Theory of Transport-Induced-Charge Electroosmotic Pumping toward

Subscriber access provided by Kaohsiung Medical University

Article

Theory of Transport-Induced-Charge Electroosmotic Pumping toward Alternating Current Resistive Pulse Sensing Wei-Lun Hsu, Junho Hwang, and Hirofumi Daiguji ACS Sens., Just Accepted Manuscript • DOI: 10.1021/acssensors.8b00635 • Publication Date (Web): 23 Oct 2018 Downloaded from http://pubs.acs.org on October 24, 2018

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 23 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

ACS Sensors

Theory of Transport-Induced-Charge Electroosmotic Pumping toward Alternating Current Resistive Pulse Sensing Wei-Lun Hsu,* Junho Hwang, and Hirofumi Daiguji Department of Mechanical Engineering, The University of Tokyo, Tokyo 113-8656, Japan E-mail: [email protected]

Abstract In this work we study transport-induced-charge electroosmosis toward alternating current resistive pulse sensing for the next generation of biomedical applications. Transport-induced-charge electroosmosis, being a new class of electrokinetic phenomenon, occurs as a salt concentration gradient works in synergy with an electric field in ultrathin nanopores. Apart from the conventional electric double layer-governed electroosmotic flow in which the flow behavior is subject to the surface charge, it is found that the transport-induced-charge electroosmotic flow behaves independently of surface charge magnitude but can be linearly regulated by the bulk salt concentration bias. The reversal of the electric field simultaneously inverses the induced charge allowing the establishment of a unidirectional flow under the application of a periodic alternating current field. This unique phenomenon permits continuous water and nanoparticles pumping through a two-dimensional material nanopore in spite of the reversal of the electric field. Built upon this mechanism, we propose a theoretical prototype of alternating current resistive pulse sensing in a two-dimensional nanopore system.

1

ACS Paragon Plus Environment

ACS Sensors 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

Keywords Alternating current; Electrokinetic pumping; Resistive pulse sensing; Salt gradient; Twodimensional nanopore

2


Page 2 of 23

Page 3 of 23 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

ACS Sensors

Water and charged particles transport through nanopores 1,2 is pivotal in manifold nanofluidic applications including resistive pulse sensing, 3,4 drug delivery, 5 sea water desalination, 6 nanofluidic battery 7,8 and reverse electrodialysis. 9,10 According to the Hagen-Poiseuille law of fluid dynamics, 11 the flow rate of the pressure-driven flow in a cylindrical channel varies inversely proportional to the fourth power of its radius. In contrast, the Smoluchowski equation for electroosmotic flow 12 indicates the electrokinetic transport behavior is governed by the surface charge condition and the dimension of the channel has relatively marginal effects on the electroosmotic mobility. Therefore, in terms of transport of aqueous solutions in confined space, electrokinetic methods are extensively used in micro/nanofluidic systems. 13 Albeit both direct current and alternating current systems have been used for electroosmotic pumping in nanopores, 14,15 the direct current electroosmotic pumping could suffer from the notorious issues of bubble formation, electrode degradation, hydrodynamic instability, etc. originating from the redox reactions at the electrodes. These daunting problems stimulate the emergence of alternating current electroosmotic pumping as an appealing approach with potentially higher stability. 16,17 A typical kind of alternating current electroosmotic pumping was established upon the induced-charge electrokinetics theory 18–20 for dielectric materials, that the induced charge in a polarizable material simultaneously inverses as the direction of the electric field reverses maintaining a continuous flow in a consistent direction. Bazant and Ben 21 theoretically designed a three-dimensional alternating current electroosmotic pumping microfluidic system achieving high flow rates using low battery voltages. On the other hand, for nonconductive materials whose surface charge is independent of the external electric field, the working principle can rely upon the asymmetric geometry caused electroosmotic flow rectification. Kneller et al. 22 investigated alternating current electroosmotic pumping in nanofluidic funnels demonstrating both ionic current and electroosmosis rectification phenomena. In a similar vein, Wu et al. 17 reported an alternating current electroosmotic pump using a conical nanopore array membrane that a representative electroosmotic flow rectification characteristic was observed resulting in an obvious pumping

