Cation Dependent Surface Charge Regulation in Gated Nanofluidic

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Cation Dependent Surface Charge Regulation in Gated Nanofluidic Devices Marie Julia Fuest, Kaushik K. Rangharajan, Caitlin Marie Boone, A. Terrence Conlisk, and Shaurya Prakash Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.6b03653 • Publication Date (Web): 20 Dec 2016 Downloaded from http://pubs.acs.org on December 22, 2016

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Analytical Chemistry

Cation Dependent Surface Charge Regulation in Gated Nanofluidic Devices Marie Fuest, Kaushik K. Rangharajan, Caitlin Boone, A.T. Conlisk, and Shaurya Prakash* Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH 43210, USA *Corresponding author, Email: [email protected] ABSTRACT: Surface charge governs nanoscale aqueous electrolyte transport, both in engineered analytical systems and in biological entities such as ion channels and ion pumps as a function of ion type and concentration. Embedded electrodes in a nanofluidic channel, isolated from the fluid in the channel by a dielectric layer, act as active, tunable gates to systematically modify local surface charge density at the interface between the nanochannel surface and the aqueous electrolyte solution, causing significant changes in measured nanochannel conductance. A systematic comparison of transport of monovalent electrolytes (KCl, NaCl), 2:1 electrolytes (MgCl2, CaCl2), and electrolyte mixtures (KCl + CaCl2) through a gated nanofluidic device was performed. Ion-surface interactions between divalent Ca2+ and Mg2+ ions and the nanochannel walls reduced the native surface charge density by up to ~4-5 times compared to the monovalent cations. In electrolyte mixtures, Ca2+ was the dominating cation with nanochannel conductance independent of KCl concentration. Systematic changes in local electrostatic surface state induced by the gate electrode are impacted by the divalent cation-surface interactions, limiting modulation of the local surface potential by the gate electrode and resulting in cation dependent nanoscale ion transport as seen through conductance measurements and numerical models.

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KEYWORDS: Nanofluidics, Field effect, Nanochannel, Gating, Cation dependence, Fabrication


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INTRODUCTION Surface charge is a fundamental parameter that governs nanoscale aqueous electrolyte transport in engineered systems for applications in energy conversion,1,2 fluid-analogs of solidstate electronics,3-5 biosensing,6,7 and in ion channels and ion pumps for precise control over ion and small molecule transport.8 Divalent ions play a critical role in regulating the opening, selectivity, and conductance of both cation and anion biological ion channels with direct implications for physiological processes such as neuronal excitability, epithelial fluid secretion, cancer cell proliferation, and blood pressure regulation.9-11 In ion channels and ion pumps the nanochannel

structure,

conformation,

sub-units

with

local

binding

sites,

relative

hydrophobicity characteristics, local electrostatic domains at channel entrances and within ion channels, and most importantly, surface charge have been identified as important parameters governing ion flux, selectivity, and levels of ion conductance and rectification.10,12-14 Yet, engineered systems such as lab-on-chip (LoC) or micro-total analysis systems (µ-TAS) that attempt to mimic many of these ideal biological functions for the variety of applications listed above suffer from incomplete understanding of surface charge regulation15-18 in contrast to biological systems, especially with multi-valent ions and electrolyte mixtures. Specifically, for gated LoC nanofluidic devices the effect of local variation of electrostatic properties on transport of multi-valent electrolytes and electrolyte mixtures, which underlie most practical applications, remains poorly understood with minimal reporting in existing peer-reviewed literature. Nanoscale architectures built with insulating materials such as glass, oxides, polymers, or a combination of these materials are commonly used substrates for numerous LoC devices for characterizing and manipulating nanoscale flows over the past decade.1,3,4,6,19-22 While, it is



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well known that oxide and polymer surfaces in contact with electrolyte solutions develop a net surface charge that can be passively controlled by regulating the electrolyte pH,23-25 active control over surface charge has been desired for real-time control over ionic transport for analytical operations in engineered nanoscale conduits. Active control can be achieved through embedded electrodes in the walls of nanofluidic channels that act as tunable gates to systematically modify local surface potential and/or surface charge density at the dielectricfluid interface.3,4 The gate potential thus influences the electric field throughout the nanochannel depth,4,19 allowing direct electrostatic manipulation of ions and molecules in the fluid volume.4,26,27 However, systematically evaluating the efficacy of electrostatic gating towards engineering transport of multi-valent and multi-component electrolyte solutions is critical towards advancing nanofluidics for highly functional LoC or µ-TAS devices. Basic transport phenomena in gated or field-effect nanofluidic devices remains an open area of research.28,29 Consequently, nearly all reports to date on gated nanofluidic devices have focused on transport of KCl,3,4,22,28,30-36 with limited evaluation of HCl37,38 and glycine based buffers.39 In the case of multi- or polyvalent electrolyte solutions, including mixtures, fundamental research for ungated nanofluidic devices shows that ion-surface and/or ion-ion interactions must be considered depending on the electrolyte type and composition along with ion concentration and surface charge density.15,17,40 Systematic comparison of gated transport for monovalent, 2:1 electrolytes, and simple electrolyte mixtures is further complicated by device to device variation, specifically by observed inconsistency of the surface charge density across fabricated devices.4,41 In this report, a systematic comparison of transport of monovalent electrolytes (KCl, NaCl), 2:1 electrolytes (MgCl2, CaCl2), and electrolyte mixtures (KCl + CaCl2) through a gated


