How does a star chain (nanooctopus) crawl through a nanopore?

The ultrafiltration of star-like polystyrene chains with different arm lengths (LA) and arm numbers (f) passing through a nanopore (20 nm) under an elongational flow field was investigated in terms of the flow-rate dependent relative retention ((C0 − C)/C0), where C0 and C are the polymer concentrations before and after the ultrafiltration. Our results reveal that for a given LA, the critical flow rate (qc,star), below which star chains are blocked, dramatically increases with f; but for a given f, is nearly independent on LA, contradictory to the previous prediction made by de Gennes and Brochard-Wyart. We have revised their theory in the region fin < fout, where fin and fout are the numbers of arms inside and outside the pore, respectively; and also accounted for the effective length of each blob. In the revision, we show that qc,star is indeed independent of LA but related to both f and fin in two different ways, depending on whether fin ≤ f/2 or ≥ f/2. A comparison of our experimental and calculated results reveals that most star chains pass through the nanopores with fin ∼ f/2. Further study of the temperature dependent (C0 − C)/C0 of polystyrene in cyclohexane shows that there exists a minimum of qc,star at ∼38 °C, close to the theta temperature of polystyrene star chains.