Tuning Ion Transport through a Nanopore by Self-Oscillating Chemical

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Tuning Ion Transport through a Nanopore by Self-Oscillating Chemical Reactions Xiaoling Zhang, Xianwei Han, Shizhi Qian, Yuanjian Yang, and Ning Hu Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b05823 • Publication Date (Web): 05 Mar 2019 Downloaded from http://pubs.acs.org on March 12, 2019

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Analytical Chemistry

Tuning Ion Transport through a Nanopore by Self-Oscillating Chemical Reactions Xiaoling Zhang,† Xianwei Han,† Shizhi Qian,‡ Yuanjian Yang,§ Ning Hu†,* †

Key Laboratory of Biorheological Science and Technology, Ministry of Education, Chongqing University, Chongqing 400030, PR China ‡

Department of Mechanical and Aerospace Engineering, Old Dominion University, Norfolk, VA 23529, USA

§

School of Safety Engineering, Chongqing University of Science and Technology, Chongqing 401331, PR China

ABSTRACT: Ion transport in nanofluidic devices and biological ion channels are highly dependent on the local environmental conditions in the electrolyte solution. Many life processes in living systems are in dynamic electrolyte solutions, and many of them are self-oscillated. Tuning ion transport through a nanofluidic diode by the self-oscillating chemical reactions is demonstrated by modelling the electrokinetic ion transport process with a validated continuum model, which includes the time-dependent PoissonNernst-Planck equations for the ionic mass transport of multiple ionic species with both volumetric and surface chemical reactions, and Stokes equations for the flow field. A pH oscillator caused by oscillating chemical reactions (i.e., bromate-sulfite-ferrocyanide system) is added at the tip side of the nanopore to periodically change its surface charge properties, consequently tuning the ion selectivity and ion transport through the nanopore. Results show that both the surface charge density of the nanopore and the electrokinetic ion transport phenomena oscillate simultaneously with the pH oscillation generated by the self-oscillating chemical reactions. The numerical results obtained by our model qualitatively agree with the published experimental observations.

KEYWORDS: pH oscillator, Bromate-sulfite-ferrocyanide system, Ion transport, Nanofluidic, Ion selectivity

INTRODUCTION The synthetic nanopores have received significant attention as a research model of biological ion channels1-8. Fundamental understandings on the ion transport and the related phenomena in a nanopore are essential for the researches of biological ion channels and the advance of synthetic nanopores9. Several important phenomena, such as ion selectivity10,11, ion concentration polarization12, ion current rectification (ICR)13, have been found in the confined nano space. Tuning ion transport and the related phenomena in a nanopore could be achieved by changing the surface properties of nanopore12, the nanopore geometry14, the properties of fluids11 (including pH value, ionic species and concentration), the applied electric potential, etc. For example, recently Nandigana et al.15 reported a nanofuidic diode that produces rectification factors in excess of 1000 in conical nanopores by simply introducing asymmetry to the fluidic reservoirs. Many previous studies assumed that the nanopore was filled with a monovalent salt, such as KCl NaCl, and LiCl3,16-19. For example, Hsu et al.17 investigated the influences of three types of salt solutions, LiCl, NaCl, and KCl, on ICR in a conical nanopore, and found that the rectification factor for the case of LiCl is always the largest when the electroosmotic flow was not considered. In addition, ion transport in a nanofluidic channel filled with a multivalent electrolyte solution has been investigated to illustrate the influences of salt valences on the nanoscale electrokinetic transport20-27, and charge inversion by multivalent ions25-27 have been discovered. Since many nanofluidic applications use electrolyte mixtures instead of a single salt solution, recently, several studies21,28-31 investigated the nanoscale electrokinetic transport of electrolyte mixtures containing a number of different types of salts without volumetric reactions. For example, Prakash et al.31 reported that the addition of Mg2+ to NaCl solutions increased the maximum electroosmotic velocity, and Na+ was found to be preferentially attracted to the negatively charged silica wall compared with Mg2+. Fuest et al.21 systematically compared the transport of monovalent and divalent electrolytes and electrolyte mixtures through a gated nanofluidic device. Although many studies have been conducted on the theories and experiments of the ion transport and the related phenomena in a nanopore9-12,16-21,28-36, most of these studies usually investigated the ionic mass transport through a nanopore or nanofluidic channel under a steady-state environment, in which the electrolyte concentrations do not change with time. In living systems, however, many life processes are in dynamic environments and are sensitive to environmental pH change37-39. Many environments are selfoscillated, and such self-oscillation plays a very important role in living systems. Electrochemical oscillators could be used to create systems that mimic the behavior of oscillatory biological systems. Recently, Zhang et al. reported an oscillatory nanofluidic device,

