LAPLACE, CNRS UMR 5213, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex, France.
RAPSODEE, CNRS UMR 5203, Université de Toulouse, IMT Mines Albi, Campus Jarlard, 81013 Albi CT Cedex 09, France.
J Phys Chem A. 2023 Mar 2;127(8):1988-1997. doi: 10.1021/acs.jpca.2c06893. Epub 2023 Feb 20.
The distributed activation energy model (DAEM) is widely used in chemical kinetics to statistically describe the occurrence of numerous independent parallel reactions. In this article, we suggest a rethink in the context of a Monte Carlo integral formulation to compute the conversion rate at any time without approximation. After the basics of the DAEM are introduced, the considered equations (under isothermal and dynamic conditions) are respectively expressed into expected values, which in turn are transcribed into Monte Carlo algorithms. To describe the temperature dependence of reactions under dynamic conditions, a new concept of null reaction, inspired from null-event Monte Carlo algorithms, has been introduced. However, only the first-order case is addressed for the dynamic mode due to strong nonlinearities. This strategy is then applied to both analytical and experimental density distribution functions of the activation energy. We show that the Monte Carlo integral formulation is efficient in solving the DAEM without approximation and that it is well-adapted due to the possibility of using any experimental distribution function and any temperature profile. Furthermore, this work is motivated by the need for coupling chemical kinetics and heat transfer in a single Monte Carlo algorithm.
分布活化能模型（DAEM）在化学动力学中被广泛用于统计描述大量独立平行反应的发生。在本文中，我们建议在蒙特卡罗积分公式的背景下重新思考，以便在没有近似的情况下计算任何时间的转化率。在介绍了 DAEM 的基础知识之后，我们将考虑的方程（在等温条件和动态条件下）分别表示为期望值，而这些期望值又被转录为蒙特卡罗算法。为了描述动态条件下反应的温度依赖性，我们从空事件蒙特卡罗算法中引入了一个新的空反应概念。然而，由于强烈的非线性，仅针对动态模式处理了一阶情况。然后，该策略应用于活化能的分析和实验密度分布函数。我们表明，蒙特卡罗积分公式在没有近似的情况下有效地解决了 DAEM，并且由于可以使用任何实验分布函数和任何温度分布，因此非常适合。此外，这项工作的动机是需要在单个蒙特卡罗算法中耦合化学动力学和传热。
