La parametration des fonctions de distribution des masses moleculaires

Abstract

Several methods for fitting molecular weight distributions by a series of Laguerre polynomials are studied. The most usual method of fitting by moments yields a series giving back the exact moments of the distribution. The shape of the curve corresponding to this series can however depart widely from the true distribution curve. If the regression method is used, the curve fitting can be made as good as one wants but, in the case of relatively short series. the moments of the series can differ markedly from those of the true distribution. By an appropriate combination of these two methods, it is possible to eliminate the aforementioned unwanted features and obtain a series that not only reproduces the shape of the distribution within experimental error but also gives back the exact values of an arbitrary number of the distribution moments. With the current experimental accuracy of the distribution data, and because not many moments are generally known, this combination method only requires a few terms in the series for the most common molecular weight distributions. For high negative skewness or for bimodal distributions, more terms are needed to reproduce the same amount of information. The method is applied to both analytical artificial distributions and experimental data.