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nanofluidic device is demonstrated for the first time. Ion-surface interactions regulate the nanochannel surface charge density as a function of cation type, resulting in distinct cation dependent gating behavior. The glass-PDMS based devices here are cation selective under conditions of interacting electric double layers (EDLs); therefore, the cation was varied across electrolyte solutions for a fixed anion. The purpose of this paper is to demonstrate that systematic changes in local electrostatic surface state induced by a gate electrode are impacted by ion-surface interactions leading to surface charge regulation and consequently the resulting nanoscale ion transport is strongly affected by cation type in gated nanofluidic devices. In particular, divalent cation-surface interactions reduce the surface charge density and limit the current modulation under some of the tested gating conditions. A multi-species numerical model confirmed that ion-surface interactions had a significant impact on the surface charge density at pH ≥ 6 for CaCl2. Ionsurface interactions between the charged walls and the divalent cations in the electrolyte regulate the surface charge density thus limiting the ability of the gate electrode to alter the net surface charge density and consequently modulate nanochannel conductance. EXPERIMENTAL PROCEDURES The gated nanofluidic device consisted of two microfluidic channels (8 µm deep x 50 µm wide x 3 cm long) which served as fluidic reservoirs to a bank of three nanofluidic channels (16 nm deep x 30 µm wide x 2.5 mm long). Four individually addressable Au gate electrodes were embedded in the roof of the nanofluidic channels and separated from the electrolyte in the nanochannel by a polydimethyl siloxane (PDMS) dielectric layer (PDMS thickness ~ 0.7 µm)19,42. Only one active gate electrode was used for this work. The micro- and nanofluidic network was patterned on a borosilicate glass substrate using UV lithography and



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wet etching techniques. Individually addressable Au gate electrodes were patterned onto a second glass substrate. A PDMS dielectric layer was spun onto the glass cover containing the electrode array. The cover with embedded electrodes and the glass substrate with the patterned channel network were bonded via O2 plasma bonding to form sealed channels. Details on device fabrication and basic device operation and characterization have been reported previously.19,42 The device testing setup included two power supplies (Keithley 3390 function generators) used to supply independent axial ( ) and gate ( ) potentials. The axial potential used here was = 3 and = 5, as discussed below, and the gate potential ranged from −3 ≤ ≤ 3. Current ( ) through the nanochannels was monitored using a Keithley 6485 picoammeter (Figure 1b). Devices were first tested with the gate electrodes floating at each respective concentration, pH, or electrolyte composition in order to measure the intrinsic (i.e., = 0 V) nanochannel conductance. All electrical measurements were conducted in an earth-grounded Faraday cage. Dedicated devices for each type of electrolyte were used to avoid contamination, with the obvious exception of devices used for electrolyte mixtures. Electrolyte solutions were prepared for concentrations ranging from 0.01 mM to 100 mM at pH 7 ± 0.2. Each device was initially tested with deionized water (18 MΩ, 10-7 M salt) to provide the same baseline for comparison between devices. Only devices with an initial DI conductance within 4.4 ± 0.5 pS were used for comparison of results across devices as a function of cation type. The gate was located at = 0.43 ± 0.02 L for all devices, where is the length of the nanochannel, as dependence of device operation on gate location has been reported previously.19 After initial conductance measurements with deionized water, electrolyte concentrations were tested in ascending order of concentration. After the electrolyte concentration was


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increased, the device was thoroughly rinsed with the next highest concentration, similar to previously reported procedures.43 Monovalent electrolytes (KCl and NaCl) were tested at 6 concentrations including DI water and concentrations ranging from 0.01 mM to 100 mM in order of magnitude increments. Divalent electrolytes (CaCl2 and MgCl2) were tested at those concentrations with the addition of 0.33 mM and 3.33 mM to match the ionic strength for KCl and NaCl at 1 mM and 10 mM respectively. Overall data trends were verified over multiple devices with data for each experimental condition comprising several data runs over multiple days. RESULTS AND DISCUSSION Three nanofluidic channels with one active embedded gate electrode connect two microchannel reservoirs (Figure 1). The axial potential, , drives ionic transport through the nanochannel. An independently controlled potential applied to the gate electrode, , modified the local surface charge density (and electric field) at the dielectric-electrolyte interface enabling field-effect control over ionic transport, quantified by changes in the measured current.

