Acta Chimica 128. (1991)
2. szám - Major György: Mathematical modelling of diffuse light scattering – Polynomial approximatiion of the concentration dependence
184 MAJOR: DIFFUSE LIGHT SCATTERING verify that the dependences for different density functions cannot be brought into fitting by linear transformation. The remittance data of a concentration series give possibility to draw up a calibration curve for quantitative analysis. However, it is more suitable to have a mathematical relation for calculating the remission or concentration. Many authors describe the Kubelka—Munk-Gurevitsch (KM) function (Eq. 2) according to which, the dependence of к/s vs. concentration gives a linear plot [6, 7, 8]. It is however valid only for a narrow concentration range, therefore, we examined the possibility of curve fitting. ' к/s = V - R-)l 2 R„ (2) Dependences of —In (Лте) vs. concentration or absorptivity give curves similar to a parabola. Because of this we studied fitting with quadratic, cubic and biquadratic polynomials. In case of model distributions we obtained proper fittings using second order polynomials. In case of measured data the calculations showed that for greater accuracy it is more expedient to use biquadratic polynomials. Results and Discussion We assembled concentration sets, diluting coloured powders with colourless powder in weight percent and measured remittance data of these samples on Pye Unicam SP8-100 spectrophotometer, using a diffuse reflectance accessory and fitted the data on a desktop computer with polynomials using the method of least squares. For comparison we examined the accuracy of the KM function. Table I shows data of concentration sets of pulverized K2Cr04 diluted with pulverized KBr; remittances were measured at 400 nm. Table II contains data of concentration sets of Kieselgel HR powder coloured with Astrazon Blue G from alcoholic solution, diluted with colourless Kieselgel HR, remittances were measured also at 400 nm. We made fittings with quadratic, cubic and biquadratic order polynomials for the dependences g = —In R^j100 vs. concentration according to Eq. 3 and first order fitting for the dependence of k/s vs. concentration according to Eq. 4. For fittings we used all measured data of several concentration sets. Tables III and IV show constants of fitted polynomials for the two series samples (I, II), respectively. к/s = A -f- Be q = A -j- Be -f- Cc2 -(- Dc3 -(- Ec4 (3)