An Experimental Approach to Systematically Probe Charge

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An Experimental Approach to Systematically Probe Charge Inversion in Nanofluidic Channels Kuang-Hua Chou, Christopher McCallum, Dirk Gillespie, and Sumita Pennathur Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b04736 • Publication Date (Web): 21 Dec 2017 Downloaded from http://pubs.acs.org on December 23, 2017

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An Experimental Approach to Systematically Probe Charge Inversion in Nanofluidic Channels Kuang-Hua Chou+, Christopher McCallum+, Dirk Gillespie^, and Sumita Pennathur+* +

University of California, Santa Barbara, CA, USA, 93106

^

Rush University Medical Center, Chicago, IL, USA, 60612

* Corresponding author: [email protected], +1 805-893-5510

ABSTRACT Charge inversion of the surfaces of nanofluidic channels occurs in systems with high-surface charge and/or highly charged ions, and is of particular interest because of applications in biological and energy conversion systems. However, the details of such charge inversion have not been clearly elucidated. Specifically, although we can experimentally and theoretically show charge inversion, understanding at what conditions charge inversion occurs, as well how much the charge-inverting ions change the surface, are not known. Here, we show a novel experimental approach for uniquely finding both the ζ-potential and adsorption time of charge inverting ions in aqueous nanofluidic systems. KEYWORDS ζ-potential, electric double layer, current monitoring, charge inversion

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INTRODUCTION In electrokinetic nanofluidic channels, ions can significantly affect the fluid flow and generate unique interactions with a charged channel surface. For example, complex ions are known to induce a change in sign of the apparent surface charge, known as charge inversion.1,2 Charge inversion is particularly relevant as it applies to biological applications such as DNA condensation and drug delivery,3-5 and can be exploited for manipulation of apparent DNA mobility to improve the accuracy of DNA sequencing.7,8 A stationary ITP-like front between two electrolytes can also be produced with local charge inversion, 9 opening the door to charge-based manipulation of biomolecules. Researchers have studied charge inversion in micro- and nanofluidics, both experimentally and theoretically. To observe charge inversion with multivalent species, researchers have performed streaming potential measurements in nanochannels1 and current rectification measurements in nanopores,2 as well as open potential measurements through varying relative reservoir concentrations.10 Researchers have also shown ion-ion correlations and charge inversion in trivalent electrolytes between mica surfaces.11 Atomistic models have predicted charge inversion and flow reversal in


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nanofluidic systems,12-14 and some have shown good agreement with current experimental data,15 but they are quite computationally intensive. Simpler continuum theories have reproduced experimental results in broad terms, but rely on fitted parameters like slip-plane location.16,17 Lastly, some attempt has been made to explain the physics of charge inversion through modified mean-field theories.18,19 While all these analyses have strengthened our fundamental understanding of the electrical double layer and charge inversion, theory still does not match the experiments. We believe this is due to a fundamental gap in knowledge regarding the physics of charge inversion, which is in part a consequence of a lack of robust experimental protocols to characterize it. Therefore, a need persists for an experimental setup and protocol to truly assess charge inversion in electrokinetic nanofluidic systems. In this paper, we employed current monitoring (CM),20,21 in which one electrolyte displaces another of different conductivity in an electrokinetic nanofluidic channel, to systematically identify two crucial parameters: the change in ζ-potential (electrostatic potential at the shear plane) and the adsorption time of charge inverting ions to change the surface of a nanofluidic channel. These parameters depend on the ion species and its concentration, both of


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which we explore in this manuscript. The CM method requires a simpler experimental setup than for streaming currents from pressure-driven flow. Moreover, even with high pressures, streaming currents are in the pA range, while our experiments produce nA currents without requiring specialized equipment. RESULTS AND DISCUSSION

Figure 1. Schematic of a current monitoring (CM) experiment. (Timepoint a) Low concentration solution is in the entire channel and negative well, with high concentration solution in the positive well only. A power supply and ammeter, Keithley 6517a, is connected to platinum electrodes which are placed in both reservoirs (see Fig. S5). (Timepoint b) High concentration solution is electroosmotically driven into the channel. (Timepoint c) The current approaches a constant value, meaning the high concentration solution has filled whole channel.