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which is composed of a bullet-shaped nanochannel and a chemical oscillator, to generate periodic and continuous ion currents40. A pH oscillator was incorporated into the tip side of the bullet-shaped nanochannel to periodically change the surface charge properties of the nanochannel, and then the nanofluidic device oscillates between low and high ion-conductivity, leading to periodic ion current properties in the nanofluidic device40. Inspired by this device, we study, for the first time, the fundamental mechanism of tuning the electrokinetic ion transport in a conical nanopore by the self-oscillating chemical reactions. The theoretical model adopted in this study includes the Stokes equations for the flow field and the Poisson-Nernst-Planck (PNP) equations for the ionic transport of multiple ionic species with both volumetric and surface chemical reactions. In contrast to most previous studies reviewed in the aforementioned paragraphs which only considered the steady-state process with only a few ionic species and did not consider volumetric chemical reactions among the ionic species, in this study, a chemical oscillator occurring at the tip side of the nanopore induces time-dependent local environmental conditions, resulting in temporal and spatial changes of the charge properties of the nanopore wall and accordingly the ionic transport phenomena. Twelve ionic species (three cations and nine anions) and two kinds of molecules were considered in this study to model the self-oscillating chemical reactions. Compared with the previous studies using a fixed concentration gradient or pH gradient to tune ion transport in a nanopore11,41-43, both the ionic concentration gradient and pH gradient exist and they are also time-dependent in the current study. Our model is validated by the existing experimental results, and would be useful for the design of self-oscillating system for tuning the ionic transport process in nanofluidic systems.

MATHEMATICAL MODEL A conical nanopore of length LN is considered as schematically shown in Fig. 1. The radii of the tip and base side are, respectively, RT and RB, and the nanopore connects two big reservoirs on its both ends. The two reservoirs are of the same size with axial length LR and radius RR. The left reservoir (i.e., the tip side) is filled with an oscillating reaction solution of 75 mM NaBrO3, 90 mM Na2SO3, 15 mM K4Fe(CN)6, and 7.5 mM H2SO4. Both the nanopore and the right reservoir (i.e., the base side) are filled with a stable solution of 75 mM NaBr, 90 mM Na2SO4, 15 mM K3Fe(CN)6, and 7.5 mM K2SO4 at fixed pH = 10. The solutions are incompressible, Newtonian fluids with the same fluid properties such as density ρ and viscosity μ. We assume that the concentrations of ionic species on segment FG recover the values for the stable solution and that the concentrations of ionic species on segment OA recover the results of the ideal continuously-fed stirred tank reactor (CSTR) without considering the diffusion effects. An external electric potential bias, V0, is applied between segments OA and FG (i.e., the ends of the reservoirs) that are far from the nanopore. Considering the axially symmetric property of the conical nanopore, a cylindrical coordinate system (r, z) with origin at point O is used. The axial z coordinate is parallel to the axis of the nanopore while the radial r coordinate is perpendicular to that.

Figure 1. Geometry of a conical nanopore connecting two reservoirs. An electric potential bias was applied between segments OA and FG to produce an ionic current. Points C, M and D are on the inner nanopore wall, and points c, m and d are on the axis of the nanopore.

