small particles, external stresses are unlikely to overcome internal forces,
while this may be easy for large particles. Gels made of particles generally
are firmer for smaller particles.
Sedimentation rateis the result of opposite forces acting on a particle,
gravitational and frictional, leading to a proportionality tod^2 (Section 13.3).
Again, it is more difficult to separate small particles from the continuous
phase than large particles. Table 9.4 gives examples; notice that for small
molecules Brownian motion tends to be much faster than sedimentation,
whereas the opposite is true for large particles.
Coalescence of emulsion droplets tends to occur more readily for
larger droplets (Section 13.4).
Altogether, dispersions of small particles tend to be more stable, often
to a considerable extent, than those of large particles.
9.2.3 Optical Properties
Hardly ever do we see light directly emanating from a light source; it is
nearly always scattered.Scatteringof light, which can be due to reflection,
refraction, or diffraction, occurs at sites where the refractive index changes,
for instance at a phase boundary; see Figure 9.7. This means that we can see
such a boundary.
Refraction. The refractive index n of a homogeneous material
equals the ratio of the wavelength of the light in vacuum over that in the
material. The value ofnalso depends on the wavelength of the lightl;it
generally decreases with increasing l. The refractive index is commonly
given asnD, i.e., atl¼589 nm (the sodium D line). Table 9.2 gives some
values.ndecreases with increasing temperature.
TABLE9.4 Motion of Spherical Particles of Various Sizes in Water
Diameter (mm) 0.001 0.01 0.1 1 10
Brownian motion 1200 390 120 39 12
Sedimentation by gravity 0.02 2 200 2 6104
Same, centrifuge at 1000g 0.2 20 2000
Same, ultracentrifuge at 10^5 g 20 2000
Room temperature. Root-mean-square displacementð<x^2 >^0 :^5 Þinmm by brownian motion
over one hour. Sedimentation rate inmm per hour, assuming the particles to differ in density
from water by 100 kg?m^3