以解析方法推導複雜反應網路之速率表達式

Abstract

估計反應速率在動力學建模中很重要，而動力學建模是各種化學領域的基礎，例如開發新材料和優化反應條件以最大化產率或改進合成策略。傳統上，可以在不同條件下進行動力學實驗來推導速率定律式。然而，在實際情況下，這種方法往往耗時，且經驗速率定律式的普遍性經常受到限制，因為它通常將異構體和反應混為一談，因此不能準確地描述複雜的反應體系。為了解決這個問題，我們開發了一種分析方法來解決複雜反應網絡的反應速率。該方法通過推導能量速率表達式（energetic rate expression, ERE）將理論計算和實驗聯繫起來，該表達式通過假設中間體的穩態來提供任何反應網絡的動力學信息。如果過渡態理論適用，任何反應網絡的反應速率都可以通過其在自由能面的分佈來計算反應速率。若將ERE應用於靈敏度分析，可以預測速率控制（degree of rate control, DRC）的排序、以判定速率決定態，有助於理解反應機制並有助於反應器設計。在本研究中，給出了ERE的推導以及ERE分析複雜反應網路的應用實例，且研究結果顯示我們的模型與現有方法有很好的吻合。

Estimating reaction rate is important in kinetic modeling, and kinetic modeling is fundamental in various chemic al fields such as developing new materials and optimizing reaction conditions to maximize the yield or improve the synthesis strategy. In principle, kinetic experiments can be carried out under different conditions to derive the rate law. However, in practice, this approach is time-consuming and the generalizability of an empirical rate law is usually limited because it usually lumps important isomers and reactions, and hence cannot always accurately describe a complex reaction system. To address this issue, we developed an analytical approach to solve the reaction rate of a complex reaction network. This method connects theoretical computations and experiments by deriving an energetic rate expression (ERE), which provides kinetic information of any reaction network by assuming steady state for the intermediates. Using ERE, the reaction rate of any reaction network can be estimated by its free energy profile if the transition state theory is applicable. When ERE is applied to the sensitivity analysis, it is possible to predict the general degree of rate control (DRC) and the critical state of the reaction network, which helps to understand the mechanism and aids in reactor design. In this work, the derivation of ERE is given along with practical examples of application of ERE in complex reaction analysis and the results show that our model agrees well with existing methods.