Uniqueness of relaxation times determined by dielectric spectroscopy
Uniqueness of relaxation times determined by dielectric spectroscopy
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DOI：
10.1088/1361-648x/acbcb8
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发表时间：
2023-05-10
影响因子：
2.7
通讯作者：
Schneider，Gerald J.
中科院分区：
文献类型：
--
作者：
Wu，Mengchun;Bichler，Karin J.;Schneider，Gerald J.
介电谱是研究分子动力学的一个非常强大的工具，因为它具有非常宽的频率范围。通常，多个过程会导致光谱扩展到几个数量级，其中一些贡献部分隐藏。为了说明，我们选择了两个例子，（i）正常模式的高摩尔质量聚合物部分隐藏的导电性和极化和（ii）轮廓长度波动部分隐藏的爬行使用充分研究的聚异戊二烯熔体作为例子。描述实验光谱和提取弛豫时间的直观方法是两个或多个模型函数的相加。在这里，我们使用经验Havriliak-Negami函数来说明提取的弛豫时间的模糊性，尽管与实验数据的拟合非常吻合。我们表明，有一个完美的描述实验数据可以实现无限数量的解决方案。然而，一个简单的数学关系表明弛豫强度和弛豫时间对的唯一性。牺牲弛豫时间的绝对值使得能够以高精度找到参数的温度依赖性。对于这里研究的特定情况，时间温度叠加（TTS）是非常有用的，以确认该原则。然而，推导不是基于特定的温度依赖性，因此，独立于TTS。我们比较了新的和传统的方法，并发现相同的趋势的温度依赖性。新技术的重要优点是弛豫时间的准确性的知识。根据峰值清晰可见的数据确定的弛豫时间在传统技术和新技术的实验准确度内是相同的。然而，对于主导过程隐藏峰值的数据，可以观察到实质性偏差。我们的结论是，新的方法是特别有帮助的情况下，需要确定弛豫时间，而无需访问相关的峰值位置。
Dielectric spectroscopy is extremely powerful to study molecular dynamics, because of the very broad frequency range. Often multiple processes superimpose resulting in spectra that expand over several orders of magnitude, with some of the contributions partially hidden. For illustration, we selected two examples,(i) normal mode of high molar mass polymers partially hidden by conductivity and polarization and (ii) contour length fluctuations partially hidden by reptation using the well-studied polyisoprene melts as example. The intuitive approach to describe experimental spectra and to extract relaxation times is the addition of two or more model functions. Here, we use the empirical Havriliak-Negami function to illustrate the ambiguity of the extracted relaxation time, despite an excellent agreement of the fit with experimental data. We show that there are an infinite number of solutions for which a perfect description of experimental data can be achieved. However, a simple mathematical relationship indicates uniqueness of the pairs of the relaxation strength and relaxation time. Sacrificing the absolute value of the relaxation time enables to find the temperature dependence of the parameters with a high accuracy. For the specific cases studied here, the time temperature superposition (TTS) is very useful to confirm the principle. However, the derivation is not based on a specific temperature dependence, hence, independent from the TTS. We compare new and traditional approaches and find the same trend for the temperature dependence. The important advantage of the new technology is the knowledge of the accuracy of the relaxation times. Relaxation times determined from data for which the peak is clearly visible are the same within the experimental accuracy for traditional and new technology. However, for data where a dominant process hides the peak, substantial deviations can be observed. We conclude that the new approach is particularly helpful for cases in which relaxation times need to be determined without having access to the associated peak position.