Enrico Bibbona, Daniele Cappelletti, Paola Siri, Elena Sabbioni, Rebeka SZABÓ, Gábor Lente: 

Final nanoparticle size distribution under unusual parameter regimes

A kinetic model of nanoparticle formation is examined, where the first step is called nucleation, in which some monomer units (n) come together to form a nucleus. This nucleus can then grow incrementally by adding one monomer unit at a time to the nanoparticle, with the exclusion of the aggregation and any reversible reactions. Let γ  denote the rate constant of the growth process and ν the rate constant of nucleation. It is well-known that when γ~ O(1/N), and ν~O(1/N(n-1)), the stochastic model converges to the solution of the Becker-Döring equations, and the final size distributions of the stochastic model can be approximated by using Lifshitz-Slyozov-Wagner’s theory. We are investigating another parameter regime where the process appears to exhibit an interesting final size distribution that we are attempting to characterize. So far, a simulation study is conducted first by using the exact Gillespie algorithm, then it is compared with some sophisticated versions of the tau-leap method. The results will be carefully analyzed.

Zoom link is available from the organizer of the seminar. Please contact János Tóth at jtoth(at)math.bme.hu.