Subscriber access provided by Iowa State University | Library
Communication
Atomic-scale Fluidic Diodes Based on Triangular Nanopores in Bilayer Hexagonal Boron Nitride Binquan Luan, and Ruhong Zhou Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b04208 • Publication Date (Web): 10 Jan 2019 Downloaded from http://pubs.acs.org on January 10, 2019
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
Atomic-scale Fluidic Diodes Based on Triangular Nanopores in Bilayer Hexagonal Boron Nitride Binquan Luan∗ and Ruhong Zhou Computational Biological Center, IBM Thomas J. Watson Research, Yorktown Heights, NY 10598, USA. E-mail:
[email protected] Abstract Nanofluidic diodes based on nanochannels have been studied theoretically and experimentally for applications such as biosensors and logic gates. However, when analyzing attoliter-scale samples or enabling high-density integration of lab-on-a-chip devices, it is beneficial to miniaturize the size of a nanofluidic channel. Using molecular dynamics simulations, we investigate conductance of nanopores in bilayer hexagonal Boron Nitride (h-BN). Remarkably, we found that triangular nanopores possess excellent rectifications of ionic currents while hexagonal ones do not. It is worth highlighting that the pore length is only about 0.7 nm which is about the atomic limit for a bipolar diode. We determined scaling relations between ionic currents I and pore sizes L for small nanopores, that are I ∼ L1 in a forward biasing voltage and I ∼ L2 in a reverse biasing voltage. Simulation results qualitatively agree with analytical ones derived from the one-dimensional Poisson-Nerst-Planck equations.
Key words: h-BN, bi-layer, fluidic diode, 2D nanopore, rectification. 1
ACS Paragon Plus Environment
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 19
Similar to electronic diodes that permit one-directional electron currents, nanofluidic channels with tailored surface charge densities (so called fluidic diodes) can rectify ionic currents under external biasing voltages. 1,2 Generally, fluidic diodes are bipolar when channelsurface contains oppositely charged segments 3 or uni-polar when one surface segment is charged whereas the rest is neutral. 4 For a nanochannel with uniformly charged surface to rectify currents, ion concentrations need to be different in two reservoirs outside the nanochannel 5 or the nanochannel is required to be in a cone shape. 6 It is also desirable to combine effects of surface charge pattern, channel geometry, ion-concentration gradients and gate voltages to achieve the enhanced rectification. 7–10 Typically, to yield a high rectification ratio, nanochannels need to be long (∼ µm) and ionic concentrations need to be low so that the Debye screening length λ is comparable to the channel radius R (for a cylindrical channel). Short nanochannels, i.e. nanopores, have also been widely studied for rectifying ionic currents. 11–14 The advantages of nanopores compared with long nanochannels include relatively larger currents, minimal usage of sample fluid, faster response to electric signals and higher sensitivity for a single biomolecule. For the interest of miniaturization, there is a lower length-limit for nanopores to operate as diodes. For a bipolar nanopore, its length Hmin must be at least the width of a depletion zone at the interface of oppositely charged channel segments. Namely, it satisfies 15 r Hmin =
V R . σ
(1)
where V is the biasing voltage; is the absolute permittivity of water; and ±σ are surface charge densities of two oppositely charged segments in a bipolar nanopore. For a biopolar diode, Hmin ≥0.7 nm, which is set by the atomic limit. To approach this limit, according to Eq. 1, the nanopore radius should be small while the surface charge density should be high. In this letter, we are motivated to explore the possibility of achieving such an atomic scale
2
ACS Paragon Plus Environment
Page 3 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
fluidic diode. Given recent advances of two dimensional (2D) heterostructures stacked together by different 2D materials (such as graphene, hexagonal boron nitride (h-BN) and MoS2 ), 16,17 a nanopore in a bilayer heterostructure 18,19 (resembling a miniaturized nanotube heterojunctions 3 ) satisfies the requirement H ∼0.7 nm. More challengingly, the pore surface must contain two layers of oppositely charged atoms. Experimentally, it was recently demonstrated for the h-BN nanosheet that a nitrogen-terminated triangular nanopore (negatively charged) can be formed as defects in CVD synthesis 20–22 or made by the electron-beam drilling with an atomic size-control (down to mono or several atoms vacancy). 