Reversible Clustering under the influence of a periodically modulated binding rate

We study cluster-cluster aggregation and fragmentation with a periodically modulated binding rate. Using the Smoluchowski mean-field equations, we derive exact solutions for the cluster size distribution for two time courses of the binding rate: (i) harmonic modulations and (ii) on-off switching of the binding rate with dwell times τb and τf. In both cases, the asymptotic cluster size distribution is oscillatory in time. The formation of small-sized clusters is enhanced compared to a constant binding rate below a critical cluster size sc. There is another critical cluster size sp close to which the size distribution becomes quasistationary. We calculate analytically the dependence of the critical points sc and sp on the relevant system parameters for on-off switching of the binding rate. Our results are relevant whenever clustering can be externally controlled