Phase-sensitive detection in potential-modulated in situ absorption and probe beam deflection techniques: Theoretical considerations

A mathematical framework is presented for the quantitative analysis of in situ potential modulation spectroelectrochemical techniques based on phase-sensitive detection for the study of solution-phase redox systems under strict diffusion control. In the case of arrangements in which the probing beam is parallel to the electrode surface, the phase of the optical signal with respect to the applied potential, assuming negligible double-layer charging currents, was found to be proportional to y(ω/2D)^1/2, where y is the distance normal to the electrode, ω is the frequency of the perturbating signal, and D is the diffusion coefficient of the species responsible for absorption or refraction. Good agreement was found between theoretical predictions and the few available experimental results for both absorption and probe beam deflection-type experiments. In particular, in the case of solutions containing the chromophore trianisylamine and nonabsorbing p-benzoquinone, the phase angle difference between absorption and diffraction calculated from theory and measured experimentally yielded a common value of ∼30°.