### 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 language | English |
---|---|

Pages (from-to) | 1671-1676 |

Number of pages | 6 |

Journal | Journal of the Electrochemical Society |

Volume | 140 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1993 Jan 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

**Theoretical Aspects of Potential Modulation Normal Incidence Reflection Absorption UV-Visible Spectroscopy under Forced Convection.** / Zhao, Ming; Scherson, Daniel Alberto.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Theoretical Aspects of Potential Modulation Normal Incidence Reflection Absorption UV-Visible Spectroscopy under Forced Convection

AU - Zhao, Ming

AU - Scherson, Daniel Alberto

PY - 1993/1/1

Y1 - 1993/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0027610886&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027610886&partnerID=8YFLogxK

U2 - 10.1149/1.2221621

DO - 10.1149/1.2221621

M3 - Article

VL - 140

SP - 1671

EP - 1676

JO - Journal of the Electrochemical Society

JF - Journal of the Electrochemical Society

SN - 0013-4651

IS - 6

ER -