Electrolyte negative differential resistance, nanoparticle dynamics in nanopores, and nanobubble generation at nanoelectrodes

This dissertation presents experimental and computational investigations of electrolyte negative differential resistance, nanoparticle dynamics in nanopores, and nanobubble formation at nanoelectrodes. Chapter 1 provides an introduction to negative differential resistance and other nonlinear electrical responses in nanopores, an overview of resistive pulse analysis of nanoparticles using nanopores, and current nanobubble research. Chapter 2 describes the first example of electrolyte negative differential resistance (NDR) discovered in nanopores, where the current decreases as the voltage is increased. The NDR turn-on voltage was found to be tunable over a ~1 V window by adjusting the applied external pressure. Finite-element simulations yielded predictions of the NDR behavior that are in qualitative agreement with the experimental observations. Chapter 3 presents the extension of NDR to an aqueous system and demonstrates the potential for chemical sensing based on NDR behavior. Solution pH and Ca2+ in the solution were separately employed as the stimulus to investigate the surface charge density dependence of the NDR behavior. The NDR turn-on voltage was found to be exceedingly sensitive to the nanopore surface charge density, suggesting possible analytical applications in detecting as few as several hundred of molecules. Chapter 4 discusses the technique of controlling the dynamics of single 8 nm diameter gold nanoparticles in nanopores, which is extended from traditional resistive pulse analysis of nanoparticles. A pressure was applied to balance electrokinetic forces acting on the charged Au nanoparticles as they translocate through a ~10 nm diameter orifice at an electric field. This force balance provides a means to vary the velocity of nanoparticles by three orders of magnitude. Finite-element simulations yielded predictions in semiquantitative agreement with the experimental results. Chapter 5 reports the electrochemical generation of individual H2 nanobubbles at Pt nanodisk electrodes immersed in a H2SO4 solution. A sudden drop in current associated with the transport-limited reduction of protons was observed in the i-V response at Pt nanodisk electrodes of radii less than 50 nm. Finite element simulation based on Fick's first law, combined with the Young-Laplace equation and Henry's Law, were employed to investigate the bubble formation and its stabilization mechanism.

ELECTROLYTE NEGATIVE DIFFERENTIAL RESISTANCE, NANOPARTICLE DYNAMICS IN NANOPORES, AND NANOBUBBLE GENERATION AT NANOELECTRODES by Long Luo A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Chemistry The University of Utah May 2014 Copyright © Long Luo 2014 All Rights Reserved The Uni v e r s i ty of Ut ah Gr adua t e Sch o o l STATEMENT OF DISSERTATION APPROVAL The dissertation of Long Luo has been approved by the following supervisory committee members: Henry S. White Chair Dec. 10, 2013 Date Approved Cynthia J. Burrows Member Dec. 10, 2013 Date Approved Joel M. Harris Member Dec. 10, 2013 Date Approved Marc D. Porter Member Dec. 10, 2013 Date Approved Rebecca M. Brannon Member Dec. 10, 2013 Date Approved and by Cynthia J. Burrows Chair/Dean of the Department of ________________________Chemistry and by David B. Kieda, Dean of The Graduate School. ABSTRACT This dissertation presents experimental and computational investigations of electrolyte negative differential resistance, nanoparticle dynamics in nanopores, and nanobubble formation at nanoelectrodes. Chapter 1 provides an introduction to negative differential resistance and other nonlinear electrical responses in nanopores, an overview of resistive pulse analysis of nanoparticles using nanopores, and current nanobubble research. Chapter 2 describes the first example of electrolyte negative differential resistance (NDR) discovered in nanopores, where the current decreases as the voltage is increased. The NDR turn-on voltage was found to be tunable over a ~1 V window by adjusting the applied external pressure. Finite-element simulations yielded predictions of the NDR behavior that are in qualitative agreement with the experimental observations. Chapter 3 presents the extension of NDR to an aqueous system and demonstrates the potential for chemical sensing based on NDR behavior. Solution pH and Ca2+ in the solution were separately employed as the stimulus to investigate the surface charge density dependence of the NDR behavior. The NDR turn-on voltage was found to be exceedingly sensitive to the nanopore surface charge density, suggesting possible analytical applications in detecting as few as several hundred of molecules. Chapter 4 discusses the technique of controlling the dynamics of single 8 nm diameter gold nanoparticles in nanopores, which is extended from traditional resistive pulse analysis of nanoparticles. A pressure was applied to balance electrokinetic forces acting on the charged Au nanoparticles as they translocate through a ~10 nm diameter orifice at an electric field. This force balance provides a means to vary the velocity of nanoparticles by three orders of magnitude. Finite-element simulations yielded predictions in semiquantitative agreement with the experimental results. Chapter 5 reports the electrochemical generation of individual H2 nanobubbles at Pt nanodisk electrodes immersed in a H2SO4 solution. A sudden drop in current associated with the transport-limited reduction of protons was observed in the i-V response at Pt nanodisk electrodes of radii less than 50 nm. Finite element simulation based on Fick's first law, combined with the Young-Laplace equation and Henry's Law, were employed to investigate the bubble formation and its stabilization mechanism. iv TABLE OF CONTENTS ABSTRACT........................................................................................................................... iii LIST OF ABBREVIATIONS..............................................................................................viii LIST OF FIGURES................................................................................................................. x ACKNOWLEDGEMENTS.................................................................................................xix CHAPTERS 1. INTRODUCTION............................................................................................................ 1 1.1 Negative differential resistance................................................................................ 1 1.2 Resistive pulse analysis of nanoparticles................................................................9 1.3 Nanobubbles............................................................................................................ 15 1.4 References ............................................................................................................... 19 2. TUNABLE NEGATIVE DIFFERENTIAL ELECTROLYTE RESISTANCE IN A CONICAL NANOPORE IN GLASS...................................................................................24 2.1 Introduction............................................................................................................. 24 2.2 Experimental section...............................................................................................28 2.2.1 Chemicals and materials...............................................................................28 2.2.2 Glass nanopore membranes (GNMs) fabrication.......................................28 2.2.3 Cell configuration and data acquisition...................................................... 29 2.2.4 Finite-element simulations............................................................................30 2.3 Results and discussion............................................................................................ 30 2.3.1 Negative Differential Resistance (NDR).................................................... 30 2.3.2 Finite-element simulations of the nanopore NDR phenomenon................33 2.4 Conclusions............................................................................................................. 43 2.5 Appendix ..................................................................................................................44 2.6 References............................................................................................................... 54 3. CHEMICAL SENSING BASED ON NEGATIVE DIFFERENTIAL ELECTROLYTE RESISTANCE IN A SOLID-STATE NANOPORE............................ 57 3.1 Introduction............................................................................................................. 57 3.2 Experimental section...............................................................................................60 3.2.1 Chemicals and materials...............................................................................60 3.2.2 Glass nanopore membrane (GNM)..............................................................61 3.2.3 Experimental set-up and data acquisition................................................... 61 3.2.4 Finite-element simulations............................................................................63 3.3 Results and discussion............................................................................................ 63 3.3.1 Negative Differential Resistance (NDR) in aqueous solutions.................63 3.3.2 Chemical sensing based on NDR.................................................................71 3.4 Conclusions............................................................................................................. 78 3.5 Appendix..................................................................................................................79 3.5.1 i-t recording of NDR response and NDR curves as a function of solution pH.............................................................................................................. 79 3.5.2 Finite element simulation..............................................................................81 3.5.3 Estimation of sensing zone surface area..................................................... 86 3.6 References............................................................................................................... 91 4. CONTROLLING NANOPARTICLE DYNAMICS IN CONICAL NANOPORES .94 4.1 Introduction............................................................................................................. 