βν-Correlation Analysis: A Modified Two-Dimensional Infrared Correlation Method for Determining Relative Rates of Intensity Change

A modified two-dimensional infrared (2D IR) correlation method called βν correlation analysis is introduced for quantitatively determining the relative rates of intensity change and the degree of coherence between intensity variations in a discrete set of dynamic spectra. In a βν correlation analysis, a mathematical cross correlation is performed between a set of n spectra undergoing some dynamic intensity variation, i.e. f (ν, n ), against a simple mathematical function. In the present case this is a sine function. Correlation intensities are a function of the phase angle (β) of the sinusoidal function and the spectral frequency (ν). The maximum positive correlation intensity will be observed at one point in the asynchronous (β, ν) correlation plot for the range 360° > β ≥ 0°. This point is used to define a new parameter, the effective phase angle, β e, of f (ν, n ), where β e is simply equal to β + 90°. In graphical terms, β e is the point of maximum positive correlation intensity in the asynchronous β vs. ν plot. The β e value quantitatively reveals the relative rates of change and the degree of coherence between the signal variations in a set of dynamic spectra. Some other desirable properties of βν correlation analysis include: (1) βν correlation plots are relatively easy to calculate in that they require no Fourier transformations; (2) the effective phase angle, β e, is a direct result of the correlation analysis, therefore no additional calculations are required; (3) in appropriate situations β e values from different experiments may be compared; and (4) noise is observed at a lower level in a βν correlation plot than the standard 2D IR maps. In this article, simple β e -relative rate models are introduced, and model calculations are used to help determine the level of uncertainty that can be expected in the β e values for a set of simulated dynamic spectra. Finally, an application of βν correlation analysis to the solid−solid-phase transition (“rotator“ transition) of n -nonadecane ( n -C 19 H 40 ) is presented.