Response characteristics of optical sensors for oxygen: models based on a distribution in tau(o) or kappa(q)

The features of two popular models used to describe the observed response characteristics of typical oxygen optical sensors based on luminescence quenching are examined critically. The models are the 'two-site' and 'Gaussian distribution in natural lifetime, tau(o),' models. These models are used to characterise the response features of typical optical oxygen sensors; features which include: downward curving Stern-Volmer plots and increasingly non-first order luminescence decay kinetics with increasing partial pressures of oxygen, pO(2). Neither model appears able to unite these latter features, let alone the observed disparate array of response features exhibited by the myriad optical oxygen sensors reported in the literature, and still maintain any level of physical plausibility. A model based on a Gaussian distribution in quenching rate constant, k(q), is developed and, although flawed by a limited breadth in distribution, rho, does produce Stern-Volmer plots which would cover the range in curvature seen with real optical oxygen sensors. A new 'log-Gaussian distribution in tau(o) or k(q)' model is introduced which has the advantage over a Gaussian distribution model of placing no limitation on the value of rho. Work on a 'log-Gaussian distribution in tau(o)' model reveals that the Stern-Volmer quenching plots would show little degree in curvature, even at large rho values and the luminescence decays would become increasingly first order with increasing pO(2). In fact, with real optical oxygen sensors, the opposite is observed and thus the model appears of little value. In contrast, a 'log-Gaussian distribution in k(o)' model does produce the trends observed with real optical oxygen sensors; although it is technically restricted in use to those in which the kinetics of luminescence decay are good first order in the absence of oxygen. The latter model gives a good fit to the major response features of sensors which show the latter feature, most notably the [Ru(dpp)(3)(2+)(Ph4B-)(2)] in cellulose optical oxygen sensors. The scope of a log-Gaussian model for further expansion and, therefore, application to optical oxygen sensors, by combining both a log-Gaussian distribution in k(o) with one in tau(o) is briefly discussed.