23 Additionally, for multiple-layer h-BN, the triangular pore can be drilled layer-by-layer with the top pore-containing layer acting as a mask, thus yielding same-sized triangular pores in lower layers. 23 In the bilayer case, remarkably, such nanopore in one layer is nitrogen-terminated while the nanopore in the other layer is boron-terminated as shown in Figure 1a, resulting in negatively and positively charged surface-segments in the entire nanopore. Note that although in general the boron-terminated nanopore in a single h-BN nanosheet is not stable, in the bilayer case both boron and nitrogen atoms on the pore surface miss one coordination and can form vertical out-of-plane B-N bonds (similar to vertical covalent bonds on the surface of nanopores in a h-BN/graphene heterostructure 24 ), leading to a stable bipolar nanopore surface (without any dangling bond). It is expected that a large opening (∼100 nm) can be drilled through a multiple layer (bulk-like ) h-BN until it reaches the bottom twolayers where the final triangular nanopore is further drilled. Under different electron beam conditions, interestingly, the nanopore shape can be hexagonal 23 instead of being triangular (Figure 1b). Notably, due to the symmetry, the hexagonal pore surface is not bipolar. We emphasize that the bipolar surface is not present in nanopores in other 2D materials (such as graphene and MoS2 ) and so far only exists in triangular nanopores in the h-BN bilayer. Here, to prove the principle, we combine the molecular dynamics (MD) method and continuum theories to analyze the current rectification by nanopores in bilayer h-BN which
3
ACS Paragon Plus Environment
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 4 of 19
represents the smallest bipolar diodes. We highlight how pore geometry, ion concentrations and pore sizes can affect rectification ratios of the atomic-scale fluidic diode. a
c
b
E
Figure 1: Modeling ionic currents through nanopores in bilayer h-BN. a) The perspective bottom view of a triangular nanopore in the h-BN bilayer. The length of each side of the equilateral triangle l=7.5 Å. b) The perspective view of a hexagon nanopore in the h-BN bilayer. Areas of nanopores shown in b) and c) are similar. c) Simulation system: atoms in h-BN nanosheets are shown as van der Waals spheres (boron: pink; nitrogen: blue); water is shown transparently; and K+ and Cl− ions are colored in tan and cyan.
To model ionic currents through a nanopore in the h-BN bilayer, we performed allatom molecular dynamics simulations using the program NAMD. 25 Figure 1c illustrates the simulation system in a hexagonal prism: the cross-section area of the base is about 94 nm2 and the height h is about 11 nm. Two h-BN nanosheets (separated by 3.4 Å) are on top of each other and the distance between neighboring boron and nitrogen atoms in each sheet is 1.4 Å. 22 Different triangular nanopores were formed by removing atoms in various triangular plates around the center of the h-BN bilayer; resulting nanopores are terminated by nitrogen and boron atoms in the upper and lower nanosheets respectively (Figure1a). For comparison, we also modeled ionic currents through a hexagonal nanopore in the h-BN bilayer (Figure 1b), where boron and nitrogen atoms alternate on the pore surface. All built nanopores were further solvated with a KCl electrolyte with the bulk number concentration ρb = 0.06, 0.3 or 0.6 nm−3 (corresponding to molar concentrations of 0.1, 0.5 or 1.0 M, 4
ACS Paragon Plus Environment
Page 5 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
respectively). In MD simulation, atoms in the h-BN were fixed at their initial lattice positions. After system equilibration at 300 K (by applying the Langevin thermostat 26 ) and 1 bar (by applying the Nosé-Hoover method 27 ), production runs were carried out at NVT ensemble (T =300 K) with biasing electric fields E (the resulting biasing voltages V =Eh). We applied the TIP3P model 28,29 for water molecules and the standard force field 30 for the ions. The force field for the h-BN bilayer was adopted from a previous study: 31 B (+0.4e) and N(-0.4e) where e is the elementary charge, yielding a charge density of +1.8 e/nm2 and -1.8 e/nm2 for boron- and nitrogen-terminated pore surface respectively (See Fig. S2 in Supporting Information for further discussion of charge parameters, which shows that the current rectification is not sensitive to the BN partial charges used). The pair-wised vdW interaction was computed using a smooth (10-12 Å) cutoff, while the long-range Coulomb interaction was calculated using the particle-mesh Ewald (PME) method with a mesh size of about 1 Å. Periodic boundary conditions were applied in all three dimensions. The simulation