- Reaction-limited aggregation. This occurs ifWis larger than a
critical value (of the order of 100?); presumably, the critical value
is smaller for larger particles. The regime has not (yet) been
seriously considered by colloid scientists.
Further Complications. The theory as discussed in this section,
when applied todilutesuspensions (since at not very smalljthe diffusion
distance of the particles is smaller than presumed) ofsmallparticles (say,
< 1 mm) underquiescentconditions (see Section 13.2.3), has been successful
in predicting a number of observations, at least for the first few aggregation
steps. This concerns (a) the reaction being second order; (b) the value oft0.5
being inversely proportional to N 0 ; (c) the distributions of multiplets
obtained; and (d) the effect of viscosity on the aggregation rate. Also the
absolute rate is often well predicted (within a factor of two or three) if it is
sure thatfast aggregationoccurs; this rate is often called the ‘‘Smoluchowski
limit.’’ However, the values of thecapture efficiencyoften deviate markedly
from the prediction, even for smooth spherical particles.
For electrostatic repulsion, it has been reasoned that during the
approach of two particles, the electric double layer may not be in
equilibrium: for the surface potential to remain constant, the surface charge
has to change, and this may not happen fast enough, since ions in the double
layer have to diffuse out of the gap. The effect is larger for larger particles,
and it follows that the influence of particle size on the height of the repulsive
barrier is smaller than predicted. Also surface roughness of the particles
tends to decrease the effect of particle size on DLVO interaction. If the
roughness is of the order of 1/k, the magnitude of the roughness, rather than
the interparticle distance, tends to determine the effective magnitude ofh.
Deaggregationof particle doublets may occur, thereby reducing the
effective aggregation rate. This can readily occur for DLVO-type interac-
tions if the aggregation is ‘‘in the secondary minimum’’ (see Figure 12.1). It
appears that deaggregation can also occur from a primary minimum, if the
differenceVmaxVminis not too large (say,< 10 kBT). This is because,
again, the value ofh*/atends to be small. Deaggregation may also occur for
other types of interaction.
Forpolymer-stabilizedparticles (Section 12.3.1), calculation ofWfrom
theory is often not possible (and this may also be the case if some other
interactions are involved: see Section 12.4). Moreover, hydrodynamic
retardation would not be according to the theory outlined above. In these
cases, it is often very difficult to predict capture efficiencies.
The particle surface may havereactive patches, often called ‘‘hot
spots.’’ Emulsion droplets, for instance, may have an adsorbed layer with
patches of protein (surface area fractiony), while the remainder is covered