94 4.2 Experimental section...............................................................................................97 4.2.1 Chemicals and materials...............................................................................97 4.2.2 Pipettes........................................................................................................... 99 4.2.3 Glass nanopore fabrication...........................................................................99 4.2.4 Resistive pulse sensing measurements and data analysis........................100 4.2.5 Finite element simulations..........................................................................100 4.3 Results and discussion.......................................................................................... 101 4.3.1 Detecting nanoparticles at the threshold of the pore size........................ 101 4.3.2 Particle capture and release........................................................................ 104 4.3.3 Controlling nanoparticle dynamics by applied pressure and applied potential....................................................................................................106 4.3.4 Factors governing particle velocity............................................................112 4.3.5 Finite element simulations..........................................................................114 4.3.6 The effects of salt concentration and particle charge on nanoparticle dynamics............................................................................................................... 116 4.3.7 Factors affecting resistive pulse peak shape............................................. 118 4.4 Conclusion............................................................................................................. 119 4.5 Appendix............................................................................................................... 120 4.5.1 Nanoparticle dynamics control by applied pressure.................................120 4.5.2 Surface charge density of the Au nanoparticle estimated from the zeta potential in an extremely diluted electrolyte solution.............................. 120 4.5.3 The geometry and boundary conditions for a simulation of the particle velocity in 100 mM and 200 mM NaCl solutions............................... 125 4.5.4 The geometry and boundary conditions for a simulation of the particle velocity in 1.0 M NaCl solution............................................................126 4.5.5 Considerations on the polarization of the nanoparticle surface charge ...126 4.6 References............................................................................................................. 127 vi 5. ELECTROGENERATION OF SINGLE NANOBUBBLES AT SUB-50 NM RADIUS PLATINUM NANODISK ELECTRODES.......................................................129 5.1 Introduction........................................................................................................... 129 5.2 Experimental section............................................................................................ 132 5.2.1 Chemicals.....................................................................................................132 5.2.2 Nanodisk electrode fabrication and characterization............................... 132 5.2.3 Electrochemical apparatus..........................................................................133 5.2.4 Finite element simulation............................................................................133 5.3 Results and discussion.......................................................................................... 133 5.3.1 Electrochemical formation of a single nanobubble ..................................133 5.3.2 Possible mechanism of electrochemical nanobubble formation..............138 5.3.3 Concentration dependence......................................................................... 141 5.3.4 Size dependence.......................................................................................... 143 5.3.5 Residual current inb..................................................................................... 145 5.4 Conclusion............................................................................................................. 148 5.5 Appendix................................................................................................................ 149 5.6 References............................................................................................................. 155 vii LIST OF ABBREVIATIONS 2D - two-dimensional A.C. - alternating current AFM - atomic force microscope Ag/AgCl - silver/silver chloride Au - gold CaCl2 - calcium chloride D.C. - direct current eq - equation GNM - glass nanopore membrane h - hour H+ - proton H2 - hydrogen H2SO4 - sulfuric acid i - current ICR - ion current rectification K2HPO4 - potassium phosphate dibasic KH2PO4 - potassium phosphate monobasic kHz - kilohertz KCl - potassium chloride M - moles per liter mC - millicoulomb mM - millimolar mmHg - millimeter mercury ms - millisecond MQ - megaohm nA - nanoampere NaCl - sodium chloride NaCN - sodium cyanide NDR - negative differential resistance nm - nanometer nM - nanomolar O2 - oxygen pA - picoampere pm - picometer Pt - platinum rms - root mean square SEM - scanning electron microscope TEM - transmission electron microscopy V - voltage |im - micrometer |is - microsecond LIST OF FIGURES Figure Page 1.1. (a) i-V response of an Esaki diode or tunnel diode recorded by an oscilloscope. The negative differential resistance (NDR) region is highlighted in blue. (b) Schematic symbol of a tunnel diode. Tunnel diodes are heavily doped p-n junctions. The heavy doping results in a broken band gap, in which the conduction band of the n+ part aligns with the valence band of the p+ part. A small voltage bias can drive the electrons on the n+ part to tunnel through the band gap to the p+ part. A further increased voltage bias elevates the energy level of the conduction band of n+ part, and therefore, fewer electrons in the conduction band on the n+ part can tunnel to the hole states on the p+ part due to the energy mismatch................................................................................................................ 2 1.2. Schematic representation of ion current rectification in conical-shaped glass nanopores................................................................................................................................ 4 1.3. (a) Ion current rectification (ICR, blue line) and negative differential resistance (NDR, red dash line). (b) and (c) Schematic representation of ion current rectification in a conical glass nanopore. At a positive voltage (internal vs. external), the nanopore is occupied by high-conductive solution due to the electro-osmosis (red arrows) pushing the internal solution outwards. Conversely, at a negative voltage, low-conductive solution fills the nanopore, resulting from an oppositely directed electro-osmosis..........................7 1.4. (a) Schematic illustration of electric field-driven resistive pulse analysis of nanoparticles. A voltage bias (EM) is applied across the membrane containing a single carbon nanotube channel, driving ions and charged particles through the nanopore. (b)-(d) show the typical current-time traces at different EM. Each pulse or decrease of current represents a single nanoparticle translocation. Particle size and surface charge are calculated based on the duration time At and pulse height Ai. Reference 26 Ito, T.; Sun, L.; Henriquez, R. R.; Crooks, R. M. Acc. Chem. Res. 2004, 37, 937-945. Copyright, 2004 American Chemical Society..................................................................................................11 1.5. A schematic drawing of the driving forces acting on a negatively charged 8-nm-diameter nanoparticle as the nanoparticle translocates through a conical-glass nanopore at a positive voltage and negative pressure. The sign is defined by the difference between internal and external potentials or pressures........................................................................14 1.6. Theoretical prediction of the internal pressure of a nanobubble as a function of nanobubble radius using the Young-Laplace equation.......................................................17 2.1. a) Schematic illustration of the NDR experiment and the glass nanopore membrane (GNM). A potential difference is applied between the two Ag/AgCl electrodes. The internal solution is an aqueous 5 mM KCl solution and the external solution is a 3:1 (v/v) DMSO/H2O mixture containing 5 mM KCl. b), c) and d) show the interfacial zone outside, right on the orifice and inside the nanopore orifice.............................................. 26 2.2. i-V response of the 380 nm radius GNM as a function of the applied positive pressure (internal vs. external). The voltage was scanned from 2 to -2 V at a rate of 200 mV/s. Internal and external solutions were an aqueous 5 mM KCl solution and a DMSO/water (v:v 3:1) mixture containing 5 mM KCl, respectively. (b) i-t recording of the 380 nm radius GNM when a 20 mmHg positive pressure was applied across the nanopore, and the voltage was cycled between -2 V (Point A) and 2 V (Point C) at a scan rate of 200 mV/s. Point B is the voltage where NDR occurs................................................................ 31 2.3. Simulation of electro-osmosis induced ICR behavior. (a) Simulated steady-state i-V response of a 400 nm radius GNM in the absence of an applied pressure. In the simulation, the external solution (z > 0) initially contained a solution of 5 mM KCl in DMSO/water mixture (volume fraction of DMSO = 0.8), while the internal aqueous solution (z < 0) initially contained 5 mM KCl. The surface of nanopore is negatively charged (-26 mC/m2). (b) is simulated steady-state volume fraction distributions of DMSO at -1 V and 1 V (internal vs. external). r = 0 is the symmetry axis of the GNM geometry, while z = 0 corresponds to the nanopore orifice................................................36 2.4. Simulation of NDR behavior in a nanopore. (a) Simulated i-V curves of a 400 nm radius nanopore at 5 mmHg pressure (red line) and in the absence of pressure (blue line).The other initial settings are the same as Figure 2.3. (b) The volume fraction distributions of DMSO at selected voltages ranging from -0.2 to -1 V.............................38 2.5. Simulated steady-state DMSO flux in the 400 nm radius GNM at an applied voltage of -0.77 V (internal vs. external). The color surface indicates the net DMSO flux magnitude. The flux vectors at the opening of nanopore indicate the directions and relative magnitudes of the convective (black arrows) and diffusive DMSO fluxes (red arrows)................................................................................................................................... 