pH Oscillator. The NaBrO3-Na2SO3-K4Fe(CN)6-H2SO4 system, which is also called the Bromate-sulfite-ferrocyanide system (BSF system), was selected as the chemical oscillator on the tip side of the nanopore. Oscillating chemical reactions were employed in a CSTR arrangement (Fig. 2). On the tip side of nanopore, initial mixture of NaBrO3-Na2SO3-K4Fe(CN)6-H2SO4 has a reaction volume Vreactor. A solution of NaBrO3 was pumped slowly into the left reactor (i.e., the tip side of the nanopore) from inlet 1 at a certain flow rate (Qflow/2) and a mixture of Na2SO3, K4Fe(CN)6, and H2SO4 was pumped slowly from inlet 2 at the same rate (Qflow/2); meanwhile, the well-mixed reaction solution was pumped out at the flow rate of Qflow. In the BSF system, several factors could affect the oscillation state, including the initial concentrations, the normalized flow rate k0 (defined as the flow rate of feed solutions Qflow divided by the reaction volume Vreactor), and temperature. The original reaction model of the BSF system was proposed by Rábai, Kaminaga, and Hanazaki (i.e., RKH model)44. We employed the extended RKH model proposed by Sato et al45, as described in Table 1, to study the pH oscillation. The reactions, rate laws, and rate constants of the BSF system at 40 °C used in the simulation are also listed in Table 1. The extended RKH model, which includes the protonation equilibrium of ଶି ସ , is more accurate45, thus, is adopted in the current study.

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Figure 2. A schematic illustration of the experimental arrangement.

Table 1. Kinetic Model for Self-Oscillating Reactions45 Reaction

Rate law

Rate constant (40 °C)

R1

ି ା ଶି ଷ ൅ ֖ ଷ

ି ା r1 = k1[ଶି ଷ ][ ]-k’1[ଷ ]

k1=5.0×1010 M-1 s-1 k’1=5.0×103 s-1

R2

ା ି ଷ ൅ ֖ ଶ ଷ

ା r2 = k2[ି ଷ ][ ]-k’2[ଶ ଷ ]

k2=6.0×1010 M-1 s-1 k’2=1.0×109 s-1

R3

ି ଶି ି ା ͵ି ଷ ൅ ଷ ՜ ͵ସ ൅ ൅ ͵

ି r3 = k3[ି ଷ ][ଷ ]

k3=9.8×10-2 M-1 s-1

R4

ଶି ି ା ͵ଶ ଷ ൅ ି ଷ ՜ ͵ସ ൅ ൅ ͸

r4 = k4[ଶ ଷ ][ି ଷ]

k4=22.0 M-1 s-1

R5

ସି ା ି ି ଷ ൅ ͸ ሺሻ଺ ൅ ͸ ՜ ൅ ͸ ሺሻଷି ൅ ͵ ଶ ଺

r5 = k5[ ା ]/(k’5+ሾ ା ሿ)

k5=2.9×10-5 M s-1 k’5=8.0×10-4 M

R6

ା ൅ ି ֖ ଶ

r6 = k6[ ା ][ ି ]- k’6

k6=1.4×1011 M-1 s-1 k’6=1.4×10-3 M s-1

R7

ି ା ଶି ସ ൅ ֖ ସ

ି ା r7 = k7[ଶି ସ ][ ]-k’7[ସ ]

k7=1.0×1011 M-1 s-1 k’7=1.0×109 s-1

Governing equations for flow and ionic mass transport. A continuum-based model, which is comprised of highly coupled Stokes equations and Poisson-Nernst-Planck (PNP) equations14,46-48, is used to investigate the hydrodynamics, electrostatics, and ionic mass transport in the nanopore: Owing to extremely low Reynolds number of the electroosmotic flow, Stokes equations are used to describe the flow. ߩ

డ‫ܝ‬ డ௧

ൌ െ‫ ݌׏‬൅ ߤ‫׏‬ଶ ‫ ܝ‬൅ ۴ ,

(1) (2)

‫ ׏‬ή ‫ ܝ‬ൌ Ͳ, σே ௜ୀଵ ܿ௜ ऊ௜ ሻ‫߶׏‬

as the body force where u is the fluid velocity vector, F represents the electrostatic force with ۴ ൌ െߩ௘ ‫ ߶׏‬ൌ െሺ‫ܨ‬ on the fluid, and p is the fluid pressure. In the above, F is the Faraday constant, N is the total number of ionic species, ϕ is the electric potential, and zi and ci are, respectively, the valence and concentration of the ith ionic species. Nonslip boundary condition (i.e., u=0) is used on segments BC, CD, and DE (the entire nanopore wall) in Fig. 1. Since the walls of the two reservoirs are far from the nanopore, a normal flow with no external pressure gradient, i.e., p=0, is imposed on segments OA and FG, and slip boundary conditions are specified on the side walls of reservoirs (AB and EF). On the axis of the nanopore (segment OG), an axisymmetric boundary condition is applied. For the mass transport of multiple ionic species in the electrolyte solution, time-dependent Poisson-Nernst-Planck (PNP) equations are used for the electric potential ϕ and the concentration of ionic species ci. െߝ଴ ߝ௙ ‫׏‬ଶ ߶ ൌ ߩ௘ ൌ ‫ ܨ‬σே (3) ௜ୀଵ ܿ௜ ऊ௜ , డ௖೔ డ௧

൅ ‫ ׏‬ή ‫ۼ‬௜ ൌ ܴ௜ ,

(i=1,…,N).

