There has recently been an extensive amount of work regarding the development of optical, electrical, and mechanical (bio)sensors employing planar arrays of surface-bound nanoparticles. The sensor output for these systems is dependent on the rate at which analyte is transported to, and interacts with, each nanoparticle in the array. There has so far been little discussion on the relationship between the design parameters of an array and the interplay of convection, diffusion, and reaction. Moreover, current methods providing such information require extensive computational simulation. Here we demonstrate that the rate of analyte transport to a nanoparticle array can be quantified analytically. We show that such rates are bound by both the rate to a single NP and that to a planar surface (having equivalent size as the array), with the specific rate determined by the fill fraction: the ratio between the total surface area used for biomolecular capture with respect to the entire sensing area. We characterize analyte transport to arrays with respect to changes in numerous parameters relevant to experiment, including variation of the nanoparticle shape and size, packing density, flow conditions, and analyte diffusivity. We also explore how analyte capture is dependent on the kinetic parameters related to an affinity-based biosensor, and furthermore, we classify the conditions under which the array might be diffusion- or reaction-limited. The results obtained herein are applicable toward the design and optimization of all (bio)sensors based on nanoparticle arrays.

Institute of Photonics and Electronics Academy of Sciences of the Czech Republic Chaberská 57 Prague 18251 Czech Republic

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