time-step was 2 fs; non-electric (e.g. vdW and bonded) and electric interactions were calculated every 2 fs and 4 fs, respectively. At each applied biasing voltage, ionic currents I in the simulated system emerging from P the transport of ions through a nanopore in the h-BN bilayer can be calculated as i qi vi /H, where H is the height of the simulation system; qi and vi are the charge and the velocity of the ith ion, respectively. Instead of plotting noisy current data, we show in Figure 2a the R total transported charges Q (= I(t)dt) through a triangular nanopore whose side length l (determined by the size of a removed triangle plate, Figure 1a) is 3a, where a (=2.5 Å) is the distance between two nearest boron atoms (or lattice constant). When ρb =0.3 nm−3 , with forward biasing voltages of 0.5, 1.0 and 1.5 V, there are a significant number of ions driven through the nanopore over the simulation time (Figure 2a). In contrast, with reverse biasing voltages of -0.5, -1.0 and -1.5 V, strikingly only a few ions moved through the pore. Therefore, as suggested by the slopes (Figure 2a), forward currents are much higher than
5
ACS Paragon Plus Environment
Nano Letters
the reverse ones. It is worth noting that the bilayer h-BN is the minimal structure to harbor a triangular nanopore with the biploar surface that is prerequisite for the observed current rectification. Therefore, the current rectification cannot occur either in a triangular nanopore in a single-layer h-BN as demonstrated in previous experiment 22 or in a nanopore in bilayer heterostructure without the bipolar surface. 18,19 a
250
1.5 V 1.0 V 0.5 V -0.5 V -1.0 V -1.5 V
200
Q (e)
150 100
50 0
0
b
1
0.6
0 -3
20
10
0.3
I (nA)
2
I (nA)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 6 of 19
30
t (ns)
40
Hexagon
0
-0.3
-0.6 -1 -0.5
-2
0
V (V)
0.5
-1
1
0
V (V)
1
2
3
Figure 2: Ionic currents through nanopores in bilayer h-BN when ρb =0.3 nm−3 . a) Total charges of ions moving through the nanopore (l=7.5 Å) vs. time t, at various applied biasing voltages. b) I-V curves for the nanopore in the h-BN bilayer. Ionic current rectification is strong for the triangular nanopore but is not present for the hexagonal nanopore (inset).
The entire I-V curve for this nanopore is shown in Figure 2b, which demonstrates an excellent rectification effect. The rectification ratio calculated by I(3V)/I(-3V) is about 50, suggesting that this nanopore system is an outstanding fluidic diode. Noticeably, currents increase slowly with voltages (near zero) which is due to the energy barrier (both entropic and dielectric) for ions to enter the small nanopore; such barrier becomes less relevant at large biasing voltages (because of large electric driving forces on ions). At intermediate biasing voltages (positive), measured currents increase linearly with voltages. The deviation from the linear relation occurs at larger biasing voltages (e.g. 3 V), which is due to the en6
ACS Paragon Plus Environment
Page 7 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
hanced water compactness inside a short nanopore 32 and thus larger frictional forces (smaller electrophoretic mobilities) for ions. Although the rectification ratio can be enhanced at high biasing voltages with the leakage current remaining negligible (e.g. -3 V), to avoid potential damage to the structure of h-BN bilayer, experiment is suggested to conduct at low voltages (e.g. 1 V as further studied below). In contrast to the triangular nanopore with polar surface, the I-V curve for the hexagonal nanopore is symmetric (Figure 2b), i.e. no rectification effect. Structure-wise, as shown in Figure 1b and Fig. S1, both the front and the back of the hexagonal nanopore are identical, showing that the charge densities of both pore-entrance and pore-exit are zero (i.e. the pore surface is not bipolar). As shown in the triangular nanopore (Figure 2a and Fig. S1) where charge densities of pore-entrance and pore-exit are +1.8 e/nm2 and -1.8 e/nm2 respectively, with such polar surface the current rectification occurs. Under the same electron beam condition as for the hexagonal pore, a nanopore with a large size (e.g. 10-nm-in-diameter) could be circular. For the same reason of the charge polarity, no current rectification is expected for the circular pore as well. From the simulation trajectories, we obtained representative snapshots of ion transport through the triangular nanopore (l=3a) under the forward and reverse biasing voltages (Figure 3a). With a forward biasing voltage, the dipole moment of the pore surface is parallel with the applied electric field E, which synergistically drives K+ and Cl− into the pore from the bottom and the top respectively (Figure 3a, left panel). However, with a reverse biasing voltage, the dipole moment is anti-parallel with the applied biasing electric field, which is counterproductive because the applied electric field attempts to drive K+ and Cl− into positively and negatively charged openings respectively (Figure 3a, right panel). To show the ion distribution quantitatively, we calculated the ion density in a triangular prism passing through the triangular nanopore. The triangular prism is perpendicular to the h-BN bilayer and the base area is same as the one of a triangular nanopore. Calculated ion densities ρ(z) were averaged in each plate (thickness: 1 Å) along the prism. When