(4)

The flux density Ni is defined as ‫ۼ‬௜ ൌ ‫ܿܝ‬௜ െ ‫ܦ‬௜ ‫ܿ׏‬௜ െ ऊ௜

஽೔ ோ்

‫ܿܨ‬௜ ‫ ߶׏‬,

(5)

where ε0 and εf are, respectively, the permittivity of the vacuum and the relative permittivity of the electrolyte solution; Ri is the reaction rate of the ith species described in Table 2; and Di, T and R are the diffusion coefficient, the absolute temperature, and the universal gas constant, respectively.


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Table 2. Reaction Rate of ionic species i

species

Ri

1

ା

-r1-r2+3r3+6r4-6r5-r6-r7

2

-r1 r1-r2-3r3

4

ଶି ଷ ଷି ସି

5

ଶ ଷ

r2-3r4

6

ି ଷ ଶି ସ ି

3r3+3r4-r7

3

7 8 9 10 11

r7 -r3-r4-r5

r3+r4+r5

ሺሻସି ଺ ሺሻଷି ଺ ି

-6r5

6r5 -r6

12

13

ା

0

14

H2O

3r5+r6

ା

0

The electric potential between the nanopore is imposed on the reservoirs’ ends (OA and FG), i.e., ϕ(on the anode) = V and ϕ(on the cathode) = 0. The concentrations of ionic species on FG recover the values for the stable solution, while the concentrations of ionic species on OA recover the ideal CSTR reaction results without considering the diffusion effects. In other words, the concentration of each species at boundary OA is specified based on the results of the CSTR system. Zero surface charge (i.e., ‫ ܖ‬ή ‫ ߶׏‬ൌ Ͳ) boundary condition and zero normal ionic fluxes (i.e., ‫ ܖ‬ή ‫ۼ‬௜ ൌ Ͳ) are applied on segments AB and EF (the side wall of the reservoirs). The entire nanopore surface (segments BC, CD, and DE) is ion-impenetrable (i.e., ‫ ܖ‬ή ‫ۼ‬௜ ൌ Ͳ) and also bears a surface charge density σw (i.e., െ‫ ܖ‬ή ‫ ߶׏‬ൌ ߪ௪ Τሺߝ଴ ߝ௙ ሻ). Here, n is the unit normal vector of these surfaces. Along the axis of the nanopore (segment OG), the boundary conditions for the ionic concentration ci and electric potential ϕ are specified by an axial symmetry condition. Assuming that the nanopore is made of a polymeric material containing the acidic functional group AH with dissociation reaction ՞ ି ൅ ା , thus the reaction could be regulated by the local concentration of H+. The surface charge density of the nanopore stemming from the above surface dissociation reaction is49,50 ߪ௪ ൌ െ‫ܨ‬ሺȞ୅ష ሻ ൌ െ‫ ܨ‬ቄ

௄ఽ ே ఽ ௄ఽ ାሾୌశ ሿೢ

ቅ.

(6)

Here, KA is the equilibrium constant of the dissociation reaction, and NA is the number site density of AH group on the inner wall of the nanopore. σw relies on the nanopore material’s properties (pKA and NA), and the local concentration of H+ (i.e., local pH value) on its wall surface. Thus, the self-oscillating reactions can influence σw of the nanopore. For the polymeric nanopores, pKA is approximately 3.8, and NA ranges from 1 to 1.5 nm-2 51 and choose NA = 1 nm-2 in this study. The induced ionic current through the nanofluidic device is calculated by integrating the current density along the electrode surface14,46-48. (7) ‫ ܫ‬ൌ ‫ܨ ׬‬ሺσே ௜ୀଵ ऊ௜ ‫ۼ‬௜ ሻ ή ‫ܵ݀ܖ‬ǡ with S being the opening of either reservoir.

