Analysis of Kinetic Langmuir Model. Part I: Integrated Kinetic Langmuir Equation (IKL): A New Complete Analytical Solution of the Langmuir Rate Equation
Analysis of Kinetic Langmuir Model. Part I: Integrated Kinetic Langmuir Equation (IKL): A New Complete Analytical Solution of the Langmuir Rate Equation
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DOI：
10.1021/la1010049
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发表时间：
2010-10-05
期刊：
影响因子：
3.9
通讯作者：
Marczewski, Adam W.
中科院分区：
文献类型：
--
作者：
Marczewski, Adam W.
本文推导了一种新的综合动力学朗缪尔方程（IKL）。IKL方程是动力学朗缪尔模型的一种简单易分析的完整解析解。并与n阶、混合1阶、2阶和多指数动力学方程进行了比较。解释了平衡覆盖theta（eq）和相对平衡摄取is对动力学的影响。采用新引入的Langmuir批平衡因子f(eq)，即两个参数theta（eq）和u（eq）的乘积来确定总体动力学行为。通过对IKL方程的分析，我们可以充分理解Langmuir动力学，解释其与经验伪一阶（PM，即Lagergren）、伪二阶（PSO）和混合1、2阶动力学方程的关系，并在Langmuir模型的基础上显示了它们可能应用的条件。分析了初始吸附速率对系统性质的依赖关系，并与先前发表的近似方程进行了比较。
In the article, a new integrated kinetic Langmuir equation (IKL) is derived. The IKL equation is a simple and easy to analyze but complete analytical solution of the kinetic Langmuir model. The IKL is compared with the nth-order, mixed 1,2-order, and multiexponential kinetic equations. The impact of both equilibrium coverage theta(eq) and relative equilibrium uptake is, on kinetics is explained. A newly introduced Langmuir batch equilibrium factor f(eq), that is the product of both parameters theta(eq)u(eq) is used to determine the general kinetic behavior. The analysis of the IKL equation allows us to understand fully the Langmuir kinetics and explains its relation with respect to the empirical pseudo-first-order (PM, i.e., Lagergren), pseudo-second-order (PSO), and mixed 1,2-order kinetic equations, and it shows the conditions of their possible application based on the Langmuir model. The dependence of the initial adsorption rate on the system properties is analyzed and compared to the earlier published approximate equations.