We study binary one-dimensional exchange-mediated A+B→0 reactions in the absence of diffusion. Using the Kirkwood superposition approximation to decouple the infinite hierarchy of many-particle densities a closed set of integrodifferential equations is derived. A comparison to simulation calculations shows that the approximation reproduces the correct long-time asymptotic decay of reactant concentration as well as the correct spatial correlations of the segregation pattern.

Nanoparticles functionalized with photo-switchable ligands can be assembled into a broad range of structures by controlled light exposure. In particular, alternating light exposures provide the means to control formation of assemblies of various sizes and symmetries. Here, we use scaling arguments and Kinetic Monte Carlo simulations to study the evolution of reversible aggregates in a solution of periodically irradiated photo-switchable nanoparticles. Scaling estimates of the characteristic size and the mean separation of aggregates agree with the simulations. The transition probabilities in the Kinetic Monte Carlo scheme are derived from a renormalized master equation of the diffusion process. Simulations on a system of nanoparticles, interacting through Lennard-Jones pair potentials that change their character from repulsive to attractive depending on the light exposure, show that the slow diffusion of particles at low effective temperatures (where the attractions are much higher than the thermal energy) results in the formation of small, “kinetically frozen” aggregates. On the other hand, aggregation does not occur at high effective temperatures, where the attractions are comparable to the thermal energy. In the intermediate range of effective temperatures, “fluctuating” aggregates form that can be stabilized by applying light pulses of specific lengths and frequencies. The aggregate sizes increase by increasing the packing fraction and the aggregates undergo transition to a percolated “network” at high packing fractions. Light-control of inter-particle interactions can either inhibit or promote nucleation and growth, and can reduce gel and glass formation.