Size effect in ion transport through angstrom-scale slits

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Science  27 Oct 2017:
Vol. 358, Issue 6362, pp. 511-513
DOI: 10.1126/science.aan5275

Squeezing through a hole

Transport of an ion is usually directly related to its hydrated radius and assumed to be nonflexible. Either a hydrated ion fits through an aperture or it does not, and shape should play a dominant role rather than charge. Esfandiar et al. created nanofluidic devices by stacking structured bulk materials, including graphite, boron nitride, and molybdenum disulfide. They investigated the transport of ions in aqueous solutions through the nanochannels in the devices. Unexpectedly, they observed different behavior for ions of similar hydrated size but opposite charge.

Science, this issue p. 511


In the field of nanofluidics, it has been an ultimate but seemingly distant goal to controllably fabricate capillaries with dimensions approaching the size of small ions and water molecules. We report ion transport through ultimately narrow slits that are fabricated by effectively removing a single atomic plane from a bulk crystal. The atomically flat angstrom-scale slits exhibit little surface charge, allowing elucidation of the role of steric effects. We find that ions with hydrated diameters larger than the slit size can still permeate through, albeit with reduced mobility. The confinement also leads to a notable asymmetry between anions and cations of the same diameter. Our results provide a platform for studying the effects of angstrom-scale confinement, which is important for the development of nanofluidics, molecular separation, and other nanoscale technologies.

Many natural materials and phenomena involve pores of angstrom-scale dimensions (14). Examples are angstrom-size ion channels in cellular membranes, which are crucial for life’s essential functions, and ion-exchange membranes used in desalination, dialysis, and other technologies (14). To mimic and better understand functioning of such ion-transport systems, it is desirable to controllably fabricate and investigate artificial channels with similar dimensions. Unfortunately, channels fabricated with standard lithography techniques and conventional materials are limited in size by the intrinsic roughness of materials’ surfaces, which typically exceeds the hydrated diameter DH of small ions by at least one order of magnitude (5, 6). Ion transporters with nanometer dimensions have also been demonstrated, including smooth-walled carbon and boron nitride nanotubes (79), nanopores made in monolayers of MoS2 and graphene (1015), and interlayer passages in graphene oxide laminates (1618). These nanochannels still have sizes considerably exceeding those typical for inorganic ions and suffer from the presence of many defects and, especially, built-in electric charges (5, 13, 19, 20). Although the latter systems delivered many insights, it has often been difficult to disentangle various mechanisms that contribute to ion transport through them, including exit-entry effects, surface charges, steric exclusion and others. Recently, we reported atomically flat slits down to several angstroms in height, which were controllably fabricated by van der Waals (vdW) assembly (21). Unlike quasi–one-dimensional nanotubes and biological channels, our capillaries are two-dimensional and, in contrast to synthetic and biological ion transporters, have chemically inert and atomically smooth walls. In this paper, we investigate ion transport under such ultrastrong confinement.

The slit devices were fabricated following the recipe described in (21, 22). In brief, our channels comprised two relatively thick (~100-nm) crystals obtained by mechanical exfoliation. For the present study, we chose graphite, hexagonal boron nitride (hBN), and molybdenum disulfide (MoS2). The crystals were placed on top of each other, separated by stripes of bilayer (2L) graphene or monolayer (1L) MoS2, which served as spacers (fig. S1). The assembly was kept together by vdW forces, and the resulting channels had the height h of ~6.6 and 6.7 Å, given by the vdW thicknesses of 1L MoS2 and 2L graphene, respectively (Fig. 1A). This height is comparable to the diameter of aquaporins (1), for example, and is our smallest achievable h because slits with thinner spacers were intrinsically unstable, collapsing due to vdW attraction between opposite walls (21). The reported angstrom-scale slits had the width w ≈ 0.13 μm and the length L of several micrometers. The tricrystal stack was placed on top of a silicon nitride membrane with a rectangular opening of 3 μm × 25 μm, which served as a mechanical support and a partition between two liquid reservoirs (fig. S2). The reservoirs were thoroughly isolated from each other to ensure that ion transport occurred only through angstrom-scale slits (Fig. 1A).

