Revisiting the Flow-Driven Translocation of Flexible Linear Chains through Cylindrical Nanopores: Is the Critical Flow Rate Really Independent of the Chain Length?

Abstract

We aim to clarify how the chain length influences the critical flow rate (qc) for flexible linear chains translocating through cylindrical nanopores in the whole length range (9.5 > R/r > 1.0), where R and r represent the chain size and the pore size, respectively. By studying the translocation behavior of both mono- and polydisperse polystyrenes through 20 nm nanopores, we have, for the first time, experimentally revealed that there exist two different translocation regimes, i.e., strong and moderate confinement regimes. In the strong confinement regime (R/r > λ*), qc is found to be independent of the chain length, consistent with the prediction by classical theories, while in the moderate confinement regime (R/r < λ*), qc increases with the chain length significantly, where λ* represents the critical relative chain length. Theoretically, λ* is determined by the critical penetration length (l*), at which the free energy change (ΔE) of a translocating chain reaches its maximum value (ΔE ∼ kBT). For longer chains (R/r > λ*), they always reach the position l* of the barrier (Ebar*) before being completely confined in the channel; but for shorter chains (R/r < λ*), they could overcome the energy barrier before reaching l*. By considering the variation of both position (L) and height (Ebar) of the energy barrier in the moderate confinement regime, a normalization equation has been proposed to correlate the normalized critical flow rate (qc/qc*) with the normalized confined length (L/l*) and energy barrier (Ebar/Ebar*), i.e., qc/qc* = (2L/l* – Ebar/Ebar*)/(L/l*)2, where qc*, l*, and Ebar* are the corresponding physical quantities in the strong confinement regime. The theoretical equation describes our experimental data well. In addition, we discuss the possibility of utilizing single membrane-based ultrafiltration for linear polymer fractionation. The experimental result demonstrates that one single membrane is enough to simultaneously tailor the boundaries of low and high molar masses of polymer fractions in ultrafiltration fractionation. As an example, we experimentally show how one can “dynamically” regulate the effective pore size of a given membrane, by properly choosing the flow rates, to fractionate a polydisperse sample (Mw/Mn ∼ 3.25) into a series of monodispersed samples (1.08 ≤ Mw/Mn ≤ 1.30) with different boundary molar masses. The current work not only strengthens our understanding of the length-dependent translocation behavior of linear polymers but also provides a versatile method for linear chain fractionation.