“…In addition to the widely investigated nucleation rate, the evolution of transient cluster size distribution is also important for nucleation processes. Against this background, Z. Kožíšek et al 24,25 proposed a transient nucleation model to study the nucleation kinetics of different molecules on active sites such as the formation of diamond clusters on Si-substrates, 26 the initial crystallization of polymers, 27 and the transient nucleation of ethanol 28,29 and ethanol-hexanol systems. 30 In this model, the transient attachment/detachment frequencies of single molecules to/from the cluster surface were used to describe the growth/decay of cluster size, and then the evolution of cluster size distribution was obtained without any parameter tting.…”
“…In addition to the widely investigated nucleation rate, the evolution of transient cluster size distribution is also important for nucleation processes. Against this background, Z. Kožíšek et al 24,25 proposed a transient nucleation model to study the nucleation kinetics of different molecules on active sites such as the formation of diamond clusters on Si-substrates, 26 the initial crystallization of polymers, 27 and the transient nucleation of ethanol 28,29 and ethanol-hexanol systems. 30 In this model, the transient attachment/detachment frequencies of single molecules to/from the cluster surface were used to describe the growth/decay of cluster size, and then the evolution of cluster size distribution was obtained without any parameter tting.…”
“…Hereafter, we will shortly summarize the basic kinetic equations. Formation of nuclei within standard nucleation theory, when the addition of "growth units" (atoms, molecules, or repeating unit of polymer chain) plays a dominant role and the coalescence of nuclei is neglected, is governed by 1,[18][19][20]…”
Kinetic equations describing nucleation on active centers are solved numerically to determine the number of supercritical nuclei, nucleation rate, and the number density of nuclei for formation both of droplets from vapor and also crystalline phase from vapor, solution, and melt. Our approach follows standard nucleation model, when the exhaustion of active centers is taken into account via the boundary condition, and thus no additional equation (expressing exhaustion of active centers) is needed. Moreover, we have included into our model lowering of supersaturation of a mother phase as a consequence of the phase transition process within a confined volume. It is shown that the standard model of nucleation on active centers (Avrami approach) gives faster exhaustion of active centers as compared with our model in all systems under consideration. Nucleation rate (in difference to standard approach based on Avrami model) is equal to the time derivative of the total number of nuclei and reaches some maximum with time. At lower nucleation barrier (corresponding to higher initial supersaturation or lower wetting angle of nucleus on the surface of active center) the exhaustion of active centers is faster. Decrease in supersaturation of the mother phase is faster at higher number of active centers.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.