Polymer chains dissolved in a solvent take random conformations due to large internal degrees of freedom and are characterized geometrically by their average shape and size. The diffusive dynamics of such large macromolecules play an indispensable role in a plethora of engineering applications. The influence of the size of the polymer chain on its diffusion is well studied, whereas the same cannot be said for the shape of the polymer chain. In the present work, the influence of the shape on the diffusion dynamics of the star-shaped chains in solution is investigated using multi-particle collision dynamics. Star-shaped chains of varying degrees of functionality are modeled in a good solvent at infinite dilution. The radius of gyration (R_g) of the star-shaped chains follows a functionality-independent scaling law with the molecular weight (N), R_g ∼ N^ν, where ν ∼ 0.627. The shape of the polymer chains is calibrated by relative shape anisotropy (κ²). We obtain nearly constant translational diffusion coefficients for the star polymers having the same hydrodynamic radius (R_h), calculated using the Zimm theory. The rotational diffusion coefficient (D_R) of the star polymer is found to be inversely proportional to its relative shape anisotropy at a constant hydrodynamic radius, i.e., D_R ∝ 1/κ².

中文翻译：

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星形大分子在稀溶液中的扩散动力学

溶解在溶剂中的聚合物链由于内部自由度大而呈现随机构象，并通过其平均形状和尺寸进行几何表征。这种大分子的扩散动力学在众多的工程应用中发挥着不可或缺的作用。聚合物链的尺寸对其扩散的影响已得到充分研究，但对于聚合物链的形状却不能说同样的情况。在目前的工作中，利用多粒子碰撞动力学研究了形状对溶液中星形链扩散动力学的影响。不同功能程度的星形链在无限稀释的良溶剂中建模。星形链的回转半径 ( R _{g ) 遵循与分子量 (} N ) 无关的功能缩放定律，R _g ∼ N ^ν，其中 ν ∼ 0.627。聚合物链的形状通过相对形状各向异性 (κ ² ) 进行校准。我们使用 Zimm 理论计算得到具有相同流体动力学半径 ( R _h )的星形聚合物的几乎恒定的平移扩散系数。发现星形聚合物的旋转扩散系数( D _R )与其在恒定流体动力学半径下的相对形状各向异性成反比，即D _R ∝ 1/κ ²。