  The size distribution of marine microplastics provides a fundamental data
source for understanding the dispersal, break down, and biotic impacts of the
microplastics in the ocean. The observed size distribution at the sea surface
generally shows, from large to small sizes, a gradual increase followed by a
rapid decrease. This decrease has led to the hypothesis that the smallest
fragments are selectively removed by sinking or biological uptake. Here we
propose a new model of size distribution without any removal of material from
the system. The model uses an analogy with black-body radiation and the
resultant size distribution is analogous to Planck's law. In this model, the
original large plastic piece is broken into smaller pieces once by the
application of "energy" or work by waves or other processes, under two
assumptions, one that fragmentation into smaller pieces requires larger energy
and the other that the probability distribution of the "energy" follows the
Boltzmann distribution. Our formula well reproduces observed size distributions
over wide size ranges from micro- to mesoplastics. According to this model, the
smallest fragments are fewer because large "energy" required to produce such
small fragments occurs more rarely.
