CEA, Nuclear Energy Division, RadioChemistry and Processes Department, Actinides Chemistry and Conversion Laboratory, F-30207 Bagnols-sur-Cèze, France.
J Phys Chem B. 2010 Sep 2;114(34):11027-38. doi: 10.1021/jp102120m.
This study is devoted to the characterization of ion exchange inside a microsphere of carboxylic resin. It aims at describing the kinetics of this exchange reaction which is known to be controlled by interdiffusion in the particle. The fractional attainment of equilibrium function of time depends on the concentration of the cations in the resin which can be modelized by the Nernst-Planck equation. A powerful approach for the numerical resolution of this equation is introduced in this paper. This modeling is based on the work of Helfferich but involves an implicit numerical scheme which reduces the computational cost. Knowing the diffusion coefficients of the cations in the resin and the radius of the spherical exchanger, the kinetics can be hence completely determined. When those diffusion parameters are missing, they can be deduced by fitting experimental data of fractional attainment of equilibrium. An efficient optimization tool coupled with the implicit resolution has been developed for this purpose. A monovalent/trivalent cation exchange had been experimentally characterized for a carboxylic resin. Diffusion coefficients and concentration profiles in the resin were then deduced through this new model.
本研究致力于羧酸树脂微球中离子交换的特性描述。目的在于描述这种交换反应的动力学过程，该反应通常由颗粒内的扩散控制。达到平衡时的分数随树脂中阳离子浓度的变化而变化，这可以用能斯特-普朗克方程进行模拟。本文引入了一种强大的数值求解方法。这种模型基于 Helfferich 的工作，但涉及到一个隐式数值方案，降低了计算成本。已知树脂中阳离子的扩散系数和球形交换器的半径，就可以完全确定动力学过程。当这些扩散参数缺失时，可以通过拟合平衡时的分数实验数据来推断它们。为此目的，开发了一种有效的优化工具与隐式求解相结合。通过实验对羧酸树脂的一价/三价阳离子交换进行了表征。然后通过该新模型推导出树脂中的扩散系数和浓度分布。