Figure 1. Device layout along with scanning electron microscope (SEM) images. (a) Schematic showing the different functional layers of the nanofluidic device. Two 7 ACS Paragon Plus Environment


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microchannels (8 µm deep x 50 µm wide x 3 cm long) served as reservoirs to a bank of three nanochannels (16 nm deep x 30 µm wide x 2.5 mm long). The micro- and nanochannel network was fabricated on a borosilicate glass substrate with individually addressable gold (Au) gate electrodes patterned on the glass cover. A polydimethyl siloxane (PDMS) dielectric layer supported on the glass cover isolated the gate electrodes from the aqueous electrolytes in the nanochannels. (b) Side-view schematic of the nanochannel, showing the active gate electrode for the data reported. Electrical connections are shown with yellow lines. (c) Scanning electron microscope (SEM) image of an open nanochannel cross section. The slit-like channel cross section lies between the arrows. The dashed red lines denote the locations on the physical device where the SEMs were taken. The channel height was ~16 nm, as expected from previous reports on device fabrication and characterization.19,42 (d) SEM image of PDMS bonded to glass in regions where no channel is expected. Cation Dependence. The intrinsic nanochannel device conductance ( = / ) was first measured with = 0 V as a function of cation type (Figure 2a and 2b) at pH = 7 ± 0.2. In agreement with previous results for KCl4,44,45 and anomalous transport of NaCl with respect to KCl,43 the two monovalent cations showed similar intrinsic (i.e., = 0V) conductance ( ). for both KCl and NaCl followed known surface charge governed (SCG) transport at < ~1 mM and had a linear dependence on concentration at > ~1 mM indicating bulk transport behavior. To satisfy electroneutrality, the total space charge within the nanochannel volume must balance the total surface charge on the nanochannel walls. is thus the summation of the surface charge governed and the bulk conductance,16,44 = +

'

2 | | !ℎ = + # $ %$ & $

[1]

$()


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where

is the surface charge density (negative for both PDMS and glass) on the nanochannel

walls, $ is the mobility of species *, $ is the bulk electrolyte concentration, and , , and ℎ are the channel width, length, and height respectively.28 The dominant term in equation (1) ( or ) depends on the bulk electrolyte concentration.28,44 At the transition

a

b

102 KCl NaCl

101

100 10-7 10-6 10-5 10-4 10-3 10-2 10-1

Intrinsic Conductance (pS)

concentration, ct, the bulk and SCG conductances are similar.


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102 CaCl2 MgCl2

101

100 10-7 10-6 10-5 10-4 10-3 10-2 10-1

Concentration (M)

Concentration (M)

Figure 2. Cation depedent intrinsic nanochannel conductance, measured with the gate electrode floating ( = 0 V). (a) The two monovalent cations showed similar intrinsic conductance in agreement with previous results for anomalous transport of NaCl with respect to KCl.43 (b) The decrease in conductance from expected surface charge governed behavior at ≈ 0.1 mM for MgCl2 and ≈ 1 mM for CaCl2 is caused by a decrease in the magnitude of the surface charge density, due to ion-surface interactions between divalent cations and the negatively charged walls as discussed in the main text. The dashed lines are intended as eyeguides.

Three of the nanochannel walls in our device are borosilicate glass and one is PDMS supported on borosilicate glass. It is worth noting that the surface charge governed transport of KCl demonstrated in our PDMS-glass device has been reported for a wide variety of 9 ACS Paragon Plus Environment


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nanofluidic devices4,44-46 showing that the baseline data trends for the most commonly studied electrolyte for these types of devices match those reported previously. In contrast to NaCl and KCl, CaCl2 and MgCl2 showed cation dependent intrinsic conductance behavior as a function of electrolyte concentration that deviated from the wellknown KCl intrinsic conductance profile. for CaCl2 and MgCl2 (Figure 2b) was independent of bulk concentration at ≤ ~ 0.1 mM, also suggesting SCG transport for divalent cations. Intrinsic conductance of MgCl2 showed a marked decrease from 4.5 pS at = 0.1 mM to 1.2 pS at = 1 mM. CaCl2 conductance decreased from 4.0 pS for = 1 mM to 0.8 pS for = 3.33 mM showing a change in conductance per unit concentration of 1.37 pS/mM for CaCl2 and 3.67 pS/mM for MgCl2 before transitioning to linear concentration dependence in the bulk transport regime. Since, is proportional to

for dilute electrolyte solutions (i.e, in the surface charge

governed regime),3,4,28,43-45 the decrease in for divalent ions corresponds to ~ 3.75x reduction in

for MgCl2 between = 0.1 mM and = 1 mM and ~ 5x reduction in

for CaCl2 between = 1 mM and = 3.33 mM. As shown in Figure 2b, two distinct transition concentrations were observed for intrinsic conductance of divalent cations: (i) sharp reduction in intrinsic conductance at concentrations that would typically correspond to SCG behavior for monovalent cations with ≈ 0.1 mM for MgCl2 and ≈ 1 mM for CaCl2 and (ii) the subsequent transition from this reduced conductance to bulk transport behavior with increasing concentration observed at , ≈ 1 mM for MgCl2 and , ≈ 3.33 mM for CaCl2. We hypothesize that the observed reduction in measured intrinsic conductance is due to reduction of

caused by ion-surface interactions, providing further support of this claim below.


