Kν Correlation Analysis. A Quantitative Two-Dimensional IR Correlation Method for Analysis of Rate Processes with Exponential Functions

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A modified two-dimensional infrared correlation technique called kν correlation analysis is introduced. In this method, a mathematical asynchronous cross-correlation is performed between a set of N infrared spectra undergoing a dynamic intensity variation against a set of exponential functions that encompass a user-defined range of rate constants. The observed correlation intensities are a function of the rate constant of the exponential function and the spectral frequency. The kν correlation plots reveal the rate relationships between different molecular groups in terms of a quantitative and tangible parameter, k, which is the rate constant of the exponential function used in the correlation. A new parameter, the effective rate constant, keff, is defined as the point of maximum correlation intensity at particular frequencies in the plot of k vs ν. The calculated values of keff represent the relative rates at which the intensities of the spectral bands change during the course of the dynamic experiment. As a result, these keff values are comparable and can be used to assign quantitative rate relationships. By using simulated IR spectra, it was shown that the keff parameter is sensitive to the relative order in which the intensity change occurs, while the size of the correlation peaks gives an indication of the magnitude of the intensity change. Spectral bands whose rate of intensity change varies through a dynamic data set are distinguished by the presence of both positive and negative peaks in the kν correlation plots. We applied the kν correlation analysis method to the time-dependent IR spectra of the photoinitiated polymerization reaction of ethyl 2-cyanoacrylate. Analysis of the keff effective rate constants showed that vibrational modes corresponding to the monomeric and polymeric cyanoacrylate molecules react differently depending on whether an inhibitor is present.