diffusion coefficient, and $ \tau $= time interval.

• Track some 3μm (Samples A & B) and 5μm (Samples C & D) microspheres.
• Estimate the diffusion coefficient of these microspheres suspended in solutions of varying viscosities. For reference, Sample A contains 3μm spheres suspended in water.
• Consider how many particles you should track and for how long. What is the uncertainty in your estimate?

See: this page for more discussion of Brownian motion and a Matlab simulation. </div>
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