7
ACS Paragon Plus Environment
Nano Letters
a
+ −
+ −
E
E
b
ρ/ρ0
10
c
1V
-1 V
1V
-1 V
+
K Cl
5 0 3 2
ρ/ρ0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 8 of 19
1
0
-40
-20
0
z (Å)
20
40
-40
-20
0
z (Å)
20
40
Figure 3: Distributions of ion concentrations around the triangular nanopores under the forward biasing voltage (1 V, left panels) and the reverse biasing voltage (-1 V, right panels). a) Illustration of ion distributions around the pore under two opposite biasing voltages (K+ : tan; Cl− : cyan; B: pink; N: blue). The h-BN bilayer is shown transparently and atoms on the front triangle-pore surface are not shown, allowing to view ions inside the pore. b,c) Distribution of ions along the z direction through the pore. l=3a (b) and 6a (c).
8
ACS Paragon Plus Environment
Page 9 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Nano Letters
l=3a and V = 1 V, as shown in Figure 3b (left panel), K+ concentrations peak at the nitrogen-terminated pore opening (z ∼-4 Å) while Cl− concentrations peak at the boronterminated pore opening (z ∼4 Å). Due to the proximity to the charged pore openings and the accumulation of counterions, the peak values are an order of magnitude higher than the bulk concentration ρb . Note that the concentrations approach the bulk value at about 1 nm away from the nanopore, suggesting that the height (11 nm) of our simulation system is large enough. For the same reason, when exiting the nanopore K+ and Cl− (coions of pore surface) concentrations are significantly reduced. Other peaks in the density distribution indicate the induced layering effect for ions close to nanopore openings. Overall, the distribution of ions yields a conducting state of the fluidic diode. On the other hand, with a reverse biasing voltage (V =-1 V), ions inside and around the nanopore are diminished as shown in the density distribution in Figure 3b (right panel), yielding a current-blocking state. Overall, the resulting rectification ratio, defined as I(+1 V)/I(-1 V), is 30.0 (Table 1), i.e. an excellent fluidic diode. When increasing the ion concentration to 0.6 nm−3 , due to the stronger electric screening, the rectification ratio is reduced to 9.1. Remarkably, when reducing the ion concentration to 0.06 nm−3 , the reverse current is nearly zero during the simulation time (likely due to the enhanced entropy barrier and significant overlap of electric double layers inside the nanopore), resulting in an infinitely large rectification ratio. For a larger nanopore l=6a, the Debye screening length (∼4.2 Å for the 0.3 nm−3 ion concentration) is smaller than the pore size and thus the charged surface only moderately influences the ion distribution. For example, with the forward biasing voltage (1 V), K+ concentrations (compared with ρ0 ) only increase and decrease by the same factor of 2 at the pore’s entrance and exit respectively (Figure 3c, left panel). With a reverse biasing (-1 V), ion concentrations are greatly reduced (Figure 3c, right panel), leading to a rectification ratio of 5.1 (Table:1). When changing ion concentrations to 0.06 and 0.6 nm−3 , rectification ratios slightly increase and decrease respectively (Table:1), suggesting that, when a pore is larger, factors other than the pore surface charge become more relevant for pore currents
9
ACS Paragon Plus Environment
Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
(see below). Table 1: Bulk concentration dependent rectification ratios, I(+1 V)/I(-1 V), when l=3a and l=6a. ρb (nm−3 ) 0.06 0.3 0.6 ratio (l=3a) ∞ 30.0 9.1 ratio (l=6a) 5.3 5.1 4.0 Besides varying ion concentrations, we further modeled ionic currents through nanopores with various sizes (l ≤28a) while fixing the ion concentration at 0.3 nm−3 . In each case, the calculated current was averaged over at least 40 ns of simulation time. Taking into account van der Waals radii of ions, sizes of water molecules associated with each ion and with pore-surface atoms, as well as energy barriers for entering a small pore, ionic currents are negligible when l
