Continuous relaxation spectra for constitutive models in medium-amplitude oscillatory shear
Continuous relaxation spectra for constitutive models in medium-amplitude oscillatory shear
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DOI：
10.1122/1.5025080
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发表时间：
2018-09-01
影响因子：
3.3
通讯作者：
Ewoldt, Randy H.
中科院分区：
文献类型：
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作者：
Martinetti, Luca;Soulages, Johannes M.;Ewoldt, Randy H.
我们推导并演示了应变控制的中幅振荡剪切(MAOS)的解析解如何与驰豫时间的连续分布相耦合。这通常适用于现有的大量MAOS型号，包括那些不受时间限制的型号。理论结果对于提高模型参数的确定性很重要，因为与松弛时间的离散分布相比，模型参数的数量可以显著减少。我们通过模拟由聚乙烯醇和四硼酸钠(硼砂)半稀溶液形成的暂态网络的实验数据来举例说明这种连续光谱MAOS方法。仅用5个参数对全频率相关MAOS特征进行了很好的拟合：3个线性参数用于对数正态分布，2个非线性参数用于非线性的强度及其截止时间尺度。值得注意的是，较长的模(tau>；tau(W))在渐近非线性区域不被激活。虽然这可能与切变非线性的可能机制相一致，但时间尺度硬截止的原因目前尚不清楚。我们的结果还表明，三次谐粘性非线性的符号变化位置可能对控制末端弛豫时间多分散性的大尺度结构特征(如摩尔质量分布或长链分支)敏感。(C)2018年流变学学会。
We derive and demonstrate how analytical solutions for strain-controlled medium-amplitude oscillatory shear (MAOS) can be coupled with a continuous distribution of relaxation times. This applies generally to the vast library of existing MAOS models, including those that are not time-strain separable. The theoretical results are important for improved certainty in model parameters, since their number can be reduced dramatically compared to a discrete distribution of relaxation times. We exemplify this continuous spectrum MAOS approach by modeling experimental data for a transient network formed from an aqueous semidilute unentangled solution of poly(vinyl alcohol) and sodium tetraborate (Borax). The full frequency-dependent MAOS signatures are fit well by only five parameters: three linear parameters for a log-normal spectral distribution and two nonlinear parameters for the strength of the nonlinearity and its cutoff time scale. Remarkably, longer modes (tau > tau(w)) are not activated in the asymptotically nonlinear regime. Although this may be compatible with the possible mechanisms for the shear nonlinearities, the reason for the hard cutoff of time scales is currently unknown. Our results also suggest that the sign change location for the third-harmonic viscous nonlinearity may be sensitive to large-scale structural features (such as molar mass distribution or long-chain branching) that control the polydispersity of terminal relaxation times. (C) 2018 The Society of Rheology.