The Eckart co-rotating frame is used to analyze the dynamics of star polymers under shear flow, either in melt or solution and with different types of bonds. This formalism is compared with the standard approach used in many previous studies on polymer dynamics, where an apparent angular velocity ω is obtained from the relation between the tensor of inertia and angular momentum. A common mistake is to interpret ω as the molecular rotation frequency, which is only valid for rigid-body rotation. The Eckart frame, originally formulated to analyze the infrared spectra of small molecules, dissects different kinds of displacements: vibrations without angular momentum, pure rotation, and vibrational angular momentum (leading to a Coriolis cross-term). The Eckart frame co-rotates with the molecule with an angular frequency Ω obtained from the Eckart condition for minimal coupling between rotation and vibration. The standard and Eckart approaches are compared with a straight description of the star's dynamics taken from the time autocorrelation of the monomer positions moving around the molecule's center of mass. This is an underdamped oscillatory signal, which can be described by a rotation frequency ω_R and a decorrelation rate Γ. We consistently find that Ω coincides with ω_R, which determines the characteristic tank-treading rotation of the star. By contrast, the apparent angular velocity ω < Ω does not discern between pure rotation and molecular vibrations. We believe that the Eckart frame will be useful to unveil the dynamics of semiflexible molecules where rotation and deformations are entangled, including tumbling, tank-treading motions and breathing modes.

中文翻译：

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Eckart框架在软物质上的应用：剪切流下星形聚合物的旋转

Eckart同向旋转框架用于分析剪切流动下的星形聚合物在熔体或溶液中以及具有不同键类型的动力学。将该形式主义与先前许多关于聚合物动力学的研究中使用的标准方法进行了比较，在该方法中，从惯性张量和角动量之间的关系获得了视在角速度ω。一个常见的错误是解释ω作为分子旋转频率，仅对刚体旋转有效。最初设计用于分析小分子红外光谱的Eckart框架剖析了各种位移：无角动量的振动，纯旋转和振动角动量（导致科里奥利交叉项）。Eckart框架以从Eckart条件获得的角频率Ω与分子共同旋转，以最大程度地减少旋转和振动之间的耦合。将标准方法和Eckart方法与对恒星动力学的直接描述进行了比较，该恒星动力学是从围绕分子质心移动的单体位置的时间自相关得出的。这是阻尼不足的振荡信号，可以用旋转频率ω来描述_R和去相关率Γ。我们一致发现， Ω恰逢ω _[R ，它决定了明星的特点坦克践踏旋转。相比之下，表观角速度ω < Ω在纯旋转和分子振动之​​间无法辨别。我们认为，Eckart框架将有助于揭示纠缠旋转和变形的半柔性分子的动力学，包括翻滚，踩踏运动和呼吸方式。