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

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Abstract

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.

Original languageEnglish
Pages (from-to)1671-1676
Number of pages6
JournalJournal of the Electrochemical Society
Volume140
Issue number6
DOIs
Publication statusPublished - 1993 Jan 1
Externally publishedYes

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Forced convection
Rotating disks
Modulation
Spectroscopy
Electrodes
Absorption spectroscopy
Eigenvalues and eigenfunctions
Optics
Differential equations
Hydrodynamics
Boundary conditions
Electric potential
Chemical analysis

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Renewable Energy, Sustainability and the Environment
  • Surfaces, Coatings and Films
  • Electrochemistry
  • Materials Chemistry

Cite this

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title = "Theoretical Aspects of Potential Modulation Normal Incidence Reflection Absorption UV-Visible Spectroscopy under Forced Convection",
abstract = "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.",
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AB - 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.

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