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Conductance of gated nanochannels. Changes in the local surface charge density and electric field were induced by the gate electrode to modulate ionic transport and, therefore, the measured current.3,4,32,33 To our knowledge, this is the first systematic comparison of gating across electrolyte types, and further, the first presentation of gating data for NaCl, MgCl2, and CaCl2. It is worth noting that gating of ionic transport is essential to numerous analytical applications as discussed in the introduction section. The current was monitored at electrolyte concentrations between 0.01 and 100 mM for +3 V ≤ ≤ -3 V at a fixed axial potential ( ).19 A representative plot of measured current as function of gate voltage for various cations is shown in Figure S1 (Supporting Information). Following previously reported analysis for gated devices,5,37 the total measured current arises from two components and can be written as = + . Here, is the intrinsic nanochannel conductance ( = 0) and is the transconductance (dI/dVg).5,19,37 To further verify that the two components of the current were independent, transconductance data was taken at = 3V and = 5V for all data sets. The dimensionless conductance ratio, ⁄ , compares the transconductance to the intrinsic nanochannel conductance (Figure 3). For the monovalent cations, the maximum value of ⁄ was observed at the transition concentration, , ≈ 1 mM (i.e., the transition between surface charge governed and bulk transport). Limited gating was observed for KCl and NaCl at concentrations that correspond to bulk intrinsic conductance behavior (that is, 10 mM and 100 mM here). The data trends reported here for ⁄ (and for as noted above) for KCl are consistent with previously reported results for KCl in TiO2 nanopores and HCl in silica nanopores.5,37 Similar to the intrinsic conductance (Figure 2), no significant cation dependence was observed between KCl and NaCl within experimental error as shown in Figure 3a. Our 11 ACS Paragon Plus Environment


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results show that NaCl follows the same concentration dependent gating behavior as the other monovalent symmetric electrolytes reported previously,5,37 with the maximum conductance ratio ( ⁄ ) at the transition concentration to bulk electrolyte transport. As with intrinsic conductance, cation dependent behavior was observed for ⁄ for CaCl2 and MgCl2. For MgCl2, ⁄ at = 0.1 mM was 0.2 compared to ~ 0.6 for monovalent ions even though KCl, NaCl, and MgCl2 have comparable at 0.1 mM. Starting at 0.1 mM gate modulation increased with concentration for MgCl2, with the maximum value of ⁄ at 1 mM, which is the transition concentration to bulk transport behavior for MgCl2. For CaCl2, ⁄ showed a local maxima at 3.33 mM, which is the transition concentration to bulk transport behavior. ⁄ for Ca2+ decreased from 0.9 at 0.33 mM to ~ 0.3 at 1 mM (which was transition from SCG to the reduced conductance, ). Consequently, the gate electrode showed reduced modulation for both divalent ions at their respective values of (0.1 mM for MgCl2 and 1 mM for CaCl2). Near this concentration ( ), ion-surface interactions reduce the surface charge density, as discussed above, and appear to limit the current modulation under gating conditions (Figure 3b). In contrast to Mg2+, a second maxima was observed for CaCl2 at 0.33 mM. This second maxima was observed for CaCl2 and not MgCl2 likely since all concentrations used in gating experiments fall within the concentration range where ion-surface interactions regulate the surface charge density for MgCl2 ( = 0.1 mM for MgCl2) but not for CaCl2 ( = 1 mM for CaCl2). At concentrations > , bulk transport behavior is known to dominate thus modulation of the surface charge density will have a limited impact on nanochannel conductance and ion-surface interactions are thus expected to effect the magnitude of / in the range - , . 12 ACS Paragon Plus Environment

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a

b

1.2

1.2 MgCl2

KCl NaCl

1.0

1.0

CaCl2

0.8 Gg / Ga

0.8 Gg / Ga

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0.6 0.4

0.6 0.4

0.2

0.2

0.0

0.0 10-4

10-3

10-2

Concentration (M)

10-1

10-4

10-3

10-2

10-1

Concentration (M)

Figure 3. Conductance ratio as a function of cation type for (a) monovalent cations and (b) divalent cations. The conductance ratio ⁄ is a non-dimensional parameter that compares

the transconductance , to the intrinsic nanochannel conductance, . The dashed lines are

intended as an eye-guide.

Ion mixtures. Most practical applications and real biological systems contain electrolyte solutions comprising multiple ionic species. However, systematic study of transconductance for electrolyte mixtures has not yet been reported. KCl and CaCl2 were selected for comparison given the broader set of knowledge existing for these two electrolytes and the vital role of calcium ions in many biological systems with nanoscale critical length scales.10,47,48 Electrolyte mixtures of KCl and CaCl2 were evaluated at pH = 7 ± 0.2 at a fixed ionic strength to ensure a consistent Debye length across experiments. The relative composition of the electrolyte solution was altered from 0% CaCl2 (i.e., 1 mM KCl) to 100 % CaCl2 (0.33 mM CaCl2) with a complete summary of the prepared electrolyte compositions in Table S1. The highest measured (Figure 4a) was at 0% CaCl2. As CaCl2 percentage was increased from 0 to 25% the intrinsic conductance decreased from ~ 2.8 pS to 1.4 pS. Further increasing the CaCl2 percentage from 25 to 50% caused the intrinsic conductance to decrease from 1.4 pS to 1.2 pS,



