Here an analytical solution of Fick’s 2^nd law is used to predict the diffusion and the stochastic adsorption of single diluted solute molecules on flat and patterned surfaces. The equations are then compared to the results of several numerical Monte Carlo simulations using a random walk model. The 1D diffusion simulations clarify that the dependence of the solute-surface collision rate on the observation-time (measurement time resolution) is because of the multiple collisions of the same molecules over different time regions. It also surprisingly suggests that due to the self-mimetic fractal function of diffusion, the equation should be corrected by a factor of two. The absorption rate of solute on an adsorptive surface is found to follow a power-law decay function due to an evolving concentration gradient near the surface along with the depletion of the bulk solute molecules on the surface, for example, in a self-assembled monolayer adsorption kinetics. Thus, the analytical equations developed to calculate the collision at a fixed measuring frequency can be extended to map the whole curve over time. In the last section of this work, 3D diffusion simulations suggest that the analytical solution is valid to predict the adsorption rate of the bulk solute to a small group of adsorptive target molecules/area on a bouncing surface, which is a critical process in analyzing the kinetics of many bio-sensing platforms.

这是菲克^第二定律用于预测单个稀释的溶质分子在平坦和有图案的表面上的扩散和随机吸附。然后将这些方程与使用随机游走模型的几个数值蒙特卡洛模拟的结果进行比较。一维扩散模拟表明，溶质表面碰撞速率与观察时间（测量时间分辨率）的相关性是由于相同分子在不同时间区域上的多次碰撞所致。还令人惊讶地暗示，由于扩散的自模拟分形函数，该方程式应校正为两倍。发现吸附表面上的溶质吸收速率遵循幂律衰减函数，这是由于表面附近浓度梯度的变化以及表面上本体溶质分子的耗竭，例如在自组装单层中吸附动力学。因此，可以扩展用于在固定测量频率下计算碰撞的分析方程式，以绘制整个曲线随时间的变化。在这项工作的最后一部分中，3D扩散模拟表明，该分析溶液可有效预测本体溶质对弹跳表面上的一小部分吸附目标分子/区域的吸附速率，这是分析吸附过程中的关键过程。许多生物传感平台的动力学。可以扩展用于在固定测量频率下计算碰撞的分析方程式，以绘制整个曲线随时间的变化。在这项工作的最后一部分中，3D扩散模拟表明，该分析溶液可有效预测本体溶质对弹跳表面上的一小部分吸附目标分子/区域的吸附速率，这是分析吸附过程中的关键过程。许多生物传感平台的动力学。可以扩展用于在固定测量频率下计算碰撞的分析方程式，以绘制整个曲线随时间的变化。在这项工作的最后一部分中，3D扩散模拟表明，该分析溶液可有效预测本体溶质对弹跳表面上的一小部分吸附目标分子/区域的吸附速率，这是分析吸附过程中的关键过程。许多生物传感平台的动力学。