Fig. 1 Ion transport under angstrom-scale confinement.

(A) Schematic of our measurement setup. (B) I-V characteristics of a device with 200 channels in parallel; w ≈ 0.13 μm, L ≈ 7 μm, 1L MoS2 spacers. KCl concentrations vary from 10−3 to 10−1 M. For clarity, the curves for low C are magnified by the color-coded factors. (C) Conductance for two representative devices with 2L graphene and 1L MoS2 as spacers (symbols). For KCl concentrations ≤10−4 M, the measured G was comparable to typical electrical leakage, as indicated in gray. (D) Conductance of slit devices made from graphite, hBN, and MoS2, using 2L graphene spacers; L ≈ 7 μm. In (C), the dashed curve is a fit assuming a constant surface charge, whereas the solid curves in (C) and (D) represent fits using the variable charge model. Error bars indicate the accuracy of determining G for individual I-V curves. Insets show schematics of the used slits.

First, we tested individual slits and measured their ionic conductivity using KCl solutions with the same molar concentration C in both reservoirs (fig. S3). The recorded current-voltage (I-V) characteristics were linear at small biases (<30 mV), exhibiting only slight nonlinearity over the studied voltage range up to ±0.2 V. The linear-response conductance G was ~0.5 nS for C = 1 M, in agreement with the known bulk conductivity of the KCl solution for the given geometry. By decreasing the KCl concentration, we rapidly reached our detection limit set by leakage currents (fig. S3). The typical leakage corresponded to ~10 pS, as found using reference devices without spacers. To increase sensitivity, we therefore opted to work with devices containing 200 slits in parallel (22). At large C, they exhibited the same conductance per channel as that found for single-channel devices (fig. S3). Typical I-V characteristics for 200-channel devices are shown in Fig. 1B and fig. S3. Their linear response G is plotted in Fig. 1C. At high salt concentrations, G is proportional to C and agrees with the KCl bulk conductivity inside the angstrom-scale slits. G starts to deviate from the linear dependence at ~10−2 M and then saturates to the leakage level of ~10 pS (Fig. 1C). As an additional test, we studied large ion exclusion using tetramethyl-, tetraethyl-, and tetrabutylammonium chloride solutions. No ionic current could be detected above the leakage limit for salts with DH > 13 Å (fig. S4). We carried out similar experiments for angstrom-scale slits with hBN and MoS2 walls (Fig. 1D) and found the dependences G(C) close to that for graphite walls. However, the saturation at low C occurred with notably higher values of G. Such behavior is well known in nanofluidics and is attributed to electric charges present on capillary surfaces (5, 6, 8, 15). We evaluated the surface charge density Θ using the standard analysis (22), which yielded ~120 and 300 μC m−2 for hBN and MoS2 surfaces, respectively. For graphite walls, the finite leakage allowed only the upper-bound estimate Θ ≤ 20 μC m−2. These values are three to four orders of magnitude smaller than those reported for carbon and hBN nanotubes [~10 and 100 mC m−2, respectively (8, 9)], silica channels, graphene oxide laminates, and pores in monolayer crystals, which typically exhibit Θ ~ 100 mC m−2 (5, 13, 15, 17). Even for our slits with MoS2 walls, an average distance between charged defects is >20 nm. We also find no difference in Θ between channels with side walls (spacers) made from graphene and MoS2 (Fig. 1C), as expected for the low aspect ratios h/w < 0.01. We believe that the low surface charge density in our capillaries is due to their extreme cleanliness. Their top and bottom walls contain virtually no surface defects being mechanically exfoliated from quality bulk crystals (21, 22), in contrast to low-dimensional materials grown by processes such as chemical vapor deposition.

The employed surface-charge model provides a good description of the experiment at both high and low C (dashed curve in Fig. 1C; see also fig. S5), but the measured G is notably higher than expected for intermediate C ≈ 10−2 to 10−4 M. Such deviations are usually assigned to the surface charge that depends on C [the so-called charge-regulation model (9)]. The solid curves in Fig. 1, C and D, show that this model describes our results better. The variable charge can be attributed to OH adsorption on capillary walls (8, 9). This agrees with our measurements of KCl conductance under pH values ranging from 2 to 10, which showed (22) that G was practically constant under acidic conditions but rapidly increased for high basic pH (fig. S6). Note that both constant and variable charge models yield the same intrinsic charge density.