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with no measured change beyond 50% CaCl2. Therefore, starting at 25% Ca2+ in the solution, was independent of K+ concentration. With 0% CaCl2 as the baseline, was estimated as a function of electrolyte composition by assuming a constant surface charge density across electrolyte compositions,43-45 and that the proportion of K+ to Ca2+ in the bulk was preserved in the nanochannel18 (SI). The estimated values for did not match experimentally measured as shown in Figure 4a, indicating that one or both of the main assumptions (i.e., constant surface charge density across electrolyte compositions or that the relative concentrations of K+ to Ca2+ in the nanochannel matches the relative concentration in the bulk) may be problematic for matching theoretical estimates to the experimental measurements. The difference between the measured and estimated values is not explained by the ratio of K+ to Ca2+ in the nanochannel alone, as the estimated and measured intrinsic conductances for 100% CaCl2 also did not match. Therefore, the constant surface charge density and, consequently, the constant space charge density assumption fails for in the case of KCl + CaCl2 mixtures. Instead, using the measured at each electrolyte composition, the surface charge density was estimated as a function of electrolyte composition relative to the 0% CaCl2 case (SI). The estimated relative

(Table S2) showed that the magnitude of

decreased by more than ½ as

CaCl2 composition goes from 0 to 25% (Figure 4b). As the relative concentration was increased beyond 25% CaCl2,

remained constant indicating Ca2+ is the dominating ion in the

mixture and regulates the surface charge.


a

b

3.2 Measured Estimated

2.8 2.4 2.0 1.6

1.2 1.0

σEC / σ0

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0.8 0.6 0.4 0.2

1.2 0

25

50

75

100

Composition (% CaCl2)

0.0

0

25

50

75

100


Figure 4. Intrinsic nanochannel conductance and deduced surface charge density for electrolyte mixtures. (a) The measured intrinsic nanochannel conductance as a function of electrolyte composition for a fixed ionic strength of 1 mM. The estimated values for intrinsic conductance were calculated using 0% CaCl2 as a baseline case and assuming a constant surface charge density. (b) The deduced surface charge density as a function of electrolyte composition calculated from the measured intrinsic nanochannel conductance at each electrolyte composition and equations (S3, S5, S6, and S8). The surface charge density for each electrolyte composition (

/ )

is shown relative to the surface charge density for the 0%

CaCl2, or 1 mM KCl, case ( 0 ). Similar to the trends in Figure 4a, introduction of Ca2+ suppressed transconductance ( ) (Figure 5a). The highest was observed at 0% CaCl2 with approximately equivalent transconductance for electrolyte compositions greater than 25% CaCl2. The decrease in between 0% CaCl2 and 25% CaCl2 was 43% compared to 68% for . Considering / (Figure 5b) and the above observations about the ability of the gate to modulate conductance, it is likely that the effect of the gate electrode is reduced at electrolyte compositions greater than 25% CaCl2 because the gate is unable to manipulate the surface potential due to interactions between Ca2+ and the charged wall. Electrostatic gating is known to alter the surface



potential,4,19,41 which influences the local electrostatic and chemical interactions (including ion adsorption), and thus the net surface charge density in the gated region.19,41

b

1.4

0.7

1.2

0.6

1.0

0.5 Gg / Ga

a Transconductance (pS)

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0.8 0.6

0.4 0.3

0.4

0.2

0.2

0.1

0.0

0

25

50

75

100

0.0


0

25

50

75

100


Figure 5. Transconductance and conductance ratio ( / ) as a function of electrolyte composition at a fixed ionic strength of 1 mM. (a) The transconductance decreases as % CaCl2 was increased from 0% to 25%, consistent with the trend for intrinsic conductance as a function of electrolyte composition. (b) The conductance ratio ( / ) showed that gate modulation decreased with % CaCl2 greater than 25%, with an approximately constant value of / beyond 25% CaCl2.

Electrolyte pH manipulation. In addition to local control over the surface charge density enabled by the gate electrode, it is well known that

can be manipulated by altering the

electrolyte pH. In order to further evaluate the surface charge regulation hypothesis, the intrinsic nanochannel conductance was measured as a function of pH for a representative 1 mM KCl and 0.33 mM CaCl2. A detailed, multi-species numerical model was developed and implemented using COMSOL Multiphysics for each electrolyte solution to estimate the surface charge density from the measured conductance of the nanochannels as a function of pH. The Poisson-Nernst-Planck 16 ACS Paragon Plus Environment

