Flow-injection of branched polymers inside nanopores

– Flexible chains (linear or branched) can be forced to enter into a narrow capillary by using a hydrodynamic flow. Here, we correct our earlier description of this problem by considering the progressive nature of the suction process. We find that the critical current for penetration, Jc, is controlled by the entry of a single blob of the capillary size, and that its scaling structure is the same for branched and linear chains. Introduction. – Confined polymer chains show up in many sectors ranging from filtration problems to DNA permeation [1]. In good solvent conditions, the concentration of linear chains in a pore smaller than the coil size, in equilibrium with a dilute bulk solution, is exponentially small [2]. However, the chain may be sucked in the pore by a flow (with an overall current J) if the current is beyond a certain threshold given by [3]: Jc ≃ kBT/η (1) where η is the solvent viscosity and kBT is the thermal energy. Note that this critical current is independent of both the molecular weight of the chains and the capillary size. Ten years ago, some of us tried to extend this discussion to the case of branched chains [3, 4]. The hope was that the threshold current could bring new informations on the properties of branched objects. It turns out, however, that our discussion was incorrect! The purpose of the present letter is to improve on that. The incorrect result was based on an “inside approach”, where the confined chain is considered independently of the entry. The implicit assumption was that the structure of a partly sucked chain may be represented by that of a completely confined chain. Below, after recalling some basic conformational principles of branched polymers, we summarize the earlier argument and show its weakness. We then present a Flory type argument for a partly sucked branched chain and discuss the progressive nature of the confining process.