Cation Dependent Surface Charge Regulation in Gated Nanofluidic

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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, Ohio 43210, United States

*S Supporting Information

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 [potassium chloride (KCl), sodium chloride (NaCl)], 2:1 electrolytes [magnesium fl chloride (MgCl2), calcium chloride (CaCl2)], and electrolyte mixtures (KCl + CaCl2) through a gated nano uidic 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.

urface charge is a fundamental parameter that governs applications, remains poorly understood with minimal report- S nanoscale aqueous electrolyte transport in engineered ing in the existing peer-reviewed literature. systems for applications in energy conversion,1,2 fluid-analogs Nanoscale architectures built with insulating materials such − of solid-state electronics,3 5 biosensing,6,7 and in ion channels as glass, oxides, polymers, or a combination of these materials and ion pumps for precise control over ion and small molecule are commonly used substrates for numerous LoC devices for transport.8 Divalent ions play a critical role in regulating the characterizing and manipulating nanoscale flows over the past − opening, selectivity, and conductance of both cation and anion decade.1,3,4,6,19 22 While it is well-known that oxide and biological ion channels with direct implications for physio- polymer surfaces in contact with electrolyte solutions develop fl a net surface charge that can be passively controlled by logical processes such as neuronal excitability, epithelial uid − secretion, cancer cell proliferation, and blood pressure regulating the electrolyte pH,23 25 active control over surface − regulation.9 11 In ion channels and ion pumps, the nano- charge has been desired for real-time control over ionic channel structure, conformation, subunits with local binding transport for analytical operations in engineered nanoscale sites, relative hydrophobicity characteristics, local electrostatic conduits. Active control can be achieved through embedded domains at channel entrances and within ion channels, and electrodes in the walls of nanofluidic channels that act as most importantly, surface charge have been identified as tunable gates to systematically modify local surface potential 3,4 important parameters governing ion flux, selectivity, and levels and/or surface charge density at the dielectric−fluid interface. − of ion conductance and rectification.10,12 14 Yet, engineered The gate potential thus influences the electric field throughout 4,19 systems such as lab-on-chip (LoC) or micrototal analysis the nanochannel depth, allowing direct electrostatic 4,26,27 systems (μ-TAS) that attempt to mimic many of these ideal manipulation of ions and molecules in the fluid volume. biological functions for the variety of applications listed above However, systematically evaluating the efficacy of electrostatic suffer from incomplete understanding of surface charge gating toward engineering transport of multivalent and − regulation15 18 in contrast to biological systems, especially multicomponent electrolyte solutions is critical toward with multivalent ions and electrolyte mixtures. Specifically, for gated LoC nanofluidic devices, the effect of local variation of Received: September 15, 2016 electrostatic properties on transport of multivalent electrolytes Accepted: December 20, 2016 and electrolyte mixtures, which underlie most practical Published: December 20, 2016

Figure 1. Device layout along with scanning electron microscope (SEM) images. (a) Schematic showing the different functional layers of the nanofluidic device. Two microchannels (8 μm deep × 50 μm wide × 3 cm long) served as reservoirs to a bank of three nanochannels (16 nm deep × 30 μm wide × 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 polydimethylsiloxane (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. fl μ ≥ − advancing nano uidics for highly functional LoC or -TAS density at pH 6 for CaCl2. Ion surface interactions between devices. the charged walls and the divalent cations in the electrolyte Basic transport phenomena in gated or field-effect nano- regulate the surface charge density and consequently limit the fluidic devices remain an open area of research.28,29 ability of the gate electrode to alter the net surface charge Consequently, nearly all reports to date on gated nanofluidic density and modulate nanochannel conductance. devices have focused on transport of potassium chloride − (KCl),3,4,22,28,30 36 with limited evaluation of hydrochloric acid ■ EXPERIMENTAL PROCEDURES 37,38 39 (HCl) and glycine based buffers. In the case of multi- or The gated nanofluidic device consisted of two microfluidic polyvalent electrolyte solutions, including mixtures, fundamen- channels (8 μm deep × 50 μm wide × 3 cm long) which served tal research for ungated nanofluidic devices shows that ion− as fluidic reservoirs to a bank of three nanofluidic channels (16 