简谐势中链的Doi-Edwards格林函数修正及其对应力光学规则的意义
Correction of Doi-Edwards' Green Function for a Chain in a Harmonic Potential and its Implication for the Stress-Optical Rule
摘要：
本文给出了二维各向异性谐振势中高分子链的修正格林函数。该格林函数是Doi和Edwards首先导出的描述被限制在周围缠结聚合物的管状域中的聚合物链的修改版本[J. Chem. Soc. Farad. II 74（1978）1802]。与Ianniruberto和Marrucci（IM）在应用Doi-Edwards Green函数[J. Non-Newtonian Fluid Mech.79（1998）225]时发现的结果相反，我们发现，如果使用校正的Green函数，则对于任何圆形或椭圆形管势，都违反了应力光学规则。违反是由于存在的虚拟弹簧，以限制在管中的链，而不是各向异性的限制潜力。另一方面，土井和爱德华兹使用他们的格林函数仅用于估计沿原始路径的单体密度，我们发现只有一个小的修正。由于他们没有将其用于流变学计算，因此应力-光学规则对于Doi-Edwards模型似乎是安全的。
英文摘要：
We provide a corrected Green's function for a polymer chain trapped in a two-dimensional anisotropic harmonic potential with a fixed boundary condition. This Green's function is a modified version of what Doi and Edwards first derived to describe the polymer chain confined in the tube-like domain of surrounding entangled polymers [J. Chem. Soc. Farad. Trans. II 74 (1978) 1802]. In contradiction to the results found by Ianniruberto and Marrucci (IM) when applying the Doi-Edwards Green function [J. Non-Newtonian Fluid Mech. 79 (1998) 225], we find that the stress-optical rule is violated for any tube potential either circular or elliptic if the corrected Green's function is used. The violation is due to the presence of the virtual springs to confine the chain in the tube rather than the anisotropy of the confinement potential. On the other hand, Doi and Edwards used their Green's function only for estimation of the monomer density along the primitive path where we find just a small correction. Since they did not use it for rheological calculations, the stress-optic rule appears to be safe for the Doi-Edwards model.
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