COMPARATIVE ANALYSIS OF THE POSSIBILITIES OF POLYNOMIAL AND ANALYTICAL APPROXIMATIONS OF POLARIZATION-OPTICAL RESPONSES OF MAGNETIC NANOFLUIDS

A quantitative comparison of the possibilities of polynomial and analytical approximation of weak polarization-optical responses of dilute magnetic nanofluids (NF) is carried out. Estimates of the coefficients of determination are used as criteria for comparing different approximation methods. It is shown quantitatively that for all studied values of the magnetic field, the dependences of the values of weak polarization-optical responses of magnetic NF on concentration are similar in the concentration range of more than three orders of magnitude. The possibilities of using the approximation coefficients for estimating the parameters of the NF under study are considered. The considered methods for approximating experimental data of NF polarization-optical responses are equivalent, since the coefficients of determination for these methods are close to each other. The advantage of the approximation method using an analytical function is that one of the approximation coefficients is directly related to the concentration of the analyzed NF. As a result, there is no need to use calibration curves and perform interpolation in order to estimate the concentration, in contrast to approximation with polynomials. Analytical approximation of the responses of the studied NF by means of dependencies using hyperbolic functions is more sensitive to the outliers in the experimental data than the approximation method based on polynomials. If a polynomial response model is used, the method of estimating concentrations through calibration curves can be successfully applied even when there are noticeable outliers in the experimental data.