3


ACS Sensors 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

characteristic. Nevertheless, both alternating current electroosmotic pumping scenarios cannot be applied to nanopore resistive pulse sensing. Not only does the integration of dielectric materials onto a nanopore require sophisticated fabrication techniques, but the interaction between the analytes and electrically polarized dielectric material will also significantly hinder the translocation events. Not to mention the current leakage through the dielectric material would be another formidable challenge. For asymmetric nanopores although they could facilitate recapture of molecules for investigating individual translocation events, 23 the oscillating flow directions would lead to inaccurate results when estimating the analyte concentration. Furthermore, it has been observed that the electric double layer-based electroosmotic response behaves nonlinearly to the surface charge density at the nanoscale due to the presence of viscoelectric effects arising from the orientation of water molecules in the vicinity of charged surfaces. By clarifying the concepts of viscoelectric immobile 24 and viscoelectric layers using a continuum model, Hsu et al. 25 pointed out that the electroosmotic mobility may decrease as surface charge density increases elucidating previous molecular dynamics results. 26 Confronting these obstacles, undoubtedly a new alternating current electroosmotic pumping strategy is needed to pave a way toward alternating current resistive pulse sensing for the next generation of diagnosis applications. We herein suggest a different approach to control electroosmotic flow using the transportinduced-charge mechanism via the manipulation of a salt concentration gradient across ultrathin nanopores, instead of utilizing the charges from an electric double layer. Prior research 27,28 has shown that ionic charges can be induced in nanoconfinement filled with an electrolyte solution during the ion transport process in a nonuniform electric field intensity environment (which can be accomplished by adding a salt concentration gradient). Employing a classical transport model using the Possion-Nernst-Planck and Navier-Stokes equations, Zhu et al. 27 indicated that the local transport-induction of inversed screening charges in a nanochannel could give rise to vortical electroosmosis. He et al. 28 revealed that

4


Page 4 of 23

Page 5 of 23 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

ACS Sensors

the salt-gradient-induced ionic charge accummulation at the junction of the nanopore and reservoir could significantly influence the DNA translocation behavior through a nanopore. Inspired by these untypical charge and flow behaviors, in this study we propose a transportinduced-charge-based alternating current electroosmotic pumping strategy for alternating current resistive pulse sensing applications. We identify that the transport-induced-charge electroosmotic flow can provide a unidirectional flow under an alternating current field. The physical mechanism and effects of key parameters (including nanopore dimensions, solute concentration, operating frequency, ionic diffusivity and surface charge density) on the transport-induced-charge electroosmotic flow behavior are investigated. Finally, we show the alternating current resistive pulse sensing system accomplishes continuous transport of nanoparticles though a two-dimensional material nanopore for current blockage measurements.

MODELING Transport-Induced-Charge Phenomena in Ultrathin Nanopores Firstly, we investigate direct current transport-induced-charge behavior for an uncharged nanopore (20 nm in length 𝐿 and 5 nm in diameter 𝑑) connecting with two electrolyte solutions carrying different potassium chloride concentrations. The average bulk potassium chloride concentration 𝑛0 (being the arithmetic mean of the electrolyte concentrations in two reservoirs) is assigned at 1 M. 3,29,30 As an electrolyte concentration difference ∆𝑛0 is imposed, the higher salt concentration in the left reservoir 𝑛H and lower salt concentration in the right reservoir 𝑛L become 𝑛0 + ∆𝑛0 /2 and 𝑛0 − ∆𝑛0 /2, respectively. In addition to the salt concentration gradient, an electric potential difference ∆𝜑 (being defined as 𝜑right − 𝜑left , where 𝜑right and 𝜑left are the electric potential in the right and left reservoirs, respectively) is concurrently applied across the nanopore. The electrokinetic behavior of the incompressible electrolyte solution is simulated by employing the Possion-Nernst-Planck, continuity and 5


ACS Sensors 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

Navier-Stokes equations as follows :

31

∇ · 𝜖∇𝜑 = −

𝜌

Page 6 of 23

𝜌e 𝜖0

(1)

[︁ (︁ )︁]︁ 𝜕𝑛𝑖 + ∇ · 𝑛𝑖 𝑣 − 𝐷𝑖 ∇𝑛𝑖 + 𝜇𝑖 𝑛𝑖 ∇𝜑 = 0 𝜕𝑡

(2)

∇ · (𝜌𝑣) = 0

(3)

(︁ 𝜕𝑣 𝜕𝑡

)︁

+ 𝑣 · ∇𝑣 = −∇𝑝 + ∇ · 𝜂∇𝑣 − 𝜌e ∇𝜑

(4)

In these expressions, 𝜖, 𝜖0 , 𝜑, 𝜌𝑒 , 𝑣, 𝜌, 𝑝 and 𝜂 are the dielectric constant, permittivity of vacuum, electric potential, space charge density, velocity vector of the solution, solvent density, pressure and viscosity, respectively. 𝐷𝑖 , 𝑛𝑖 and 𝜇𝑖 (=

𝑞𝑖 𝐷𝑖 𝑘B 𝑇a

where 𝑞𝑖 is the charge

of ions, 𝑘B is Boltzmann’s constant and 𝑇a is the absolute temperature) are the diffusivity, concentration and mobility of the ionic species 𝑖, respectively, where the subscript 𝑖 denotes “ + ” for cations and “ − ” for anions. In the Navier-Stokes equation (Eq.(4)), the pressure force −∇𝑝, viscous drag ∇ · 𝜂∇𝑣 and electric body force −𝜌e ∇𝜑 are taken into account where the variation of 𝜂 due to the influence of local electric field is neglected. It is worth mentioning that for steady-state direct current electroosmotic pumping,

𝜕𝑛𝑖 𝜕𝑡

= 0 and

𝜕𝑣 𝜕𝑡

=

0. At the nanopore and electrolyte solution interface, we consider the surface is non-slip and impermeable to ions and both the nanopores and nanoparticles are nonconductive. These lead to the following boundary conditions :

