排除体积相互作用的环状链的分子内距离和形状因子
Intramolecular distances and form factor of cyclic chains with excluded volume interactions
摘要：
数值模拟孤立的循环链排除体积。报告了形状因子S（x）的数据，其中x是约化散射变量，还报告了分子内单元之间距离的平均值和分布。距离的平均值与两个替代表达式进行比较，描述它们与分离单元的段数的依赖性。分布函数的结果进行了比较与des Cloizeaux形式。最后，S（x）的数据进行了比较，也来自des Cloizeaux表达式的分布函数的理论函数。此外，还得到了这些函数的低x展开式和渐近展开式.基于这些展开式，提出了在整个x值范围内对模拟数据进行良好描述的简单公式。还包括与线性链的类似结果的比较。
英文摘要：
Numerical simulations are performed for isolated cyclic chains with excluded volume. Data are reported for the form factor, S(x), where x is the reduced scattering variable, and also for averages and distributions of the distance between intramolecular units. The averages of distances are compared with two alternative expressions describing their dependence with the number of segments separating the units. The distribution function results are compared with the des Cloizeaux form. Finally the S(x) data are compared with theoretical functions also derived from the des Cloizeaux expression for the distribution function. Moreover, the low x and asymptotic expansions of these functions are obtained. Based on these expansions, simple formulas are proposed to give a good description of the simulation data in the whole range of values of x. A comparison with similar results for linear chains is also included.
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