40 2.6. Experimental NDR behavior for a 230 nm radius GNM with a scan rate of 10 mV/s and 20 mmHg pressure applied across the membrane. NDR behavior occurs over a potential difference of ~7 mV (from -0.852 to -0.859 V). Internal and external solutions were an aqueous 5 mM KCl solution and a DMSO/water (v:v 3:1) mixture containing 5 mM KCl, respectively. The volume fraction distributions of DMSO before and after the NDR point are taken from Figure 2.4 (-0.770 and -0.778V) to reiterate the origin of the NDR behavior....................................................................................................................... 42 2.7. Optical microscope images of a sharpened Pt wire sealed at the end of a glass capillary at different stages during the polishing process to expose a Pt disk. (Note: the "two wires" in the third photo corresponds to a single folded wire.)............................... 45 xi 2.8. i-V response of the nanopore filled with and immersed in an aqueous 1 M KCl solution. The i-V response exhibits ohmic behavior in the 1 M KCl solution..................46 2.9. Experimental i-V responses of an 857 nm radius nanopore using an internal aqueous 5 mM KCl solution and an external DMSO/H2O mixture (v:v 3:1) containing 5 mM KCl. Positive pressures were applied from 0 mmHg to 280 mmHg...........................................47 2.10. Experimental i-V responses of a 330 nm radius GNM with an internal aqueous 5 mM KCl solution and an external DMSO/water mixture (v:v 3:1) containing 5 mM KCl. A positive pressure (internal vs. external) ranging from 20 mmHg to 80 mmHg was applied across the GNM. Scan rate = 200 mV/s. The i-V curves show the forward and reverse scan responses at each pressure............................................................................... 48 2.11. The steady-state potential profile along the center axis (left) and potential distribution (right) when -0.77 V is applied across a 400 nm radius GNM. Internal solution: 5 mM KCl in H2O; external solution: 5 mM KCl in DMSO/H20 ..................... 49 2.12. The 2D axial-symmetric geometry of the GNM and the mesh for the finite-element simulation (red dash line: the symmetry axis). The initial interface between the internal 5 mM KCl aqueous solution and the 5 mM KCl external DMSO/H2O solution is located at the pore orifice, z = 0.............................................................................................................50 2.13. (a) Viscosity and (b) diffusion coefficients of K+ and Cl" in DMSO/H2O mixtures. The diffusion coefficients of K+ and Cl- were calculated based on Stokes-Einstein equation (eq 2.3) using the values of viscosity reported in ref. 53 and are plotted. The polynomial fittings of data points shown on the graphs were used in the finite element simulation. In addition, in computing the potential and ion distributions, a linear relation between dielectric constant of the DMSO/H2O mixture and the mole fraction of DMSO in the mixture was assumed, as described in ref. 54........................................................... 51 2.14. i-V responses of a 380 nm radius GNM at zero applied pressure. (A) Blue curve: internal and external aqueous solutions containing 5 mM KCl; (B) red curve: internal aqueous solution containing 5 mM KCl and external 3:1 (v/v) DMSO/H2O mixed solution containing 5 mM KCl. The voltage was scanned from -2 to 2 V at a rate of 200 mV/s. . 52 3.1. (a) Illustration of pressure-driven and voltage-engendered electro-osmotic flows that give rise to negative differential resistance (NDR) in the i-V response of a negatively charged, conical nanopore that separates high and low ionic strength solutions. The color surface indicates the magnitude of the net flow velocity; red and blue denote higher and lower velocities, respectively. Pressure-driven flow out o f the pore occurs along the central axis of the nanopore (red arrow), while an opposing electro-osmotic flow (EOF) into the pore occurs along the negatively charged nanopore surface (white arrows). NDR observed in the i-V response of the nanopore results from positive feedback associated with an increase in EOF as the voltage is increased: an increased flux of the external low-conductivity solution into the nanopore orifice results in a decreased ionic conductivity of solution in the nanopore causing a further increase in EOF and a sudden drop in the nanopore conductivity at a critical voltage, V\. (b) Profiles of the total ion concentration xii (K+ plus Cl-) in the nanopore for applied voltages above (V > V*,, high conductivity state) and below (V < V*, low conductivity state) the conductivity switching potential, V*.....59 3.2. Schematic drawing of the experimental set-up. A glass nanopore membrane (GNM) at the end of a glass capillary separates the high (internal) and low (external) concentration KCl solutions. A positive pressure (inside vs. outside nanopore) is applied across the GNM to generate an outward pressure-driven flow. A 1 kHz, 10 mV (rms) sine wave superimposed on a slowly varying voltage (10 mV/s) is applied between the two Ag/AgCl electrodes located on opposite sides of the nanopore. The lock-in amplifier is used to analyze the A.C. component of the current.........................................................62 3.3. NDR behaviors in a nanopore. (a) A series of NDR curves as a function of the external KCl concentration measured using a 260-nm-radius nanopore. The KCl concentration of the external solution was varied between 5 and 25 mM KCl, while the internal KCl concentration (50 mM) was held constant; pH = 7.0. A 10 mmHg pressure (internal vs. external) was applied. (b) Conductance values measured from the slopes of i- V responses at voltages positive and negative of the NDR switching potential as a function of the external solution KCl concentration........................................................... 64 3.4. Simulation of NDR behavior in a nanopore. (a) Simulated i-V curve of the 260-nm-radius nanopore with an external KCl concentration of 5 mM and an internal KCl concentration of 50 mM (corresponding to the experimental data (gray line) in Figure 3.3a). A pressure of 10 mmHg and a surface charge density of -12.5 mC/m2 were used in the simulation. (b) The corresponding solution volumetric flow rate at the orifice as a function of the applied voltage. Negative values of flow rate correspond to solution flow from the bulk solution into the nanopore. (c) The total ion concentration profiles ( CK+ + Ccl- ) as a function of applied voltage.......................................................................67 3.5. Positive feedback mechanism associated with the NDR switch.................................69 3.6. Simulated NDR curves for a 260-nm-radius nanopore at 5 mmHg pressure as a function of nanopore surface charge density. The simulation corresponds to 50 (internal) and 5 mM (external) KCl solutions...................................................................................... 72 3.7. Reversible NDR response to Ca2+ in the external electrolyte solution for a 270-nm-radius nanopore. Experimental conditions: 54 mmHg; 1 M internal and 100 mM external KCl solutions; pH = 7.8; Ca2+ concentration (when present in solution) = 2 mM; scan rate: 100 mV/s........................................................................................................................ 74 3.8. D.C. and A.C. NDR signals recorded simultaneously using a potentiostat and lock-in amplifier for a 470-nm-radius glass nanopore at pH 7.2, 8 mmHg and a scan rate of 10 mV/s. KCl solution concentrations: 0.1 M external and 1 M internal. On the right is the expansion of the NDR switching region.............................................................................. 76 3.9. pH-dependence study. (a) pH-dependent NDR behavior for a 370-nm-radius nanopore. Pressure: 80 mmHg; KCl solution concentrations: 0.1 M external and 1 M internal; 10 mV/s scan rate; 1 kHz and 10 mV (rms) sine wave. (b) Dependence of xiii conductivity switching potential on surface charge density, estimated from eqs 3.1 and 3.3........................................................................................................................................... 77 3.10. i-t trace recorded at a data acquisition rate of 50 kHz while scanning the voltage at 10 mV/s from -3 V to -6 V across a 350-nm-radius nanopore. The internal and external KCl solution concentrations are 1 M and 100 mM, respectively. The pressure is 80 mmHg; pH = 4.9. The insert shows switch completed within ~60 ms or ~0.6 mV. The temporal resolution of the measurement is limited by the instrumentation bandwidth of ~20 kHz..................................................................................................................................80 3.11. The 2D axial-symmetric geometry of the glass nanopore with a radius of 260 nm and the mesh used for the finite-element simulation (the red dash line corresponds to the axis of symmetry). The surface charge density was varied to match the experimental results (Figure 3.3 and Figure 3.4) for a 260-nm-radius glass nanopore (-12.5 mC/m2). The initial concentration of KCl within the solution domain was set to 50 mM. Pressure, concentration, and voltage boundary conditions, corresponding to the bulk values of the internal and external solutions are shown in the figure...................................................... 