25

𝑣=0

(5)

𝑛 · 𝐽𝑖 = 0

(6)

𝑛 · ∇𝜑 =

6

𝜎 𝜖𝜖0


(7)

Page 7 of 23 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

ACS Sensors

Figure 1: Boundary conditions applied on a hybrid mesh consisting of structured and unstructured grids in two-dimensional cylindrical coordinates (𝑟, 𝑧). The origin is anchored at the center of the nanopore. (︁ )︁ where 𝐽 𝑖 = 𝑛𝑖 𝑣 − 𝐷𝑖 ∇𝑛𝑖 + 𝜇𝑖 𝑛𝑖 ∇𝜑 is the ionic flux of the ionic species 𝑖 and 𝜎 denotes the nanopore surface charge density. In the bulk, we consider the flow is fully developed, the ion concentrations are equal to the solute concentration and the constant electric potential is assigned according to the applied electric potential bias. These boundary conditions are summarized as shown Figure 1. These coupled partial differential equations are numerically resolved by an implicit finite volume method 32 in a hybrid mesh consisting of structured and unstructured grids. The simulation results of ionic concentration distributions are shown in Figure 2 (see Supporting Information 1 for a sensitivity analysis). Figure 2a,b indicates that as an electric potential difference is applied to an electrolyte concentration biased nanopore, the electroneutrality could be locally unsatisfied inside the nanopore (although it must be achieved if considering the whole solution). 27,33 A similar phenomenon has been reported in a much larger system of lithium ion batteries by Rademaker et al. 33 who concluded that the deviations of electroneutrality do exist in a nonuniform concentration solution but are marginal enough to be ignored (< 10−7 % of the electrolyte concentrations). However, since the miniaturization of the system elevates the ionic concentration gradient and electric field magnitudes, these electroneutrality deviations become remarkable at the nanoscale. It must be pointed out that the sign of this transport-induced-charge dependents upon

7


ACS Sensors 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

Figure 2: Contours of the ion concentration difference 𝑛+ −𝑛− in an uncharged nanopore, (a) as the salt concentration gradient ∇𝑛0 is in the same direction to the external electric field 𝐸 (Case I) and (b) as ∇𝑛0 is opposite to 𝐸 (Case II), at the average salt concentration 𝑛0 = 1 M, bulk concentration difference ∆𝑛0 = 0.4 M, electric potential difference |∆𝜑| = 10 V, pore length 𝐿 = 20 nm and pore diameter 𝑑 = 5 nm. Variations of (c) the ion concentrations 𝑛+ , 𝑛− for the Case I (the solid and dashed curves indicate 𝑛+ and 𝑛− , respectively) and (d) the ion concentration difference 𝑛+ − 𝑛− (the solid curves are for the Case I and dashed curves are for the Case II where 𝑧 = 0 is anchored at the center of the nanopore) at different ∆𝑛0 . The gray shadow areas in (c) and (d) highlight the nanopore region. the relative directions of the salt concentration gradient ∇𝑛0 and electric field 𝐸. When ∇𝑛0 is in the same direction to 𝐸 (referred as Case I), negative charges appear in the surfaceuncharged nanopore. In contrast, as the direction of 𝐸 is reversed to the opposite direction to ∇𝑛0 (referred as Case II), positive charges are induced, meaning the local concentration of cations 𝑛+ is higher than that of anions 𝑛− . When ∆𝑛0 between the two reservoirs is enlarged, the magnitude of the local ion concentration difference 𝑛+ − 𝑛− increases implying that the local charge intensity can be controlled by altering the bulk salt concentrations as shown in Figure 2c,d. 8


Page 8 of 23

Page 9 of 23 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

ACS Sensors

Figure 3: Schematic illustrations of the (a) conventional electric double layer electroosomtic flow (EDL EOF) in a charged nanopore filled with a uniform bulk salt concentration solution and (b) transport-induced-charge electroosmotic flow (TIC EOF) in an uncharged nanopore simultaneously imposed with a salt concentration gradient ∇𝑛0 and an electric field 𝐸 in the axial direction. 𝐽 +,cond , 𝐽 −,cond , 𝐽 +,diff and 𝐽 −,diff represent the conductive ionic flux of cations, conductive ionic flux of anions, diffusive ionic flux of cations and diffusive ionic flux of anions, respectively. (c) Variaions of 𝐽 +,diff and 𝐽 −,diff in the 𝑧-direction along the nanopore centerline. The gray shadow area highlights the nanopore region.

