Determination of the kinetic parameters of complex condensed phase reactions using a nonlinear model

This research introduces a novel nonlinear model that can be used in the modified Friedman method to determine activation energy <i>via</i> linear regression with a trial-and-error approach. Its application in a simulated reaction enhanced precision in activation energy determination and accurately captured the trend in activation energy variation with temperature compared to quadratic regression. The nonlinear model can also predict nonlinearity in compensation effect relationships, aiding in the assessment of pre-exponential factor, rate constant, and conversion function in complex reactions, ensuring more precise results compared to linear model. By incorporating random noise into the simulated reaction’s isoconversional kinetic data, which follows a normal distribution, we observed that both nonlinear and quadratic regressions produce comparable activation energy values. However, the nonlinear compensation effect approach yields more precise results for the pre-exponential factor, rate constant, and conversion function compared to the linear model in the presence of random errors. The novel approach based on the nonlinear model was applied, in conjunction with the linear and quadratic Friedman methods featuring linear compensation effect, to compute the kinetic parameters of a polymer coating on a commercial optical fiber as well as a polyethylene. Gnu Octave/MATLAB codes were also made available for estimating the kinetic parameters of complex reactions exhibiting a single peak in reaction rate curves using the linear, quadratic, and nonlinear Friedman methods, along with the application of linear and nonlinear compensation effects. These codes can be customized by users to estimate the kinetic parameters of their own kinetic data.

本研究提出了一种新型非线性模型，可结合改进的弗里德曼（Friedman）法，通过试错法结合线性回归求解活化能。相较于二次回归，该模型应用于模拟反应时，可提升活化能求解精度，并准确捕捉活化能随温度变化的趋势。该非线性模型还可预测补偿效应关系中的非线性特征，有助于评估复杂反应中的指前因子、速率常数及转化函数，相比线性模型可获得更精准的结果。我们在模拟反应的等转化率动力学数据中引入服从正态分布的随机噪声，结果显示，非线性回归与二次回归所得活化能数值相近。但在存在随机误差的场景下，非线性补偿效应方法在指前因子、速率常数及转化函数的求解上，相比线性模型具备更高的精度。本研究将基于该非线性模型的新型方法，与具备线性补偿效应的线性、二次弗里德曼法相结合，用于计算商用光纤表面聚合物涂层及聚乙烯的动力学参数。同时，本研究还提供了Gnu Octave/ MATLAB代码，可通过线性、二次及非线性弗里德曼法，结合线性与非线性补偿效应，估算反应速率曲线呈单峰特征的复杂反应的动力学参数；用户可对这些代码进行自定义修改，以适配自身动力学数据的参数估算需求。