surface and/or ion−ion interactions must be considered nm deep × 30 μm wide × 2.5 mm long). Four individually depending on the electrolyte type and composition along addressable gold (Au) gate electrodes were embedded in the with ion concentration and surface charge density.15,17,40 roof of the nanofluidic channels and separated from the Systematic comparison of gated transport for monovalent, 2:1 electrolyte in the nanochannel by a polydimethylsiloxane electrolytes, and simple electrolyte mixtures is further (PDMS) dielectric layer (PDMS thickness ∼0.7 μm).19,42 complicated by device to device variation, specifically by Only one active gate electrode was used for this work. The observed inconsistency of the surface charge density across micro- and nanofluidic network was patterned on a borosilicate fabricated devices.4,41 glass substrate using UV lithography and wet etching In this report, a systematic comparison of transport of techniques. Individually addressable Au gate electrodes were monovalent electrolytes [KCl, sodium chloride (NaCl)], 2:1 patterned onto a second glass substrate. A PDMS dielectric electrolytes [magnesium chloride (MgCl2), calcium chloride layer was spun onto the glass cover containing the electrode (CaCl2)], and electrolyte mixtures (KCl + CaCl2) through a array. The cover with embedded electrodes and the glass gated nanofluidic device is demonstrated for the first time. substrate with the patterned channel network were bonded via − Ion surface interactions regulate the nanochannel surface O2 plasma bonding to form sealed channels. Details on device charge density as a function of cation type, resulting in distinct fabrication and basic device operation and characterization have cation dependent gating behavior. The glass-polydimethylsilox- been reported previously.19,42 ane (PDMS) based devices here are cation selective under The device testing setup included two power supplies conditions of interacting electric double layers (EDLs); (Keithley 3390 function generators) used to supply independ- therefore, the cation was varied across electrolyte solutions ent axial (Va) and gate (Vg) potentials. The axial potential used fi for a xed anion. here was Va = 3 V and Va = 5 V, as discussed below, and the − ≤ ≤ The purpose of this paper is to demonstrate that systematic gate potential was in the range of 3V Vg 3 V. Current (I) changes in local electrostatic surface state induced by a gate through the nanochannels was monitored using a Keithley 6485 electrode are impacted by ion−surface interactions leading to picoammeter (Figure 1b). Devices were first tested with the surface charge regulation, and consequently, the resulting gate electrodes floating at each respective concentration, pH, or nanoscale ion transport is strongly affected by cation type in electrolyte composition in order to measure the intrinsic (i.e., fl − gated nano uidic devices. In particular, divalent cation surface Vg = 0 V) nanochannel conductance. All electrical measure- interactions reduce the surface charge density and limit the ments were conducted in an earth-grounded Faraday cage. current modulation under some of the tested gating conditions. Dedicated devices for each type of electrolyte were used to A multi-species numerical model confirmed that ion−surface avoid contamination, with the obvious exception of devices interactions had a significant impact on the surface charge used for electrolyte mixtures. Electrolyte solutions were

1594 DOI: 10.1021/acs.analchem.6b03653 Anal. Chem. 2017, 89, 1593−1601 Analytical Chemistry Article ∼ prepared for concentrations ranging from 0.01 to 100 mM at dependence on concentration at cbulk > 1 mM indicating bulk pH 7 ± 0.2. Each device was initially tested with deionized transport behavior. water (18 MΩ,10−7 M salt) to provide the same baseline for To satisfy electroneutrality, the total space charge within the comparison between devices. Only devices with an initial nanochannel volume must balance the total surface charge on ± deionized (DI) conductance within 4.4 0.5 pS were used for the nanochannel walls. Ga is thus the summation of the surface comparison of results across devices as a function of cation charge governed and the bulk conductance,16,44 type. The gate was located at L = 0.43 ± 0.02L for all devices, g m where L is the length of the nanochannel, as dependence of 2wμσ+|| Fwh GG=+= G + μ zc2 bulk device operation on gate location has been reported aSCGbulk ∑ i ii L L (1) previously.19 i=1 After initial conductance measurements with deionized where σ is the surface charge density (negative for both PDMS water, electrolyte concentrations were tested in ascending μ and glass) on the nanochannel walls, i is the mobility of order of concentration. After the electrolyte concentration was bulk species i, ci is the bulk electrolyte concentration, and w, L, increased, the device was thoroughly rinsed with the next and h are the channel width, length, and height, respectively.28 highest concentration, similar to