beta nu-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 betav correlation analysis is introduced for quantitatively determining the rela tive rates of intensity change and the degree of coherence between intensit y variations in a discrete set of dynamic spectra. In a betav correlation a nalysis, a mathematical cross correlation is performed between a set of n s pectra undergoing some dynamic intensity variation, i.e. f (v, n), against a simple mathematical function. In the present case this is a sine function . Correlation intensities are a function of the phase angle (beta) of the s inusoidal function and the spectral frequency (v). The maximum positive cor relation intensity will be observed at one point in the asynchronous (beta ,v) correlation plot for the range 360 degrees > beta greater than or equal to 0 degrees. This point is used to define a new parameter, the effective phase angle, beta (e), of (v, n), where beta (e), is simply equal to beta 90 degrees. In graphical terms, beta (e) is the point of maximum positive correlation intensity in the asynchronous beta vs. v plot. The beta (e) val ue quantitatively reveals the relative rates of change and the degree of co herence between the signal variations in a set of dynamic spectra. Some oth er desirable properties of betav correlation analysis include: (1) betav co rrelation plots are relatively easy to calculate in that they require no Fo urier transformations; (2) the effective phase angle, beta (e) is a direct result of the correlation analysis, therefore no additional calculations ar e required; (3) in appropriate situations beta (e) values from different ex periments may be compared; and (4) noise is observed at a lower level in a betav correlation plot than the standard 2D IR maps. In this article, simpl e beta (e)-relative rate models are introduced, and model calculations are used to help determine the level of uncertainty that can be expected in the beta (e) values for a set of simulated dynamic spectra. Finally, an applic ation of betav correlation analysis to the solid-solid-phase transition ("r otator" transition) of n-nonadecane (eta -C19H40) is presented.