Statistical significance of polymer-size scaling in Langevin diffusion

Determine whether the apparent reduction in scatter produced by scaling the Langevin-dynamics diffusion data by the polymer radius of gyration is statistically significant.

Background

The paper compares polymer diffusion in Langevin-dynamics simulations, which omit explicit hydrodynamic interactions, with diffusion in lattice-Boltzmann molecular-dynamics simulations. For the Langevin data, the authors first introduce a phenomenological dependence on the crowder-to-monomer size ratio, represented by the factor ln(1+R/r), to account for the strong effect of crowder size. They then additionally scale the data by the polymer radius of gyration, R_g, and observe a reduction in scatter across the simulated systems.

The authors suggest that this apparent R_g dependence could reflect correlated motion induced by excluded-volume interactions among mobile colloidal crowders, potentially producing hydrodynamic-like effects at the polymer scale even in Langevin dynamics. However, the simulations and available statistics do not establish whether the observed reduction in scatter is statistically meaningful, leaving the significance of polymer-size scaling unresolved.