previously reported proce- 43 The dominant term in eq 1 (GSCG or Gbulk) depends on the bulk dures. Monovalent electrolytes (KCl and NaCl) were tested electrolyte concentration.28,44 At the transition concentration, at 6 concentrations including DI water and concentrations ct, the bulk and SCG conductances are similar. ranging from 0.01 to 100 mM in order of magnitude Three of the nanochannel walls in our device are borosilicate increments. Divalent electrolytes (CaCl2 and MgCl2) were glass, and one is PDMS supported on borosilicate glass. It is tested at those concentrations with the addition of 0.33 and worth noting that the surface charge governed transport of KCl 3.33 mM to match the ionic strength for KCl and NaCl at 1 demonstrated in our PDMS−glass device has been reported for fi − and 10 mM, respectively. Overall data trends were veri ed over a wide variety of nanofluidic devices4,44 46 showing that the multiple devices with data for each experimental condition baseline data trends for the most commonly studied electrolyte comprising several data runs over multiple days. for these types of devices match those reported previously. In contrast to NaCl and KCl, CaCl2 and MgCl2 showed ■ RESULTS AND DISCUSSION cation dependent intrinsic conductance behavior as a function Three nanofluidic channels with one active embedded gate of electrolyte concentration that deviated from the well-known fi electrode connect two microchannel reservoirs (Figure 1). The KCl intrinsic conductance pro le. Ga for CaCl2 and MgCl2 ≤ axial potential, Va, drives ionic transport through the nano- (Figure 2b) was independent of bulk concentration at cbulk channel. An independently controlled potential applied to the ∼0.1 mM, also suggesting SCG transport for divalent cations. fi gate electrode, Vg, modi ed the local surface charge density Intrinsic conductance of MgCl2 showed a marked decrease (and electric field) at the dielectric−electrolyte interface from 4.5 pS at cbulk = 0.1 mM to 1.2 pS at cbulk = 1 mM. CaCl2 enabling field-effect control over ionic transport, quantified by conductance decreased from 4.0 pS for cbulk = 1 mM to 0.8 pS changes in the measured current. for cbulk = 3.33 mM showing a change in conductance per unit Cation Dependence. The intrinsic nanochannel device concentration of 1.37 pS/mM for CaCl2 and 3.67 pS/mM for fi conductance (Ga = I/Va) was rst measured with Vg =0Vasa MgCl2 before transitioning to linear concentration dependence function of cation type (Figure 2a,b) at pH = 7 ± 0.2. In in the bulk transport regime. 4,44,45 Since, G is proportional to σ for dilute electrolyte solutions agreement with previous results for KCl and anomalous a − transport of NaCl with respect to KCl,43 the two monovalent (i.e, in the surface charge governed regime),3,4,28,43 45 the ∼ × cations showed similar intrinsic (i.e., V = 0 V) conductance decrease in Ga for divalent ions corresponds to 3.75 g σ (Ga). Ga for both KCl and NaCl followed known surface charge reduction in for MgCl2 between cbulk = 0.1 mM and cbulk =1 ∼ ∼ × σ governed (SCG) transport at cbulk < 1 mM and had a linear mM and 5 reduction in for CaCl2 between cbulk =1mM and cbulk = 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 ca 0.1 mM for ≈ MgCl2 and ca 1 mM for CaCl2 and (ii) the subsequent transition from this reduced conductance to bulk transport ≈ behavior with increasing concentration observed at ct 1mM ≈ for MgCl2 and ct 3.33 mM for CaCl2. We hypothesize that the observed reduction in measured intrinsic conductance is due to reduction of σ caused by ion−surface interactions, providing further support of this claim below. Figure 2. Cation depedent intrinsic nanochannel conductance, Conductance of Gated Nanochannels. Changes in the fl measured with the gate electrode oating (Vg = 0 V). (a) The two local surface charge density and electric field were induced by monovalent cations showed similar intrinsic conductance in agreement the gate electrode to modulate ionic transport and, therefore, with previous results for anomalous transport of NaCl with respect to 3,4,32,33 43 the measured current. To our knowledge, this is the first KCl. (b) The decrease in conductance from expected surface charge ≈ ≈ systematic comparison of gating across electrolyte types and, governed behavior at ca 0.1 mM for MgCl2 and ca 1 mM for CaCl2 fi is caused by a decrease in the magnitude of the surface charge density, further, the rst presentation of gating data for NaCl, MgCl2, due to ion−surface interactions between divalent cations and the and CaCl2. It is worth noting that gating of ionic transport is negatively charged walls as discussed in the main text. The dashed lines essential to numerous analytical applications as discussed in the are intended as eye-guides. introduction. The current was monitored at electrolyte

