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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Classical nucleation theory ： ウィキペディア英語版 Classical nucleation theory Nucleation is the first step in the formation of either a new thermodynamic phase or a new structure via self-assembly or self-organisation. Nucleation is typically defined to be the process that determines how long we have to wait before the new phase or self-organised structure appears. Classical nucleation theory (CNT) is the most common theoretical model used to understand why nucleation may take hours or years, or in effect never happen.〔H. R. Pruppacher and J. D. Klett, ''Microphysics of Clouds and Precipitation'', Kluwer (1997)〕〔P.G. Debenedetti, ''Metastable Liquids: Concepts and Principles'', Princeton University Press (1997)〕〔 == Outline of classical nucleation theory == This is the standard simple theory for nucleation of a new thermodynamic phase, such as a liquid or a crystal. It should be borne in mind that it is approximate. The basic CNT nucleation of a new phase provides an approximate but physically reasonable prediction for the rate at which nuclei of a new phase form, via nucleation on a set of identical nucleation sites. This rate, ''R'' is the number of, for example, water droplets nucleating in a uniform volume of air supersaturated with water vapour, per unit time. So if a 100 droplets nucleate in a volume of 0.1m3 in 1s, then the rate ''R''=1000/s. The description here follows modern standard CNT.〔 The prediction for the rate ''R'' is ::$R\backslash \; =\backslash \; N\_S\; Zj\backslash exp\; \backslash left(\; \backslash frac\; \backslash right)$ where : *$\backslash Delta\; G^$ * is the free energy cost of the nucleus at the top of the nucleation barrier, and ''k''BT is the thermal energy with ''T'' the absolute temperature and ''k''B is the Boltzmann constant. : *$N\_S$ is the number of nucleation sites. : *$j$ is the rate at which molecules attach to the nucleus causing it to grow. : *$Z$ is what is called the Zeldovich factor Z. Essentially the Zeldovich factor is the probability that a nucleus at the top of the barrier will go on to form the new phase, not dissolve. This expression for the rate can be thought of as a product of two factors: The first, $N\_S\; \backslash exp\; \backslash left(\; -\backslash Delta\; G^$ */k_BT \right), is the number of nucleation sites multiplied by the probability that a nucleus of critical size has grown around it. It can be interpreted as the average, instantaneous number of nuclei at the top of the nucleation barrier. Free energies and probabilities are closely related in general, by definition. The probability of a nucleus forming at a site is proportional to $\backslash exp(G^$ */kT ). So if $\backslash Delta\; G^$ * is large and positive the probability of forming a nucleus is very low and nucleation will be slow. Then the average number will be much less than one, i.e., it is likely that at any given time none of the sites has a nucleus. The second factor in the expression for the rate is the dynamic part, $Zj$. Here, $j$ expresses the rate of incoming matter and $Z$ is the probability that a nucleus of critical size (at the maxiumum of the energy barrier) will continue to grow and not dissolve. The Zeldovich factor is derived by assuming that the nuclei near the top of the barrier are effectively diffusing along the radial axis. By statistical fluctuations, a nucleus at the top of the barrier can grow diffusively into a larger nucleus that will grow into a new phase, or it can lose molecules and shrink back to nothing. The probability that a given nucleus goes forward is $Z$. To see how this works in practice we can look at an example. Sanz and coworkers have used computer simulation to estimate all the quantities in the above equation, for the nucleation of ice in liquid water. They did this for a simple but approximate model of water called TIP5P/2005. At a supercooling of 19.5 °C, i.e., 19.5 °C below the freezing point of water in their model, they estimate a free energy barrier to nucleation of ice of $\backslash Delta\; G^$ *=275k_BT. They also estimate a rate of addition of water molecules to an ice nucleus near the top of the barrier of ''j'' = 1011/s and a Zeldovich factor ''Z'' = 10−3 (note that this factor is dimensionless because it is basically a probability). The number of water molecules in 1 m3 of water is approximately 1028. Putting all these numbers into the formula we get a nucleation rate of approximately 10−83/s. This means that on average we would have to wait 1083s (1076 years) to see a single ice nucleus forming in 1 m3 of water at -20 °C! This is a rate of homogeneous nucleation estimated for a model of water, not real water—in experiments we cannot growing nuclei of water and so cannot directly determine the values of the barrier ''ΔG *'', or the dynamic parameters such as ''j'', for real water. However, it may be that indeed the homogeneous nucleation of ice at temperatures near -20 °C and above is ''extremely'' slow and so that whenever we see water freezing temperatures of -20 °C and above this is due to heterogeneous nucleation, i.e., the ice nucleates in contact with a surface. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Classical nucleation theory」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.