[AOS21-P04] 海洋マイクロプラスチックのサイズ分布に関する統計力学的アプローチ
キーワード：海洋マイクロプラスチック、粒径分布、統計力学
The observed size distribution of marine microplastics generally shows, from large to small sizes, a gradual increase followed by a rapid, but smooth decrease (Figure). This decrease is puzzling because breaking up a plastic piece into smaller fragments naturally increases the number of fragments. This apparent discrepancy has led to a speculation that smaller plastic fragments somehow disappear ("missing plastics" problem). The present study aims to provide an alternative explanation for this size distribution, borrowing ideas from statistical mechanics. In our model, we assume that a flat plastic piece is fragmented into n x n equal cells that have a uniform size in a crush event. We further assume that the fragmentation of each piece is caused by “crush energy”, whose magnitude is assumed to be inversely proportional to the size of the cell, and whose occurrence probability follows the Boltzmann distribution. Under these assumptions and the constraint of the volume conservation of the plastics, we finally obtain the size distribution of the fragments, which follows Planck's formula for black body radiation. In our model, the total available "crash energy" is an unknown parameter. After adjusting it for the curve to fit the data, the Planck distribution agrees well with the observed distribution (Figure). In our model, smaller fragments beyond the peak of the distribution are fewer because the probability of getting "crash energy" large enough to produce such small fragments is low. Our formula predicts that the peak of the size distribution shifts to a smaller size and the total amount of the microplastics becomes larger with increasing crush energy. As a future extension, sink of plastic fragments may be included by the inclusion of an analogue of chemical potential.