RESULTS AND DISCUSSIONS The developed model is numerically solved by COMSOL Multiphysics 5.3 (www.comsol.com). In the present study, the radius of the nanopore’s tip is RT = 7 nm and its base RB = 43 nm. To reduce the scale of computation, the conical nanopore has a relatively short length with LN = 200 nm. The axial length and radius of both reservoirs are LR = RR = 200 nm, respectively. A small fillet is used to smooth the connections between the nanopore and the reservoirs and the radius of the fillet is 0.2RT. The following parameters’ values are used in the computation: μ = 1 × 10-3 Pa·s, ε0 = 8.854187817 × 10-12 F/m, εf = 80, ρ = 1 × 103 kg/m3, R = 8.31 J/(K·mol), T = 313.15 K, and F = 96490 C/mol. The valences (zi) and the diffusion coefficients (Di) of related ionic species and molecules are given in Table 3. pH Oscillator. Edblom et al.52 discovered the oscillation phenomena in the BSF system when conducting oxidations of ଶି ଷ and ି ሺሻସି ଺ by ଷ . The pH of this system oscillates between ~3 and ~7. The original RKH model including only R1-R5 is not sufficiently accurate45, and has a large discrepancy from the experimental results in the minimum of pH value, which is less than ି 45 ା nearly 2 pH units. Later, the RKH model was improved by adding R7 ሺଶି ସ ൅ ֖ ସ ) . In this study, we use the extended RKH model to study the pH oscillation phenomena of the BSF system. We use the Reaction Engineering module in COMSOL to simulate the pH oscillating reactions. The initial concentrations used in the simulation are [NaBrO3]0 = 75 mM, [Na2SO3]0 = 90


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mM, [K4Fe(CN)6]0 = 15 mM, and [H2SO4]0 = 7.5 mM. The flow rate of feed solutions is set to 2 × 10-6 m3/min, and the reaction volume of the CSTR is set to 4× 10-5 m3, thus the normalized flow rate k0 is 0.05 min-1. The stirring rate is not considered in this simulation. Table 3. Valences and Diffusion Coefficients species

zi

Di (cm2/s)

References

ା

+1

9.0e-5

53

ଶି ଷ

-2

1.1e-5

53

ଷି

-1

1.5e-5

53

ସି

-1

1.33e-5

53

ଶ ଷ

0

1.6e-5

53

ି ଷ

-1

1.485e-5

54

ଶି ସ ି

-2

1.065e-5

53

-1

2.084e-5

54

ሺሻସି ଺

-4

0.735e-5

53

ሺሻଷି ଺

-3

0.309e-5

55

ି

-1

5.26e-5

53

ା

+1

1.334e-5

54

ା

+1

1.96e-5

9

H2O

0

2.13e-5

Fig. 3 shows our numerical results of the reaction system. The black, red, blue, violet and green lines correspond to the concenି ସି ି ଶି ି + + tration profiles of ሾଶି ଷ ሿ, ሾଷ ሿ, ሾ ሺሻ଺ ሿ, [H ], and ሾଷ ሿ, respectively. [H ] oscillates in antiphase with ሾଷ ሿ, ሾଷ ሿ, ସି ି 45,53 ሾ ሺሻ଺ ሿ and ሾଷ ሿ, which is consistent with the simulation results from the literatures . The corresponding pH showing in Fig. 3B agrees well with the result from Sato et al.45, which is depicted by the dashed line in Fig. 3B. At the equilibrium state, the pH of the reacting system oscillates between 3.52 and 6.67 at 40 °C, and the period of pH oscillation is ~547 s.

ି ૝ି ି + Figure 3. (A) Concentrations profiles of ሾ‫۽܁‬૛ି ૜ ሿ, ሾ۰‫۽ܚ‬૜ ሿ, ሾ۴‫܍‬ሺ۱‫ۼ‬ሻ૟ ሿ, [H ], and ሾ۶‫۽܁‬૜ ሿ, respectively. (B) oscillating pH.


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Figure 4. The pH oscillator result and the local pH at Points C, M and D (A) and ionic current (B) in a nanopore under an applied voltage of 1V.

