A semi-empirical constitutive equation is suggested for the model comb polymer with the purpose to simultaneously describe the intrinsic medium amplitude oscillatory shear (MAOS) behaviors and transient behaviors in start-up elongational experiments. The molecular stress and hierarchical relaxation of comb polymers are discussed on the basis of the orientation-stretch coupled conformation tensor of both backbone and arm, which are governed by the same evolution equation with different relaxation times. The discrete Baumgaertel–Schausberger–Winter spectrum is adopted for the backbone relaxation. The model has four parameters that are fully determined from the linear spectrum. The equation set is solved analytically by the perturbation method under MAOS and solved numerically under start-up extensional flows. The predictions on the nonlinear rheological behaviors are well consistent with the experiments.

中文翻译：

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缠结梳型聚合物的取向-拉伸耦合模型

为梳型聚合物提出了一个半经验本构方程，目的是在启动伸长实验中同时描述本征介质振幅振荡剪切（MAOS）行为和瞬态行为。在主链和臂的取向-拉伸偶联构象张量的基础上讨论了梳形聚合物的分子应力和分层弛豫，它们由相同的演化方程控制，具有不同的弛豫时间。离散的Baumgaertel–Schausberger–Winter频谱用于骨干松弛。该模型具有四个参数，这些参数是完全根据线性频谱确定的。该方程组通过MAOS下的摄动法进行解析求解，并在启动扩展流下进行数值求解。