Modelled diffusion-controlled response and recovery behaviour of a naked optical film sensor with a hyperbolic-type response to analyte concentration

Abstract

The diffusion-controlled response and recovery behaviour of naked optical film sensor (i.e., with no protective memberane) with a hyperbolic-type response [i.e., S₀/S=(1 +Kc), where S is the measured value of the absorbance or luminescence intensity of one form of the sensor dye in the presence of the analyte, S₀ is the observed value of S in the absence of analyte and K is a constant] to changes in analyte concentration, c, in a system under test is approximated using a simple model, and described more accurately using a numerical model; in both model it is assumed that the system under test represents an infinite reservoir. Each model predicts the variations in the response and recovery times of such an optical sensor, as a function of the final external analyte concentration, the film thickness (l) and the analyte diffusion coefficient (D). From an observed signal versus time profile for a naked optical film sensor it is shown how values for K and D/l² can be extracted using the numerical model. Both models provide a qualitative description of the often cited asymmetric nature of the response and recovery for hyperbolic-type response naked optical film sensors. It is envisaged that the models will help in the interpretation of the response and recovery behaviour exhibited by many naked optical film sensors and might be especially apposite when the analyte is a gas.