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Theory of Fluorescence Depolarization by Anisotropic Brownian Rotations. Discontinuous Distribution Approach

机译:各向异性布朗旋转的荧光去极化理论。非连续分布方法

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In this paper, we generalize to molecules devoid of symmetry the phenomenological treatment of depolarization of the fluorescence by the Brownian rotations of a spherical molecule due to Spencer and Weber. There are six ways in which a system of orthogonal coordinates rigidly bound to the molecule may be made to coincide with the laboratory coordinates. The transitions between these permissible orientations gives rise to a system of six differential equations of transport, the solution of which entails that of a differential equation of sixth order. However, because of the equivalence of some of the rotations as regards the depolarizing effects, on account of the symmetry conditions, the solution of a differential equation of third order is only necessary. Consequently, after an instantaneous light pulse, a polarized component of the fluorescence will show a maximum of three exponential decays and the difference of parallel and perpendicular components a maximum of only two decays. The steady‐state fluorescence polarization from a completely assymetric molecule is given by a simple expression containing as only parameters a mean rotational rate, the variance of three orthogonal rates of rotation, and an average of these rates weighted according to their angles with the emission oscillator. A qualitative comparison of this treatment with previous theories of depolarization that make use of classical rotary diffusion theory shows that the former is better suited to an intuitive understanding of the phenomena and to experimental usage.
机译:在本文中,我们将斯宾塞和韦伯通过球形分子的布朗旋转对荧光去极化的现象学处理推广到缺乏对称性的分子。有六种方法可以使刚性结合到分子的正交坐标系统与实验室坐标重合。这些允许方向之间的跃迁产生了一个由六个输运微分方程组成的系统,其解需要六阶微分方程的解。然而,由于一些旋转在去极化效应方面是等价的,由于对称性条件,只需要求解三阶微分方程。因此,在瞬时光脉冲之后,荧光的偏振分量将显示最多三个指数衰减,平行分量和垂直分量的差异最多只有两个衰减。来自完全非对称分子的稳态荧光偏振由一个简单的表达式给出,该表达式仅包含平均旋转速率、三个正交旋转速率的方差以及根据它们与发射振荡器的角度加权的这些速率的平均值作为参数。将这种处理与以前使用经典旋转扩散理论的去极化理论进行定性比较表明,前者更适合于对现象的直观理解和实验用途。

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