Polymer稀溶液的粘度函数和流变光学性质：FENE-Fraenkel哑铃模型与棒状模型的比较
Viscometric Functions and Rheo-optical Properties of Dilute Polymer Solutions: Comparison of FENE-Fraenkel Dumbbells with Rodlike Models
摘要：
刚性大分子或聚合物链的持久性长度的数量级的轮廓长度（或更大），传统上被建模为杆或非常刚性的弹簧。FENE-Fraenkel弹簧哑铃，这是一个可伸缩的非零自然长度与可调谐波刚度，是一个这样的模型，以前已被证明重现珠棒行为的流体动力学相互作用的情况下。FENE-Fraenkel弹簧的力定律对于适当选择的弹簧参数值简化为Hookean或FENE弹簧力定律。因此，可以通过适当地改变参数来探索珠弹簧和珠杆行为的极限之间的交叉区域。在这项研究中，使用半隐式预测-校正布朗动力学算法，FENE-Fraenkel弹簧模拟杆与流体动力学相互作用时，弹簧刚度，可扩展性和模拟时间步长仔细选择。通过放松弹簧刚度和可延伸性，FENE-Fraenkel弹簧还可以再现类似弹簧的行为，例如粘度与剪切速率的幂律比例从$-1/3$转换到$-2/3$，以及第二法向应力差从正变为负。此外，与高纵横比的刚性大分子的粘度和线性二色性的实验数据的比较表明，FENE-Fraenkel弹簧的可延伸性和刚度允许与棒状模型相比，在建模不灵活的分子时具有相同或更高的精度。
英文摘要：
Rigid macromolecules or polymer chains with persistence length on the order of the contour length (or greater) have traditionally been modelled as rods or very stiff springs. The FENE-Fraenkel-spring dumbbell, which is finitely extensible about a non-zero natural length with tunable harmonic stiffness, is one such model which has previously been shown to reproduce bead-rod behaviour in the absence of hydrodynamic interactions. The force law for the FENE-Fraenkel spring reduces to the Hookean or FENE spring force law for appropriately chosen values of the spring parameters. It is consequently possible to explore the crossover region between the limits of bead-spring and bead-rod behaviour by varying the parameters suitably. In this study, using a semi-implicit predictor-corrector Brownian dynamics algorithm, the FENE-Fraenkel spring is shown to imitate a rod with hydrodynamic interactions when spring stiffness, extensibility and simulation timestep are chosen carefully. By relaxing the spring stiffness and extensibility, the FENE-Fraenkel spring can also reproduce spring-like behaviour, such as a crossover from $-1/3$ to $-2/3$ power-law scaling in the viscosity with shear rate, and a change from positive to negative second normal stress difference. Furthermore, comparisons with experimental data on the viscosity and linear dichroism of high aspect ratio, rigid macromolecules shows that the extensibility and stiffness of the FENE-Fraenkel spring allows for equal or improved accuracy in modelling inflexible molecules compared to rodlike models.
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