Determining proton diffusion in polymer films by lifetimes of luminescent complexes measured in the frequency domain

Polymer-supported luminescent metal complexes represent an important class of oxygen, pH, and ion sensors. The diffusion properties of the analyte into the sensing film are important for rational sensor and support design and development. We describe a technique using lifetime measurements in the frequency domain for determining the diffusion coefficient of hydrochloric acid through various polymeric pH sensor films. Two types of polymers are doped with [Ru(4,7-diphenyl-1,10-phenanthroline)2(4,4'-dicarboxy-2,2'-bipyridine)]Cl2. We monitor the phase shift of luminescence (from which we calculate the apparent lifetime, tau(app)) versus time after applying a step increase in the aqueous HCl concentration at the surfaces of the film. We model the decrease in tau(app) as a function of time using the diffusion coefficient of HCl in the polymer as the only adjustable parameter. The model accurately predicts the lifetime versus time curves, and the resulting diffusion coefficients are highly dependent on the polymer. Relative to bulk water, diffusion of protons within very hydrophilic hydrated D4 polymer (a polyethylene oxide cross-linked siloxane ring polymer) films is hindered approximately 4-fold, while within a more hydrophobic sol gel it is hindered by over 1 order of magnitude. The methodology is adaptable for measuring diffusion coefficients of a variety of analytes in different sensor films as long as the bound and unbound forms luminescence and the excited states have different lifetimes.