9


ACS Sensors 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 10 of 23

The transport-induced-charge mechanism can be elucidated by analyzing the nonequivalent ionic fluxes of cations 𝐽 + and anions 𝐽 − through the nanopore summarized in Figure 3 (where Figure 3a illustrates the conventional electric double layer system for comparison). The ionic fluxes 𝐽 + and 𝐽 − in the axial direction, composed of the advective ionic flux 𝐽 𝑖,adv , diffusive ionic flux 𝐽 𝑖,diff and conductive ionic flux 𝐽 𝑖,cond , can be described as follows :

𝐽 + = 𝑛+ 𝑣 +(−𝐷+ ∇𝑛+ ) + (−𝜇+ 𝑛+ 𝐸) ⏟ ⏞ ⏟ ⏞ ⏟ ⏞

(8)

𝐽 − = 𝑛− 𝑣 +(−𝐷− ∇𝑛− ) + (−𝜇− 𝑛− 𝐸) ⏟ ⏞ ⏞ ⏟ ⏟ ⏞

(9)

𝐽+,adv

𝐽−,adv

𝐽+,diff

𝐽−,diff

𝐽+,cond

𝐽−,cond

Provided that the advective fluxes 𝐽 +,adv and 𝐽 −,adv do not contribute to the driving force, they are herein neglected in this discussion but will be included in our simulations. As illustrated in Figure 3b, when 𝐸 is applied toward the high concentration end, the directions of 𝐽 +,diff and 𝐽 +,cond are opposite to each other whereas both 𝐽 −,diff and 𝐽 −,cond point toward the low concentration end. As the concentration difference is present, the conductivity difference between two reservoirs renders unequal 𝐽 𝑖,cond between the nanopore junctions. Therefore, a difference between 𝐽 +,diff and 𝐽 −,diff is initiated to satisfy the conservation of ions (given that the integral of 𝐽 𝑖 over the cross-sectional area along the 𝑧-direction is constant). The variations of 𝐽 +,diff and 𝐽 −,diff along the nanopore centerline are plotted in Figure 3c. Clearly, due to the opposite directions of 𝐽 +,diff and 𝐽 +,cond , 𝐽 +,diff at the high concentration junction becomes larger than 𝐽 −,diff and an opposite trend occurs at the low concentration end, yielding different distributions of 𝑛+ and 𝑛− inside the nanopore. As a response to the electric force imposing onto the transport-induced-charge, the charged solution inside the nanopore is electroosmotically driven as shown in Figure 4a,b. In case of negative transport-induced-charge (i.e., the Case I), the electric force drags the solution toward the opposite direction of 𝐸 resulting in a transport-induced-charge elec-

10


Page 11 of 23 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

ACS Sensors

Figure 4: Contours of the flow field |𝑣| with streamlines in an uncharged nanopore, (a) as ∇𝑛0 is in the same direction to 𝐸 (Case I) and (b) as ∇𝑛0 is opposite to 𝐸 (Case II), at 𝑛0 = 1 M, ∆𝑛0 = 0.4 M, |∆𝜑| = 10 V, 𝐿 = 20 nm and 𝑑 = 5 nm. Variations of the average flow velocity 𝑣ave and maximum flow velocity 𝑣max in the middle of the nanopore (c) as a function of ∆𝑛0 at different pore diameter 𝑑 (𝑛0 = 1 M, |∆𝜑| = 10 V and 𝐿 = 20 nm) and (d) as a function of pore length 𝐿 at different |∆𝜑| (𝑛0 = 1 M, ∆𝑛0 = 0.4 M and 𝑑 = 5 nm). troosmotic flow from the high concentration end to the low concentration end. On the other hand as the positive charges are induced (i.e., the Case II), the solution is propelled toward the direction of 𝐸 opposite to that of ∇𝑛0 . Consequently, regardless of the inversion of charge, the transport-induced-charge electroosmosis flows in a consistent direction from the high concentration reservoir to low concentration reservoir for both cases. For potassium chloride solutions where the ionic diffusivities of cations and anions are approximately equal (≈ 2×10−9 m2 /s), the flow magnitudes of two cases are identical. Figure 4c shows the effects of ∆𝑛0 on the flow velocity 𝑣 in the nanopores with different pore diameter 𝑑. It is worth highlighting that in an ultrasmall nanopore (e.g., 𝑑 = 5

11


ACS Sensors 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 12 of 23

nm), 𝑣 responses directly proportional to ∆𝑛0 while this linear dependence vanishes in larger nanopores (e.g., at 𝑑 = 10 nm), suggesting that the transport-induced-charge electroosmotic flow can be linearly controlled by the bulk concentrations in ultra-tiny nanopores. Figure 4d reveals the uniqueness of transport-induced-charge electroosmosis to the nanoscale that 𝑣 drops rapidly with the increase of 𝐿. Within the investigated |∆𝜑| range (i.e., 5 V and 10 V), the transport-induced-charge electroosmotic flow becomes negligible as the pore is longer than 100 nm. When the nanopore is elongated, both ∇𝑛0 and 𝐸 decrease mitigating transport-induced-charge effects. At the other extreme, when the nanopore length is ultimately thin (e.g., for two-dimensional material nanopores), a subtle concentration difference due to ion concentration polarization across the charged nanopore could trigger significant transport-induced-charge electrokinetic phenomena (even without the presence of a bulk salt concentration difference). Under such circumstances, the superposition of the electric double layer electroosmosis and transport-induced-charge electroosmosis leads to nonlinear DNA translocation behavioir (see Supporting Information 2 in more detail).