1595 DOI: 10.1021/acs.analchem.6b03653 Anal. Chem. 2017, 89, 1593−1601 Analytical Chemistry Article ≤ ≤ concentrations between 0.01 and 100 mM for +3 V Vg charge density, as discussed above, and appear to limit the − fi 19 3 V at a xed axial potential (Va). A representative plot of current modulation under gating conditions (Figure 3b). measured current as a function of gate voltage for various In contrast to Mg2+, a second maxima was observed for cations is shown in Figure S1. CaCl2 at 0.33 mM. This second maxima was observed for 5,37 Following previously reported analysis for gated devices, CaCl2 and not MgCl2 likely since all concentrations used in the the total measured current arises from two components and can gating experiments fall within the concentration range where − be written as I = GaVa + GgVg. Here, Ga is the intrinsic ion surface interactions regulate the surface charge density for nanochannel conductance (Vg = 0) and Gg is the trans- MgCl2 (ca = 0.1 mM for MgCl2) but not for CaCl2 (ca =1mM 5,19,37 conductance (dI/dVg). To further verify that the two for CaCl2). At concentrations c > ct, bulk transport behavior is components of the current were independent, transconduc- known to dominate; thus, modulation of the surface charge tance data was taken at Va = 3 V and Va = 5 V for all data sets. density will have a limited impact on nanochannel conductance, − ff The dimensionless conductance ratio, Gg/Ga, compares the and ion surface interactions are expected to e ect the − transconductance to the intrinsic nanochannel conductance magnitude of Gg/Ga in the range of ca ct. (Figure 3). For the monovalent cations, the maximum value of Electrolyte 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 ± fi CaCl2 were evaluated at pH = 7 0.2 at a xed 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) Figure 3. Conductance ratio as a function of cation type for (a) with a complete summary of the prepared electrolyte monovalent cations and (b) divalent cations. The conductance ratio compositions in Table S1. The highest measured Ga (Figure Gg/Ga is a nondimensional parameter that compares the trans- 4a) was at 0% CaCl2. As CaCl2 percentage was increased from conductance, Gg, to the intrinsic nanochannel conductance, Ga. The dashed lines are intended as an eye-guide.

≈ Gg/Ga was observed at the transition concentration, ct 1mM (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 and 100 mM here). The data trends reported here for Gg/Ga (and for Ga 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 Figure 4. Intrinsic nanochannel conductance and deduced surface intrinsic conductance (Figure 2), no signiﬁcant cation depend- charge density for electrolyte mixtures. (a) The measured intrinsic ence was observed between KCl and NaCl within experimental nanochannel conductance as a function of electrolyte composition for ﬁ error as shown in Figure 3a. Our results show that NaCl follows a xed ionic strength of 1 mM. The estimated values for intrinsic the same concentration dependent gating behavior as the other conductance were calculated using 0% CaCl2 as a baseline case and 5,37 assuming a constant surface charge density. (b) The deduced surface monovalent symmetric electrolytes reported previously, with charge density as a function of electrolyte composition calculated from the maximum conductance ratio (Gg/Ga) at the transition the measured intrinsic nanochannel conductance at each electrolyte concentration to bulk electrolyte transport. composition and eqs S3, S5, S6, and S8. The surface charge density for σ As with intrinsic conductance, cation dependent behavior each electrolyte composition ( EC) is shown relative to the surface was observed for Gg/Ga for CaCl2 and MgCl2. For MgCl2, charge density for the 0% CaCl , or 1 mM KCl, case (σ ). ∼ 2 0 Gg/Ga at cbulk = 0.1 mM was 0.2 compared to 0.6 for monovalent ions even though KCl, NaCl, and MgCl2 have ∼ comparable Ga at 0.1 mM. Starting at 0.1 mM, gate modulation 0% to 25%, the intrinsic conductance decreased from 2.8 to increased with concentration for MgCl2, with the maximum 1.4 pS. Further increasing the CaCl2 percentage from 25% to value of Gg/Ga at 1 mM, which is the transition concentration 50% caused the intrinsic conductance to decrease from 1.4 to to bulk transport behavior for MgCl2. 1.2 pS, with no measured change beyond 50% CaCl2. 2+ For CaCl2, Gg/Ga showed a local maxima at 3.33 mM, which Therefore, starting at 25% Ca in the solution, Ga was is the transition concentration to bulk transport behavior. independent of K+ concentration. 2+ ∼ Gg/Ga for Ca decreased from 0.9 at 0.33 mM to 0.3 at 1 With 0% CaCl2 as the baseline, Ga was estimated as a mM (which was transition from SCG to the reduced function of electrolyte composition by assuming a constant 43−45 conductance, ca). Consequently, the gate electrode showed surface charge density across electrolyte compositions and reduced modulation for both divalent ions at their respective that the proportion of K+ to Ca2+ in the bulk was preserved in 18 values of ca (0.1 mM for MgCl2 and 1 mM for CaCl2). Near this the nanochannel (Supporting Information). The estimated − concentration (ca), ion surface interactions reduce the surface values for Ga did not match experimentally measured Ga as

