Wormlike Chains Near the Rod Limit: Translational Friction Coefficient
Wormlike Chains Near the Rod Limit: Translational Friction Coefficient
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DOI：
10.1021/ma60068a032
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发表时间：
1979-03
期刊：
影响因子：
5.5
通讯作者：
T. Norisuye;M. Motowoka;H. Fujita
中科院分区：
文献类型：
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作者：
T. Norisuye;M. Motowoka;H. Fujita
采用蠕虫香肠模型，根据Oseen-Burgers方法的Yamakawa-Fujii公式计算了Kratky-Porod（KP）蠕虫链在杆极限附近的平移摩擦系数.这里的蠕虫状香肠指的是两端有半球的蠕虫状圆柱体。得到的表达式在L= d的极限处收敛于斯托克斯定律，其中L是轮廓长度，d是香肠的直径。它与忽略端部效应的Yamakawa-Fujii表达式的比较表明，端部校正出乎意料地小。实际上，Yamakawa-Fujii理论的精确度可达L/d~ 4。其中，Kratky-Porod蠕虫状链（KP链）的平移摩擦系数的最精确公式是由Ya-makawa和Fujii用他们称之为蠕虫状圆柱的模型得出的。然而，它仍然是不完整的，因为它忽略了来自圆柱端部的贡献。根据Broersma 7对直圆柱体的研究判断，可以预期，随着KP链变短，端部对流体动力学行为的影响应该变得显著。本文的目的是估计这种影响，使用蠕虫状香肠模型的KP链。这个模型是一个蠕虫状的圆柱体，两端有两个半球，如图1所示。假设香肠的中心轴具有KP链的柔性特性。我们还假设，无论香肠以何种方式变形，垂直于中心轴的每个半球的横截面都保持圆形。我们的计算将仅限于杆极限附近的香肠，因为通过这样做，前面推导出的力矩8（R2 m（R* u 0）n）（m，n=
The translational friction coefficient,, of the Kratky-Porod (KP) wormlike chain near the rod limit is calculated according to the Yamakawa-Fujii formulation of the Oseen-Burgers method, with a wormlike sausage model assumed for the chain. Here wormlike sausage means a wormlike cylinder capped with hemispheres at its ends. The resulting expression for converges to the Stokes law at the limit of L= d, where L is the contour length and d is the diameter of the sausage. Its comparison with the Yamakawa-Fujii expression, which ignores end effects, shows that end corrections to are unexpectedly small. In fact, the Yamakawa-Fujii theory is accurate down to as short a chain as L/d~ 4.Among others, 1™ 5 the most accurate formulation of the translational friction coefficient,, of the Kratky-Porod wormlike chain6 (KP chain) is one worked out by Ya-makawa and Fujii5 with a model that theycall the wormlike cylinder. However, it is still incomplete in that it neglects contributions from the ends of the cylinder. Judging from a study by Broersma7 on straight cylinders, one may anticipate that end effects on hydrodynamic behavior should become significant as the KP chain gets shorter. The purpose of the present paper is to estimate such effects on, using a wormlike sausage model for the KP chain. This model is a wormlike cylinder capped with two hemispheres at its ends, as illustrated in Figure 1. It is assumed that the central axis of the sausage has a flexibility characteristic of the KP chain. We also assume that the cross-section of each hemisphere perpendicular to the central axis stays circular in whatever way the sausage is deformed. Our calculation will be restricted to the sausage near the rod limit, because by so doing the previously derived moments8 (R2m (R* u0) n)(m, n=