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equations for nanofluidic transport of four ions (H+, OH-, K+, Cl- or H+, OH-, Ca2+, Cl-) were solved, where

was the fit parameter used to match the experimentally measured and

simulated intrinsic conductances. A complete description of the modeling methodology, which is consistent with several previous reports, is given in the Supporting Information (SI).21,49 As noted above, the nanofluidic device here comprises three glass and one PDMS wall. Given that nanoscale transport is directly controlled by surface charge,4,44,45 especially at dilute electrolyte concentrations (larger Debye lengths) in the surface charge governed regime, it is reasonable to expect that different nanochannel walls could add another layer of complexity to nanofluidic transport. Moreover, it is known that the electroosmotic velocity is different for PDMS microchannels compared to glass microchannels.50,51 Capillary electrophoresis experiments in microchannels have shown that the magnitude of the ζ potential for PDMS is between 0.25x and 0.75x the magnitude of the ζ potential for glass.51 For the experimental conditions here, this difference in the magnitude of the ζ potential corresponds to a ~0.25x to 0.75x difference in the magnitude of the surface charge density. On the other hand, some other previous reports have indicated that silica and PDMS have similar 12 values and thus approximately the same change in surface charge density as a function of pH.24,52 Therefore, we systematically evaluate the effect of heterogenous wall charge on intrinsic nanochannel conductance through a detailed, parametric numerical calculation. Two numerical models were implemented using COMSOL for each electrolyte as a function of pH to determine the effect of likely unequal surface charge density of PDMS and glass. The first COMSOL model considered a homogenous surface charge distribution (

345

=

66 )

and the second considered the most extreme expected difference in surface

charge density between the top and bottom walls, with a 4x higher surface charge density on



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the bottom (glass) wall compared to the surface charge density of the top (PDMS) wall (4

345

=

66 ).

pH (i.e., ()

For both cases the total surface charge was held constant as a function of

345

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= 89:; ≈ 5@> or = > ≈ 12B> ) since at such low pH, bulk transport behavior for HCl is expected.43 Interestingly, the increase in conductance due to H+ ions was observed experimentally for CaCl2 but not for KCl, though the computed conductance for CaCl2 at pH 2 was still ~2.4x the experimentally measured value. While the anomalous experimental result for KCl at pH 2 is in agreement with past observations of Duan et al.,43 the discrepancy between theory and experiments was attributed to an active proton-cation exchange process56 and lack of incorporating size and layering effects in models for nanochannels with multiple ionic species.57 Given that this anomalous transport behavior for nanofluidic channels is a recent finding beginning with the work of Duan et al., the discrepancies between theory and experiments remains an active area of research with little consensus in existing literature.57 The COMSOL model for the surface charge density confirmed that at 0.33 mM CaCl2 and pH ≥ 6, Ca2+ regulates the value of the surface charge density, as discussed above. In the case



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of multivalent ions, interactions between counter ions (i.e., those with opposite polairty to the wall charge) in the electrolyte with the charged wall and/or with each other are known to cause charge inversion, or the reversal of the polarity of the effective surface charge density at sufficiently high electrolyte concentration.15,16,40 Charge inversion is generally attributed to either transverse correlations between ions and charged surface sites, including electrostatic interactions and chemical binding, or lateral ion-ion correlations (as in strongly correlated liquid theory).16,40,58,59 Advanced numerical methods60 such as molecular dynamics simulations61-63 include effects of the discrete nature of charged surface sites,40,59,64 ions,40,64 water molecules,40,64 and size effects. 40,64,65 However, no consensus exists with regard to the actual mechanism by which charge inversion occurs for divalent ions or the critical electrolyte concentration for charge inversion. Past reports for nanochannels indicate that the critical concentration for 2:1 electrolytes is 350 mM or higher15,40,66 while one recent work reported charge inversion for 10 mM MgCl2 in agreement with the predicted critical concentration for strongly correlated liquid (SCL) theory.16 Notably, the applicability of SCL theory is determined by the magnitude of ion-ion correlations, which is quantified by the interaction parameter.15,59,67,68 The interaction parameter depends on the magnitude of the bare surface charge density and the ion valence. Considering the value of the interaction parameter for the system reported here (see Supporting Information) and the concentration range used in this work (pH data for 0.33 mM CaCl2 with relevant transitions observed well below even 10 mM), neither lateral correlations (i.e., ion-ion interactions) nor charge inversion are expected in our system and have therefore not been considered in the COMSOL model. The surface charge regulation at pH ≥ 6 evident from the


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pH dependent intrinsic conductance of CaCl2 is therefore attributed to transverse ion-surface correlations.40,59,67 Transconductance (pS)

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Figure 7. Transconductance as a function of pH for 1 mM KCl and 0.33 mM CaCl2 with equivalent ionic strength for both solutions. A local maximum for the transconductance was observed at pH = 8. The transconductance increased between pH 4 and pH 2 for CaCl2 in agreement with observed trends for intrinsic nanochannel conductance as a function of pH. The dashed lines are intended as eye-guides only.

As now expected, transconductance of the divalent cation (Figure 7), Ca2+ as a function of pH showed significantly different behavior than the monovalent K+ ion. for K+ between pH 8 – pH 10 was nearly independent of pH (Figure 6a), with a similar trend for Ca2+ filled nanochannels. However, for K+ filled channels increased from pH 6 to pH 8, before sharply decreasing at pH 10. Interestingly, as pH was increased from pH 6 to pH 10, the Ca2+ followed similar trends as K+ with the B < @ at pH 8, further suggesting that Ca2+ limits modulation of the surface potential at the dielectric/fluid interface by the gate electrode. Ca2+ filled nanochannels showed the highest measured at pH 2, in-line with trends, which