The small Θ and little dependence on walls’ chemistry provide an opportunity to examine more subtle effects in ion transport. Because h is comparable to DH for small ions, we investigated whether, in addition to the found complete exclusion of large (>13 Å) ions, our angstrom-scale slits provide any size effect for common inorganic salts, as widely discussed in the literature and important for applications (13). To this end, several chloride solutions were chosen, with cations’ DH values ranging from ~6.6 to 12.5 Å. Chloride’s DH is 6.6 Å. Despite reaching the limit h < DH, our channels exhibited no abrupt steric exclusion (Fig. 2A and fig. S4B), contrary to what is often assumed when modeling ion transport. As reported above (Fig. 1), the conductivity σ of KCl, where both ions had DHh, changed relatively little with respect to its bulk conductivity. The chloride solutions with larger cations exhibited a notable reduction in their σ, which reached a factor of 4 for Al3+ and ~50 for tetramethylammonium (their DH values are ~1.5 and 2 times larger than h, respectively). These observations clearly show that ions under confinement do not act as hard balls but are able to partially shred or flatten their hydration shells (14, 23).

Fig. 2 Size effect in ionic conductivity.

(A) Conductivity of various 0.1 M solutions for a device with graphite walls and 1L MoS2 spacers (blue circles). Chlorides’ cations are listed along the top x axis, and their DH values are shown along the bottom x axis. The solid curve is a guide for the eye. Open squares denote bulk conductivity of the salts. (B) Angstrom-scale slits’ resistance 1/G as a function of L (graphite walls; 2L graphene spacers). Solid lines represent linear fits. Error bars indicate SDs in determining G from I-V curves.

It is known that edges of nanopores and nanotubes have a profound effect on their ionic conductance (10, 11, 13, 15, 18). To find out whether similar entry-exit effects contribute to ion transport through our angstrom-scale slits, we studied dependence of their G values on the channel length L. An example is shown in Fig. 2B for two chloride solutions. The measured resistance 1/G increases linearly with L and, within our accuracy, the linear fits extrapolate to zero. This indicates little contribution from entry-exit barriers, proving that the conductance is dominated by ion diffusion inside the slits.

To gain more information about the influence of angstrom-scale confinement on ion transport, we performed drift-diffusion experiments (8, 13, 15, 17). The two reservoirs were again filled with various chloride solutions, but now in different concentrations. Specifically, we used 10 and 100 mM solutions in the permeate and feed reservoirs, respectively (Fig. 3A). Because cations and anions generally diffuse at different rates, a finite ion current arises even in the absence of applied voltage; consequently, I-V curves become shifted along the voltage axis (Fig. 3A). A positive current at zero V corresponds to higher mobility of anions, μ, compared to that of cations, μ+. For example, the curves in Fig. 3A show that K+ and Al3+ diffuse through our angstrom-scale slits faster and slower than Cl, respectively. The zero-current potential Em allows us to find the mobility ratio, μ+ (13, 17), using the Henderson equation (24) Embedded Image(1)where z+ and z are the valences of cations and anions, respectively; F is the Faraday constant; R is the universal gas constant; T = 300 K; and Δ is the ratio of C in the feed and permeate containers. In our experiments, Δ = 10 and z = –1. Figure 3B plots μ+ obtained using Eq. 1. The mobility ratio changes by one order of magnitude with increasing DH from K+ to Al3+ but is indifferent to the wall material. We also used reference capillaries with size Embedded Image DH where no steric effects were expected (22). The latter devices exhibited μ+ values very close to those reported in the literature for bulk solutions, confirming the accuracy of our analysis for angstrom-scale slits (figs. S7 to S9).

Fig. 3 Ion mobility under angstrom-scale confinement.