83 3.12. Simulation for 25 mM (external) and 50 mM (internal) KCl solutions. (a) Simulated i-V response for a 260 nm radius nanopore (external solution: 25 mM KCl and internal solution: 50 mM KCl; 10 mmHg). (b) Simulated total ion distribution near the nanopore orifice at voltages from -0.4 to -1.4 V..................................................................................84 3.13. Simulation for 5 mM (external) and 50 mM (internal) KCl solutions. (a) Simulated i-V response for a 260 nm radius nanopore (external solution: 1 mM KCl and internal solution: 50 mM KCl; 10 mmHg). (b) Simulated total ion distribution near the nanopore orifice at voltages from -0.4 to -1.4 V..................................................................................85 3.14. Schematic representation of the sensing zone surface for a 370-nm-radius glass nanopore. (The bold lines a and b are not drawn to scale.) The colored surface is the simulated electro-osmotic velocity profile for a = 185 nm and b = 5077 nm. The simulation shows that the influence of analyte binding on electro-osmotic velocity is largest within a small region near the nanopore orifice. The area of this region ("sensing zone") is approximately defined by the lengths a and b.....................................................87 3.15. Simulation of the dependence of v at the nanopore orifice on a. (a) Simulated electro-osmotic flow rate v at the nanopore orifice at various ring width a. (b) the maximum v (vmax) in (a) as a function of a. See Figure 3.14 for definition of the parameter a. The calculations correspond to a 370-nm-radius glass nanopore.................................. 89 3.16. Simulation of the dependence of v at the nanopore orifice on b. (a) Simulated electro-osmotic flow rate v at the nanopore orifice at various length b. (b) The maximum v (vmax) in (a) as a function of b. See Figure 3.14 for definition of parameter b. The calculations correspond to a 370-nm-radius glass nanopore..............................................90 4.1. Driving forces acting on a particle in a conical nanopore. During translocation experiments, positive potentials applied to an electrode within the pipette and negative pressures applied within the pipette both tend to draw negatively charged particles inward xiv from the external solution. The applied potential also induces a counteracting electro-osmotic force that tends to drive particles out of the pipette into the external solution. The summation of these different forces determines the particle velocity and translocation timescale................................................................................................................................ 98 4.2. Optical images of a micropipette before and after chemical etching. (a) A programmable micropipette puller was used to form a narrow opening (1 ^m) that was melted into a terminal bulb enclosing a cone-shaped cavity. (b) The terminal bulb was then sanded and briefly melted with a microforge to form a flattened geometry (dashed lines delineate the outlines of the original bulb shown in (a)). Ag/AgCl electrodes were placed across the unopened pore and hydrofluoric acid etchant was used as the external solution to form a nano-scale pore in the sanded and remelted tip. A spike in the current indicated pore formation..................................................................................................... 102 4.3. Scanning electron microscope (SEM) images of a nanopore in a micropipette tip that had been used to detect 8-nm nanoparticles. Prior to imaging, this nanopore was rinsed with deionized water, allowed to dry, and then sputtered with a ~2 nm thick layer of gold. The opening located at the center of the pipet tip has a diameter of 37 nm at the surface........................................................................................................................103 4.4. i-t traces used to determine when the pore size exceeds or is just at the threshold of the Au nanoparticle size. In these experiments, 8-nm Au nanoparticles (C= -51 mV) were placed in the external solution, and a pressure of ~0.5 atm and voltage of 250 mV were applied to drive the particles into the nanopore. (a) Square-shaped blockades of widely varying duration are observed when the pore size is smaller than the particle size. The current within these blocks sometimes increases briefly, as seen at 0.59 s and 0.68 s, but eventually returns to the base current level as seen in the dashed oval in (a) (the trace on the right is an expansion of this region). (b) Passage of a particle through another pore at the threshold of the particle size accompanied by a large current spike (dashed oval in (b)). Note that this current spike (expanded on the right) has the asymmetric shape characteristic of a typical translocation through a conical pore. The 1.0 M NaCl solution was buffered at pH 7.4 with 7 mM Na2HPO4, 21 mM KH2PO4, and contained 0.1% Triton X-100.........................................................................................................................105 4.5. i-t traces showing a single nanoparticle passing back and forth through the nanopore orifice as the applied potential is reversed. (a) A 10-Hz voltage square wave between +1000 and -1000 mV results in resistive pulses in the i-t trace shown in (b). The i-t traces in (b) are clipped to show just the relevant 50-ms portions of the square wave where translocations occur. (c) A 3-Hz square wave between only +525 and +225 mV also results in a single nanoparticle passing back and forth through the pore orifice. Both solutions contained 8-nm Au nanoparticles (C = -51 mV) in 1.0 M NaCl PBS pH 7.4 plus 0.1% Triton X-100. Particle concentration in (b) equals 50 nM, and in (d) equals 320 nM.................................................................................................................................107 4.6. Nanoparticle translocation velocity vs. applied voltage at a pressure of (a) -0.047 atm and (b) -0.35 atm. The solution conditions are for (a): 1.0 M NaCl, A ,A (C = -51 mV) and O,* (C = -15 mV), and for (b): 0.2 M NaCl: A (C = -51 mV) and O (C = -15 mV); xv 0.1 M NaCl: A (£=-51 mV) and O (£=-15 mV). All solutions were buffered at pH 7.4 with 7 mM Na2HPO4, 21 mM KH2PO4, and contained 0.1% TritonX-100. The filled and open symbols in (a) represent two consecutive sets of data collected under identical conditions. Dashed lines through data points represent linear least squares fits. Representative i-t traces for particular translocations at different voltages are shown. . 109 4.7. Schematic depicting control of nanoparticle velocity in conical nanopores. The voltage-dependent peak widths presented in Figure 4.6 result from the summed contributions of different forces acting on the charged nanoparticle. The applied pressure (-0.047 atm) remains constant throughout all measurements, but the particle-dependent electrophoretic and particle-independent electro-osmotic forces change at different rates with varying voltage. As a result, the more highly charged particles (£ = -51 mV) obtain a minimum velocity at ~300 mV, while the less charged particles (£ = -15 mV) obtain a minimum velocity at ~200 mV...........................................................................................110 4.8. Simulations of nanoparticle velocities at the pore orifice. (a) Simulated velocity profile for a nanoparticle (£ = -15 mV) in a 0.2 M NaCl solution, at 0.35 atm pressure and applied voltages between 100 and 500 mV corresponding to the turquoise lines in Figure 4.6b and Figure 4.8c. (b) and (c) are plots of particle velocities corresponding to the data in Figure 4.6a and b, respectively. The data point colors and symbols follow the same scheme used to plot experimental data in Figure 4.6. Parameters and other details of the finite element simulation are presented in 4.5 Appendix................................................. 117 4.9. Forward and reverse translocation of three nanoparticles as a function of the applied pressure. A nanopore having a resistance of 117 MQ measured in 1.0 M NaCl was used to observe 8-nm diameter Au nanoparticles at constant applied potential (250 mV). In (a), three particles enter the pore between 1.2 and 1.6 s as negative pressure (-0.25 atm) is applied to the pipette. A pore block between 1.8 and 2.8 s is removed by applying a positive pressure (0.5 atm), pushing the three particles out of the pipette between 3.1 and 3.3 s. A negative pressure (-0.25 atm) is then applied at 4.5 s to draw the three particles back through the nanopore between 5 s and 7 s. Although the standard deviation in the particle size distribution was only ± 0.6 nm, distinct peak shapes seen in the i-t expansions shown in (b) reflect subtle differences in the particle sizes, and allow identification of individual particles. The applied positive pressure was greater than the applied negative pressures, resulting in increased translocation velocity and therefore narrower peak widths...........................................................................................................121 4.10. Simulated potential profile generated by a -9 mC/m2 charged Au nano-particle with a diameter of 8 nm............................................................................................................... 122 4.11. Geometry and boundary conditions for the finite-element simulation in a 100 mM or 200 mM NaCl solution and P = 0.35 atm......................................................................123 4.12. Geometry and boundary conditions for the finite-element simulation in a 1.0 M NaCl solution with P = 0.047 atm...................................................................................... 124 xvi 5.1. Schematic representation of the electrochemical formation of an individual nanobubble at a Pt nanodisk electrode with a radius a < 50 nm. The Pt nanodisk is shrouded in glass. The hemispherical shape of the nanobubble is drawn here for schematic purposes and is unlikely to represent the actual shape....................................131 5.2. Cyclic voltammograms of hydrogen nanobubble formation at a nanoelectrode. (a) Cyclic voltammogram recorded at a 27-nm-radius Pt electrode immersed in a deoxygenated 0.5 M H2SO4 solution (scan rate = 100 mV/s). The transport-limited current associated with the transport-limited electroreduction of H+ drops suddenly at ~- 0.4 V vs Ag/AgCl due to the nucleation and rapid growth of a H2 nanobubble. The peak current at which nanobubble formation occurs is labeled as ip, . The insert shows a residual current inb of -0.4 nA after the formation of a nanobubble. (b) Cyclic voltammetric response for the same 27-nm-radius Pt electrode recorded at scan rates ranging from 10 to 200 mV/s.............................................................................................134 5.3. A typical i-t trace during nanobubble formation. (a) i-t trace recorded while scanning the voltage at 100 mV/s from 1 V to -1 V at the 27-nm-radius Pt nanodisk immersed in 0.5 M H2SO4. (b) Expansion of (a) shows that the formation of a nanobubble is described in a two-step mechanism, with the initial step occurring on a time scale of a few hundred microseconds, followed by a slower growth process on the time scale of a few milliseconds. In this particular example, the current reaches the steady-state residual value, inb, is ~3 ms. The temporal resolution of the measurement is limited by the instrumental10 kHz bandwidth...........................................................................................137 5.4. Simulated H2 distribution (surface) near a 27-nm-radius Pt nanodisk at the experimentally measured critical current i1, of -21 nA. The black line is the 0.1 M H2 contour line, within which the concentration of H2 (C h 2) is higher than the saturation concentration CHfd (~0.10 M, see text) required to form a spherical nanobubble with a diameter of 20 nm................................................................................................................ 140 5.5. Cyclic voltammetric response at a 27-nm-radius Pt nanodisk as a function of H2SO4 solution concentration: (a) 0.01 to 0.05 M and (b) 0.1 to 0.5 M. Scan rate = 100 mV/s. The drop in current due to single nanobubble formation occurs in solutions containing greater than ~0.1 M H2SO4................................................................................................. 