Stochastic Adsorption of Diluted Solute Molecules at Interfaces
2020
Here an analytical solution
of Fick’s 2nd 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.
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