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arXiv 1707.09170cond-mat.soft
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Eckart框架在软物质中的应用:剪切流下星形聚合物的旋转

Application of the Eckart frame to soft matter: rotation of star polymers under shear flow

Jurij Sablić, Rafael Delgado-Buscalioni, Matej Praprotnik

摘要:

Eckart同向旋转框架用于分析剪切流动下星形聚合物的动力学,无论是在熔体或溶液中,并具有不同类型的键。这种形式主义相比,在许多以前的聚合物动力学研究中使用的标准方法,其中一个表观角速度$ω$是从张量的惯性和角动量之间的关系。一个常见的错误是将$ω$解释为分子旋转频率,这只对刚体旋转有效。最初用于分析小分子红外光谱的Eckart框架剖析了不同类型的位移: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框架与分子以角频率$Ω$共同旋转,该角频率从用于旋转和振动之间的最小耦合的Eckart条件获得。标准和Eckart的方法进行了比较,从时间自相关的单体位置移动的分子的质量质心的恒星的动态的直接描述。这是欠阻尼振荡信号,其可以由旋转频率$ω_R$和去相关速率$Γ$来描述。我们一致地发现$Ω$与$ω_R$一致,这决定了恒星的特征性坦克踩踏旋转。相比之下,表观角速度$ω< Ω$不能区分纯旋转和分子振动。我们相信Eckart框架将有助于揭示半柔性分子的动力学,其中旋转和变形纠缠在一起,包括翻滚,坦克踩踏运动和呼吸模式。

英文摘要:

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 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 monomers 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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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