1596 DOI: 10.1021/acs.analchem.6b03653 Anal. Chem. 2017, 89, 1593−1601 Analytical Chemistry Article shown in Figure 4a, indicating that one or both of the main A detailed, multi-species numerical model was developed and assumptions (i.e., constant surface charge density across implemented using COMSOL Multiphysics for each electrolyte electrolyte compositions or the relative concentrations of K+ solution to estimate the surface charge density from the to Ca2+ in the nanochannel match the relative concentration in measured conductance of the nanochannels as a function of the bulk) may be problematic for matching theoretical pH. The Poisson-Nernst-Planck equations for nanofluidic estimates to the experimental measurements. The difference transport of four ions (H+,OH−,K+,Cl− or H+,OH−,Ca2+, between the measured and estimated values is not explained by Cl−) were solved, where σ was the fit parameter used to match the ratio of K+ to Ca2+ in the nanochannel alone, as the the experimentally measured and simulated intrinsic con- estimated and measured intrinsic conductances for 100% CaCl2 ductances. A complete description of the modeling method- also did not match. Therefore, the constant surface charge ology, which is consistent with several previous reports, is given density and, consequently, the constant space charge density in the Supporting Information.21,49 assumption fails for Ga in the case of KCl + CaCl2 mixtures. As noted above, the nanofluidic device here comprises three Instead, using the measured Ga at each electrolyte glass and one PDMS wall. Given that nanoscale transport is composition, the surface charge density was estimated as a directly controlled by surface charge,4,44,45 especially at dilute function of electrolyte composition relative to the 0% CaCl2 electrolyte concentrations (larger Debye lengths) in the surface case (Supporting Information). The estimated relative σ (Table ff σ charge governed regime, it is reasonable to expect that di erent S2) showed that the magnitude of decreased by more than nanochannel walls could add another layer of complexity to 1/2 as CaCl2 composition goes from 0% to 25% (Figure 4b). nanofluidic transport. Moreover, it is known that the As the relative concentration was increased beyond 25% CaCl2, ff σ 2+ electroosmotic velocity is di erent for PDMS microchannels remained constant indicating Ca is the dominating ion in compared to glass microchannels.50,51 Capillary electrophoresis the mixture and regulates the surface charge. 2+ experiments in microchannels have shown that the magnitude Similar to the trends in Figure 4a, introduction of Ca of the zeta (ζ) potential for PDMS is between 0.25× and 0.75× suppressed transconductance (G )(Figure 5a). The highest G 51 g g the magnitude of the ζ potential for glass. For the experimental conditions here, this difference in the magnitude of the ζ potential corresponds to a ∼0.25−0.75× 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 pK 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 heterogeneous 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 Figure 5. Transconductance and conductance ratio (Gg/Ga)asa of likely unequal surface charge density of PDMS and glass. function of electrolyte composition at a fixed ionic strength of 1 mM. The first COMSOL model considered a homogeneous surface (a) The transconductance decreases as % CaCl2 was increased from σ σ 0% to 25%, consistent with the trend for intrinsic conductance as a charge distribution ( PDMS = glass) and the second considered function of electrolyte composition. (b) The conductance ratio (G / the most extreme expected difference in surface charge density g × Ga) showed that gate modulation decreased with greater than 25% between the top and bottom walls, with a 4 higher surface CaCl2, with an approximately constant value of Gg/Ga beyond 25% charge density on the bottom (glass) wall compared to the CaCl . σ σ 2 surface charge density of the top (PDMS) wall (4 PDMS = glass). For both cases, the total surface charge was held constant as a σ σ function of pH (i.e., (wL) PDMS +(wL) glass = constant). In was observed at 0% CaCl2 with approximately equivalent 21,49 transconductance for electrolyte compositions greater than 25% agreement with past results, the transport mechanism of CaCl . The decrease in G between 0% CaCl and 25% CaCl ions in the present system was dominated by electromigration, 2 g 2 2 with convection contributing to less than 7% of the total was 43% compared to 68% for Ga. Considering Gg/Ga (Figure 5b) and the above observations about the ability of the gate to conductance. As a result, the impact on measured conductance fl modulate conductance, it is likely that the effect of the gate due to induced variation in electroosmotic ow arising from the − electrode is reduced at electrolyte compositions greater than hybrid glass PDMS system is likely negligible. Notably, for a fixed total surface charge, the intrinsic 