New Challenges in Aggregation Kinetics

聚集动力学的新挑战

• 批准号: 0703937
• 负责人: Rodolfo Rosales
• 金额: $ 11.2万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0703937&HistoricalAwards=false
• 关键词: New; Challenges; Aggregation; Kinetics

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.

Rosales0703937聚集，即单体聚合成大的、有结构的簇，是科学和工业中许多现象的核心。在一个简化的模型中，团簇的生长是一次加入或脱落单体的随机过程。Becker-Dering(BD)常微分方程组通过表面反应控制小团簇的生长。用Lifshitz-Slyozov方程描述了由周围单体扩散生长的大团簇。小星团通过自由能势垒上的波动引起的缓慢过程而成核并形成大星团。研究人员Joseph Farjoun研究了成核的以下几个方面：(A)Zeldovich成核公式与实验结果不一致。它对过饱和度的大小非常敏感，因此对团簇大小的分布也很敏感。研究人员通过将过饱和度分解到更高的阶数来寻求更准确的公式。此外，基于重整化蒙特卡罗方法的模拟提供了更多关于形核率的数据。(B)由Zeldovich形核率和LS增长率决定的团簇尺寸的长期分布是一个典型的问题。这位研究人员研究了与平滑相似解的联系：对他的博士论文中的部分答案进行了更深入的分析。(C)二维成核分析是研究人员博士论文工作的自然延伸。单体浓度对二维核的对数行为迫使成核过程在空间上是不均匀的。研究者通过将二维扩散的前人工作联系起来来研究这一点。(D)研究了聚集过程对其他物理参数的动态依赖性。具体地说，他分析了温度变化的系统中的聚集。成核速率和形成的团簇总数由降低的温度和单体的耗尽之间的平衡决定，这两个因素对过饱和度具有竞争作用。由聚集模拟的现象--凝固、沉淀和水蒸气凝聚成液滴--出现在许多生物物理和工业环境中：玻璃到晶体的转变、过冷液体和聚合物中的晶体成核、胶体结晶、超过临界胶束浓度(CMC)的球形聚集体的生长，以及通过粗化淬火进入混溶间隙的二元合金的偏析，仅举几个具体的例子。微芯片制造领域将从能够预测二维团簇的短期和长期行为的理论中受益匪浅。解决Zeldovich公式(它预测星团形成的速度)和实验之间长期存在的分歧，找到聚集过程各个阶段的时间尺度，以及二维聚集理论(所有这些都是本项目的研究主题)，可以得到更准确的预测和更好的设计。一个更现实的模型，它解释了温度的变化，可以用于蒸汽形成行业(如发电厂)的设计，以及天气预报。目前最先进的聚集状态是极端情况：在很短和很长时间内的行为，非常小或非常大的星团的行为已经被广泛研究。在这个项目中，研究人员约瑟夫·法容的工作弥合了这些差距。