维亚佐夫金高级分析

维亚佐夫金分析（Vyazovkin Analysis）是一种无模型（等转化率）的动力学分析方法，用于计算任意温度程序实验中活化能 E(α) 对转化率α的依赖关系，其中也包括动态和等温条件。

维亚佐夫金 高级方法与 维亚佐夫金方法。

鉴于无模型方法的局限性，必须始终检查该无模型方法是否有效且适用。

维亚佐夫金分析属于积分型无模型方法，首先，必须求出主要动力学方程（1）从反应开始到当前转化度α的温度积分（式1）：

\frac{d\alpha}{dt} = A(\alpha) \bullet f(\alpha) \bullet exp\left( \frac{- E(\alpha)}{RT} \right)

温度程序 T(t)（式（2））的时域积分：

\int_{0}^{\alpha}\frac{d\alpha}{A(\alpha) \bullet f(\alpha)} = \int_{t_{0}}^{t}{\exp\left( \frac{- E(\alpha)}{RT(t)} \right)dt}

对于在相同转化度 α 下的不同实验，其中i和j的数值各不相同，可写出以下公式（式（3））：

\int_{t_{0}}^{t_{\alpha i}}{\exp\left( \frac{- E(\alpha)}{RT(t)} \right)dt} = \int_{t_{0}}^{t_{\alpha j}}{\exp\left( \frac{- E(\alpha)}{RT(t)} \right)dt}

最后，应使以下函数取最小值，以求得活化能 E(α) [1,2]（式（4））：

\psi(\alpha) = \sum_{i}^{}{\sum_{j \neq i}^{}\frac{\int_{t_{0}}^{t_{\alpha i}}{\exp\left( \frac{- E(\alpha)}{RT(t)} \right)dt}}{\int_{t_{0}}^{t_{\alpha j}}{\exp\left( \frac{- E(\alpha)}{RT(t)} \right)dt}}}

Where t_αi is the time at which the conversion α is reached for the i-th measurement.

It is always necessary to simulate the curves by Vyazovkin method and compare them with experiment. This comparison helps to check if Vyazovkin method is suitable for analysis of the current reaction.

Kinetics Neo

This method is not used in Kinetics Neo. For dynamic data with constant heating rate please use Vyazovkin Analysis method in Kinetics Neo.

For arbitrary temperature program please use Friedman Analysis method in Kinetics Neo.

References

Vyazovkin, S.; Dollimore, D. Linear and Nonlinear Procedures in Isoconversional Computations of the Activation Energy of Nonisothermal Reactions in Solids. J. Chem. Inf. Comput. Sci.36(1), 42–45 (1996). https://doi.org/10.1021/ci950062m