25% CaCl2 because the gate is unable to manipulate the surface potential due to interactions between Ca2+ and the charged conductance in the case of a homogeneous charge distribution wall. Electrostatic gating is known to alter the surface and in the case of heterogeneous charge distribution between potential,4,19,41 which influences the local electrostatic and the top (PDMS) and bottom (glass) walls differed by less than chemical interactions (including ion adsorption), and thus the 2% (Figure S4) showing that the intrinsic conductance is net surface charge density in the gated region.19,41 independent of likely unequal surface charge density on the top Electrolyte pH Manipulation. In addition to local control and bottom walls. The intrinsic conductance, therefore, is over the surface charge density enabled by the gate electrode, it determined by the total surface charge of all nanochannel walls is well-known that σ can be manipulated by altering the and the resulting space charge in the nanochannel volume as a electrolyte pH. In order to further evaluate the surface charge function of pH. Our observation that experimentally measured regulation hypothesis, the intrinsic nanochannel conductance Ga and Gg/Ga for KCl match previously reported trends for was measured as a function of pH for a representative 1 mM homogeneous nanochannels (discussed above) is supported by KCl and 0.33 mM CaCl2. the modeling results which indicate that the transport is

1597 DOI: 10.1021/acs.analchem.6b03653 Anal. Chem. 2017, 89, 1593−1601 Analytical Chemistry Article governed by the total surface charge and the total change in decrease with pH for both silica and PDMS between pH 8 and surface charge. pH 1023,41,53 but does not consider ion−surface interactions. More work is needed to develop a strong understanding of Notably, at pH 10, the computed value of the surface charge the impact of heterogeneous walls; however, the glass−PDMS density for KCl filled nanochannels was ∼2.8× higher than the fi heterogeneity does not appear to be a major factor for the surface charge density for CaCl2 lled nanochannels. intrinsic conductance reported here. Our data and models Multi-valent and even monovalent ions in solution are indicate that the transport is strongly (and as expected) known to reduce the magnitude of the surface charge density of dominated by the space charge in the nanochannel volume, ungated micro- and nanofluidic channels as a function of ion which in turn is impacted by the total surface charge, i.e., an valence, electrolyte concentration, and the bare surface charge effective charge density from all four walls enclosing the fluid density (and thus pH).15,17,40 In the devices considered here, volume. In the case of transconductance, the gate electrode the magnitude of the bare surface charge density is highest at alters the local surface potential and/or surface charge density pH 10 and the magnitude of the surface charge density is likely which influences both electrostatic and chemical ion−surface regulated by cation−surface interactions for both the 2:1 and interactions. Ion−surface interactions in turn determine the 1:1 electrolytes at pH 10, causing the experimentally observed ff e ective surface charge density and subsequently the space plateau in the intrinsic conductance for KCl and CaCl2 between charge in the nanochannel volume. Quantification of specific pH 10 and pH 8. ion−surface interactions will require detailed information on As expected, the magnitude of the surface charge density surface reactions and is further complicated by the lack of (derived from the intrinsic conductance data) decreased for fi explicitly known surface reactions between ions and PDMS or both KCl and CaCl2 lled channels from pH 8 to pH 7 and ions and borosilicate glass.17 Comprehensive studies evaluating from pH 7 to pH 6, but with a lower magnitude of the surface fl fi in uence of heterogeneous nanochannel walls on nanochannel charge density for CaCl2 lled nanochannels compared to KCl transport are beyond the scope of this work and form topics for filled nanochannels. In contrast to KCl filled channels, the fi future investigations. CaCl2 lled nanochannels were isoelectric at pH 6, indicating The experimentally measured intrinsic nanochannel con- divalent cation−surface interactions reduce the magnitude of ductance for 1 mM KCl and 0.33 mM CaCl2 as a function of the surface charge density for pH ≥ 6. pH is plotted with the numerically computed intrinsic From the COMSOL model of the intrinsic conductance data, conductance in Figure 6a. The corresponding computed value the nanochannel surface was isoelectric for both KCl and CaCl2 filled channels at pH ≤ 4 consistent with previous reports which indicate the isolectric point is pH 2−3 for glass20 and pH 2−4 for PDMS.24,25 However, at pH 2, the numerically modeled intrinsic conductance did not match the experimentally measured intrinsic nanochannel conductance. The increase in the computed conductance from the 4 species numerical