Department of Chemistry, Hankuk University of Foreign Studies, Yongin 17035, Korea.
Int J Mol Sci. 2020 Feb 3;21(3):997. doi: 10.3390/ijms21030997.
We investigate how the size, the number, and the spatial arrangement of identical nonoverlapping reactive patches on a sphere influence the overall reaction kinetics of bimolecular diffusion-limited (or diffusion-controlled) reactions that occur between the patches and the reactants diffusing around the sphere. First, in the arrangement of two patches, it is known that the overall rate constant increases as the two patches become more separated from each other but decreases when they become closer to each other. In this work, we further study the dependence of the patch arrangement on the kinetics with three and four patches using the finite element method (FEM). In addition to the patch arrangement, the kinetics is also dependent on the number and size of the patches. Therefore, we study such dependences by calculating the overall rate constants using the FEM for various cases, especially for large-sized patches, and this study is complementary to the kinetic studies that were performed by Brownian dynamics (BD) simulation methods for small-sized patches. The numerical FEM and BD simulation results are compared with the results from various kinetic theories to evaluate the accuracies of the theories. Remarkably, this comparison indicates that our theory, which was recently developed based on the curvature-dependent kinetic theory, shows good agreement with the FEM and BD numerical results. From this validation, we use our theory to further study the variation of the overall rate constant when the patches are arbitrarily arranged on a sphere. Our theory also confirms that to maximize the overall rate constant, we need to break large-sized patches into smaller-sized patches and arrange them to be maximally separated to reduce their competition.
我们研究了相同的非重叠反应斑块在球体上的大小、数量和空间排列如何影响斑块与周围扩散的反应物之间发生的双分子扩散限制（或扩散控制）反应的整体反应动力学。首先，在两个斑块的排列中，已知当两个斑块彼此之间的距离越来越远时，整体速率常数会增加，但当它们彼此之间的距离越来越近时，整体速率常数会减小。在这项工作中，我们使用有限元方法（FEM）进一步研究了三个和四个斑块排列对动力学的依赖性。除了斑块排列外，动力学还取决于斑块的数量和大小。因此，我们通过使用 FEM 为各种情况计算整体速率常数来研究这种依赖性，特别是对于大型斑块，这项研究是对针对小型斑块的布朗动力学（BD）模拟方法进行的动力学研究的补充。数值 FEM 和 BD 模拟结果与各种动力学理论的结果进行了比较，以评估理论的准确性。值得注意的是，这种比较表明，我们最近基于曲率相关动力学理论开发的理论与 FEM 和 BD 数值结果吻合得很好。通过这种验证，我们使用我们的理论进一步研究了斑块在球体上任意排列时整体速率常数的变化。我们的理论还证实，为了最大化整体速率常数，我们需要将大型斑块分解成更小的斑块，并将它们排列得尽可能远离，以减少它们之间的竞争。
