Accuracy improvement of the experiment determining macromolecular weight by capillary viscometer based on Monte Carlo simulation

Abstract

In order to lower the experimental uncertainty when measuring the molecular weight of a polymer (Mw) with a glass capillary viscometer, error propagation from the measured flow times to the calculated Mw is analyzed by Monte Carlo simulation. New experimental designs are then proposed to achieve a lower experimental uncertainty for the same number of measurements in total. To simulate experiments, normally distributed relative flow time deviations are randomly generated and used to calculate Mw. It is found that the errors increase hugely from the flow times to the Mw. For example, a relative standard deviation (RSTD) of 0.5% of the flow times can lead to an RSTD of 15% to the Mw for the experiment design that measures the flow times of a pure solvent and four solutions of different concentrations in triplicate, and calculates the Mw based on them, as instructed in many laboratory manuals. Most importantly, the study reveals that the errors of the flow times corresponding to the pure solvent and solutions have a very different influence on the deviation of Mw. The flow times of the pure solvent and the solution with the lowest concentration have the most significant impact on the deviation of Mw. Finally, new experimental designs are explored and it is found that by only measuring the flow times of two solutions (the 10 g l−1 solution measured in triplicate and the 5 g l−1 solution measured nine times) and the pure solvent (measured in triplicate) the RSTD of Mw can be reduced by 33% compared with the case in which four solutions and the pure solvent are all measured in triplicate.