2.5. Derivative Spectroscopy

Derivative spectroscopy is based on the use of the derivative spectra of a zero-order spectrum. The derivative spectrum and can be expressed as:

where: n—derivative order, ⁿD_λ represents the value of the n-order derivative of an analyte at the analytical wavelength (λ), A—absorbance.

The most important properties of derivative spectrophotometry, similar to those in classic spectrophotometry, are the dependence of the derivative value on concentration and its additivity. By differentiating the expression for the Lambert–Beer law over the wavelength, the following equation is obtained [21,22]:

where ε—molar absorption coefficient (cm/mol/L), c—concentration of an analyte (mol/L), l—thickness of solution layer (cm). The derivative spectrum of the n-component mixture is a sum of derivative spectra of individual components:

A useful feature of derivative spectroscopy is the dependence of derivatisation results on the geometrical characteristic of the starting, zero-order spectrum. The shape and the intensity of the resulting derivative spectrum depend on the half-height width of the peaks in the zero-order spectrum. Due to this property, broad zero-order spectra are quenched with the generation of higher orders of derivatives, while narrow peaks undergo amplification. If the zero-order spectrum possesses two bands, A and B, which differ from their half-heights width (LB > LA), after a generation of n-order derivative a ratio of derivatives intensity can be expressed as:

Derivative spectrophotometry provides an increase in sensitivity and selectivity of the methods in comparison with the classical derivative spectrophotometry based on the same colour system. An increase in selectivity in the derivative spectrophotometry results from the fact that differentiation permits to obtain a larger amount of information contained in the basic absorption spectrum. Due to this, it is possible to take advantage of the differences in the position of the peaks (different A.max) and in the peak half-width (different L values) [21,22]. For obtaining the first derivative and second derivative spectra the Savitzky–Golay algorithm [23,24] was used with 20 points smoothing and a 3rd order polynomial using Origin 8 software (Origin, OriginLab Corperation, Northampton, MA, USA).