Living in the moment: a mathematically verified approach for molecular weight distribution analysis and application to data storage

The moments of mathematical distributions allow calculation of various statistical parameters of the distribution and provide quantitative measures of its shape. In cases where the distribution is a polymer molecular weight distribution (MWD), the moments can be used to calculate the number- and weight-average molecular weights of the sample and the standard deviation and other higher order statistical parameters of the representative (e.g., chain length and mass) distributions. In this work, the moments of distributions are used to develop powerful equations that allow the statistical parameters of any arbitrary mixture of molecular weight distributions to be calculated. These equations take the average molecular weights and mass fractions of polymer samples as inputs and provide the corresponding molecular weight averages of the mixed sample as outputs. Various statistical parameters of the representative number and weight distributions can then be easily and accurately attained using the calculated molecular weight averages. As a representative example of the power of this approach, blended polymer MWDs were encoded with characters and accurately and rapidly decoded using the developed equations. Overall, as this polymer blending approach is developed from a mathematical standpoint, there are practically no limits to the number or type of component distributions in the mixture, thus providing a much simpler route for designing polymer mixtures with tightly controlled statistical properties.