Diffusive adsorption/association is a fundamental step in almost all chemical reactions in diluted solutions, such as organic synthesis, polymerization, self-assembly, biomolecular interactions, electrode dynamics, catalysis, chromatography, air and water environmental dynamics, and social and market dynamics. However, predicting the rate of such a reaction is challenging using the equations established over 100 years ago. From dimensional analysis, we can guess a series of equations including historical ones and new ones that have the correct final unit, the number of molecules associated per second, which is constructed from concentration, diffusion coefficient, and size of the molecules only. These equations are roughly divided into two groups, continuous models and discrete models. The continuous models integrate Fick’s concentration gradient in the solution near the target to calculate the association rate, and are the historical solutions reported. The discrete models integrate the probability density function of each probe that is discretely distributed in the solution. I have introduced a key concept of the nearest neighbor diffusion time to stabilize these time-dependent solutions. These models are applied to analyze a set of experimental results for comparison to achieve consistency and clarify assumptions among models.

中文翻译：

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扩散关联率方程的量纲分析


扩散吸附/缔合是稀溶液中几乎所有化学反应的基本步骤，例如有机合成、聚合、自组装、生物分子相互作用、电极动力学、催化、色谱、空气和水环境动力学以及社会和市场动态。然而，使用 100 多年前建立的方程来预测这种反应的速率具有挑战性。通过量纲分析，我们可以猜测一系列方程，包括历史方程和新方程，它们具有正确的最终单位，即每秒关联的分子数，仅由浓度、扩散系数和分子大小构成。这些方程大致分为两组：连续模型和离散模型。连续模型整合目标附近溶液中的菲克浓度梯度来计算关联率，并且是报告的历史溶液。离散模型集成了解中离散分布的每个探针的概率密度函数。我引入了最近邻扩散时间的关键概念来稳定这些与时间相关的解。这些模型用于分析一组实验结果进行比较，以实现模型之间的一致性并澄清假设。