142 5.6. Cyclic voltammetric response as a function of the radius of the Pt nanodisk in a 0.5 M H2SO4 solution. Scan rate = 100 mV/s. Nanodisk radii are (a) from 11 to 28 nm and (b) from 54 to 226 nm................................................................................................................144 5.7. Simulation of diffusion limited proton transfer near a nanobubble. (a) Schematic illustration of a hemispherical nanobubble at a 27-nm-radius Pt nanodisk, and the dissolution of H2 gas into the solution balanced by the electroreduction of H+ at the circumference of the nanobubble. The colored surface shows the distribution of H+ at the diffusion-limited condition where the H+ concentration is driven to zero at the Pt surface (in accordance with the Nernst equation at potentials more negative than E for H+/H2 redox couple; dark red corresponds to 1 M H+ far from the electrode surface). (b) xvii Expanded illustration showing the 3-phase Pt/gas/solution boundary. (c) Simulated H+ diffusion-limited current i<db as a function of the width of uncovered Pt surface in part (b). a is the radius of the nanodisk and rnb is the radius of the semispherical nanobubble. H+ reduction occurs at the circumference of the Pt nanoelectrode on the exposed region of Pt defined by a ring of width (a - rnb) ..................................................................................... 147 5.8. The steady-state voltammetric response of Pt nanodisk electrodes with various radii immersed in a 5.0 mM ferrocene (Fc) in acetonitrile (supporting electrolyte 0.1 M TBAPF6; scan rate = 10 mV/s). The electrode radii, a, were calculated from the limiting current, ilim, using the expression ilim = 4nFDC*a, where D and C* are the diffusivity and bulk concentration of Fc and n = 1. The curves show the forward and reverse scans. See main text for other details....................................................................................................150 5.9. Cyclic voltammetric response for an 11-nm-radius Pt nanodisk in a 0.5 M H2SO4 solution recorded at scan rates between 10 and 200 mV/s...............................................151 5.10. Cyclic voltammetric response at an 11-nm-radius Pt nanodisk as a function of H2SO4 solution concentration: (a) 0.01 to 0.05 M and (b) 0.1 to 0.5 M. Scan rate = 100 mV/s 152 5.11. The 2D axial-symmetric geometry of the nanodisk electrode embedded in glass and the mesh for the finite-element simulation (red dash line: the symmetry axis)..............153 5.12. Simulated H2 distribution near a 226-nm-radius Pt nanodisk at the experimental critical current inpb of 770 nA. The white line is the 0.1 M H2 contour line, within which the concentration of H2 is greater than the saturation concentration (0.102 M) to form a spherical nanobubble with a diameter of 20 nm. See main text for discussions of the H2 saturation concentration and simulation............................................................................ 154 xviii ACKNOWLEDGEMENTS First of all, I would like to thank my PhD advisor, Dr. Henry S. White. He has been really helpful and supportive throughout my PhD study. His integrity, hard-working attitude, thoughtful guidance and extensive knowledge have been and will always be an inspiration to me. I also want to thank my committee members, Dr. Joel M. Harris, Dr. Marc D. Porter, Dr. Cynthia J. Burrows and Dr. Rebecca M. Brannon for their thoughtful suggestions. I feel grateful to the White group members and really enjoyed my stay with them during the past two and a half years. I will cherish the memories in my entire life. I also want to thank my parents for their continuous love and encouragement. I deeply apologize for not being able to go back to China and visit them in the past three and a half years. And last but not least, I want to say thank you to my beloved fiance, Yi- Ju Tsai. It is because of you that I never feel lonely when I am alone in this foreign country. CHAPTER 1 INTRODUCTION 1.1 Negative differential resistance Negative differential resistance (NDR) is a technologically important electrical phenomenon in which electrical current decreases as an applied voltage is increased. NDR behavior was first found in a semiconductor device, Esaki diode or tunnel diode, by Leo Esaki in 1958.1 In 1973, Leo Esaki was awarded the Nobel Prize in Physics for this discovery. Figure 1.1a shows the NDR electrical response of a tunnel diode (highlighted in blue), recorded by an oscilloscope. A tunnel diode is a heavily doped p-n junction, and therefore, the conduction band of the n+ part overlaps with the valence band of p+ part in terms of energy. Under a voltage bias, the free electron in the conduction band of the n+ region can tunnel through the band gap to the valence band of the p+ region and conduct current, as shown in Figure 1.1b. As the voltage bias is further increased, the energy level of the conduction band of the n+ region becomes higher, resulting in fewer electrons on the n+ side having the same energy as the hole states in the valence band of the p+ region. Under these conditions, the tunneling current starts decreasing and NDR occurs. NDR in nanopores exhibits a similar electrical response as tunnel diode, but the mechanism is completely different. The discovery of NDR response in nanopores Figure 1.1. (a) i-V response of an Esaki diode or tunnel diode recorded by an oscilloscope. The negative differential resistance (NDR) region is highlighted in blue. (b) Schematic symbol of a tunnel diode. Tunnel diodes are heavily doped p-n junctions. The heavy doping results in a broken band gap, in which the conduction band of the n+ part aligns with the valence band of the p+ part. A small voltage bias can drive the electrons on the n+ part to tunnel through the band gap to the p+ part. A further increased voltage bias elevates the energy level of the conduction band of n+ part, and therefore, fewer electrons in the conduction band on the n+ part can tunnel to the hole states on the p+ part due to the energy mismatch. 2 originates from the study of another widely investigated nonlinear electrical response in nanopores, i.e., ion current rectification (ICR). ICR is defined as the experimental departure of the current-voltage (i-V) responses of nanopores or nanochannels from the linear ohmic behavior, i.e., the magnitude of the current flowing through a nanopore between two electrodes at negative potentials is greater or smaller than the current at the same positive potentials.2 The blue line in Figure 1.2 schematically illustrates a typical ICR response. In 1997, Wei, Bard, and Feldberg first discovered ICR in quartz conical-shaped nanopipets.3 They demon­strated that the ICR behavior depends on the size of the nanopipet orifice and the ionic strength of the solution in contact with the conical-shaped nanopipets. Since then, there has been great interest in exploring ICRs in different nanopores.4-8 Martin and co-workers reported in 2004 that ICR relies primarily on the surface characteristics of the inner walls of the nanopore.9 For example, conical Au nanotubes modified with chemisorbed thiol mercapto-propionic acid exhibit ICR in a 0.1 M KF solution. They observed rectification at pH = 6.6 where the -COOH group is deprotonated to yield negative surface charge; at pH = 3.5, the surface charge is removed and rectification is eliminated. Similarly, adding positive surface charge to the nanotubes leads to rectifiers with polarity opposite that of the anionic nanotubes. It has been generally accepted that rectification behavior is strongly related to the pore size, pore surface properties, and the ionic strength of the bulk solution. For a glass conical nanopore, the surface is negatively charged at neutral pH due to the dissociation of the surface silanol groups. The electric field associated with the charged surface extends to a distance of ~5k-1, 3 Figure 1.2. Schematic representation of ion current rectification in conical-shaped glass nanopores. K 1 = l gr g0RT 2 z 2F 2c (1 1 ) 5 where k-1 is the Debye screening length, sr is the relative permittivity, s0 is the permittivity in a vacuum, R is the gas constant, T is the absolute temperature, z is the electrolyte valence, F is the Faraday constant, and c is the electrolyte concentration.10 The Debye length is ~3 and 0.3 nm for a 0.01 M and a 1 M KCl solution, respectively. Qualitatively, when the orifice size of a conical-shaped pore approaches nanometer scale and is of the order of magnitude of 5k-1, the electric field produced by the surface charge covers a great fraction of the orifice and the volume of solution in the pore orifice becomes cation selective due to the electrostatic attraction and repulsion. As a negative potential (we define all potentials and pressures reported hereinafter as values in the pore interior relative to those in the external solution) is applied across the membrane, the potassium