It is widely agreed that the classical Langmuir rate equation cannot be applied for describing the kinetics of adsorption processes whose rate is controlled by diffusive transport phenomena. To overcome this limit, we propose a modification of the Langmuir rate equation, referred to as Diffusion-Controlled Langmuir Kinetics (DCLK), assuming that the macroscopic forward rate of adsorption is inversely related to the square root of time. We tested the DCLK model on experimental adsorption kinetic data. The results indicate that the DCLK model describes the kinetic data better than the traditional pseudo-second order model. Consistently with the intraparticle adsorption/diffusion theory, the adsorption amount predicted by the DCLK model proportionally increases with the square root of time at the beginning of the process. The effect of temperature on the adsorption rate and the relative role played by kinetics and thermodynamics are discussed.

人们普遍认为经典的Langmuir速率方程不能用于描述吸附速率由扩散传输现象控制的动力学过程。为了克服这一限制，我们假设对吸附的宏观正向速率与时间的平方根成反比，我们建议对Langmuir速率方程进行修改，称为扩散控制的Langmuir动力学（DCLK）。我们根据实验吸附动力学数据测试了DCLK模型。结果表明，DCLK模型比传统的伪二级模型更好地描述了动力学数据。与颗粒内吸附/扩散理论一致，DCLK预测的吸附量在过程开始时，模型随时间的平方根成比例增加。讨论了温度对吸附速率的影响以及动力学和热力学的相对作用。