Statistical Approximation of Fourier Transform-IR Spectroscopy Data for Zinc White Pigment from Twentieth-Century Russian Paintings

Abstract

Introduction. Ageing of a paint layer is associated with various physical and chemical processes, in particular with polymerization and oxidation as the binders dry out, and also with chemical reactions when the binders react with the pigments, resulting in formation of new substances (compounds). Photoinduced changes in the binders and pigments, their chemical reactions during storage of the paintings (especially when the atmosphere is signifi cantly polluted), as well as mechanical damage to the paint and varnish layers are also possible. Study of processes associated with ageing of paintings is important for modern applied science. The corresponding results allow us to solve a number of practical problems such as restoration, determination of authenticity, and dating.Several experimental methods can be used to determine the composition of the paint layer in a painting. Optical spectroscopy is a useful tool in analysis of the molecular composition of samples (see, for example, [1,2]). The position and relative intensities of the spectral bands can be used to determine structural changes in the analyte molecules. Fourier transform-IR (FTIR) microspectroscopy is often used as a highly sensitive method, making it possible to work with micronsized samples [3]. Databases for IR spectra of paints and binders are available for interpretation of the experimental results [4,5]. Ageing causes changes in the molecular composition of the paint layers. Measurements of the spectroscopic parameters (line intensities and positions) probably can be used to determine the age of a painting. In fact, monotonic changes in the spectral lines of the oil after drying out have been demonstrated in [6]. However, polymerization and oxidation processes associated with ageing of the paint layer depend considerably on the environment (temperature, humidity, and composition of the atmosphere) and the illumination conditions. Thus identical spectral changes can be observed for paintings of different ages while the measured parameters can be quite different for two paintings of the same age.In order to solve this problem, after determining the time-dependent parameter for a set of paintings of different ages, we use statistical data processing methods. Then for an unknown painting, the parameter can be used to estimate the age. Such an approach requires knowing a specifi c mathematical model for ageing, making it possible to calculate an analytical "dating curve". Nevertheless, analysis of experimental data for a statistically signifi cant number of paintings has shown that such an approach does not work due to the signifi cant scatter in the experimental data and the lack of an adequate analytical model for ageing of paintings under unknown conditions [7]. Furthermore, the results of averaging have shown that the nature of the dependences under study are considerably nonlinear (threshold type) [7].