Acta Chimica 128. (1991)
2. szám - Major György: Mathematical modelling of diffuse light scattering – Polynomial approximatiion of the concentration dependence
Acta Chimica Hungarica 128 (2), pp. 183 —186 (1991) MATHEMATICAL MODELLING OF DIFFUSE LIGHT SCATTERING POLYNOMIAL APPROXIMATION OF THE CONCENTRATION DEPENDENCE* György Major (H-1121 Budapest, Eötvös út 51 — 53) Received October 20, 1989 Accepted for publication February 21, 1990 Mathematical modelling of diffuse scattering samples shows that the dependence of remission vs. absorptivity or concentration gives different curves for different samples. Therefore, polynomial fitting for —ln (R) vs. concentration curves gives better accuracy then the use of the Kubelka — Munk—Gurevitsch function. Mathematical modelling of diffuse light scattering gave a good possibility for the study of several relations of the phenomenon. The starting point for the modelling was the assumption that the light, falling on the light scattering object, emerges from the sample either on the illuminated side ■— remission — or in case of a thin sample, on the other side — transmission — covering different path lengths. For both light beams a distribution function can be written. The determination of loss resulting from the absorption can be calculated in consideration of the density function f(u) of these distributions according to eq. (1), where e is the absorptivity, c the concentration and u the path length [1, 2, 3] I = h ГЛи) e~eCU du (1) ö Data obtained from modelling show that the shape and measures of the density functions depend both on the thickness of sample and on the shape, size and size distribution of particles. The density function is a composition of step-lengths’ distribution by the photon inside particles following a zigzag way through the sample [4]. Because of this, the density function can have several maxima and inflexion points. This means further that for different samples its shape can be diverse and the determination of distribution function by deduction can hardly be expected. Dependences of remission vs. absorptivity (or concentration) calculated for model density functions, which are constructed from straight lines, give a good demonstration of differences for the shape of curves [5]. These data + This paper was presented at the 5th Hungarian Conference on Molecular Spectroscopy at Sárospatak, Hungary, June 19—22, 1989.