  Electrostatic interactions provide a convenient way to modulate interactions
between nanoparticles, colloids, and biomolecules because they can be adjusted
by the solution pH or salt concentration. While the presence of salt provides
an easy method to control the net interparticle interaction, the nonlinearities
arising from electrostatic screening make it difficult to quantify the strength
of the interaction. In particular, when charged particles assemble into
clusters or aggregates, nonlinear effects render the interactions strongly
non-pairwise. Here we report Brownian dynamics simulations to investigate the
effect that the non-pairwise nature of electrostatic interactions has on
nanoparticle assembly. We compare these simulations to a system in which the
electrostatics are modeled by a strictly pairwise Yukawa potential. We find
that both systems show a narrow range in parameter space where the particles
form well-ordered crystals. Bordering this range are regions where the net
interactions are too weak to stabilize aggregated structures, or strong enough
that the system becomes kinetically trapped in a gel. The non-pairwise
potential differs from the pairwise system in the appearance of an amorphous
phase for strongly charged particles. This phase appears because the many-body
electrostatic interactions limit the maximum density achievable in an assembly.
