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Many chemical and biological systems exhibit intermittent search phenomena when participating particles alternate between dynamic regimes with different dimensionality. Here we investigate theoretically a dynamic search process of finding a small target at two dimensional surface starting from the bulk solution, which is an example of such intermittent search process. Both continuum and discrete-state stochastic descriptions are developed. It is found that depending on the scanning length $\lambda$, which describes the area visited by the reacting molecule during one search cycle, the system can exhibit three different search regimes: (i) For small $\lambda$, the reactant finds the target mostly via three dimensional bulk diffusion, (ii) for large $\lambda$, the reactant molecule associates to the target mostly via the surface diffusion, and (iii) for intermediate $\lambda$, the reactant reaches the target via a combination of three-dimensional and two dimensional search cycles. Our analysis also shows that the mean search times have different scaling as the function of the size of the surface segment depending on the nature of the dynamic search regime. Search dynamics is also sensitive the to the position of the target for large scanning lengths. In addition, it is argued that the continuum description underestimates mean search times and not always correctly describes the most optimal conditions for the surface-assisted dynamic processes. The importance of our findings for real natural systems is discussed.
This article was published in the following journal.
Name: The journal of physical chemistry. B
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