Matsumoto M
Department of Chemistry, Faculty of Integrated Arts and Sciences, University of Tokushima, Josanjima, Tokushima, Japan.
Biophys Chem. 1996 Jan 16;58(1-2):173-83. doi: 10.1016/0301-4622(95)00097-6.
The time-dependent rotational diffusion equation for rigid macromolecules in solution has been approximately solved for two cases in order to extend the electric birefringence technique to streaming-electric birefringence. One is for the initial period through the application of a rectangular electric pulse to the solution immersed in a low shear flow. The purpose of this is expansion of the distribution function into a function series made by the product of the powers of reduced time (= Thetat) and hydrodynamic field alpha (= G Theta , G: velocity gradient, Theta: rotary diffusion constant) and a surface harmonic P(i)(j)cos jphi. The solution for the build-up process at arbitrary electric field strength is found, but is limited to low hydrodynamic fields. The other is for the response when an alternating electric field is applied to the solution in a shear flow. Here, instead of reduced time, the maximum electric field E(0) is chosen as a parameter for the expansion. The expressions for the intensity of the transmitted light through crossed Nicols are derived in two optical systems where the polarizer is set at an angle of 45 degrees and 0 degrees to the direction of the electric field. The results in the former case show that we can determine four parameters, the ratio of velocity gradient to rotary diffusion constant, the axial ratio of a particle, the anisotropy of electric polarizability, and the optical anisotropy factor, from four values observed in two optical systems, namely, two light intensities before applying an electric field and two initial slopes of the build-up after applying an electric field. On the other hand, when a low alternating electric field with extremely high frequency is applied, the build-up of the light intensity in the former case is the same as that of electric birefringence for pure induced dipole orientation. The build-up for the latter optical system is the same as the expression for pure induced dipole orientation of Eq. (38) shown in a previous work.
为了将电场双折射技术扩展到流动电场双折射，针对溶液中刚性大分子的时间相关旋转扩散方程，在两种情况下进行了近似求解。一种情况是在低剪切流中，对浸没的溶液施加矩形电脉冲后的初始阶段。这样做的目的是将分布函数展开为一个函数级数，该级数由约化时间（=θt）和流体动力场α（=Gθt，G：速度梯度，θt：旋转扩散常数）的幂次与一个面谐函数P(i)(j)cos jφ的乘积构成。得到了任意电场强度下建立过程的解，但仅限于低流体动力场。另一种情况是在剪切流中对溶液施加交变电场时的响应。这里，选择最大电场E(0)作为展开的参数，而不是约化时间。在偏振器相对于电场方向设置为45度和0度的两个光学系统中，推导了通过正交尼科耳棱镜的透射光强度的表达式。前一种情况下的结果表明，我们可以从在两个光学系统中观测到的四个值，即施加电场前的两个光强度和施加电场后建立过程的两个初始斜率，确定四个参数，即速度梯度与旋转扩散常数的比值、粒子的轴比、电极化率的各向异性以及光学各向异性因子。另一方面，当施加极低频率的低交变电场时，前一种情况下光强度的建立与纯感应偶极取向的电场双折射相同。后一种光学系统中的建立与先前工作中所示的式(38)的纯感应偶极取向表达式相同。
