Geometric relationship between the projected surface area and mass of a plastic particle

The quantification of the mass of meso/microplastic (MMP) particles is crucial for assessing the global inventory of ocean plastics and assessing environmental and human health risks. Herein, linear regression models between mass and projected surface area on a log scale were established by directly measuring the masses of 4390 MMP particles collected at 35 sites in 17 Japanese rivers with an ultramicrobalance. The linear regression models estimated mass concentrations more accurately than any previous method based on geometric volume assuming several three-dimensional shapes. Additionally, linear regression models were quite reasonable for determining the geometric relationships of idealized cuboid particles. The slope of the linear regression models was dependent on the three-dimensional shapes of the particles, and their intercept was determined according to their third dimension. Moreover, the third dimension led to uncertainty in the mass estimation of particles; thus, the accuracies of the previous methods were relatively poor. Nevertheless, two limitations for mass measurement by linear regression models were identified, which determined the size range of the MMP particles on the projected surface area (ranging from 10^-4 mm² to 10² mm²) that is applicable for mass estimation of the particles collected from riverine and marine environments. Our results could be used to accurately estimate the mass concentrations in aquatic environments and provide insights into the geometric relationships between the mass and size of MMP particles.