Diffusion Models of Mass Transport for the Characterisation of Amperometric Gas Sensors

A diffusion model for the analysis of chronoamperometric data in response to a concentration step is developed for amperometric gas sensors. This analysis avoids the difficulties with standard potentiodynamic measurements at the large specific area, high capacitance electrodes employed in these sensors. Despite the fact that typical devices comprise multiple layers with varying thicknesses and diffusivities, we show that typical chronoamperometric traces can be fitted to a simple diffusion model with a single parameter tau=L2D ${\tau ={{{L}<^>{2}}\over{D}}}$ where L is an overall effective thickness of the diffusion barrier and D is an effective diffusion coefficient. Through a comparison of the transient and steady-state current, independent estimates of L and D in the devices can be made. The model is also extended to cover cases with interfacial kinetic barriers; such kinetic limitations lead to a change in the effective values L and D, but the simple diffusion model remains a good fit to the data. This analysis shows that transient sensor responses can be characterised by a single parameter tau and conversely that deviations from this regression model cannot be assigned to (i) complex layer architectures or (ii) interlayer kinetic barriers. Instead, we show that non-uniform accessibility effects arising from a distribution of diffusion rates across the device lead to deviations from the simple regression model, but that they may be captured approximately by a more complex model in which tau has a probability distribution. Diffusion models for the response of commercial amperometric gas sensors to a concentration step of the analyte are analysed. Effective values of barrier thickness and diffusion coefficient can be extracted for devices with complex layered architectures and possible interfacial phase transfer barriers. Small deviations of the experimental data from the model reflect a distribution of diffusivities in the devices. image