Cation-controlled permeation of charged polymers through nanocapillaries

Molecular dynamics simulations are used to study the effects of different cations on the permeation of charged polymers through flat capillaries with heights below 2 nm. Interestingly, we found that, despite being monovalent, ${\mathrm{Li}}^{+}$, ${\mathrm{Na}}^{+}$, and ${\mathrm{K}}^{+}$ cations have different effects on polymer permeation, which consequently affects their transmission speed throughout those capillaries. We attribute this phenomenon to the interplay of the cations' hydration free energies and the hydrodynamic drag in front of the polymer when it enters the capillary. Different alkali cations exhibit different surface versus bulk preferences in small clusters of water under the influence of an external electric field. This paper presents a tool to control the speed of charged polymers in confined spaces using cations.

Figure 1

Schematic of the simulation setup. The feed and permeate reservoirs are connected by a narrow flat capillary. External electrical field is applied on the charged particles pulling a negatively charged polymer from the feed reservoir into the capillary and subsequently it diffuses into the permeate reservoir. Cyan and orange particles represent cations (${\mathrm{K}}^{+}$, ${\mathrm{Na}}^{+}$, ${\mathrm{Li}}^{+}$) and anions (${\mathrm{Cl}}^{-}$), respectively. For ease of illustration, water molecules are depicted as tiny points.

Figure 2

Time evolution of the polymer center of mass for five different KCl ion concentrations subjected to different voltages across the system: 5 V(a), 12 V(b), 25 V(c), and 50 V (d).

Figure 3

Polymer mean velocity inside the capillary versus the cation concentration for KCl, NaCl and LiCl electrolytes at 25 V (left) and 50 V (right). The curves are guide to the eye.

Figure 4

Polymer time-displacement curves for three different systems including without ions, with ions, and with ions frozen at particular positions. The upper and lower rows, respectively, are for KCl and LiCl electrolytes, and the columns from left to right are for 0.5 M, 0.75 M and 1 M solute concentrations.

Figure 5

(a) Number of cations inside the capillary of height 1.8 nm for potassium and lithium electrolytes versus time. The curves at the time intervals in which the polymer resides inside the capillary are bolded. (b) Time-displacement curves. The capillary gave a bias to lithium electrolyte in a way that the polymer in potassium electrolyte felt a barrier when entering the capillary. Panels (c), (d) and (e), (f) are the same quantities as (a), (b), respectively, for capillaries of height 1.4 nm and 2.4 nm. In the 1.4 nm capillary, the polymer felt a barrier in both cases while for the 2.4 nm capillary there is no entrance barrier.

Figure 6

Free energy (solid lines) and internal energy (dashed lines) as a function of cation distance from the water cluster center of mass for two cations, ${\mathrm{K}}^{+}$ and ${\mathrm{Li}}^{+}$. In the upper panels, there is no external electric field, while in the lower panels there is an external electric field of 3 V/nm. Panels on the left show results for the nonpolarizable model, while panels on the right show results for the polarizable model.