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

The ultrafiltration of star-like polystyrene chains with different arm lengths (L-A) 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 ((C-0 - C)/C-0), where C-0 and C are the polymer concentrations before and after the ultrafiltration. Our results reveal that for a given L-A, the critical flow rate (q(c,star)), below which star chains are blocked, dramatically increases with f; but for a given f, is nearly independent on L-A, contradictory to the previous prediction made by de Gennes and Brochard-Wyart. We have revised their theory in the region f(in) < f(out), where f(in) and f(out) 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 q(c,star) is indeed independent of L-A but related to both f and f(in) in two different ways, depending on whether f(in) <= f/2 or >= f/2. A comparison of our experimental and calculated results reveals that most star chains pass through the nanopores with f(in) similar to f/2. Further study of the temperature dependent (C-0 - C)/C-0 of polystyrene in cyclohexane shows that there exists a minimum of q(c,star) at similar to 38 degrees C, close to the theta temperature of polystyrene star chains.