sitytends to enhance the aggregation rate somewhat, even for spheres,
because the effects of particle size on collision radius and mutual diffusion
coefficient then do not exactly cancel in Eq. (13.2).
‘‘Slow’’ Aggregation. There are several reasons why aggregation
rate can be slower than that predicted by Eq. (13.1). Smoluchowski
introduced astability factor W, by which the calculated result would have to
be divided to obtain the experimental result, without giving theory for the
magnitude ofW. Others speak of thecapture efficiencya, defined as the
probability that two particles stick upon closely encountering each other. It
is generally assumed thatW¼1/a. Equations (13.1) and (13.2) should be
multiplied bya, and Eq. (13.3) be divided by it (or be multiplied byW).
An obvious cause for the slowing down of aggregation is the presence
of a repulsive free energyVat some distancehbetween the particles, as
discussed in Chapter 12. A particle approaching the ‘‘central’’ particle will
FIGURE13.2 Perikinetic aggregation. The relative particle number concentration
as a function of the timetafter aggregation has started over the halving timet0.5.N
refers to number,N 0 to initial total number, and the subscripts 1, 2, 3, etc. to the
numbers of particle monomers, dimers, trimers, etc. The equation for the number of
k-mers is also given.