Ionic transport in a nanopore. Fig. 4A depicts the pH caused by the pH oscillator and the local pH at the nanopore wall (i.e., Points C, M and D in Fig. 1) as a function of time. After the first cycle, pH of the CSTR system (at the boundary OA) continuously oscillates between 3.52 and 6.67. As the nanopore wall is negatively charged and H+ ions are attracted towards the nanopore wall, pH at Points C, M, D are typically lower than the bulk pH caused by the pH oscillator. Fig. 4B shows an oscillating ionic current through the nanopore when ϕ(on the anode) = 1 V. Under the applied voltage of 1 V, the period of the ion current oscillation is approximately 547 s with the amplitude of approximately 46.5 nA after reaching the equilibrium state (the second period). In addition, the ionic current oscillates simultaneously with the pH variation caused by BSF system. Although the amplitude of the ion current has a small deviation from the experimental data from Zhang et al.40, which could be caused by the differences of the applied voltage and nanopore geometry, the trend of the oscillating ion current obtained by our model is quite consistent with the experimental results from the literature40. Since pH of the solution oscillates during the process, local surface charge density,σw, temporally oscillates and becomes spatially dependent. Fig. 5 illustrates the surface charge density, σw, at three points (Points C, M and D in Fig.1) along the inner nanopore wall versus time. Obviously, the surface charge density varies temporally and spatially along the nanopore wall. Compared with those located at Points M and D, σw at Point C has the largest variation. It is because Point C connects the left reservoir, where the pH oscillating reactions mainly occur. As shown in Fig. 4A, the oscillation amplitude of pH decreases as the distance from the left reservoir increases. Since σw highly depends on the local pH, the oscillation magnitude of σw also decreases as the distance from the left reservoir (the tip side) increases. After reaching the equilibrium state, σw oscillates between -44.2 (at corresponding pH =3.52) and -116.0 mC/m2 (at corresponding pH =6.67) at the middle of the nanopore wall (Point M). The concentration of H+ decreases (increases) from pH=3.52 to pH=6.67 (from pH=6.67 to pH=3.52), thus inducing more (less) negatively charged A− dissociated from the AH groups on the nanopore wall, yielding higher (lower) negative surface charge density. Since the stable solution at the end of the right reservoir is maintained at pH=10, the nanopore wall near the right reservoir is more negatively charged, resulting in higher negative surface charge density on point D than the points of C and M.


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Figure 5. Surface charge density (σw) at three points (Points C, M, D in Fig. 1) along the inner nanopore wall.

Figure 6. Cp at three points (Points C, M, and D) along the inner nanopore wall.

To further understand the ion transport regulated by the pH oscillator, Fig. 6 shows the total ionic concentration of positive ions (Na+, K+, and H+) at three points (Points C, M and D in Fig. 1), Cp=[Na+]+[K+]+[H+]. Since the nanopore wall is negatively charged, many positive ions are accumulated inside the nanopore due to electrostatic interaction. Owing to the oscillation of the surface charge density as shown in Fig. 5, ionic concentration, Cp, also oscillates. This trend is consistent with the distribution of the surface charge density as presented in Fig. 5. After reaching equilibrium state, at the same time the concentration of positive ions at the middle of the nanopore is lower than that at the base, which is higher than that at the tip. In the BSF system, Na+ and K+ ions do not participate in the chemical reactions, and initially have a uniform distribution in the entire nanopore and reservoirs. Thus, the re-distributions of Na+ and K+ are mainly caused by the electrostatics force arising from the external electric field and the charged nanopore wall. As local pH increases from 3.52 to 6.67 (from t=1000.9 s to t=1262.9 s), the magnitude of the nanopore’s negative surface charge density increases, leading to more Na+ and K+ ions electrostatically attracted into the nanopore and accordingly an increase in the concentration of positive ions. When pH decreases from 6.67 to 3.52, the surface charge density decreases, yielding less positive ions accumulated in the nanopore. Note that at high negative surface charge density near the tip, the corresponding concentration of H+ ions is low. This is why the total concentration of positive ions is lower than that at the middle of the nanopore due to less H+ ions. Fig. 7 illustrates the magnitude of fluid velocity at three points (Points c, m, d in Fig. 1) and the variation in flow rate with time when a positive potential bias is applied on the anode. The flow rate also oscillates with the pH oscillator. As the nanopore wall is negatively charged, cations always dominate over anions inside the nanopore, and the EOF is always directed from the tip of the nanopore to the base. In addition, as the pH increases from 3.52 to 6.67 (from t=1000.9 s to t=1262.9 s), the EOF velocity increases due to the increase in the magnitude of negative surface charge density. The flow rate increases, implying that the nanopore state changes from closed to open status. Although there is no pressure gradient is imposed at both ends of the nanopore, due to the geometric variation of the conical nanopore, a pressure gradient is induced inside the nanopore, especially near the tip. The temporal variation of the surface charge density also induces an oscillating pressure gradient with respect to time, as shown in Fig.S1 of the Supporting Information. The flow is driven by the externally applied electric field and the induced pressure-gradient. Due to the spatial change of the cross-section area, the axial electric field inside the nanopore is not uniform along its axis. Fig.S2 of the Sup-


