Buffle Jacques, Startchev Konstantin, Galceran Josep
Analytical and Biophysical Environmental Chemistry, Dept of Inorganic, Analytical and Applied Chemistry, Sciences II, 30 quai E. Ansermet, CH-1211, Geneva 4.
Phys Chem Chem Phys. 2007 Jun 14;9(22):2844-55. doi: 10.1039/b700913e. Epub 2007 Apr 17.
In complicated environmental or biological systems, the fluxes of chemical species at a consuming interface, like an organism or an analytical sensor, involve many coupled chemical and diffusion processes. Computation of such fluxes thus becomes difficult. The present paper describes an approximate approach, based on the so-called reaction layer concept, which enables one to obtain a simple analytical solution for the steady-state flux of a metal ion at a consuming interface, in the presence of many ligands, which are in excess with respect to the test metal ion. This model can be used for an unlimited number of ligands and complexes, without limit for the values of the association/dissociation rate constants or diffusion coefficients. This approximate solution is compared with a rigorous approach for the computation of the fluxes based on an extension of a previously published method (J. Galceran, J. Puy, J. Salvador, J. Cecília, F. Mas and J. L. Garcés, Phys. Chem. Chem. Phys., 2003, 5, 5091-5100). The comparison is performed for a very wide range of the key parameters: rate constants and diffusion coefficients, equilibrium constants and ligand concentrations. Their combined influence is studied in the whole domain of fully labile to non-labile complexes, via two combination parameters: the lability index, L, and the reaction layer thickness, mu. The results show that the approximate solution provides accurate results in most cases. However, for particular combinations of metal complexes with specific values of L or mu, significant differences between the approximate and rigorous solutions may occur. They are evaluated and discussed. These results are important for three reasons: (i) they enable the use of the approximate solution in a fully reliable manner, (ii) when present, the differences between approximate and rigorous solution are largely due to the coupling of chemical reactions, whose importance can thus be estimated, (iii) due to its simple mathematical expression, the individual contribution of each metal species to the overall flux can be computed.
在复杂的环境或生物系统中，在诸如生物体或分析传感器等消耗界面处化学物质的通量涉及许多耦合的化学和扩散过程。因此，计算此类通量变得困难。本文描述了一种基于所谓反应层概念的近似方法，该方法能够在存在多种相对于测试金属离子过量的配体的情况下，获得消耗界面处金属离子稳态通量的简单解析解。该模型可用于无限数量的配体和配合物，对缔合/解离速率常数或扩散系数的值没有限制。将此近似解与基于先前发表方法的扩展（J. Galceran、J. Puy、J. Salvador、J. Cecília、F. Mas和J. L. Garcés，《物理化学化学物理》，2003年，5卷，5091 - 5100页）的通量计算的严格方法进行了比较。在非常广泛的关键参数范围内进行了比较：速率常数和扩散系数、平衡常数和配体浓度。通过两个组合参数：活性指数L和反应层厚度μ，在从完全不稳定到非不稳定配合物的整个范围内研究了它们的综合影响。结果表明，近似解在大多数情况下提供了准确的结果。然而，对于具有特定L或μ值的金属配合物的特定组合，近似解和严格解之间可能会出现显著差异。对这些差异进行了评估和讨论。这些结果之所以重要有三个原因：（i）它们能够以完全可靠的方式使用近似解；（ii）当存在差异时，近似解和严格解之间的差异很大程度上是由于化学反应的耦合，因此可以估计其重要性；（iii）由于其简单的数学表达式，可以计算每种金属物种对总通量的单独贡献。
