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The size distribution of marine microplastics provides a fundamental datasource for understanding the dispersal, break down, and biotic impacts of themicroplastics in the ocean. The observed size distribution at the sea surfacegenerally shows, from large to small sizes, a gradual increase followed by arapid decrease. This decrease has led to the hypothesis that the smallestfragments are selectively removed by sinking or biological uptake. Here wepropose a new model of size distribution without any removal of material fromthe system. The model uses an analogy with black-body radiation and theresultant size distribution is analogous to Planck's law. In this model, theoriginal large plastic piece is broken into smaller pieces once by theapplication of "energy" or work by waves or other processes, under twoassumptions, one that fragmentation into smaller pieces requires larger energyand the other that the probability distribution of the "energy" follows theBoltzmann distribution. Our formula well reproduces observed size distributionsover wide size ranges from micro- to mesoplastics. According to this model, thesmallest fragments are fewer because large "energy" required to produce suchsmall fragments occurs more rarely.

A model for the size distribution of marine microplastics: a statistical mechanics approach