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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 Kuhn length ： ウィキペディア英語版 Kuhn length The Kuhn length is a theoretical treatment, developed by Werner Kuhn, in which a real polymer chain is considered as a collection of $N$ Kuhn segments each with a Kuhn length $b$. Each Kuhn segment can be thought of as if they are freely jointed with each other.〔Flory, P.J. (1953) ''Principles of Polymer Chemistry'', Cornell Univ. Press, ISBN 0-8014-0134-8〕〔Flory, P.J. (1969) ''Statistical Mechanics of Chain Molecules'', Wiley, ISBN 0-470-26495-0; reissued 1989, ISBN 1-56990-019-1〕〔Rubinstein, M., Colby, R. H. (2003)''Polymer Physics'', Oxford University Press, ISBN 0-19-852059-X〕 Each segment in a freely jointed chain can randomly orient in any direction without the influence of any forces, independent of the directions taken by other segments. Instead of considering a real chain consisting of $n$ bonds and with fixed bond angles, torsion angles, and bond lengths, Kuhn considered an equivalent ideal chain with $N$ connected segments, now called Kuhn segments, that can orient in any random direction. The length of a fully stretched chain is $L=Nb$ for the Kuhn segment chain.〔 〕 In the simplest treatment, such a chain follows the random walk model, where each step taken in a random direction is independent of the directions taken in the previous steps, forming a random coil. The average end-to-end distance for a chain satisfying the random walk model is $\backslash langle\; R^2\backslash rangle\; =\; Nb^2$. Since the space occupied by a segment in the polymer chain cannot be taken by another segment, a self-avoiding random walk model can also be used. The Kuhn segment construction is useful in that it allows complicated polymers to be treated with simplified models as either a random walk or a self-avoiding walk, which can simplify the treatment considerably. For an actual homopolymer chain (consists of the same repeat units) with bond length $l$ and bond angle θ with a dihedral angle energy potential, the average end-to-end distance can be obtained as :$\backslash langle\; R^2\; \backslash rangle\; =\; n\; l^2\; \backslash frac\; \backslash cdot\; \backslash frac$, ::where $\backslash langle\; \backslash cos(\backslash textstyle\backslash phi\backslash ,\backslash !)\; \backslash rangle$ is the average cosine of the dihedral angle. The fully stretched length $L\; =\; nl\backslash ,\; \backslash cos(\backslash theta/2)$. By equating $\backslash langle\; R^2\; \backslash rangle$ and $L$ for the actual chain and the equivalent chain with Kuhn segments, the number of Kuhn segments $N$ and the Kuhn segment length $b$ can be obtained. For worm-like chain, Kuhn length equals two times the persistence length.〔Gert R. Strobl (2007) ''The physics of polymers: concepts for understanding their structures and behavior'', Springer, ISBN 3-540-25278-9〕 ==References== 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「Kuhn length」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.