Alternating Current Transport-Induced-Charge Electroosmotic Pumping The unique characteristic of the transport-induced-charge electroosmotic flow shown in Figure 4a,b allows the direct control of a unidirectional flow in nanopores using alternating current fields. As a time-dependent sinusoidal electric potential difference ∆𝜑(𝑡) :

∆𝜑(𝑡) = 𝜑max sin (2𝜋𝑓 𝑡)

(10)

is applied across the nanopores (where 𝜑max , 𝑓 and 𝑡 are the peak voltage, frequency and time, respectively), an alternating current transport-induced-charge electroosmotic flow from the high to low concentration ends is established despite the reversal of 𝐸 as depicted in Figure 5a.

12


Page 13 of 23 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

ACS Sensors

Figure 5: (a) Schematic illustration of the nanofluidic alternating current transport-inducedcharge electroosmotic pumping. Transient variation of the average flow velocity 𝑣ave at different (b)(c) frequency 𝑓 in a neutral nanopore for potassium chloride solutions, (d) solute species (at 𝑓 =100 Hz in a neutral nanopore) and (e) surface charge density 𝜎 (at 𝑓 =10 Hz for potassium chloride solutions), at 𝑛0 = 1 M, ∆𝑛0 = 0.4 M, 𝜑max = 10 V, 𝐿 = 20 nm and 𝑑 = 5 nm. (The positive and negative values indicate the flow directions to the low and high concentration ends, respectively. The dashed lines in (e) represent the time averaged mean velocity magnitude of the first five cycles at different nanopore surface charge condition.) The average flow velocity 𝑣ave at different frequency is examined in Figure 5b,c. At low 𝑓 (1 and 10 Hz), a continuous unidirectional flow is generated which becomes stable after a few cycles. At high 𝑓 (100 and 1000 Hz), two notable changes are observed : (i) the flow magnitude significantly decreases and (ii) the flow behaviors less predictable oscillating between both ends. The former behavior could because of that when 𝑓 is high, 𝐸 reverses before the transport-induced-charge is fully developed suppressing transport-induced-charge effects. Furthermore, the sudden change of 𝐸 prohibits instantaneously redistribution of

13


ACS Sensors 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

ions inside the nanopore for the inversion of charge resulting in a temporal reversal of the transport-induced-charge electroosmotic flow. This effect is mitigated as the ionic diffusivity increases. As evidenced in Figure 5d, 𝑣ave for the high ionic diffusivity hydrogen chloride (HCl) and potassium hydroxide (KOH) solutions is about 2 to 3 times higher than that for the sodium chloride (NaCl) and potassium chloride (KCl) solutions (where the ionic diffusivities of proton 𝐷H+ , chloride ions 𝐷Cl− , potassium ions 𝐷K+ , hydroxide 𝐷OH− and sodium ions 𝐷Na+ are 9.31×10−9 m2 /s, 2.03×10−9 m2 /s, 1.96×10−9 m2 /s, 5.27×10−9 m2 /s and 1.33×10−9 m2 /s, respectively). In case of charged nanopores, the superposition of the electric double layer electroosmotic flow and transport-induced-charge electroosmotic flows gives rise to complex flow behavior as shown in Figure 4e. However, since the time averaged mean velocity due to the electric double layer electroosmotic flows under an alternating current field in a nonconductive cylindrical pore vanishes, the net flow rate is simply attributed by the transport-induced-charge electroosmotic flow resulting in a similar time averaged mean velocity at different surface charge density (represented by the dashed lines). In other words, the mean pumping performance is dominated by the bulk salt concentrations controlled transport-induced-charge phenomena but insensitive to the nanopore surface charge condition.

Alternating Current Resistive Pulse Sensing in a Two-Dimensional Nanopore Next, we propose an alternating current resistive pulse sensing system for bionanosensing applications using alternating current transport-induced-charge electroosmotic pumping. One essential difficulty for the alternating current resistive pulse sensing using the conventional electric double layer electroosmotic flow for nanoparticles transport through nanopores (nonconductive) comes from the independence of the interfacial charge and the external electric field. The reversal of the electric field simultaneously reverses the direction of the electric double layer electroosmotic flow yielding null fluxes of the solution and nanoparticles. The 14