Experimental method: Current monitoring20,21 is a decades-old technique that indirectly measures electroosmotic flow (EOF) and ζ-potential via the simple measurement of voltage-driven current through a channel. Specifically, we first fill a


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glass nanochannel with the low concentration electrolyte by capillary action. After filling, the positive reservoir is filled with high concentration electrolyte. We then simultaneously apply a voltage (30V) and monitor the change in current through the channel (Keithley 6517a). Due to the negative surface charge, the excess counter-ions in the EDL induce fluid flow from positive well to negative well, and the higher conductivity electrolyte fills the channel, decreasing the total resistance of the channel and increasing the overall current measured (Figure 1). We record the current every 30 ms (Figure 1, Timepoint b). When the current trace is flat, the nanochannel has been filled by the high concentration electrolyte (Figure 1, Timepoint c). To calculate the EOF rate, 𝑢𝑢𝐸𝐸𝐸𝐸𝐸𝐸 , we divide the time interval ∆t (from point a to c) from the length of

the nanochannel L, and for a nanochannel with thin electric double layers, the ζ𝐿𝐿 𝜇𝜇

potential is ζ = − 𝛥𝛥𝛥𝛥 𝜖𝜖𝜖𝜖, where μ is the fluid viscosity, ϵ is the permittivity, and E is the applied electric field. Note that this assumes thin electric double layers, which is generally the case with concentrations of solutions greater than 1mM.22 Charge-Inverting Ions: Figure 2 shows the results of a CM experiment using the charge inverting ion La3+. In this particular experiment, the two aqueous solutions were a mixture of 10 mM LaCl3 with 10 mM Tris-buffer (conductivity = 4.068 mS/cm) and


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a 24.70 mM Tris buffer (conductivity = 3.063 mS/cm). First, we performed a simple current monitoring experiment with different concentrations of Tris buffer (as in Figure 1) to ensure that the channel performed as expected (i.e., no bubbles or clogs in the channel, see Figure S1 for a typical CM experiment with Tris only). With the channel filled with 24.70 mM of Tris, we replaced one reservoir with the Tris-buffered LaCl3. We then immediately applied an external potential, 30 V, into the well with the LaCl3 and recorded the current, shown in Figure 2 (top, Timepoint a). In all experiments, current originally rises (from point a to b), indicating that LaCl3 + Tris, the higher conductivity solution, is filling the channel. However, after 30 s, the current decreases and continues to decrease until the channel is re-filled the original fluid again, the lower conductivity solution. This strongly suggests that the decrease of current corresponds to flow reversal. This makes sense if La3+ induced charge inversion of the surface, i.e., changed the ζ-potential on the channel to a positive value and thus reversed the direction of the flow.1 Presumably, when the LaCl3 solution enters the channel, La3+ ions gradually adsorb on the wall, leading to charge inversion. Consistent with this idea, the current does not seem to reach steady state as the Tris buffer is refilling the channel. Instead, there is a long and slow decrease in conductivity to steady state corresponding


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to the La3+ ions slowing coming off the channel wall. In addition, now that the channel is coated, the ζ-potential is smaller and thus the contribution of surface currents is reduced, making the absolute value of current lower than when the experiment started. To confirm our hypothesis, we performed a slightly more complicated experiment, with results shown in Figure 2 (bottom). Here, like in the previous experiment, the Tris buffer is loaded in the channel first and the 10 mM Tris-buffered LaCl3 is placed in a reservoir with a positive voltage applied (Figure 2, bottom, Timepoint a). As before, the current rises when an electric field is applied. However, unlike before, once the current reached its maximum value, we cut off the power and replaced the buffer well with 20 mM Tris-buffered LaCl3 (conductivity = 7.299 mS/cm) (Figure 2, bottom, Timepoint c). This replacement allows us to determine whether the channel walls were chargeinverted. If so, the current would continue to rise and level off at the current corresponding to where the 20mM + LaCl3 would fill the channel. If the charge had not inverted, the current would not rise, but rather level off, as in typical current monitoring experiment. In Figure 2 (bottom, Timepoint d), we show that the current indeed rises to


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Figure 2. (top) Experimental results of CM experiment with Tris-buffered LaCl3 solution, 10 mM LaCl3 + 10 mM Tris and 24.70 mM Tris buffer. The figure on the left shows the average of 3 trials with error-propagated 95% confidence intervals of the data. On the right are schematics of the solutions in the channel corresponding to the timepoints in the current monitoring plot. Timepoint a: initial Tris filled channel with 10 mM LaCl3 + 10 mM Tris added to positive well only. Timepoint b: La3+ induces flow reversal. Timepoint c: concentration front retreats. (bottom) Experimental results of a CM experiment with different concentrations of Tris-buffered LaCl3 solution, 10 mM LaCl3 + 10 mM Tris, 20 mM LaCl3 + 10 mM Tris, and 10 mM Tris buffer. Timepoint a-b: same as in the top panel. Timepoint c: current reaches maximum, and 10 mM Tris-buffered LaCl3 was replaced with 20 mM Tris-buffered LaCl3. Timepoint d: Due to the charge inversion, the flow goes from right to left, electroosmotically driving the 20 mM Trisbuffered LaCl3 into the channel, causing the current to keep rising and finally leveling off (Timepoint d). the expected level based on the conductivities, and then stabilizes because the channel has filled with the high conductivity 20 mM Tris-buffered LaCl3 solution. Theoretical Description: Although currently no theory of ions can exactly reproduce


