Biology Reference
In-Depth Information
Figure 14.1
compares these forces for two spherical particles of a
given size (e.g., two particles each having a radius of 1 mm) and a density
equivalent to that of water, which is approximately the density of biological
cells. For particles here on Earth, obviously the greatest gravitation force will
be the one between a particle and the Earth itself. Therefore,
Fig. 14.1
also
shows the predicted force of gravitation between the Earth and a particle of
a given size. As the size of the two interacting particles decreases to less than
10
m, electromagnetic forces, like the van der Waals force, become
the preeminent force. Not surprisingly, a bacterium with a density of ~1 g cm
3
to 10
5
3
and length scale of 10
6
m exists solely within the realm of electromagnetic
forces.
10
-9
10
-6
10
-3
10
0
10
3
10
6
10
15
10
15
10
10
10
10
Earth-particle
10
5
10
5
10
0
10
0
vdw
10
-5
10
-5
10
-10
10
-10
particle-particle
10
-15
10
-15
10
-20
10
-20
10
-9
10
-6
10
-3
10
0
10
3
10
6
radius of particle (m)
Figure 14.1.
Log-log plot of the theoretical gravitational and van der Waals forces
between two similarly sized particles that are in contact with one another. The
dashed line describes the gravitational force between two particles of the same size.
To determine the gravitational force, a particle's mass was converted to radius by
assuming the particle was a solid homogeneous sphere with a density of 1 g cm
.
The interacting distance was the sum of the radii of the two interacting particles. The
shaded region outlines the boundaries of the expected van der Waals force between
the two particles of the same size. Values for the Hamaker constant ranged from
10
3
J, which is appropriate for biological and inorganic solids,
7
and contact
was deined as an effective separation between particles of 0.2 to 2 nm.
9
The solid
line is the gravitational attraction between a particle of a given radius and the Earth
(mass = 5.97
20
to 10
21
10
24
kg). For the Earth-particle gravitational force, the interaction
distance was set as 6.4
s
s
10
6
m (i.e., radius of the Earth).
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