Page 14 of 23

Page 15 of 23 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

ACS Sensors

issue could be circumvented by employing the alternating current transport-induced-charge electroosmotic pumping. Due to its special unidirectional flow characteristic, the nanoparticles are able to migrate in a consistent direction despite the reversal of the electric field enabling continuous transport of nanoparticles through nanopores even under alternating current fields. The envisaged scenario will become valid when transport-induced-charge electrosmotic effects are predominant over the summation of electric double layer electrosmotic and electrophoretic effects, where the both terms are directly influenced by the external electric field direction. According to the analysis in Figure 4c,d, we concurrently adopt two approaches to enhance transport-induced-charge effects that we (i) minimize the nanopore length and (ii) maximize the salt concentration difference. The behavior of a negatively charged (the particle surface charge density 𝜎p = −10 mC/m2 ) spherical nanoparticle (non-conductive and non-permeable and the particle diameter 𝑑p = 2 nm) passing through a highly salt concentration biased (the potassium chloride concentrations of 3 M and 0.01 M are supplied in the high and low concentration reservoirs, respectively) two-dimensional monolayer molybdenum disulfide (MoS2 ) nanopore (𝐿 = 0.65 nm, 𝑑 = 5 nm and 𝜎 = -46.94 mC/m2 ) 34 at different applied electric potential is elucidated by computational simulation, as the geometry and the surface charge densities of the simulated system are summarized in Figure 6a. The hydrodynamic force 𝐹 d and electric force 𝐹 e on the nanoparticle are derived from the Maxwell stress tensor 𝜏E and hydrodynamic stress tensor 𝜏H over nanoparticle’s surface 𝑆, respectively :

3

∫︁ ∫︁ 𝐹 e = 𝜖𝜖0

]︂ ∫︁ ∫︁ [︂ 1 𝜏E · 𝑛𝑆 𝑑𝐴 = 𝜖𝜖0 𝐸𝐸 − (𝐸 · 𝐸)𝐼 · 𝑛𝑆 𝑑𝐴 2 𝑆 𝑆

∫︁ ∫︁

∫︁ ∫︁

[︀ [︀ ]︀]︀ −𝑝𝐼 + 𝜂 ∇𝑣 + (∇𝑣)𝑇 · 𝑛𝑆 𝑑𝐴

𝜏H · 𝑛𝑆 𝑑𝐴 =

𝐹d = 𝑆

(11)

(12)

𝑆

in which 𝑛𝑆 is the unit normal vector on the particle surface, 𝐼 represents the unit tensor, 𝑇 is the matrix transpose and 𝑑𝐴 denotes an infinitesimal area element. The particle velocity 15


ACS Sensors 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

Figure 6: (a) Computational mesh and geometry of a nanoparticle translocating through a monolayer molybdenum disulfide (MoS2 ) nanopore under an alternating current field at 𝐿 = 0.65 nm, 𝑑 = 5 nm (2.5 nm in radius), 𝜎 = −46.64 mC/m2 , the nanoparticle diameter 𝑑p = 2 nm (1 nm in radius) and the particle surface charge density 𝜎p = −10 mC/m2 . Contours of the flow field |𝑣| with streamlines, (b) as ∇𝑛0 is in the same direction to 𝐸 and (c) as ∇𝑛0 is opposite to 𝐸. (d) Nanoparticle velocity 𝑣p map and (e) current variation 𝜆 map for alternating current resistive pulse sensing at 𝑛H = 3 M, 𝑛L = 0.01 M and |∆𝜑| = 0.5 V, . 𝑣p is estimated using a pseudo-steady-state condition that 𝐹 total (= 𝐹 e + 𝐹 d ) on the particle equals zero. 35 Since the translocation time (which can be approximately estimated by 𝐿/|𝑣p | ≈ 10 ns) is much shorter than the period of an alternating current cycle (1/𝑓 = 0.1 s at 𝑓 = 10 Hz), each translocation event is simulated at a constant applied voltage. The ionic current 𝐼c is derived based on the integral of the products of ionic charge and ionic flux

16


Page 16 of 23

Page 17 of 23 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

ACS Sensors

𝑞+ 𝐽 + and 𝑞− 𝐽 − over the nanopore cross-sectional area 𝐴c , viz : ∫︁ ∫︁

(︁

𝐼c =

)︁ 𝑞+ 𝐽 + + 𝑞− 𝐽 − · 𝑛𝐴 𝑑𝐴

(13)

𝐴c

where 𝑛𝐴 is the unit normal vector on the nanopore cross section area. Figure 6b,c shows typical flow fields inside the nanopore as the nanoparticle is translocating through the nanopore at 𝑛H = 3 M, 𝑛L = 0.01 M and |∆𝜑| = 0.5 V. As ∇𝑛0 and 𝐸 are pointing toward the same direction, the transport-induced-charge electroosmosis and electric double layer electroosmosis are in the opposite directions (the former flows to the low concentration end whereas the latter flows to the high concentration end). However, due to the dominance of the transport-induced-charge electroosmosis, both the solution inside the nanopore and therefore the nanoparticle migrate to the low concentration reservoir. If 𝐸 is reversed to the opposite direction of ∇𝑛0 , both the transport-induced-charge and electric double layer electroosmotic flows drive the nanoparticle toward the low concentration end despite the opposite electrophoretic force. As a result, the nanoparticle translocates from the high concentration reservoir to the low concentration reservoir under either situation. A nanoparticle velocity map plotted across a range of applied potentials is shown in Figure 6d. Due to the presence of transport-induced-charge effects, the nanoparticle migrates in a consistent direction (i.e., toward the low concentration end when 𝑣p is positive) at arbitrary electric potential. The corresponding ionic current variation of Figure 6d is shown in Figure 6e. Here the current variation 𝜆 is defined as

𝐼c −𝐼c,0 𝐼c,0

× 100 %, where 𝐼c,0 is the

current for the open nanopore without the presence of the nanoparticle. Finally, depending upon a similar sensing mechanism with the classical direct current resistive pulse sensing, the particle properties (e.g., charge or size) can be revealed by these current blockage signals.

