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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 Distortion free energy density ： ウィキペディア英語版 Distortion free energy density The Distortion free energy density is a quantity that describes the increase in the free energy density of a liquid crystal caused by distortions from its uniformly aligned configuration. It also commonly goes by the name Frank free energy density named after Frederick Charles Frank. ==Nematic Liquid Crystal== The Distortion free energy density in a nematic liquid crystal is a measure of the increase in the Helmholtz free energy per unit volume due to deviations in the orientational ordering away from a uniformly aligned nematic director configuration. The total free energy density for a nematic is therefore given by: :$\backslash mathcal\_=\backslash mathcal\_+\backslash mathcal\_$ where $\backslash mathcal\_$ is the total free energy density of a liquid crystal, $\backslash mathcal\_$ is the free energy density associated with a uniformly aligned nematic, and $\backslash mathcal\_$ is the contribution to the free energy density due to distortions in this order. For a non-chiral nematic liquid crystals $\backslash mathcal\_$ is commonly taken to consist of three terms given by: :$\backslash mathcal\_=\backslash fracK\_1(\backslash nabla\backslash cdot\backslash mathbfK\_2(\backslash mathbf\})^2+\backslash fracK\_3(\backslash mathbf\})^2$ The unit vector $\backslash mathbf\}|=1)$, which describes the nature of the distortion. The three constants $K\_i$ are known as the Frank constants and are dependent on the particular liquid crystal being described. They are usually of the order of $10^$ dyn. Each of the three terms represent a type of distortion of a nematic. The first term represents pure splay, the second term pure twist, and the third term pure bend. A combination of these terms can be used to represent an arbitrary deformation in a liquid crystal. It is often the case that all three Frank constants are of the same order of magnitude and so it is commonly approximated that $K\_1=K\_2=K\_3=K$. This approximation is commonly referred to as the one-constant approximation and is used predominantly because the free energy simplifies when used to the much more computationally compact form: :$\backslash mathcal\_=\backslash fracK((\backslash nabla\backslash cdot\backslash mathbf\})^2)=\backslash fracK\backslash partial\_n\_\backslash partial\_n\_$ A fourth term is also commonly added to the Frank free energy density called the saddle-splay energy that describes the surface interaction. It is often ignored when calculating director field configurations since the energies in the bulk of the liquid crystal are often greater than those due to the surface. It is given by: :$\backslash fracK\_\backslash nabla\backslash cdot((\backslash mathbf\}-\backslash mathbf(\backslash nabla\backslash cdot\; \backslash mathbf\_=-\backslash oint\backslash fracW(\backslash mathbf\})^2\backslash mathrmS$ The anchoring energy is given by $W$ and the unit vector $\backslash mathbf\{\backslash hat\{\backslash nu\}\}$ is normal to the particles 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「Distortion free energy density」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.