model from pH 4 to pH 2 is due to the higher concentration of H+ ions and the significantly higher mobility of H+ compared to + 2+ μ + ≈ μ + μ + ≈ μ 2+ K and Ca ( H 5 K or H 12 Ca ) since, at such low pH, bulk transport behavior for HCl is expected.43 Interestingly, the increase in conductance due to H+ ions was Figure 6. Use of solution pH to modify surface charge density. (a) observed experimentally for CaCl2 but not for KCl, though the ∼ × Experimentally measured and numerically calculated intrinsic nano- computed conductance for CaCl2 at pH 2 was still 2.4 the channel conductance as a function of pH. (b) The average surface experimentally measured value. While the anomalous exper- charge density computed with the numerical model. The surface σ fi imental result for KCl at pH 2 is in agreement with past charge density, ,wasthe t parameter used to match the observations of Duan and Majumdar,43 the discrepancy experimentally measured and simulated intrinsic conductances based 49,54,55 between theory and experiments was attributed to an active on well-established ion transport theory in nanochannels. − 56 Dashed lines are intended as eye-guides. proton cation exchange process and lack of incorporating size and layering effects in models for nanochannels with multiple ionic species.57 Given that this anomalous transport of the effective surface charge density for all four walls at each behavior for nanofluidic channels is a recent finding beginning pH is shown in Figure 6b. It is worth noting for practical with the work of Duan and Majumdar,43 the discrepancies applications that the average surface charge density reported between theory and experiments remains an active area of here, which governs the nanoscale ion transport at dilute research with little consensus in existing literature.57 electrolyte concentrations, for PDMS−glass devices falls within The COMSOL model for the surface charge density 2 4 fi ≥ 2+ the lower range for silica [∼−0.001 to −0.1 C/m ], which is con rmed that, at 0.33 mM CaCl2 and pH 6, Ca regulates known to vary based on fabrication methods. The exper- the value of the surface charge density, as discussed above. In imentally measured intrinsic conductance was independent of the case of multi-valent ions, interactions between counterions pH for both electrolytes between pH 10 and pH 8 with similar (i.e., those with opposite polarity to the wall charge) in the intrinsic conductance measured for KCl at pH 10 and pH 8 and electrolyte with the charged wall and/or with each other are CaCl2 at pH 10 and pH 8, consistent with experimental known to cause charge inversion or the reversal of the polarity 17 ff ffi measurements for 1 mM KNO3 in microchannels. The nearly of the e ective surface charge density at su ciently high constant intrinsic conductance corresponds to a nearly constant electrolyte concentration.15,16,40 Charge inversion is generally value of the surface charge density for each electrolyte. This is attributed to either transverse correlations between ions and in contrast with the classical behavior (see Supporting charged surface sites, including electrostatic interactions and Information), which predicts the surface charge density should chemical binding, or lateral ion−ion correlations (as in strongly

1598 DOI: 10.1021/acs.analchem.6b03653 Anal. Chem. 2017, 89, 1593−1601 Analytical Chemistry Article correlated liquid theory).16,40,58,59 Advanced numerical meth- ■ SUMMARY AND CONCLUSIONS − ods60 such as molecular dynamics simulations61 63 include This paper presented for the first time a systematic comparison 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, of cation dependent transconductance as a function of no consensus exists with regard to the actual mechanism by monovalent, divalent, and polyvalent mixtures for gated which charge inversion occurs for divalent ions or the critical nanochannels, where local change in the surface potential at −fl electrolyte concentration for charge inversion. Past reports for the dielectric uid interface was induced by an embedded gate nanochannels indicate that the critical concentration for 2:1 electrode. A broad parametric study with 16 nm deep electrolytes is 350 mM or higher15,40,66 while one recent work nanochannels for a large range of evaluated electrolyte −7− −1 reported charge inversion for 10 mM MgCl2 in agreement with concentrations (10 10 M), one of the widest reported the predicted critical concentration for strongly correlated pH ranges (pH 2−10), and electrolyte mixtures, with first 16 liquid (SCL) theory. reported transconductance for NaCl, CaCl2,andMgCl2, Notably, the applicability of SCL theory is determined by the demonstrated that systematic changes in local electrostatic magnitude of ion−ion correlations, which is quantified by the − 15,59,67,68 surface state are impacted by ion surface interactions for interaction parameter. The interaction parameter divalent cations at pH ≥ 6, and the resulting nanoscale ion depends on the magnitude of the bare surface