#### Presentation Title

Using the Fast Fourier Transform to Determine the Components of a Mixture from an Infrared Spectrum

#### Faculty Mentor

Laura S. Chowdhury, Paula K. Hudson

#### Start Date

17-11-2018 8:45 AM

#### End Date

17-11-2018 9:00 AM

#### Location

C323

#### Session

Oral 1

#### Type of Presentation

Oral Talk

#### Subject Area

physical_mathematical_sciences

#### Abstract

Infrared (IR) spectra provide qualitative and quantitative information about compounds and are unique to every compound. The IR spectrum of a mixture, a combination of compounds, follows the additivity of Beer’s law, a linear combination of the spectra of individual compounds. Given the IR spectrum of an unknown mixture, we would like to determine its composition in terms of the individual components and their relative concentrations. We have measured IR spectra for compounds at select concentrations, but not all possible concentrations. Thus, we model the spectrum of an individual compound at any concentration by employing a linear combination of two experimental spectra at different concentrations. To determine the unknown components and respective concentrations within a mixture, we fit a linear combination of the modeled spectra to the measured spectrum of the mixture. For the model fitting procedure, we apply the Fast Fourier Transform (FFT) to all spectra and minimize the least squares error for the imaginary part of the FFT. The results yield the individual concentrations of the compounds that compose the mixture. For this study, we measured IR spectra of short chain C2 – C5 α-, ω- dicarboxylic acids, and mixtures thereof, using a Fourier transform infrared (FTIR) spectrometer. These compounds, prevalent components of atmospheric aerosol, can directly interact with incoming solar radiation and outgoing terrestrial radiation causing either a warming or cooling effect at the Earth's surface. So far, we have been able to model the spectra of four dicarboxylic acids at any given concentration. In addition, our initial results indicate successful identification of individual components and respective concentrations of the dicarboxylic acid mixture with small relative error.

Using the Fast Fourier Transform to Determine the Components of a Mixture from an Infrared Spectrum

C323

Infrared (IR) spectra provide qualitative and quantitative information about compounds and are unique to every compound. The IR spectrum of a mixture, a combination of compounds, follows the additivity of Beer’s law, a linear combination of the spectra of individual compounds. Given the IR spectrum of an unknown mixture, we would like to determine its composition in terms of the individual components and their relative concentrations. We have measured IR spectra for compounds at select concentrations, but not all possible concentrations. Thus, we model the spectrum of an individual compound at any concentration by employing a linear combination of two experimental spectra at different concentrations. To determine the unknown components and respective concentrations within a mixture, we fit a linear combination of the modeled spectra to the measured spectrum of the mixture. For the model fitting procedure, we apply the Fast Fourier Transform (FFT) to all spectra and minimize the least squares error for the imaginary part of the FFT. The results yield the individual concentrations of the compounds that compose the mixture. For this study, we measured IR spectra of short chain C2 – C5 α-, ω- dicarboxylic acids, and mixtures thereof, using a Fourier transform infrared (FTIR) spectrometer. These compounds, prevalent components of atmospheric aerosol, can directly interact with incoming solar radiation and outgoing terrestrial radiation causing either a warming or cooling effect at the Earth's surface. So far, we have been able to model the spectra of four dicarboxylic acids at any given concentration. In addition, our initial results indicate successful identification of individual components and respective concentrations of the dicarboxylic acid mixture with small relative error.