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nano 2007-06-23 03:39

纳米材料及其材料生长过程的Ostwald ripening

【纳米科技世界论坛专题讨论】这个物理过程是材料生长，表面扩散及其界面物理化学等广泛存在的物理问题，往往容易一些混淆，也是学生，特别是初步接触这方面不容易搞懂的问题。这个专题我们的目的是先讨论清楚基本概念，再讨论在纳米材料生长中的应用。iii \@cO7O B
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[b]1. 什么是Ostwald ripening？[/b]
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(chemistry) Solution-crystallizer phenomenon in which small crystals, more soluble than large ones, dissolve and reprecipitate onto larger particles. $|9N2qLje
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[b]Ostwald ripening [/b]is an observed phenomenon in solid solutions which describes the evolution of an inhomogenous structure over time. When a phase precipitates out of a solid, energetic factors will drive some precipitates to grow, drawing from the others, which shrink. If this process continues, eventually fewer and larger crystals form inside the solid that have smaller and smaller surface-to-volume ratios compared to the smaller particles, thus reducing the energy of the entire system.
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The phenomenon was first described by Wilhelm Ostwald in 1896.[[url=http://en.wikipedia.org/wiki/Ostwald_ripening#_note-0][b]1[/b][/url]]
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In geology, it is the textural coarsening, ageing or growth of phenocrysts and crystals in solid rock which is below the solidus temperature. It is often ascribed as a process in the formation of orthoclase megacrysts, as an alternative to the physical processes governing crystal growth from nucleation and growth rate thermochemical limitations.t&y&A2N|a6q
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In oil-in-water emulsion-type polymerizations, Ostwald ripening is the diffusion of monomer from smaller to larger droplets due to the greater solubility of the single monomer molecules in the larger monomer droplets. The rate of this diffusion process is linked to the solubility of the monomer in the continuous (water) phase of the emulsion. Ostwald ripening is a key mechanism in the destabilization of emulsions (for example, by creaming and sedimentation).

An everyday example of Ostwald ripening is the recrystallization of water within ice cream which gives old ice cream a gritty, crunchy texture. The larger ice crystals grow competitively with the smaller within the ice cream, thereby destabilizing the homogeneity of the emulsion.

In chemistry, the term refers to the growth of larger crystals from those of smaller size which have a higher solubility than the larger ones. In the process, many small crystals formed initially slowly disappear, except for a few that grow larger, at the expense of the small crystals. The smaller crystals act as fuel for the growth of bigger crystals. The process of Ostwald Ripening is fundamental in modern technology for the solution synthesis of quantum dots.oj+AYE ["N.Xy(?
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This spontaneous process occurs because larger particles are more energetically favored than smaller particles. While the formation of many small particles is kinetically favored, (i.e. they nucleate more easily) large particles are thermodynamically favored. This is because small particles have a larger surface area to volume ratio than large particles and are consequently easier to produce. Molecules on the surface are energetically less stable than the ones already well ordered and packed in the interior. Large particles, with their greater volume to surface area ratio, therefore represent a lower energy state. Hence, many small particles will attain a lower energy state if transformed into large particles and this is what we see in [b]Ostwald ripening.[/b]

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[b]2. Coarsening[/b]
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[b]Droplet ripening on thin films[/b]
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Certain fluids on a solid substrate form a configuration of droplets connected by a precursor layer. This configuration coarsens in time: The average droplet size grows while the number of droplets decreases and the characteristic distance between them increases. The evolution of the film -- described by a time-dependent height function h>0 -- is driven by the reduction of energy. In our case, the energy is a combination of the surface energy and intermolecular forces.
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[align=center]Droplet configuration at two different timesgF5b8W3~?2_
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K. Glasner und T. Witelski (in PRE 67, 2003) gave -- based on asymptotic analysis -- a heuristic argument that the system has a statistically self-similar behavior characterized by a single scaling exponent. For instance, the number density of droplets on an one-dimensional substrate scales like t*(-2/5). This scaling law is confirmed by numerical simulations.5YOrw@1p4N
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In a joint work with D. Slepcev (UCLA), we (F. Otto and T. Rump) establish rigorously an upper bound on the coarsening rate in a time-averaged sense (in [ref]). We apply a method proposed by Kohn and Otto (see [ref]) which uses the fact that the evolution of the film is a gradient flow. Our main analytical contribution is an interpolation inequality involving the Wasserstein distance which characterizes the distance between two droplet configurations. The bound on the scaling exponent is depending on the dimension. For instance, the bound on the number density in 1-d scales like t*(-2/5) (in accordance with the result of Glasner and Witelski), whereas in 2-d it scales like t*(-3/4). Our numerical experiments verify this result.
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As was also shown by Glasner and Witelski (in Physica D 209, 2005) for 1-d, there are two competing coarsening mechanisms: Collapse and collision of droplets.

* Collapse relies on mass exchange through the precursor layer: Larger droplets grow at the expense of the smaller ones. Eventually, the smaller droplets disappear, only the largest one survives. This is known as Ostwald ripening. In the picture below, the mass transfer from the smaller droplets to the largest one is depicted by the red arrows.

一个典型的[b]Ostwald ripening过程（图片和电影）[/b]/hDf @+v#{wOk
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[align=center]Ostwald ripening of droplets K$g/{l$pns
an avi :[url=http://www-mathphys.iam.uni-bonn.de/%7Erump/web/3drops.avi]video can be :downloads[/url]
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* Droplets migrate on the precursor layer, which can lead to coarsening by collision of two droplets. The mobility of a droplet depends on the choice of the mobility function in the thin film approximation; in our case we consider functions M(h)=hq, q>0. Depending on q, the mobility increases with height.
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We study the role of migration in the coarsening process for the whole range of mobility exponents q>0 in case of a two-dimensional substrate.4b3k2Q]wZ
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[[i] 本帖最后由 nano 于 2007-06-22 11:51 编辑 [/i]]

zhangdelin0000 2007-06-23 19:09

好东西，看了一篇综述，还没有能明白，楼主指点迷津了，多谢！！！

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