charge density transport is strongly affected by cation type in a gated and the ion valence. Considering the value of the interaction nanofluidic device. Results for KCl were in agreement with parameter for the system reported here (see Supporting previous reports on gated nanofluidic transport of KCl and HCl Information) and the concentration range used in this work establishing a viable baseline for the devices reported here, yet (pH data for 0.33 mM CaCl2 with relevant transitions observed well below even 10 mM), neither lateral correlations (i.e., ion− several new and unexpected observations were noted along fl ion interactions) nor charge inversion are expected in our with critical implications for nano uidic transport and system and have therefore not been considered in the subsequent use of these devices in analytical systems. COMSOL model. The surface charge regulation at pH ≥ 6 Conductance decreased for MgCl2 and CaCl2 at concen- evident from the pH dependent intrinsic conductance of CaCl2 trations typically associated with surface charge governed is therefore attributed to transverse ion−surface correla- transport for monovalent electrolytes, suggesting a decrease tions.40,59,67 in the total surface charge density due to divalent cation− As now expected, transconductance of the divalent cation surface interactions. Consequently, addition of divalent ions can (Figure 7)Ca2+ as a function of pH showed significantly 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 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 Figure 7. Transconductance as a function of pH for 1 mM KCl and 2+ regulation by Ca at % CaCl2 > 25% limits the ability of the 0.33 mM CaCl2 with equivalent ionic strength for both solutions. A gate electrode to modulate the potential at the dielectric−fluid local maximum for the transconductance was observed at pH = 8. The interface. Ion−surface interactions between the charged walls transconductance increased between pH 4 and pH 2 for CaCl2 in agreement with observed trends for intrinsic nanochannel conductance and the divalent cations in the electrolyte regulate the surface as a function of pH. The dashed lines are intended as eye-guides only. charge density and consequently limit the ability of the gate electrode to alter the net surface charge density and modulate nanochannel conductance. Our several new experimental observations, supporting ff + + di erent behavior than the monovalent K ion. Ga for K models, and detailed discussion of data trends including between pH 8 and pH 10 was nearly independent of pH matching with existing data show evidence of surface charge 2+ fi (Figure 6a), with a similar trend for Ca lled nanochannels. regulation by divalent cations for negatively charged nano- + fi However, Gg for K lled channels increased from pH 6 to pH channel walls with potentially significant impact on how such 8, before sharply decreasing at pH 10. Interestingly, as pH was 2+ devices can be used to construct analytical devices performing increased from pH 6 to pH 10, the Ca followed similar trends 19 fi + CaCl2 KCl logic operations at the nanoscale. Further quanti cation of as K with the Gg < Gg at pH 8, further suggesting that fi − Ca2+ limits modulation of the surface potential at the speci c ion surface interactions will require detailed informa- dielectric−fluid interface by the gate electrode. Ca2+ filled tion on surface reactions and is further complicated by the lack nanochannels showed the highest measured G at pH 2, in-line of explicitly known surface reactions between ions and PDMS g 17 with Ga trends, which likely indicate increased concentration of or ions and borosilicate glass. Therefore, conductance models H+ in the diffuse layer for CaCl at pH 2. In contrast, G (and of gated nanofluidic channels that include effects of both 2 g − Ga) remains nearly unchanged between pH 2 and pH 6 for electrostatic and chemical ion surface interactions continue to KCl. be a challenge.

1599 DOI: 10.1021/acs.analchem.6b03653 Anal. Chem. 2017, 89, 1593−1601 Analytical Chemistry Article ■ ASSOCIATED CONTENT (13) Lorinczi, E.; Gomez-Posada, J. C.; de la Pena, P.; Tomczak, A. P.; Fernandez-Trillo, J.; Leipscher, U.; Stuhmer, W.; Barros, F.; Pardo, *S Supporting Information L. A. Nat. Commun. 2015, 6, 6672. The Supporting Information is available free of charge on the (14) Tang, L.; Gamal El-Din, T. M.; Payandeh, J.; Martinez, G. Q.; ACS Publications website at DOI: 10.1021/acs.anal- Heard, T. M.; Scheuer, T.; Zheng, N.; Catterall, W. A. Nature 2014, chem.6b03653. 505,56−61. Further data demonstrating the dependence of measured (15) van der Heyden, F. H. J.; Stein, D.; Besteman, K.; Lemay, S. G.; current on gate voltage, characterization of gate leakage Dekker, C. Phys. Rev. Lett. 2006, 96, 224502. current, details on analytical analysis of electrolyte (16) Li, S. X.; Guan, W.; Weiner, B.; Reed, M. A. 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1601 DOI: 10.1021/acs.analchem.6b03653 Anal. Chem. 2017, 89, 1593−1601