ion (K+) flux is directed from external solution to the pore interior, while the chloride ions (Cl-) move in the opposite direction. A consequence of the cation selectivity at the pore orifice is that Cl- ions are rejected by the glass surface, resulting in an accumulation of Cl- within the pore interior, and a greater conductivity inside the pore orifice than the bulk KCl solution, as shown in Figure 1.2. As the negative potential is increased, a higher Cl- concentration and conductivity will be present and an increased conductivity will be achieved. Because the conical nanopore is characterized by the localized mass transfer resistance in the vicinity of the portion of the pore that is immediately adjacent to the pore orifice (the sensing zone), 11 the greater conductivity in the sensing zone results in a higher overall conductivity of the nanopore, reflected as an increase in the slope of the i-V curves. Conversely, when a positive potential is applied, the transport of Cl- from the external solution to the pore interior is repelled by the surface charges and Cl- is depleted within the pore. This depletion decreases the nanopore conductivity and the experimentally measured ion current, represented as a decrease in the slope of the i-V curves. Different conductivities at positive and negative voltages results in a departure from the linear ohmic behavior, or ion current rectification (ICR). White and coworkers verified this mechanism using finite element simulations which involved solving the coupled Nernst-Planck, Poisson's, and Navier-Stokes equations in a simplified 2D axial symmetric system (cylindrical coordinate) that represents the actual 3D geometry of a conical-shaped nanopore.12 In a recent article, Yusko and Mayer reported a new method to generate the ICR response in borosilicate glass nano- and micropores.13 In their experiment, two solutions with different conductivities were placed inside and outside a nano-/micropore, as illustrated in Figure 1.3b and c. At positive voltages, a voltage-induced electro-osmosis flow (EOF, red arrows in Figure 1.3b) in a nanopore is generated to push the internal high-conductive solution (KCl aqueous solution) out of the sensing zone. The EOF is caused by the electromigration of counter ions (cations) accumulating near the negatively charged glass surface in an electric field, which drags the solution through momentum transfer. At negative voltages, conversely, an oppositely-directed EOF (red arrows in Figure 1.3c) is generated to pull the external low-conductive solution (KCl in DMSO/water mixture) into the sensing zone. As a result, an ICR response was achieved (Figure 1.3a) due to different conductivities of the solutions occupying the sensing zone at positive and negative voltages. Following a similar route, Jiang and coworkers14 produced ICR response in nanopores by placing two KCl solutions with different 6 7 Figure 1.3. (a) Ion current rectification (ICR, blue line) and negative differential resistance (NDR, red dash line). (b) and (c) Schematic representation of ion current rectification in a conical glass nanopore. At a positive voltage (internal vs. external), the nanopore is occupied by high-conductive solution due to the electro-osmosis (red arrows) pushing the internal solution outwards. Conversely, at a negative voltage, low-conductive solution fills the nanopore, resulting from an oppositely directed electro-osmosis. concentrations inside and outside a nanopore. This type of ICR response can also be regarded as the transition between two conductive states at zero volts (high-conductive state at positive voltages and low-conductive state at negative voltages). The shift of this transition voltage to a negative value results in an NDR response (red dash line in Figure 1.3a), due to the need to return to the low conductivity state at more negative voltages. Chapter 2 and 3 describe how to achieve this shift in transition voltage and discuss the numerical models used to qualitatively capture the mechanism of NDR behaviors in nanopores. The highly nonlinear i-V characteristics of ICR and its strong dependence on surface properties have inspired researchers to construct biosensors by tuning the local surface charge at the pore orifice via binding of analytes. Martin et al. first demonstrated a highly sensitive and selective protein biosensor based on the permanent blockage of the ionic current through biofunctionalized conical Au nanotubes.15 The Siwy group then described a new type of biosensing system for avidin, streptavidin, and the capsular polypeptide from Bacillus anthracis, by monitoring the rectification ratio (defined as currents at voltages of one polarity over currents at voltages of the opposite polarity) for the detection of an analyte.16 Ali and co-workers described another sensing paradigm of ICR in a nanochannel contained in an ion-tracked polymer membrane.17 The inner walls of the channel are decorated with horseradish peroxidase (HRP) enzyme using carbodiimide coupling chemistry for repeatedly detecting nanomolar concentrations of hydrogen peroxide (H2O2) with 2, 20-azino-bis (3-ethylbenzothiazoline-6-sulfonate) (ABTS) as the substrate. Azzaroni and Ali also reported a pH-dependent ICR by integrating polymer brushes into single conical nanochannels.18 A layer-by-layer assem­8 bly technique was developed by the same group to deposit multilayered films of poly (allylamine hydrochloride) (PAH) and poly (styrenesulfonate) (PSS) on the pore surface.19 The nanopores can then be switched reversibly between different rectifying states. In another report, Wang and Jiang attempted to attach a pH-sensitive DNA molecular motor to a synthetic poly (ethylene terephthalate) (PET) nanopore, bestowing nanopores with various pH-determined conductive states.20 Jiang and Zhu also built a biomimetic asymmetric responsive single nanochannel system in which the ICR is both pH- and temperature-sensitive.21 Based on the mechanism study, we found that NDR in nanopores was also extremely sensitive to the surface properties of nanopores. Inspired by these studies on ICR based sensing, we demonstrate the sensing applications of NDR in nanopores in this dissertation. Instead of the rectification ratio in current, the shift in the transition voltage where the NDR occurs becomes the indicator of the change of nanopore surface properties and analytes in solution. 1.2 Resistive pulse analysis of nanoparticles The resistive pulse counter, also called the Coulter counter, was invented by Dr. Wallace Coulter in 1953 to analyze micrometer size objects such as bacteria, cells, and clay particles 22 and has been extensively applied in biomedical applications and fundamental science, such as measuring the dissolution rate of air bubbles.23 A traditional Coulter counter contains two compartments separated by a 20 p,m to 2 mm diameter aperture. Particles in the solution are driven through the aperture by a voltage bias or pressure gradient. Two Ag/AgCl electrodes on either side of the aperture continuously 9 record ion current changes during the particle translocation. A single resistive pulse (a drop in current) is generated due to the replacement of conductive electrolyte solution by a transolcating nonconductive solid particle. The frequency, width and height of these pulses provide insight into the particle size distribution, concentration, shape, and surface charge properties. The development of nanopore fabrication techniques during the past ten years has enabled a resurgence of the Coulter counter paradigm as an alternate way to quickly analyze individual nanoparticles. Solid-state 24 ' 35 and biological 36 ' 38 nanopores with diameters ranging from several hundred to a few nanometers have been developed, enabling scientists to count particles in a similar size range, and to analyze the structure of biopolymers, e.g., DNA.37 In the 1970s, DeBlois et a l.39-41 reported, for the first time, the extension of Coulter counting to nanoparticles, including viruses about 60 nm in diameter and polystyrene spheres 90 nm in diameter using individual submicron pores etched in plastic sheets. Recently, the Crooks group26,42-44 reported the application of Si3N4 and PDMS membranes containing an individual multiwalled carbon nanotube (~130 nm diameter) as a nano-Coulter counter. Their experimental setup is schematically shown in Figure 1.4a. Negatively charged nanoparticles were driven through the carbon nanotube by a voltage bias (Em) while the ion current was continuously recorded. Figure 1.4b to d show current­time traces at different EM between the two Ag/AgCl electrodes. Each pulse, or current drop, represents a single particle translocation through the nanochannel. The magnitude of one pulse, Aic, can be related to particle size, the pulse duration, At, can be used to determine the charge carried by the particle, and the pulse frequency provides information about the concentration of particles in solution. This experiment clearly 10 11 Figure 1.4. (a) Schematic illustration of electric field-driven resistive pulse analysis of nanoparticles. A voltage bias (EM) is applied across the membrane containing a single carbon nanotube channel, driving ions and charged particles through the nanopore. (b)-(d) show the typical current-time traces at different EM. Each pulse or decrease of current represents a single nanoparticle translocation. Particle size and surface charge are calculated based on the duration time At and pulse height Ai. Reprinted with permission from Reference 26 Ito, T.; Sun, L.; Henriquez, R. R.; Crooks, R. M. Acc. Chem. Res. 2004, 37, 937-945. Copyright, 2004 American Chemical Society. identified the potential value of Coulter counting in modern analysis, and led to a resurgence of interest in the resistive pulse analysis of nanoparticles. The replacement of electrolyte solution within the channel by a nanoparticle causes an increase of solution resistance, AR, and therefore a decrease in current, Ai. This process is completely reversible, so when the particle exits the channel the current level recovers to the baseline level, io = Em / Ro, where Ro is the constant open channel solution resistance. With and without a nanoparticle in the channel, the solution resistance can be always calculated by eq 1.2 using different geometry factors, S(x). R = dx + Rend (1.2) 0 S where k is the solution conductivity and Rend is the spreading resistance at the ends of a nanochannel due to the