17


ACS Sensors 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

CONCLUSIONS In summary, we have proposed an alternating current electroosmotic pump for alternating current resistive pulse sensing using transport-induced-charge phenomena. The constructed system and sensing strategy have been theoretically justified by computational simulations. The investigated transport-induced-charge phenomena become predominant over the conventional electric double layer electrokinetic phenomena as nanopore’s length reduces down to the atomic level, remarkably changing its electrokinetic behavior. This finding might stimulate the birth of novel sensing strategies accompanying with new opportunities for molecule control through two-dimensional nanopores. Meanwhile, the transport-induced-charge theory could open up a new direction of resistive pulse sensing using alternating current for the next generation of nanopore biosensing.

Supporting Information Supporting Information Available : The following file is available free of charge. “Supporting Information for Theory of Transport-Induced-Charge Electroosmotic Pumping toward Alternating Current Resistive Pulse Sensing.” SI 1. Sensitivity Analysis on the Reservoir Dimensions. SI 2. Role of Transport-Induced-Charge Phenomena in Nonlinear Electrokinetics in a Charged Two-Dimensional Nanopore.

ORCID Wei-Lun Hsu : 0000-0002-5451-4301 Junho Hwang : 0000-0002-4041-7973 Hirofumi Daiguji : 0000-0001-6896-3282

18


Page 18 of 23

Page 19 of 23 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

ACS Sensors

Notes The authors declare no competing financial interest.

Acknowledgement This research was supported by a Grant-in-Aid for Young Scientists (B) under Japan Society for the Promotion of Science KAKENHI Grant Number 17K17682.

References 1. Sparreboom, W.; van den Berg, A.; Eijkel, J. C. T. Principles and Applications of Nanofluidic Transport. Nat. Nanotechol. 2009, 4, 713–720. 2. Oyarzua, E.; Walther, J. H.; Megaridis, C. M.; Koumoutsakos, P.; Zambrano, H. A. Carbon Nanotubes as Thermally Induced Water Pumps. ACS Nano 2017, 11, 9997– 10002. 3. Hsu, W.-L.; Daiguji, H. Manipulation of Protein Translocation through Nanopores by Flow Field Control and Application to Nanopore Sensors. Anal. Chem. 2016, 88, 9251– 9258. 4. Shi, W.; Friedman, A. K.; Baker, L. A. Nanopore Sensing. Anal. Chem. 2017, 89, 157– 188. 5. Losic, D.; Simovic, S. Self-Ordered Nanopore and Nanotube Platforms for Drug Delivery Applications. Expert Opin. Drug Deliv. 2009, 6, 1363–1381. 6. Dervin, S.; Dionysiou, D. D.; Pillai, S. C. 2D Nanostructures for Water Purification: Graphene and Beyond. Nanoscale 2016, 8, 15115–15131.

19


ACS Sensors 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

7. Daiguji, H.; Yang, P. D.; Szeri, A. J.; Majumdar, A. Electrochemomechanical Energy Conversion in Nanofluidic Channels. Nano Lett. 2004, 4, 2315–2321. 8. Daiguji, H. Ion Transport in Nanofluidic Channels. Chem. Soc. Rev. 2010, 39, 901–911. 9. Hwang, J.; Sekimoto, T.; Hsu, W.-L.; Kataoka, S.; Endo, A.; Daiguji, H. Thermal Dependence of Nanofluidic Energy Conversion by Reverse Electrodialysis. Nanoscale 2017, 9, 12068–12076. 10. Yeh, L.-H.; Chen, F.; Chiou, Y.-T.; Su, Y.-S. Anomalous pH-Dependent Nanofluidic Salinity Gradient Power. Small 2017, 13, 1702691–1702696. 11. Bird, B. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena, 2nd ed.; John Wiley & Sons, 2007. 12. Hunter, R. J. Zeta Potential in Colloid Science: Principles and Applications; Elsevier, 1981. 13. Cao, L.; Wen, Q.; Feng, Y.; Ji, D.; Li, H.; Li, N.; Jiang, L.; Guo, W. On the Origin of Ion Selectivity in Ultrathin Nanopores: Insights for Membrane-Scale Osmotic Energy Conversion. Adv. Funct. Mater. 2018, 28, 18041891–18041898. 14. Chen, L.; Conlisk, A. T. Electroosmotic Flow and Particle Transport in Micro/Nano Nozzles and Diffusers. Biomed. Microdevices 2008, 10, 289–298. 15. Wang, X.; Cheng, C.; Wang, S.; Liu, S. Electroosmotic Pumps and Their Applications in Microfluidic Systems. Microfluid. Nanofluid. 2009, 6, 145–162. 16. Brask, A.; Snakenborg, D.; Kutter, J.; Bruus, H. AC Electroosmotic Pump with BubbleFree Palladium Electrodes and Rectifying Polymer Membrane Valves. Lab Chip 2006, 6, 280–288. 17. Wu, X.; Rajasekaran, P. R.; Martin, C. R. An Alternating Current Electroosmotic Pump Based on Conical Nanopore Membranes. ACS Nano 2016, 10, 4637–4643. 20


