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

Abstract

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 ((C₀ − C)/C₀), where C₀ 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 ∼ f/2. Further study of the temperature dependent (C₀ − C)/C₀ of polystyrene in cyclohexane shows that there exists a minimum of q_c,star at ∼38 °C, close to the theta temperature of polystyrene star chains.