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experiments with charge inversion, density functional theory (DFT) of electrolytes and similar models have done so qualitatively, even with trivalent ions.2,16,17 Specifically, we used DFT6 to compute the electrical double layer structure of a mixture of La3+ and Tris. In Figure S4, we show how the ζ-potential can change as a function of added La3+ concentration, becoming positive to induce a reversal of fluid flow. This is due to a region of positive potential near the negatively charged wall (Figure S4, inset). However, from an ion transport point of view, it is unknown where the slip plane is located (i.e., where ion velocities in the Navier-Stokes equations are 0 and the ζpotential is located), especially for trivalent ions. Therefore, Figure S4 supports the idea of charge inversion for our experimental conditions in an equilibrium electrical double layer, but we need a different approach to model our data when ions are flowing. Because our experimental results show charge inversion reversing fluid flow due to a change of sign in the ζ-potential, we hypothesized that two parameters can describe the phenomenon: ζ2 and tads. We define ζ2 as the ζ-potential that the channel eventually reaches when the charge-inverting ion reaches a steady state (ζ1 is the ζ-potential before charge inversion), and tads as the timescale for the ion to adsorb to the channel wall. To model the data with ions flowing with these two parameters experimentally defined, we


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employed Nernst-Plank theory (see Supporting Information). Figure 3 shows our theoretical results, and how these parameters lead to different CM curves. Specifically, as ζ2 becomes more positive, the CM curve in Figure 3(a) is narrower and achieves steady state much faster. This is because the EOF in the opposite direction is faster with a larger ζ-potential. Similarly, if the adsorption time is longer, the current dips down lower and takes a longer time to reach steady state. This increase in steady-state time occurs because the charge-inverting ions need more time to attach to the surface and, therefore, it takes longer to reach steady state. Both parameters depend on each other, as well as the concentration and the flow velocity. On the right side of Figure 3, we show simulations of both the concentration front (black solid line) and the ζ-potential (red dashed line) along the channel at three different time points. These demonstrate how ζ2 and tads affect the profile of the ζpotential and conductivity along the channel. A larger tads elongates the ζ-potential transition width (top row), and the higher ζ-potential causes the concentration to move more quickly through the channel (bottom row).


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Figure 3. (a) Simulations of current monitoring with three different ζ2 and tads for a 5 mm long, 5 μm wide, 100 nm tall channel with initial ζ-potential of -43 mV. Higher ζ2 causes the current to reach steady state faster, and larger tads decreases the current minimum and increases the time to reach steady state. (b-j) Simulation results of conductivity (solid black curve) and ζ-potential (dashed red line) for given parameters (b-d vs e-g vs h-j) at 3 different times (first column: 10 s where the front is moving to the right; second column: 30 s near the current minima; third column = 90 s where the front is moving to the left). Determining Charge Inversion: Given that concentration affects both ζ2 and tads, we used these simulations to predict ζ2 and tads for a variety of concentrations of charge inverting ions, keeping ζ1 constant at -43 mV, yielding constant initial EOF. We chose to perform experiments with Ru(bpy)3Cl2, instead of LaCl3, because Ru(bpy)32+ fluoresces, allowing us to track the front of the ions as they move through the channel. We chose a ζ1 of -43 mV for our simulations because we experimentally determined the


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ζ1 of 24.7mM Tris buffer to be -43±4.17 mV, as described in SI. We first used this ion to confirm that the fluid did indeed switch directions by seeing a bright front of ions filling the channel, and then the channel dimming as the fluid flow was reversed and Tris re-filled the channel (see Electronic Supporting Information for video). Next, after determining the ζ-potential of the channel when filled with Tris buffer (ζ1) through simple CM experiments (Figure S1), we performed the same experiments with different concentrations of Ru(bpy)3Cl2 (0.1 mM, 2.5 mM and 5 mM, all in 10 mM Tris buffer) with 24.70 mM Tris in the other well. In all experiments, the current sharply decreased at the beginning after which charge inversion occurred, and the current slowly increased after the channel wall was coated, as shown in Figure 4. As expected, as the Ru(bpy)3Cl2 concentration increases, there is a more dramatic effect on the charge reversal, and the current returns to steady state more quickly. In addition to showing all the current monitoring traces in Figure 4, we also show a control experiment in the first panel without a charge-inverting ion. We compared these experiments to simulations by fitting ζ2 and tads. As expected, for increasing Ru(bpy)3Cl2 concentration ζ2 increases and tads decreases. Specifically, ζ2 ranges from 1.3 mV to 7.5 mV, showing that the ζ-potential is dependent on the


