New Challenges in Aggregation Kinetics

点击翻译按钮获取中文摘要

Rosales0703937 Aggregation, the coalescence of monomers into large,structured clusters, is found at the heart of many phenomena inscience and industry. In a simplified model, cluster growth is adiscrete stochastic process of adding or shedding monomers, oneat a time. The Becker-Doring (BD) ordinary differentialequations govern the growth of small clusters by surfacereactions. Large clusters, growing by the diffusion of thesurrounding monomers, are described by the Lifshitz-Slyozovequations. Small clusters nucleate and form large ones by a slowprocess caused by fluctuations over a free-energy barrier. Theinvestigator, Joseph Farjoun, studies the following aspects ofnucleation: (a) The Zeldovich nucleation formula disagrees with theexperimental results. It is highly sensitive to thesuper-saturation's value, and hence on the distribution ofcluster-sizes. The investigator seeks a more accurate formula byresolving the super-saturation to higher order. In addition, asimulation based on renormalized Monte-Carlo methods is providingmore data on the nucleation rate. (b) The long-term distribution of clusters sizes, as determinedby the Zeldovich nucleation rate and LS growth rate, is aclassical problem. The investigator studies a connection to thesmooth similarity-solution: A deeper analysis of the partialanswer in his PhD thesis. (c) The analysis of 2-dimensional nucleation is a naturalextension of the work in the investigator's PhD thesis. Thelogarithmic behavior of monomer concentration about nuclei in2-dimensions forces the nucleation process to be spatiallynon-homogeneous. The investigator studies this by connecting toprevious work on 2-dimensional diffusion. (d) The investigator studies the dynamic dependency of theaggregation process on other physical parameters. Specifically,he analyzes aggregation in a system with a varying temperature. The nucleation rate and the total amount of clusters formed aredetermined by a balance between the decreasing temperature andthe depletion of monomers, which have competing effects on thesuper-saturation. Phenomena that are modeled by aggregation -- solidification,precipitation, and the condensation of vapor into droplets --appear in many biophysical and industrial contexts:Glass-to-crystal transformations, crystal nucleation inunder-cooled liquids, and in polymers, colloidal crystallization,growth of spherical aggregates beyond the critical micelleconcentration (CMC), and the segregation by coarsening of binaryalloys quenched into the miscibility gap, to name but a fewspecific examples. The field of micro-chip fabrication stands tobenefit greatly from a theory capable of predicting the short-and long-term behavior of 2-dimensional clusters. Resolving thelong-standing disagreement between the Zeldovich formula (whichpredicts the rate at which clusters are created) and theexperiments, finding the time-scales of the various phases of theaggregation process, and a theory for 2-dimensional aggregation(all of which are topics of research in this project) allows formore accurate predictions and better design. A more realisticmodel, which accounts for the varying temperature, can be used inthe design of vapor-forming industries (e.g. power plants), andin weather prediction. The current state of the art inaggregation is that of extremes: the behavior at very short andvery long times, the behavior of very small or very largeclusters have been studied extensively. In this project, thework of the investigator, Joseph Farjoun, bridges these gaps.