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likely indicate increased concentration of H+ in the diffuse layer for CaCl2 at pH 2. By contrast, (and ) remain nearly unchanged between pH 2 – pH 6 for KCl. SUMMARY AND CONCLUSIONS This paper presented for the first time a systematic comparison of cation dependent transconductance as a function of monovalent, divalent, and polyvalent mixtures for gated nanochannels, where local change in the surface potential at the dielectric/fluid interface was induced by an embedded gate electrode. A broad parametric study with 16 nm deep nanochannels for a large range of evaluated electrolyte concentrations (10-7-10-1 M), one of the widest reported pH ranges (pH 2-10), and electrolyte mixtures, with first reported transconductance for NaCl, CaCl2, and MgCl2, demonstrated that systematic changes in local electrostatic surface state are impacted by ion-surface interactions for divalent cations at pH ≥ 6, and the resulting nanoscale ion transport is strongly affected by cation type in a gated nanofluidic device. Results for KCl were in agreement with previous reports on gated nanofluidic transport of KCl and HCl establishing a viable baseline for the devices reported here, yet several new and unexpected observations were noted along with critical implications for nanofluidic transport and subsequent use of these devices in analytical systems. Conductance decreased for MgCl2 and CaCl2 at concentrations typically associated with surface charge governed transport for monovalent electrolytes, suggesting a decrease in the total surface charge density due to divalent cation-surface interactions. Consequently, addition of divalent ions can be used to regulate the effective surface charge density and thereby directly affect the nanochannel conductance. A multi-species numerical model used to compute the surface charge density confirmed that ion-surface interactions had a significant impact on the surface charge density at pH ≥ 6 for 24 ACS Paragon Plus Environment

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CaCl2. Data from KCl and CaCl2 electrolyte mixtures clearly indicated that Ca2+ in the mixture is the dominating ion as determined by a decrease in surface charge density when CaCl2 was added (between 0% CaCl2 composition and 25% CaCl2 composition) and a surface charge density that was independent of KCl concentration for % CaCl2 > 25%. The transconductance data further suggests the surface charge regulation by Ca2+ at % CaCl2 > 25% limits the ability of the gate electrode to modulate the potential at the dielectric/fluid interface. Ion-surface interactions between the charged walls and the divalent cations in the electrolyte regulate the surface charge density thus limit the ability of the gate electrode to alter the net surface charge density and consequently modulate nanochannel conductance. Our several new experimental observations, supporting models, and detailed discussion of data trends including matching with existing data show evidence of surface charge regulation by divalent cations for negatively charged nanochannels walls with potentially significant impact on how such devices can be used to construct analytical devices performing logic operations at the nanoscale.19 Further quantification of specific ion-surface interactions will require detailed information on surface reactions and is further complicated by the lack of explicitly known surface reactions between ions and PDMS or ions and borosilicate glass.17 Therefore, conductance models of gated nanofluidic channels that include effects of both electrostatic and chemical ion-surface interactions continue to be a challenge.

ASSOCIATED CONTENT Supporting Information The Supporting Information contains further data demonstrating the dependence of measured current on gate voltage, characterization of gate leakage current, details on analytical analysis of electrolyte mixtures, calculation of the interaction parameter, and details on the numerical 25 ACS Paragon Plus Environment


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model implemented in COMSOL that examines the effect of possible heterogeneous surface charge density of the top and bottom walls as well as pH dependence of nanochannel conductance. This Supporting Information is available free of charge on the ACS Publications website at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *Shaurya Prakash, Email: [email protected] Author Contributions M. Fuest and S. Prakash conceived and designed the experiments, analyzed the data, and wrote the paper. M. Fuest and C. Boone performed the experiments. K.K. Rangharajan and A.T. Conlisk contributed materials and analysis tools to the manuscript. All authors reviewed and contributed to the final manuscript. CONFLICT OF INTEREST The authors declare no competing financial interest. ACKNOWLEDGEMENTS The authors acknowledge the staff at Nanotech West Laboratories at The Ohio State University for assistance with equipment during fabrication and characterization of devices. The authors would like to acknowledge partial financial support from the US Army Research Office (ARO) through grant W911NF09C0079, and the National Science Foundation (NSF) through grant CBET-1335946. M. Fuest would like to thank NSF graduate research fellowship program (GRFP) for support.


