  Self-propelled colloidal particles exhibit rich non-equilibrium phenomena and
have promising applications in fields such as drug delivery and self-assembled
active materials. Previous experimental and theoretical studies have shown that
chemically active colloids that consume or produce a chemical can self-organize
into clusters with diverse characteristics depending on the effective phoretic
interactions. In this paper, we investigate self-organization in systems with
multiple chemical species that undergo a network of reactions and multiple
colloidal species that participate in different reactions. Active colloids
propelled by complex chemical reactions with potentially nonlinear kinetics can
be realized using enzymatic reactions that occur on the surface of
enzyme-coated particles. To demonstrate how the self-organizing behavior
depends on the chemical reactions active colloids catalyze and their chemical
environment, we consider first a single type of colloid undergoing a simple
catalytic reaction, and compare this often-studied case with self-organization
in binary mixtures of colloids with sequential reactions, and binary mixtures
with nonlinear autocatalytic reactions. Our results show that in general active
colloids at low particle densities can form localized clusters in the presence
of bulk chemical reactions and phoretic attractions. The characteristics of the
clusters, however, depend on the reaction kinetics in the bulk and on the
particles and phoretic coefficients. With one or two chemical species that only
undergo surface reactions, the space for possible self-organizations are
limited. By considering the additional system parameters that enter the
chemical reaction network involving reactions on the colloids and in the fluid,
the design space of colloidal self-organization can be enlarged, leading to a
variety of non-equilibrium structures.