partially blocked mass transport.45 k is generally assumed to be constant in the nanochannel, although there are exceptions when the width of the channel or the diameter of the pore approaches the length scale of the electrical double layer. The ratio of current change during the translocation Ai / io is equal to the ratio of resistance changeAR/Ro. As a result, Ai / io is a function of the shape of nanoparticles (e.g., the diameter ds of a nanosphere) and the topology of the corresponding nanochannel (e.g., the diameter dc and length lc of a nanocylinder). For example, Ai/ io for a nanosphere translocating through a nanocylinder, derived by DeBlois,39 is 12 A _ S(dc, ds ) ----- d3 (lc + °.8dc ) (1.3) 13 o where S (d c, d s) is a correction factor that depends on the nanoparticle to nanochannel diameter ratio, ds/dc. Whends / d c < 0.8, S(dc, d s) is ~1 (± 2%).26a Similar expressions of Ai / io were derived for conical nanopores46-48 and short cylindrical nanopores (where, lc < ds)49 Nanoparticle size ds is then calculated based on experimentally measured Ai / io using eq 1.3. The duration time, At, is inversely proportional to the average translocation velocity, v. In the absence of particle/channel interactions, there are three types of external driving forces contributing to v: electrophoretic forces (EPF), electro-osmotic forces (EOF) and applied pressure. Figure 1.5 schematically illustrates these three forces exerted on a negatively charged 8 nm nanoparticle when a positive voltage and negative pressure are applied (inside vs. outside the nanopore). The EPF stems from the influence of the external electric field on a charged particle while the EOF arises from the transport of the counterions in the electrical double layer of the nanopore wall that drags water with them through viscous interactions.50 Researchers usually isolate the electrophoretic velocity component experimentally and mathematically from the other two. Then, the nanoparticle surface charge is estimated from the electrophoretic velocity, velectrophoresis, in terms of its zeta potential, Z, using the Helmholtz-Smoluchowski equation, ^ _ a grgoZ _ velectrophoresis (1 4) e n e 14 Figure 1.5. A schematic drawing of the driving forces acting on a negatively charged 8- nm-diameter nanoparticle as the nanoparticle translocates through a conical-glass nanopore at a positive voltage and negative pressure. The sign is defined by the difference between internal and external potentials or pressures. where fj.e is the nanoparticle electrophoretic mobility, E is the electric field gradient, sr is the solution dielectric constant, rj is the solution viscosity, eo is the vacuum permittivity, and A is a correction factor which depends upon the ratio of the particle diameter, ds, and the Debye length, k 1 (whends / k 1 >> 1, A = 1; when d s / k l<< 1, A = 2/3). Previous studies on the resistive pulse analysis of nanoparticles indicate that these three external driving forces (EPF, EOF and pressure) are of similar order of magnitude. Most recently, Lan et al. 51 demonstrated that fine control of a single nanoparticle translocation direction and speed is possible by adjusting the applied pressure in an electric field. By accurately adjusting all three forces, we achieved more adequate control of particle speed and moving direction through the sensing zone, which enables us to obtain more detailed information about particle size, charge, shape, and even chemical interactions. Chapter 4 reports the experimental details about controlling the dynamics of individual 8-nm-diameter gold nanoparticles, and the numerical models that semiquantitatively predicted the experimental observations. 1.3 Nanobubbles Nanobubbles are gas-containing cavities with a nanometer size in the liquid solution. The pressure difference (Ap ) between inside and outside a bubble, which is caused by the surface tension (7) at the liquid-gas interface minimizing their surface area and therefore the volume, is governed by Young-Laplace equation (eq 1.5). Eq 1.5 predicts that the internal pressure of nanobubbles (pnb) is extremely high due to its nano­scale curvature (rnb). For example, a 200-nm radius air bubble in water has an internal 15 pressure of ~ 10 atm. The theoretical prediction of nanobubble internal pressure as a function of radius is shown in Figure 1.6. . 2y AP = Pnb - Pout =- (1.5) rnb The increased pressure within the nanobubble leads to an increase of the concentration of the gas in the liquid. According to Henry's law,52 at a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid. For example, the solubility of the gas contained in 20-nm-radius bubbles is 100 fold higher than the solubility in ambient conditions. In other words, the bubbles should dissolve into the solution as soon as they are formed if the solution is not saturated with such high concentration gas. Researchers have not reached an agreement about whether these nanobubbles are able to survive in solution. A few research groups in Japan claimed that they have successfully produced solutions containing gas nanobubbles with radii less than 50 nm.53-56 In the past decade, the majority of research on nanobubbles has been on interfacial gas nanobubbles. Interfacial nanobubbles attach to a solid substrate instead of being suspended in solution. They have been successfully observed and characterized by tapping mode atomic force microscopy (TMAFM).57-66 The development of new methods of generating6677- 7700 and detecting interfacial gas nanobubbles,5577 -7722 as well as the develop­ment of the theory and mechanism of nanobubble formation and stabilization 73-77 16 Internal Pressure (atm) 17 Nanobubble radius (nm) Figure 1.6. Theoretical prediction of the internal pressure of a nanobubble as a function of nanobubble radius using the Young-Laplace equation. have greatly advanced. At present, it is possible to generate large ensembles of nanobubbles of different gas types at hydrophobic surfaces (e.g., perfluorodecyltrichlorosilane (PFDTS) and highly orientated hydrophobic pyrolytic graphite (HOPG)) using the solvent exchange technique57 or by the electrolysis of water.67 Previous studies by other researchers have shown that interfacial nanobubbles exist for hours or days, in contrast to the theoretical short lifetime due to rapid gas dissolution.78 Several mechanisms have been proposed to explain the observed long lifetime of nanobubbles, such as the role of impurities at the interface, 75, 79, 80dynamic steady-state, 69, 74 and contact line pinning, 73,77 but still no general agreement has been yet reached on the actual mechanism. Not only is the stabilization mechanism under debate, but also the mechanism of nanobubble formation remains unclear. It has been proposed that interfacial nanobubbles result from a supersaturation of gas at the interface.73,81 However, Seddon et al.82 and Dong et al.83 recently reported the formation of surface nanobubbles in solutions that were not supersaturated by the corresponding gas. How nanobubbles form at the interface and why they remain stable are still open questions. Chapter 5 presents a new electrochemical approach for investigating the formation and stability of a single H2 nanobubble at the solid substrate. 18 1.4 References (1) Esaki, L. Phys. Rev. 1958, 603-604. (2) Siwy, Z. S. Adv. Funct. Mater. 2006, 16, 735-746. (3) Wei, C.; Bard, A. J.; Feldberg, S. W. Anal. Chem. 1997, 69, 4627-4633. (4) Siwy, Z. S.; Howorka, S. Chem. Soc. Rev. 2010, 39, 1115-1132. (5) Guo, W.; Tian, Y.; Jiang, L. Acc. Chem. Res. 2013, Article ASAP. (6) Hou, X.; Guo, W.; Jiang, L. Chem. Soc. Rev. 2011, 40, 2385-2401. (7) Cheng, L.-J.; Guo, L. J. Chem. Soc. Rev. 2010, 39, 923-938. (8) Zhou, K. M.; Perry, J. 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NDR investigations recently extend far beyond traditional solid-state devices to include single-molecule based electronic junctions, and graphene/carbon nanotube based electronics.3-15 In this chapter, a simple and general method to produce NDR phenomena based on solution ion conductivity within confined nanoscale geometry is demonstrated. Our device is based on an ~50 |im thick glass membrane containing a single, electrically charged, conical shaped nanopore, which has been developed in our laboratory for nanoparticle detection,16-18 as well as for the investigations of microgel19 and liposome 20 translocation in porous media. In the NDR investigation reported here, the membrane separates two electrolyte solutions that possess significantly different ionic conductivities, as shown in Figure 2.1a. The external solution is a mixed DMSO/H2O solution (v:v 3:1) containing 5 mM KCl that has a relatively low conductivity; the internal solution is a 5 mM KCl aqueous solution which has an electrical conductivity approximately 4 times larger than the external solution. To observe the NDR behavior, a positive constant pressure is applied inside the capillary to which the membrane nanopore is attached, resulting in the high conductivity internal solution being driven outward through the pore. Simultaneously, a voltage is applied across the membrane to induce electro-osmotic flow of the external solution in the direction opposite of the pressure driven flow, a consequence of the negative surface charge of the glass. Although the internal and external solutions are completely miscible, the radius of the nanopore orifice is sufficiently small (~300 nm) to result in steady-state convergent/divergent ion fluxes and flows on the internal/external sides of the orifice. Consequently, a well-defined and relatively sharp interfacial zone is established whose position is determined by the balance of the constant pressure force and voltage-dependent electro-osmotic force. As demonstrated herein, by varying the applied voltage at a constant applied pressure, the steady-state interfacial zone can be positioned outside of the nanopore (Figure 2.1b, in the external solution), within the nanopore (Figure 2.1d, in the internal solution), or directly at the nanopore orifice (Figure 2.1c). Because the mass-transfer resistance of the nanopore is largely localized to the volume of solution immediately adjacent to the sides of the pore orifice, the voltage-dependent electro-osmotic force results in the interfacial zone passing through the region of space most sensitive to the electrolyte conductivity (the "sensing zone") as the voltage is varied; this movement of the transition zone results in a sharp increase in the nanopore resistance 25 26 Figure 2.1. a) Schematic illustration of the NDR experiment and the glass nanopore membrane (GNM). A potential difference is applied between the two Ag/AgCl electrodes. The internal solution is an aqueous 5 mM KCl solution and the external solution is a 3:1 (v/v) DMSO/H2O mixture containing 5 mM KCl. b), c) and d) show the interfacial zone outside, right on the orifice and inside the nanopore orifice. when the low conductivity solution enters this region, which is reflected as a sudden decrease in the current in i-V traces. Experimental results and computer simulations demonstrating these principles are presented in this chapter. Since the discovery of ion current rectification (ICR) in a conical shaped nanopore by Wei, Feldberg and Bard, 21 the current-voltage response of asymmetric charged nanopores and nanochannels has received significant attention due to its departure from classic linear ohmic behavior. Extensive research on the experimental and theoretical aspects of ion current rectification (ICR) associated with nanopores with asymmetric geometry or asymmetric charge distribution has been reported over the past two decades. 