Order. For very small volume fraction j, the particles in a
dispersion can be distributed at random. For higherj, there is always
someorder. This is illustrated in Figure 9.3a and 9.3b. Around a sphere of
radiusRa volume ofð 4 = 3 Þpð 2 RÞ^3 is not available for other spheres of the
same radius (taking the center of a sphere as representing its position). This
implies that random distribution is not possible. The higherj, the less
random the distribution is, and at the closest packingðjmaxÞ, monodisperse
spheres would show perfect order.
If the particles areanisometric, which means that they have different
dimensions in different directions, fairly close packing always leads to
anisotropyof the system, which means that some properties depend on the
direction considered. This is illustrated in Figure 9.3c. Anisotropy is also
possible for low volume systems, or for spherical particles: it all depends on
their arrangement. A good example of visible anisotropy is in bread, where
the gas cells are generally not spherical, but elongated. During the oven
rising, when the cells become much larger, the dough is confined by the
mold, and expansion of the cells in a horizontal direction is limited. When
cutting a slice of bread in the normal way, this is clearly observed, but when
the loaf is cut parallel to the bottom, the cells look spherical. Muscle tissue is
very anisotropic, and especially the mechanical strength greatly depends on
the direction of the force applied. The same holds true for many plant
organs, like stems.
Anisotropy can be manifest in several physical properties and at
various scales, for instance,
FIGURE9.3 Order induced when particles are present at high volume fraction in a
confined space. Illustrated for two-dimensional systems.