title: Cluster-size distribution in the autocatalytic growth model.
abstract: We generalize the model of transition-metal nanocluster growth in aqueous solution, proposed recently [J. Jȩdrak, Phys. Rev. E 87, 022132 (2013)], by introducing a more complete description of chemical reactions. In order to model time evolution of the system, equations describing chemical reaction kinetics are combined with the Smoluchowski coagulation equation. In the absence of coagulation and fragmentation processes, the model equations are solved in two steps. First, we obtain the explicit analytical form of the i-mer concentration, ξ(i), as a function of ξ(1). This result allows us to reduce considerably the number of time-evolution equations. In the simplest situation, the remaining single kinetic equation for ξ(1)(t) is solved in quadratures. In a general case, we obtain a small system of time-evolution equations, which, although rarely analytically tractable, can be relatively easily solved numerically.
authors.affiliation: Institute of Physical Chemistry, Polish Academy of Sciences, ulica Kasprzaka 44/52, 01-224 Warsaw, Poland.
authors.forename: Jakub
authors.initials: J
authors.lastname: Jedrak
mesh_terms: D003102:Colloids / Q000138:chemical synthesis*; D003198:Computer Simulation; D003460:Crystallization / Q000379:methods*; D053768:Metal Nanoparticles / Q000737:chemistry* / Q000648:ultrastructure; D008956:Models, Chemical; D008958:Models, Molecular; D010316:Particle Size; D028561:Transition Elements / Q000737:chemistry*
chemical_list: D003102:Colloids; D028561:Transition Elements