We assume that aggregation startswith a dimer formation fromtwo
non-aggregated NPs, based on the Smoluchowski principle
(Chandrasekhar, 1943), and that aggregates of any size will form with
an identical kinetic rate constant k; subsequently aggregated-NPs and/
or aggregate-aggregate interactions can occur forming unstable suspensions.
The aggregation rate constant is proportional to the slope of the
change on A over time during the early stages of the aggregation,
when formation of dimers is considered important, according to Eq. (2).
At enhanced ionic strengths the electrical double layer surrounding
the NPs is compressed, and the role of electrostatic interactions in the
aggregation process is screened. Van der Waals forces and hydrodynamic
interactions are minor and the aggregation kinetic is controlled
by Brownian diffusion. This regime is known as fast aggregation or
diffusion controlled aggregation (DCA). In contrast, at lower ionic
strengths double layer interactions between the charged NPs result in
an energy barrier. As a consequence, the aggregation rate is reduced
and the NPs remain in solution for longer. This regime is known as
slow aggregation or reaction controlled aggregation (RCA), due to
mechanistic similarities to chemical reactions.
Normalizing the slopes obtained at different salt concentrations to
the one obtained in the DCA regime, under favourable aggregation
conditions, the aggregation efficiency (α),which represents the fraction
of successful aggregation, can be calculated by: