Effects of fill fraction on the capture efficiency of nanoscale molecular transducers

We study the effects of nanotransducer fill fraction on the molecular capture efficiency contribution to overall sensor response. Contrary to expectation, we show that the relative capture efficiency can exceed the fill fraction in the transient regime. However, at thermodynamic equilibrium, the relative efficiency equals the fill fraction in the probe-limited case. When the number of target molecules in solution is the limiting factor in capture, then gains in capture efficiency can be obtained even at thermodynamic equilibrium. The important implication of these results is that significant intrinsic nanotransducer enhancement is necessary in order to provide net gain in sensor response, but that nanotransducer enhancement does not need to exceed the inverse fill fraction. In addition, net gain in overall sensor response is more readily achievable at low target concentrations.