Page 35 - Science at the nanoscale

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June 9, 2009
2.3. Brownian Motion of Nanoscale Objects
Viscosities of some common fluids.
Table 2.2
Viscosity (Pa.s)
Fluids
Acetone
0.0032
0.00018
Air
0.012
Alcohol (ethyl)
Blood (whole)
0.04
Blood plasma
0.015
Gasoline
0.006
14.9
Glycerine
1.1
Oil (light)
6.6
Oil (heavy)
Water
0.01
−1
, i.e. it falls by a distance equivalent to its size
about 1 µms
every second. If its radius is further reduced to 1 nm (i.e. an
−1
iron nanoparticle), its terminal velocity drops to 1 pms
, which
is negligible relative to its size! Furthermore, at the nanoscale, we
expect the effects of individual molecules in the fluid impacting
on the nanoparticle (Brownian motion) to become significant, and
this will be discussed next.
2.3
BROWNIAN MOTION OF NANOSCALE OBJECTS
In 1827, the English botanist Robert Brown noticed that pollen
grains suspended in water jiggled about under the lens of the
microscope, following a zig-zag path like the one pictured in 25 ch02
Fig. 2.3. It was only in 1905 when Einstein succeeded in stating
the mathematical laws governing the movements of particles on
the basis of the principles of the kinetic-molecular theory of heat.
According to this theory, microscopic bodies suspended in a liq-
uid perform irregular thermal movements called Brownian molec-
ular motion. Brownian motion became more generally accepted
because it could now be treated as a practical mathematical model.
Its universality is closely related to the universality of the normal
(Gaussian) distribution.
The 1D diffusive Brown motion probability distribution as a
function of position x and time t, P(x, t), is described by the