Page 20 of 23

Page 21 of 23 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

ACS Sensors

18. Hughes, M. AC Electrokinetics: Applications for Nanotechnology. Nanotechnology 2000, 11, 124–132. 19. Bazant, M.; Squires, T. Induced-Charge Electrokinetic Phenomena: Theory and Microfluidic Applications. Phys. Rev. Lett. 2004, 92, 0661011–0661014. 20. Bazant, M.; Kilic, M.; Storey, B.; Ajdari, A. Towards an Understanding of InducedCharge Electrokinetics at Large Applied Voltages in Concentrated Solutions. Adv. Colloid Interface Sci. 2009, 152, 48–88. 21. Bazant, M. Z.; Ben, Y. Theoretical Prediction of Fast 3D AC Electroosmotic Pumps. Lab Chip 2006, 6, 1455–1461. 22. Kneller, A. R.; Haywood, D. G.; Jacobson, S. C. AC Electroosmotic Pumping in Nanofluidic Funnels. Anal. Chem. 2016, 88, 6390–6394. 23. German, S. R.; Hurd, T. S.; White, H. S.; Mega, T. L. Sizing Individual Au Nanoparticles in Solution with Sub-Nanometer Resolution. ACS Nano 2015, 9, 7186–7194. 24. Hsu, W.-L.; Daiguji, H.; Dunstan, D. E.; Davidson, M. R.; Harvie, D. J. E. Electrokinetics of the Silica and Aqueous Electrolyte Solution Interface: Viscoelectric Effects. Adv. Colloid Interface Sci. 2016, 234, 108–131. 25. Hsu, W.-L.; Harvie, D. J. E.; Davidson, M. R.; Dunstan, D. E.; Hwang, J.; Daiguji, H. Viscoelectric Effects in Nanochannel Electrokinetics. J. Phys. Chem. C 2017, 121, 20517–20523. 26. Qiao, R.; Aluru, N. R. Scaling of Electrokinetic Transport in Nanometer Channels. Langmuir 2005, 21, 8972–8977. 27. Zhu, X.; Guo, L.; Ni, S.; Zhang, X.; Liu, Y. Transport-Induced Inversion of Screening Ionic Charges in Nanochannels. J. Phys. Chem. Lett. 2016, 7, 5235–5241.

21


ACS Sensors 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

28. He, Y.; Tsutsui, M.; Scheicher, R. H.; Fan, C.; Taniguchi, M.; Kawai, T. Mechanism of How Salt-Gradient-Induced Charges Affect the Translocation of DNA Molecules through a Nanopore. Biophys. J. 2013, 105, 776–782. 29. Hsu, W.-L.; Inglis, D. W.; Jeong, H.; Dunstan, D. E.; Davidson, M. R.; Goldys, E. M.; Harvie, D. J. E. Stationary Chemical Gradients for Concentration Gradient-Based Separation and Focusing in Nanofluidic Channels. Langmuir 2014, 30, 5337–5348. 30. Hsu, W.-L.; Harvie, D. J. E.; Davidson, M. R.; Jeong, H.; Goldys, E. M.; Inglis, D. W. Concentration Gradient Focusing and Separation in a Silica Nanofluidic Channel with a Non-uniform Electroosmotic Flow. Lab Chip 2014, 14, 3539–3549. 31. Hsu, J.-P.; Hsu, W.-L.; Chen, Z.-S. Boundary Effect on Diffusiophoresis: Spherical Particle in a Spherical Cavity. Langmuir 2009, 25, 1772–1784. 32. Harvie, D. J. E. An implicit Finite Volume Method for Arbitrary Transport Equations. ANZIAM J. 2012, 52, C1126–C1145. 33. Rademaker, T. J.; Akkermans, G. R. A.; Danilov, D. L.; Notten, P. H. L. On the Deviation of Electro-Neutrality in Li-Ion Battery Electrolytes. J. Electrochem. Soc. 2014, 161, E3365–E3372. 34. Feng, J.; Graf, M.; Liu, K.; Ovchinnikov, D.; Dumcenco, D.; Heiranian, M.; Nandigana, V.; Aluru, N. R.; Kis, A.; Radenovic, A. Single-Layer MoS2 Nanopores as Nanopower Generators. Nature 2016, 536, 197–200. 35. Liu, K.-L.; Hsu, J.-P.; Hsu, W.-L.; Yeh, L.-H.; Tseng, S. Diffusiophoresis of a Polyelectrolyte in a Salt Concentration Gradient. Electrophoresis 2012, 33, 1068–1078.

22


Page 22 of 23

Page 23 of 23 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

ACS Sensors

Graphical TOC Entry For TOC Only

23


Theory of Transport-Induced-Charge Electroosmotic Pumping toward

Recommend Documents