(A) Examples of I-V characteristics for various chloride solutions under the concentration gradient Δ = 10 (device with graphite walls and 1L MoS2 spacers). The inset shows a schematic of the drift-diffusion measurements. (B) Mobility ratio μ+ as a function of cations’ DH value for slits made from graphite, hBN, and MoS2 (color coded), using 2L graphene spacers. Open squares represent the ions’ hydration energy. (C) Ion mobility under the confinement as a function of DH (circles). The most complete data set (graphite walls) is shown. Other walls yielded similar values. Diamonds represent literature values (25) for μ+ and μ in bulk solutions. Curves in (B) and (C) are guides for the eye. Error bars indicate SDs in our measurements of the zero-current potentials.

It is more informative to find μ+ and μ rather than their ratios. To this end, we measured conductivity of various chloride solutions (as in Fig. 2A) using relatively high C = 0.1 M so that the surface-charge contribution could be neglected. The conductivity can then be described as σ ≈ F(c+μ+ + cμ), where c and c+ are the concentrations of anions and cations, respectively. Combining the latter equation with the found μ+ value, we obtained μ+ and μ. Their values are plotted in Fig. 3C. The mobility of Cl varies little for different salts (within ±15%), but its absolute value under the confinement becomes about three times smaller than in bulk solutions (Fig. 3C). In stark contrast, the cations exhibit a decrease in mobility by a factor of ~10 with increasing DH from K+ to Al3+. Despite K+ and Cl exhibiting the same DH and similar mobilities in bulk solutions (22, 25), the mobility of K+ remains practically unaffected by the confinement, whereas Cl becomes three times less mobile (Fig. 3C).

Although the reported exclusion of very large ions from our angstrom-size slits is generally expected, it is rather surprising that small ions exhibit only the modest suppression of their mobility if the sieve size h becomes notably smaller than DH (1618). A number of molecular dynamic simulations previously suggested that under such “quantum” confinement, ions can reconfigure their hydration shells that become effectively squashed (14, 23). A qualitative measure of the difficulty for such water-molecule rearrangements around ions is their hydration energy, which describes the energy that is accumulated in hydration shells and that increases with increasing DH (26, 27). We expect that coefficients describing ions’ kinetics depend exponentially on the activation energy barrier presented by involved dehydration processes. This is in conceptual agreement with the fact that the measured μ+ values evolve approximately exponentially with the hydration energy, as indicated by the use of two y axes in Fig. 3B. Furthermore, the suppression of chloride’s mobility with respect to its bulk value is puzzling, particularly because K+ ions, having the same DH, exhibit no discernable change. We attribute the asymmetry to different polarization of water molecules around cations and anions (22). The hydration shell of K+ has hydrogen atoms pointing preferentially outside (fig. S10). In contrast, the exterior of Cl is covered with OH groups. It is known (28, 29) that both graphene and hBN polarize water molecules so that OH groups are directed preferentially toward the surfaces (also in accordance with the pH dependence reported in fig. S6). This suggests that anions, compared with cations of the same size, should exhibit stronger interactions with graphene and hBN walls (28, 30). This would result in extra friction of Cl against the walls and, consequently, reduced mobility, in agreement with the observed cation-anion asymmetry. Further theory analysis is required to quantitatively describe the reported dehydration and asymmetry effects.

Our atomically flat angstrom-size slits exhibit, in the first approximation, little chemical interaction with ions and act purely as a geometric confinement. The observed changes in small ions’ mobility can be explained by distortions of their hydration shells, which become progressively more costly in terms of the energy if the ion diameter increases. Our results imply that any feasible confinement is unlikely to provide high selectivity between small ions, and living and artificial systems must rely on strategically placed electric charges inside channels or at their entries.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S10

References (3135)

References and Notes

  1. See supplementary materials.
  2. Acknowledgments: This work was supported by the European Research Council, the Royal Society, and Lloyd’s Register Foundation. B.R. and K.G. are recipients of the Leverhulme Early Career Fellowship and the Marie Curie International Incoming Fellowship, respectively. S.G. acknowledges financial support from the National Research Foundation, Prime Minister’s Office, Singapore, under the Competitive Research Program (grant NRF-CRP13-2014-03).
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