Au-coated Pd (Au/Pd) nanocubes (˜250 nm in width) connected via a network of single-walled carbon nanotubes (SWCNTs) have been employed as an electrochemical biosensor. As previously reported, these in situ Au/Pd nanocube SWCNT networks are capable of ultrasensitive amperometric sensing of glucose, with a sensitivity, detection limit, and linear sensing range greater than similar CNT-based glucose biosensors. The 3D mass diffusion of glucose molecules to the Au/Pd nanocube surfaces, forced convection environment of the testing vial, and Brownian motion of the Au/Pd nanocubes are all likely factors contributing to the strong electrochemical performance of the Au/Pd-SWCNT biosensor. In an effort to elucidate the effects of these contributing factors, this work demonstrates an analytical biosensor capture kinetics model that analyzes the analyte-biosensor mass transfer by molecular diffusion and convection due to both the fluid motion within the test vial and the Brownian motion of the Au/Pd nanocubes themselves.

The biosensor capture kinetics model incorporates a quasi steady-state integrated incident flux equation to model mass diffusion of biomolecules to the surface of a 1D planar, 2D nanowire, and 3D nanosphere surface in Cartesian, cylindrical, and spherical coordinates respectively. A Burgers vortex model is introduced to analyze the biosensor diffusion boundary layer within a test vial that experiences fluid downwelling and upwelling within the vial center and boundaries due to the rotation of a magnetic stir bar. Finally the convection-diffusion equation simplified by Stokes flow is utilized to model the diffusion boundary layer of the Au/Pd nanocubes experiencing Brownian motion.

Several key conclusions can be interfered from this model. First, a biosensor experiencing 3D mass diffusion will exhibit a greater analyte concentration flux of at least one order of magnitude greater than a biosensor experiencing 2D diffusion and 1D mass diffusion in quiescent and convective fluid environments. Additionally, mass transfer by convection increases the concentration flux to the biosensor by inhibiting the continued advancement of the analyte depletion layer around the biosensor. Furthermore, the Brownian motion model of the Au/Pd nanocubes is shown to improve the mass transfer to the biosensor surface, portraying a substantial increase in amperometric current signal output as compared to a similar electrochemical-based biosensor with stationary Au/Pd nanocubes. In summary, the results of the biosensor capture kinetics model corroborate the high sensitivities and low detection limits previously observed experimentally by Au/Pd nanocube-SWCNT biosensors.