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Figure 4. The experimental (solid black line) and simulation (dashed red line) results for different concentrations of Tris-buffered Ru(bpy)3Cl2 solution, as well as the CM results for 10 mM Tris displacing 24.7 mM Tris (dotted blue line). The 24.70 mM Tris (ζ1 = -43 mV and the conductivity = 3.063 mS/cm) filled the channel before the well was replaced with Ru(bpy)3Cl2. To match the experimental results, we found the adjustable parameters for (a) 0.1 mM Ru(bpy)3Cl2 + 10 mM Tris of ζ2 = 1.3 mV and tads = 80.96 s with a relative RMSD between the fitted curve and experiments of 1.27% (see SI), (b) 2.5 mM Ru(bpy)3Cl2 + 10 mM Tris of ζ2 = 1.4 mV and tads = 16.75 s (RMSD 2.76%), and (c) 5.0 mM Ru(bpy)3Cl2 + 10 mM Tris of ζ2 = 7.5 mV and tads = 13.96 s (RMSD 2.67%). concentration of Ru(bpy)32+ (see Figure S3 for the complete data set). The adsorption time is greatest for the lowest concentration of Ru(bpy)3Cl2, consistent with the hypothesis that the dilute solution contains an insufficient concentration of divalent ions to coat the surface as rapidly. Moreover, Figures 4(b) and (c) show that at higher concentration, the magnitude of the flow reversal increases, and the adsorption time


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decreases substantially (compared to Figure 4(a)). The simulations shown in Figure 4 produce values of tads and ζ2 which are not necessarily monotonic, and we believe that is because of our fitting assumption. In Figure S2, we show the distribution of tads and ζ2 for all our data sets as a function of Ru(bpy)3Cl2 concentration. CONCLUSION Although current monitoring has been used for decades to predict ζpotential with a combination of simulations matching experiments, we showed that one can predict the time it takes for the charge inverting ion species to adsorb and the final ζ-potential once the ion adsorption has reached steady state. This work also shows, however, that more accurate models of both charge inversion (i.e., the equilibrium electrical double layer structure) and the location of the slip plane (i.e., the height of the immobile Stern layer) are needed. While the modeling of the double layer structure has become much more accurate, a theory of which ions comprise the Stern layer is still absent and more work remains to be done. The technique developed here can be a way to produce experimental data upon which theories of the Stern layer can be built, in addition to producing data to further investigate the fundamental physics of charge inversion. MATERIALS AND METHODS


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DEVICE FABRICATION We used two pieces of fused silica to fabricate the nanochannel with our custom, optimized bonding technique. One fused silica was patterned with 5 mm long, 5 μm wide rectangles and etched 100 nm using standard photolithography and dry etching techniques. The channel was sealed using a two-step plasma activation process, with an oxygen plasma treatment first, followed by a nitrogen plasma treatment to increase the fusion bonding strength of fused silica.23 SOLUTION PREPARATION Ru(bpy)3Cl2 and LaCl3 were purchased from Sigma-Aldrich and chosen as the complex ions in this study because while both induce charge inversion, they are quite different, La3+ being a small trivalent ion24 and Ru(bpy)32+ a large, fluorescent, divalent ion.9,25 All the solutions are prepared with TrisEDTA buffer (ThermoFisher, USA), which has pH 7, and diluted with ultrapure deionized water (Milli-Q, USA). For cleaning the channel, 100 mM sodium hydroxide and 100 mM sulfuric acid were used. The conductivities of the solution were measured with a calibrated conductivity meter (OAKTON, USA). To measure the EOF solely due to the buffer, two different concentrations of Tris buffer were prepared: 24.70 mM (conductivity = 3.063 mS/cm), and 22.23 mM (conductivity = 2.845 mS/cm). NUMERICAL SIMULATIONS


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Numerical simulations were performed by solving the time-dependent Nernst-Planck equation coupled with applied electric fields and creeping fluid flow using COMSOL 5.2 (COMSOL, Inc., Stockholm, Se) for a one-dimensional channel geometry to simulate the current versus time in a nanochannel. A large number of different possible ζ2 and tads were calculated, and the resulting set of current versus time data was then least-squares fit to the experimental traces to extract both ζ2 and tads. A detailed description is given in the Supporting Information. SUPPORTING INFORMATION The supporting information is available free of

charge on the ACS Publications website. The supporting information contains further details regarding the numerical model as well as additional data showing all of our current monitoring experiments (PDF) as well as a video showing charge inversion observed via fluorescence microscopy. ACKNOWLEDGEMENTS This material is based on work supported by the National Science Foundation under Grants 1402736 (to S.P) and 1402897 (to D.G.) and by the Institute for Collaborative Biotechnologies through Grants W911NF-09-0001 and W911NF-12-1-0031 from the U.S. Army Research Office (to S.P.).


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An Experimental Approach to Systematically Probe Charge

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