Dispersing Powders in Liquids, Part 1, by Ralph D. Nelson, Jr.
The development of sophisticated computer programs for evaluating
photographs of the contours of particles gave shape analysis a
resurgence in popularity. A more complete discussion of the
mathematical analysis of shape in terms of conventional shape and
roughness measures and also of fractal geometry may be found in
Allen\dag. The following section discusses a few aspects of
shape that affect dispersions.
Shape
Although many of the equations in dispersion science are written
in terms of spheres or cubes, most fundamental and agglomerated
particles are not simple shapes. Spheres are the most preferred
shapes for industrial products because they pack to a higher
density, flow better, and have lower surfactant demand than other
shape that encloses the same equal volume.
The simplest way to adjust an equation (that was written to
describe the behavior of spheres) for nonsphericity is to use a
shape factor to correct the length, area, or volume measures.
Characterization of commercial powders and slurries is difficult
because of the broad distribution of particle volumes and shapes
within a batch of commercial powder and the all-to-frequent lack
of reproducibility of these volume and shape distributions from
batch to batch.
Small amounts of impurities or dispersants may adsorb on the
crystal faces, affecting not only the volume and shape of the
fundamental particles, but also the way in which they agglomerate
into higher level structures. If a crystal has two fast-growing
and one slow-growing face, the fast-growing faces will rapidly
grow outward to form the long axis of a needle-shaped crystal.
The slow-growing faces end up having the largest surface areas.
Considerable technical effort has been spent finding out how to
control particle shape by adding ions or surfactants that adsorb
on and retard the growth of different crystal faces.
Shape affects the way particles respond to instruments designed to
measure their size. For example, spheres will scatter light
differently than needles of the same volume. Shape also affects
the balance of forces that control the interactions of particles.
For example, if one face of a crystal is positively charged and
another face is negatively charged, the agglomerative forces will
be stronger if the particles are cubes than if they are needles.
The small ends cannot hold much charge and thus cannot have a
strong attraction to the oppositely charged sides of the needle.
Surface Roughness
Surface roughness is a major factor in reducing particle
attraction, since only smooth surfaces can come close enough over
large areas to allow strong bonding. In rare cases, the surface
irregularities between two particles will mesh, but it is
difficult to control particle formation well enough to
manufacture such a meshing structure. Surface roughness also
increases dispersant demand, and since the initially added
dispersant adsorbs in the valleys, where it is not very effective
in preventing particle agglomeration, small amounts of dispersant
are less effective for rough particles than for smooth particles.
Porosity
If a particle contains pores large enough to permit entry of the
surfactant, then porosity creates extra demand for dispersant
(beyond that required to treat the external surface). Since the
pores can attract the surfactant from all sides, they usually
adsorb surfactant more strongly than the outer surface, so the
first dispersant adsorbed is lost inside the particle and
contributes nothing to the interaction between particles.
Heterogeneous Solids
The preceding discussion assumed that the particles were either
homogeneous or were uniformly coated with a second material. In
many industrial situations this is not the case. Variations in the
composition of a solid may arise from inhomogeneous distribution
of a minor component in a solid state mix or from the presence of
a second phase -- either as a second set of particles or as the
cement between the particles. Such inhomogeneities lead to more
varied interactions than are possible for a homogeneous solid.
It is harder to manufacture a heterogeneous solid with a specific
structure than to produce homogeneous solids, because we must now
control several different chemical additions and several
precipitations (in parallel or in sequence) rather than just one.
A heterogeneous powder may be a mix of particles having different
densities, optical adsorptivities, refractive indices, x-ray
attenuation factors, and shapes. A particle size measuring
device may respond differently to two particles having the same
mass and shape, but having two different compositions.
Microscopy can help in determining whether heterogeneity is
present in a sample .
Varieties of Heterogeneity
A commercial slurry of rutile (one of the several crystalline
forms of TiO2) particles may contain aluminum in a variety of
chemical forms:
an aluminum ion in solution -- Al+++
a complex with another ion in solution -- AlOH++, AlCl4-
a solid oxide -- 
-Al2O3,
-Al2O3
a solid hydroxide -- boehmite AlOOH, gibbsite Al(OH)3
each of which may be found in a variety of physical situations
substituted or occluded inside a rutile particle
anchored as a coating on a rutile particle surface
adsorbed on the rutile particle surface
as separate particles in a physical mix with the rutile particles
Distribution of Heterogeneity
The second material (causing heterogeneity) may be uniformly
distributed within the particle, or it may be concentrated near
the surface or in pores and crevices. The mass percent of
the second material may be uniform from one particle to the next
or may vary widely.
A coating may be of uniform thickness or may be present as
islands on the surface. If the coating thickness or the amount
of surfactant adsorbed per unit area is the same for small
particles as for large particles, then small particles will
contain a higher mass percent of the second material than the
larger ones do. Changes in solution conditions from one batch to
the next may strongly affect the amount of second material
precipitated or adsorbed. Abrasion of a coating may knock off
small particles of pure coating. Since these have properties
different from the coated particles, their fouling, settling, and
elution properties will be different from the coated particles.