Modeling of luminescence-based oxygen sensors with non-uniform distribution of excitation and quenching characteristics inside active medium

A generic mathematical model was developed, which describes the integral luminescent signal (intensity and phase shift) of the quenched-luminescence oxygen sensor in the case of non-uniform distribution of the main parameters inside active medium, namely the quenching constant, oxygen and dye concentration and intensity of excitation. This approach, which describes the behaviour of various intensity-based and phase-fluorimetric oxygen sensor systems, was validated by applying it to a set of experimental calibration data obtained with heterogenous microporous sensor membranes on the basis of platinum(II)-octaethylporphine-ketone and polystyrene, and the phase-fluorimetric detector. The cases of one-, two- and three-parametric distribution of the quenching constant were analysed in detail, including discrete single- and double-exponential models and continuous distributions. The latter were represented by: Rayleigh and Maxwell distributions for one-parametric models; Gaussian, Laplace, Cauchy, Extreme Value, Logistic distributions for symmetrical two-parametric models; lognormal, Weibull, gamma and beta distributions for asymmetrical two-parametric models; mixed single-exponential model with one- and two-parametric distribution of the quenching constant-for three-parametric models. Particular models were determined, that provide satisfactory approximation with the same or smaller number of parameters than the classical single and double-exponential models. The best accuracy was achieved with: Maxwell distribution for one-parametric models; lognormal and truncated Gausian (defined only for the quenching constant values larger than distribution mode) for two-parametric models; and discrete double-exponential and mixed discrete with Maxwell distribution for three-parametric models.