We found an anomalous nonlinear behavior under large amplitude oscillatory shears, where the amplitude stress deviates strongly from the linear dependence of strain, while the time dependence of stress remains sinusoidal. This phenomenon is usually accompanied with the Payne effect of filled rubbers. In order to understand the molecular details regarding this unusual behavior, we examined a series of polybutadiene/tetradecane solutions filled with carbon black. Our results show that there is a previously unrecognized transition in the system as the matrix polymer concentration ϕ approaches and passes through a characteristic polymer concentration ϕc. Below ϕc, the system typically shows the classic nonlinearity, where the storage modulus G′ decreases as the strain amplitude γ0 increases and the resulting stress waveforms are distorted from sinusoidal waves. Above ϕc, the system displays an anomalous nonlinearity, where the stress responses at any given strain remain surprisingly sinusoidal regardless of the drop in the storage modulus G′. The critical concentration ϕc is about an order of magnitude greater than the entanglement polymer concentration ϕe. The degree of entanglement in the matrix apparently determines the occurrence of this unusual rheological event and plays a key role here. Increasing the polymer molecular weight enhances this transition.

中文翻译：

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颗粒填充聚合物溶液的流变响应：向线性-非线性二分法的过渡

我们发现了在大振幅振荡剪切下的异常非线性行为，其中振幅应力强烈偏离应变的线性相关性，而应力的时间相关性仍然是正弦曲线。这种现象通常伴随着填充橡胶的佩恩效应。为了了解有关这种异常行为的分子细节，我们检查了一系列填充炭黑的聚丁二烯/十四烷溶液。我们的结果表明，当基体聚合物浓度 φ 接近并通过特征聚合物浓度 φc 时，系统中存在以前无法识别的转变。在 ϕc 以下，系统通常表现出经典的非线性，其中储能模量 G' 随着应变幅度 γ0 的增加而减小，并且由此产生的应力波形从正弦波扭曲。在 ϕc 以上，系统显示出异常非线性，无论储能模量 G' 是否下降，任何给定应变下的应力响应都保持惊人的正弦曲线。临界浓度 ϕc 比缠结聚合物浓度 ϕe 大一个数量级。基质中的纠缠程度显然决定了这种不寻常的流变事件的发生，并在这里起着关键作用。增加聚合物分子量会增强这种转变。临界浓度 ϕc 比缠结聚合物浓度 ϕe 大一个数量级。基质中的纠缠程度显然决定了这种不寻常的流变事件的发生，并在这里起着关键作用。增加聚合物分子量会增强这种转变。临界浓度 ϕc 比缠结聚合物浓度 ϕe 大一个数量级。基质中的纠缠程度显然决定了这种不寻常的流变事件的发生，并在这里起着关键作用。增加聚合物分子量会增强这种转变。