Prokhorov General Physics Institute of the Russian Academy of Sciences, Vavilov Str. 38, 119991 Moscow, Russia.
A. V. Topchiev Institute of Petrochemical Synthesis of the Russian Academy of Sciences, Leninsky Av. 29, 119991 Moscow, Russia.
Spectrochim Acta A Mol Biomol Spectrosc. 2022 Dec 5;282:121653. doi: 10.1016/j.saa.2022.121653. Epub 2022 Jul 22.
Mathematically describing the length-dependence of vibrational fingerprints of polyenes is challenging, yet crucial in understanding and predicting polyene-associated molecular properties of industrially-important and vital substances. To this end, we develop an analytical relationship between the wavenumbers ν∼ of the Raman-active CC stretching mode in polyene sequences (CHCH)n and the polyene length (n) using classical mechanics laws. Noteworthy, this relationship is derived from Newton's equations instead of regression approximations and validated against experimental data for degraded polyvinyl chloride (PVC), t-butyl end-capped all-trans polyenes, β-carotenes, and carotenoids. Furthermore, given this fundamental tool, we carefully re-examined or validated the up-to-now applied empirical tools; we find that: (i) A phenomenological exponential regression function ν=1461+151.2×exp-0.07808n proves fairly suitable for describing polyenes with lengths below 24 in degraded PVC. (ii) The derived analytical relationship agrees more closely with a long-established reciprocal-length regression function ν=1459+720/n+1 for describing carotenoids. Moreover, extensive DFT calculation results on all-trans polyenes H(CHCH)H (n = 3-30) and polyenes end-capped with terminal vinyl chloride oligomers agree with experiment for shorter polyenes and are similar, showing that complicated calculations of ν∼ for infinite degraded PVC chains reduce to the calculations on finite polyene sequences. Noteworthy, unlike other polyene length-determination tools, the proposed analytical polyene length-determination based on intrinsic physical properties could well prove to be an even more versatile tool, as it comes with the added potential for determining or correcting the elasticity constants of carbon bonds in polyene chains.
用数学方法描述聚烯的振动指纹的长度依赖性具有挑战性，但对于理解和预测工业上重要和重要物质的聚烯相关分子性质至关重要。为此，我们使用经典力学定律，在聚烯序列（CHCH）n中的拉曼活性 CC 伸缩模式的波数 ν∼和聚烯长度（n）之间建立了一种解析关系。值得注意的是，这种关系是从牛顿方程推导出的，而不是从回归近似值中推导出的，并针对降解聚氯乙烯（PVC）、叔丁基封端全反式聚烯、β-胡萝卜素和类胡萝卜素的实验数据进行了验证。此外，给定这个基本工具，我们仔细重新检查或验证了迄今为止应用的经验工具；我们发现：（i）经验指数回归函数 ν=1461+151.2×exp-0.07808n 对于描述降解 PVC 中长度小于 24 的聚烯相当合适。（ii）所得到的解析关系与长期存在的倒数长度回归函数 ν=1459+720/n+1 更吻合，用于描述类胡萝卜素。此外，对全反式聚烯 H(CHCH)H（n=3-30）和末端氯乙烯齐聚物封端的聚烯的广泛 DFT 计算结果与实验结果吻合，对于较短的聚烯结果相似，表明复杂的无限降解 PVC 链的 ν∼计算简化为有限聚烯序列的计算。值得注意的是，与其他聚烯长度确定工具不同，基于内在物理性质的提出的解析聚烯长度确定方法可能成为更通用的工具，因为它具有确定或校正聚烯链中碳键弹性常数的附加潜力。
