where f (N) can be determined from τ c and c measured in the multi-chain simulations. The value of this concentration for regular-flexibility backbones of different chain lengths, N, in the poor solvent is shown in Fig. . If D ∼ N β and R ∼ N ν , where β and ν are scaling exponents, the scaling of f (N) ∼ N (2-β -4ν) is predicted; then, assuming that Fig. Critical concentration above which multi-chain aggregation is expected to be faster than single-chain folding as a function of polymer chain length in the poor solvent. For 10 and 20mers, there are multiple indistinguishable overlapping points present for the same chain length, calculated using τ c from multi-chain simulations at dierent concentrations. The solid circles are values calculated from the Langevin dynamics simulations (i.e. with no hydrodynamic interactions (HI)). The red curves are power-law ts to these data, either with the t parameters unconstrained (solid line) or with the power-law exponent constrained to that expected from theory (dashed line). The grey circle for N = 20 corresponds to the low-friction system and was not included in the t. Unlled squares are values corrected for HI using eqn (7). The grey curves are unconstrained (solid line) and constrained (dashed line) power-law ts to these corrected data analogous to the red lines for the uncorrected data. The value of c † at N = 180, corresponding to the work in ref. 12, calculated from the theoretical scaling both with (c † HI,theory ) and without (c † noHI,theory ) the hydrodynamic correction, is indicated on the graph. Error bars indicate two standard errors. τ s ∝ N α , eqn (5) predicts the scaling (see ESI Section S9)