论文标题
曲线坐标中蠕虫样链的修饰扩散方程的球形谐波膨胀
Spherical-harmonic Expansion of the Modified Diffusion Equation for Wormlike Chain in Curvilinear Coordinates
论文作者
论文摘要
我们使用自洽场理论研究了类似蠕虫的聚合物链，并考虑了聚合物片段之间的Onsager排除体积相互作用。聚合物链的传播器是用于研究聚合物构象的必不可少的物理量之一，该聚合物满足蠕虫样链的修饰扩散方程（MDE）。虫状链的传播器不仅取决于空间变量，还取决于方向。我们通过使用球形谐波系列分离传播器的变量，然后将MDE简化为一组耦合方程组，仅取决于本文中的空间变量。我们分别通过圆柱坐标和球形坐标中的球形谐波功能扩展了MDE。我们发现，无论在圆柱坐标或球形坐标中，都有三种设置方向的方法。但是为了方便计算，我们比较了这三种形式，并选择最简单的形式来简化MDE。而且我们得到一组方程组仅取决于空间变量。
We investigate the wormlike polymer chains using self-consistent field theory and take into account the Onsager excluded-volume interaction between polymer segments. The propagator of polymer chain is one of the essential physical quantities used to study the conformation of polymers, which satisfies the modified diffusion equation (MDE) for wormlike chain. The propagator of wormlike chain is not only dependent on the spatial variables, but also on the orientation. We separate the variables of propagator by using spherical-harmonic series and then simplify the MDE to a coupled set of equations only depends on spatial variables in this paper. We expand the MDE by spherical-harmonic functions in cylindrical coordinates and spherical coordinates, respectively. We find that there are three ways to set the orientation, no matter in cylindrical coordinates or spherical coordinates. But for the convenience of calculation, we compare these three forms and choose the simplest one to simplify the MDE. And we get a coupled set of equations only depends on spatial variables.
