Theoretical Aspects of Potential Modulation Normal Incidence Reflection Absorption UV-Visible Spectroscopy under Forced Convection

A theoretical treatment is presented for the quantitative analysis of potential-modulated normal-incidence reflection absorption UV-visible spectra of solution-phase, optically absorbing species produced at the surface of a rotating disk electrode (RDE). This novel technique is based on the application of a sinusoidal voltage of small amplitude to the RDE to generate in turn, a perturbation in the concentration profile of the absorbing species, C. Such changes introduce a modulation in the absorptivity of the solution along the axis of rotation of the RDE, and these can be monitored by (near)-normal-incidence UV-visible reflection absorption spectroscopy. A mathematical analysis of the optics and hydrodynamics for the system indicates that the ratio (I*/I _dc ), where I* is the amplitude of the ac and I _dc the magnitude of the dc components of the optical signal, is proportional to the extinction coefficient of C and to the absolute value of the integral of the time-independent function of the oscillatory concentration profile. Excellent agreement was obtained between the approximate soloutions (in terms of the eigenfunctions, eigenvalues, and coefficients of the appropriate Sturm-Liouville system) valid in a domain of frequencies low enough to achieve optimum sensitivity and those determined by rigorous numerical integration of the governing differential equation subject to the appropriate boundary conditions. This provides a means of extracting quantitative information from the experimental data based on a simple mathematical expression.