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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 Rotational diffusion ： ウィキペディア英語版 Rotational diffusion Rotational diffusion is a process by which the equilibrium statistical distribution of the overall orientation of particles or molecules is maintained or restored. Rotational diffusion is the counterpart of translational diffusion, which maintains or restores the equilibrium statistical distribution of particles' position in space. The random re-orientation of molecules (or larger systems) is an important process for many biophysical probes. Due to the equipartition theorem, larger molecules re-orient more slowly than do smaller objects and, hence, measurements of the rotational diffusion constants can give insight into the overall mass and its distribution within an object. Quantitatively, the mean square of the angular velocity about each of an object's principal axes is inversely proportional to its moment of inertia about that axis. Therefore, there should be three rotational diffusion constants - the eigenvalues of the rotational diffusion tensor - resulting in five rotational time constants. If two eigenvalues of the diffusion tensor are equal, the particle diffuses as a spheroid with two unique diffusion rates and three time constants. And if all eigenvalues are the same, the particle diffuses as a sphere with one time constant. The diffusion tensor may be determined from the Perrin friction factors, in analogy with the Einstein relation of translational diffusion, but often is inaccurate and direct measurement is required. The rotational diffusion tensor may be determined experimentally through fluorescence anisotropy, flow birefringence, dielectric spectroscopy, NMR relaxation and other biophysical methods sensitive to picosecond or slower rotational processes. In some techniques such as fluorescence it may be very difficult to characterize the full diffusion tensor, for example measuring two diffusion rates can sometimes be possible when there is a great difference between them, e.g., for very long, thin ellipsoids such as certain viruses. This is however not the case of the extremely sensitive, atomic resolution technique of NMR relaxation that can be used to fully determine the rotational diffusion tensor to very high precision. == Basic equations of rotational diffusion == For rotational diffusion about a single axis, the mean-square angular deviation in time $t$ is $$ \langle\theta^2\rangle = 2 D_r t \! where $D\_r$ is the rotational diffusion coefficient (in units of radians2/s). The angular drift velocity $\backslash Omega\_d\; =\; (d\backslash theta/dt)\_$ in response to an external torque $\backslash Gamma\_$ (assuming that the flow stays non-turbulent and that inertial effects can be neglected) is given by $$ \Omega_d = \frac where $f\_r$ is the frictional drag coefficient. The relationship between the rotational diffusion coefficient and the rotational frictional drag coefficient is given by the Einstein relation (or Einstein–Smoluchowski relation): $$ D_r = \frac where $k\_B$ is the Boltzmann constant and $T$ is the absolute temperature. These relationships are in complete analogy to translational diffusion. The rotational frictional drag coefficient for a sphere of radius $R$ is $$ f_{r, \textrm{sphere}} = 8 \pi \eta R^3 \! where $\backslash eta$ is the dynamic (or shear) viscosity.〔Landau et Lifchitz tome 4 : Mécanique des fluide p 287 〕 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「Rotational diffusion」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.