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porting Information depicts the variation of the axial electric field as functions of both time and z-axis. The axial electric field in the two reservoirs is relatively uniform, and its magnitude is much lower than that inside the nanopore. The highest axial electric field occurs at the tip of the nanopore owing to the smallest cross-section area. The axial electric field also oscillates with time due to the oscillation of the surface charge density of the nanopore wall.

Figure 7. Magnitude of fluid velocity at three points (Points c, m, d) on the axis of the nanopore (A) and the flow rate (B).

The period and magnitude of the nanofluidic oscillator could be controlled by the oscillation reactions, which could be changed by the initial concentrations, k0, temperature, and other factors. Fig. 8 shows when changing the ionic concentrations (left column) and the normalized flow rate k0 (right column), the oscillation states of nanopore could be changed. In the left column of Fig. 8, the oscillating reaction solution contains 65 mM NaBrO3, 75 mM Na2SO3, 20 mM K4Fe(CN)6, and 10 mM H2SO4. Accordingly, the stable solution contains 65 mM NaBr, 75 mM Na2SO4, 20 mM K3Fe(CN)6, and 10 mM K2SO4 at pH=10. We can see that this pH oscillator has a shorter period, ~347 s and pH oscillates between 3.64 and 5.87. Accordingly, the period and amplitude of the ion current oscillation also change (Fig. 8A) and this occurs because σw oscillates with the pH oscillator (Fig. 8B). In the right column of Fig. 8, compared with Fig. 4, the ionic concentrations keep the same, while the flow rate of feed solutions is set to 4 × 10 -6 m3/min with k0 =0.1 min-1. The period of the ion current oscillation is approximately 770.0 s and the amplitude is approximately 49.3 nA. Thus, we can control the open/closed states of nanopore and its frequency, which could be useful to detect individual molecules and mimic the behavior of oscillatory biological systems.


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Figure 8. The oscillation states changed by the ionic concentrations (left column) and k0 (right column).

CONCLUSIONS The ion transport in nanofluidic devices and biological ion channels depends on the local environmental conditions. Many life processes in living systems are in dynamic and self-oscillating electrolyte solutions. Electrokinetic ion transport in a periodically oscillating nanofluidic system was studied using a continuum-based model that consists of the coupled Poisson-Nernst-Planck equations for the ionic mass transport of multiple ion species and the Stokes equations for the flow field. Compared with most existing studies, in which only a few ionic species without reactions were studied, in this study, a chemical oscillator was added at the tip side of the nanopore, causing the pH of the background salt to oscillate between 3.52 and 6.67. Results show that the local pH, surface charge density, ionic current, and electroosmotic flow oscillate simultaneously with the oscillation of H+ concentration caused by BSF system, and the electrokinetic ion transport in the nanofluidic system can be regulated by the species concentrations and flow rate of the self-oscillating chemical reaction system, which provides another way to actuate the open/close state of the nanofluidic device.

ASSOCIATED CONTENT Supporting information Results of the variations of the axial pressure gradient (Figure S1) and the axial electric field (Figure S2) in reservoirs and across the nanopore.

AUTHOR INFORMATION ACS Paragon Plus Environment

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Corresponding Author *E-mail: [email protected].

Author Contributions All authors have given approval to the final version of the manuscript.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Nos. 21827812, 31571005, 81871450), the Fundamental Research Funds for the Central Universities (No. 2018CDXYSW0023), the Natural Science Foundation of Chongqing (No. cstc2018jcyjAX0389), and the Program of International S&T Cooperation (No. 2014DFG31380).


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Tuning Ion Transport through a Nanopore by Self-Oscillating Chemical

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