Page 36 - Science at the nanoscale

7:14
RPS: PSP0007 - Science-at-Nanoscale
June 9, 2009
Classical Physics at the Nanoscale
26
24
22
20
18
16
14
1
20
24
2
3
Z(µm)
4
5
Figure 2.3.
A microsphere that is suspended in water will exhibit Brow-
nian motion due to frequent collisions with water molecules. The figure
shows the reconstructed trajectory of such a microsphere (diameter =
0.6 µm) after its motion was tracked by optical microscopy over a period
of 20 seconds. The zig-zag path is typical of a particle exhibiting Brown-
ian motion (from author’s own work).
Gaussian distribution: 22 X(µm) 26 28 30 26 Y(µm) ch02
2
−3 −x
P(x, t) = (4πDt) 2 exp (2.15)
4Dt
where D is the diffusivity of a particle radius of R in a fluid of
viscosity η at temperature T:
kT
D = (2.16)
6πηR