Nanoparticles in sensing applications: on what timescale do analyte species adsorb on the particle surface?

The recent decade saw much interest in sensors based on nanoparticles. Such sensors typically employ sensing mechanisms that utilise the adsorption of analyte species on the nanoparticle surfaces, while adsorption induces changes in the physical properties of the nanoparticles. In this work, we introduce an analytical model for the rate of adsorption of analyte species on the nanoparticle surface. Expressions for the fractional surface coverage and the number of adsorbed molecules as a function of time are derived assuming spherical nanoparticles. Moreover, we provide values for common experimental conditions and show that for small nanoparticles (r < 10 nm) a surface coverages of 30% can be reached in less than 1 s at adsorbent concentrations as low as 50 nM.