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ABBREVIATIONS DI, deionized; KCl, potassium chloride; NaCl, sodium chloride; MgCl2, magnesium chloride; CaCl2, calcium chloride; EDLs, electric double layers; Au, gold; PDMS, polydimethyl siloxane; SEM, scanning electron microscope; SCG, surface charge governed; SCL, strongly correlated liquid REFERENCES (1) van der Heyden, F. H. J.; Bonthuis, D. J.; Stein, D.; Meyer, C.; Dekker, C. Nano Letters 2006, 6, 2232-2237. (2) Prakash, S.; Yeom, J. Nanofluidics and Microfluidics: Systems and Applications; William Andrew: Norwich, NY, 2014. (3) Guan, W.; Fan, R.; Reed, M. A. Nature Communications 2011, 2, 506. (4) Karnik, R.; Fan, R.; Yue, M.; Li, D.; Yang, P.; Majumdar, A. Nano letters 2005, 5, 943948. (5) Nam, S. W.; Rooks, M. J.; Kim, K. B.; Rossnagel, S. M. Nano letters 2009, 9, 2044-2048. (6) Prakash, S.; Pinti, M.; Bhushan, B. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 2012, 370, 2269-2303. (7) Hou, X.; Guo, W.; Jiang, L. Chemical Society Reviews 2011, 40, 2385-2401. (8) Hille, B. Ionic Channels of Excitable Membranes, Third ed.; Sinauer Associates, Inc.: Sunderland, MA, 2001, p 607. (9) Peters, C. J., Yu, H., Tien, J., Jan, Y.N., Li, M., Jan, L.Y. Proceedings of the National Academy of Sciences 2015, 112, 3547-3552. (10) Li, W., Aldrich, R.W. Proceedings of the National Academy of Sciences 2011, 108, 59465953. (11) Bichet, D., Haass, F.A., Jan, L.Y. Nature Reviews: Neuroscience 2003, 4, 957-967. (12) Aguilella, V. M.; Verdia-Baguena, C.; Alcaraz, A. Physical Chemistry Chemical Physics 2014, 16, 3881-3893. (13) Lorinczi, E.; Gomez-Posada, J. C.; de la Pena, P.; Tomczak, A. P.; Fernandez-Trillo, J.; Leipscher, U.; Stuhmer, W.; Barros, F.; Pardo, L. A. Nature Communications 2015, 6, 6672. (14) Tang, L.; Gamal El-Din, T. M.; Payandeh, J.; Martinez, G. Q.; Heard, T. M.; Scheuer, T.; Zheng, N.; Catterall, W. A. Nature 2014, 505, 56-61. (15) van der Heyden, F. H. J.; Stein, D.; Besteman, K.; Lemay, S. G.; Dekker, C. Physical Review Letters 2006, 96, 224502. (16) Li, S. X.; Guan, W.; Weiner, B.; Reed, M. A. Nano Letters 2015, 15, 5046–5051. (17) Datta, S.; Conlisk, A. T.; Li, H. F.; Yoda, M. Mechanics Research Communications 2009, 36, 65-74. (18) Martins, D. C.; Chu, V.; Conde, J. P. Biomicrofluidics 2013, 7, 034111. (19) Fuest, M.; Boone, C.; Rangharajan, K. K.; Conlisk, A. T.; Prakash, S. Nano Letters 2015, 15, 2365–2371. (20) Cheng, L.-J.; Guo, L. J. ACS Nano 2009, 3, 575-584.



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(52) Ocvirk, G.; Munroe, M.; Tang, T.; Oleschuk, R.; Westra, K.; Harrison, D. J. Electrophoresis 2000, 21, 107-115. (53) Ma, Y.; Yeh, L.-H.; Lin, C.-Y.; Mei, L.; Qian, S. Analytical Chemistry 2015, 87, 45084514. (54) Daiguji, H.; Yang, P.; Majumdar, A. Nano Letters 2004, 4, 137-142. (55) Jin, X.; Joseph, S.; Gatimu, E. N.; Bohn, P. W.; Aluru, N. R. Langmuir 2007, 23, 1320913222. (56) Raider, S. I.; Gregor, L. V.; Flitsch, R. Journal of the Electrochemical Society 1973, 120, 425-431. (57) Gillespie, D. Microfluidics and Nanofluidics 2015, 18, 717-738. (58) Besteman, K.; Zevenbergen, M. A. G.; Heering, H. A.; Lemay, S. G. Physical Review Letters 2004, 93, 170802. (59) Faraudo, J.; Travesset, A. The Journal of Physical Chemistry C 2007, 111, 987-994. (60) Conlisk, A. T. Essentials of Micro- and Nanofluidics, 1st ed.; Cambridge University Press: New York, 2013, p 552. (61) Prakash, S.; Zambrano, H. A.; Rangharajan, K. K.; Rosenthal-Kim, E.; Vasquez, N.; Conlisk, A. T. Microfluidics and Nanofluidics 2016, 20, 8. (62) Prakash, S.; Zambrano, H. A.; Fuest, M.; Boone, C.; Rosenthal-Kim, E.; Vasquez, N.; Conlisk, A. T. Microfluidics and Nanofluidics 2015, 19, 1455-1464. (63) Zambrano, H. A.; Pinti, M.; Conlisk, A. T.; Prakash, S. Microfluidics and Nanofluidics 2012, 13, 735-747. (64) Qiao, R.; Aluru, N. R. Physical Review Letters 2004, 92, 198301. (65) Greberg, H.; Kjellander, R. The Journal of Chemical Physics 1998, 108, 2940-2953. (66) He, Y.; Gillespie, D.; Boda, D.; Vlassiouk, I.; Eisenberg, R. S.; Siwy, Z. S. Journal of the American Chemical Society 2009, 131, 5194-5202. (67) Shklovskii, B. I. Physical Review E 1999, 60, 5802-5811. (68) Grosberg, A. Y.; Nguyen, T. T.; Shklovskii, B. I. Reviews of Modern Physics 2002, 74, 329-345.



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Glass PDMS Channels Gold

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