22" 46 ICR in a charged conical-shaped nanopore results from the accumulation and depletion of ions near the orifice of the nanopore, and has been detailed elsewhere. 23 ' 30 ' 32 ' 42 Siwy and coworkers reported NDR gating behavior in a conical nanopore upon surface charge reversal due to voltage dependent binding of Ca2+ to the nanopore surface.47,48 The NDR phenomenon reported here builds on this research base. Specifically, in a recent article, Yusko and Mayer described a borosilicate glass membrane containing a single nanopore that separated the same DMSO/H2O and aqueous electrolyte compositions employed in this report; these researchers reported that the degree of ICR could be enhanced by drawing the external low conductivity solution into the nanopore by electro-osmosis.49 Conversely, our laboratory recently demonstrated that ICR can be eliminated by pressure driven flow.50 These two results are combined to create a nanopore exhibiting NDR. Similar to the use of NDR based solid-state switches in electronics, a nanopore exhibiting NDR can potentially be employed to amplify small electrical perturbations. In 27 this chapter, we also demonstrate that a small change in the voltage across the nanopore (a few mV) can result in large change (-80%) in the electrical current. Such highly nonlinear electrical responses may be especially suitable for solution phase chemical sensing. 2.2 Experimental section 2.2.1 Chemicals and materials KCl (99.8%, Mallinckrodt) and DMSO (99.9%, EMD Chemical) were used as received. All aqueous solutions were prepared using water (18 MQcm) from a Barnstead E-pure H2O purification system. 2.2.2 Glass nanopore membranes (GNMs) fabrication GNMs were fabricated according to previous reports from our laboratory. 51 Briefly, a Pt wire attached to the tungsten fiber was electrochemically sharpened in a NaCN solution and then sealed in a glass capillary (Dagan Corp., Prism glass capillaries, SB16, 1.65 mm outer diameter, 0.75 mm inner diameter, softening point 700 °C) using a H2/air flame. The capillary was then polished until a Pt nanodisk was exposed, as indicated by an electronic feedback circuit. Optical images of the capillary showing the polishing process are presented in 2.5 Appendix. The Pt nanodisk was then partially etched in a 20% CaCl2 solution by applying a 6 V A. C. voltage between the Pt nanodisk and a large Pt wire counter electrode, and then the remaining Pt wire was gently removed by pulling out the tungsten fiber. The orifice radius of the resulting conical nanopore was determined from the resistance of the pore in 1.0 M KCl solution as previously described. 28 (See 2.5 Appendix.) Experimental results were obtained using three GNMs with orifice radii ranging from 240 to 380 nm. However, the NDR phenomena described in this report have been reproduced using other nanopores with similar size orifice radii. A GNM with a much larger orifice radius (857 nm) did not exhibit NDR, as reported in 2.5 Appendix. 2.2.3 Cell configuration and data acquisition A Dagan Cornerstone Chem-Clamp potentiostat and a Pine RDE4 (used as the waveform generator) were interfaced to a computer through a PCI data acquisition board (National Instruments). Current-voltage (i-V) curves were recorded by in-house virtual instrumentation written in LabVIEW (National Instrument) at a data acquisition rate of 10 kHz. A 3-pole Bessel low-pass filter was applied at a cut-off frequency of 1 kHz. The GNM was filled and immersed in a 5 mM KCl aqueous solution and the i-V curve measured to ensure the cleanness of the nanopore by checking the dependence of ICR response on applied pressure driven flow. Clean nanopores showed agreement with expectations that ICR disappears with pressure applied, based on the results in ref. 50. The GNM was then removed from solution, and excess surface liquid was wiped off. The GNM was then immersed in the 5 mM KCl DMSO/water mixture (v:v 3:1) containing 5 mM KCl and i-V measurements were recorded. Electrical contact to the solutions was made using Ag/AgCl electrodes. Pressure was applied across the GNM, Figure 2.1, using a 10 mL gastight syringe (Hamilton Co., Reno, Nevada) and measured with a Marshalltown-Tempco, Inc. pressure gauge with a sensing range between 0 to 300 mmHg. 29 2.2.4 Finite-element simulations The finite-element simulations were performed to investigate the NDR mechanism using COMSOL Multiphysics 4.1 (Comsol, Inc.). 2.3 Results and discussion 2.3.1 Negative Differential Resistance (NDR) Figure 2.2a shows the i-V response of a 380 nm radius GNM containing an aqueous internal solution and immersed in a mixed DMSO/H2O (v:v 3:1) external solution; both solutions contained 5 mM KCl. The family of curves corresponds to different constant positive pressures applied inside the capillary, ranging between 0 and 50 mmHg. The applied voltage corresponds to the potential of the internal Ag/AgCl electrode vs. the external Ag/AgCl electrode. At nonzero applied pressures, a large reversible decrease in the current occurs as the potential is scanned to negative values, Figure 2.2a. The decrease in current, as the electrical driving force is increased, corresponds to a region of NDR. Prior to and following the potential at which NDR occurs (referred to as the "turning point"), the nanopore exhibits quasi-ohmic behavior, but the conductance of the nanopore at potentials positive of the turning point (~2 x 1 0- 8 Q"- 1) is approximately one order of magnitude larger than at negative potentials (~2 x 10-9 Q-1) (determined from the slopes of the i-V curves). As the applied pressure is increased, the turning point shifted to more negative voltages. The NDR i-V curve was reversible and repeatable as the voltage was swept between -2 to 2 V, as shown in Figure 2.2b. The i-V response of a 330 nm radius GNM exhibiting nearly identical NDR behavior as a function of pressure, is presented in 30 31 (a) 10 •40 -25 (b) 15 Figure 2.2. i-V response of the 380 nm radius GNM as a function of the applied positive pressure (internal vs. external). The voltage was scanned from 2 to -2 V at a rate of 200 mV/s. Internal and external solutions were an aqueous 5 mM KCl solution and a DMSO/water (v:v 3:1) mixture containing 5 mM KCl, respectively. (b) i-t recording of the 380 nm radius GNM when a 20 mmHg positive pressure was applied across the nanopore, and the voltage was cycled between -2 V (Point A) and 2 V (Point C) at a scan rate of 200 mV/s. Point B is the voltage where NDR occurs. 2.5 Appendix and includes both forward and reverse scans which give some indication of the hysteresis in the NDR turning point (10 to 100 mV at different pressures for the data in 2.5 Appendix. The degree of hysteresis observed in the NDR turning point varied from nanopore to nanopore, and increased with increasing scan rates, but has not been fully explored. Presumably the hysteresis arises from the relatively slow redistribution of solvent and ions.37, 38 The NDR phenomenon can be qualitatively understood by considering the position of the interfacial zone between the internal high-conductivity solution and external low-conductivity solution, relative to the location of the electric potential drop at the nanopore orifice. First, it is important to note that because the pore is conical shaped, the fluxes of ions and solvent molecules are radially convergent (or divergent, depending on the direction of the current and applied pressure), resulting in a steady-state i-V response at slow scan rates and a steady-state distribution of ions and molecules. Consequently, a well-defined and relatively sharp interfacial zone exists between the solutions, with a location that is determined by the balance of the constant pressure force and the voltage-dependent electro-osmotic force. Conversely, the location of electric potential drop across the nanopore is largely voltage independent, and is distributed over a region of solution on both sides of the orifice; the width of this sensing zone is of the same order of magnitude as the pore radius, as previously demonstrated 52 (see 2.5 Appendix for an example of the potential distribution across a 400 nm nanopore). By varying the applied voltage at a constant applied pressure, the variable electro-osmotic force can be used to scan the position the interfacial zone between the internal and external solutions across the sensing zone. Qualitatively, a high nanopore conductance 32 state exists at low negative voltages or at high applied pressures, corresponding to the interfacial zone located on the external side of the orifice, and the internal aqueous 5 mM KCl solution occupying the sensing zone; conversely, a low nanopore conductance state exists at high negative voltages or at low applied pressures, corresponding to the interfacial zone located on the internal side of the orifice, and the external DMSO/H2O 5 mM KCl solution occupying the sensing zone. For a particular combination of applied pressure and voltage, the NDR turning point occurs when interfacial zone passes through the orifice. 2.3.2 Finite-element simulations of the nanopore NDR phenomenon Steady-state finite element simulations using COMSOL Multiphysics were performed to provide a more quantitative description of the experimental results. The internal solution was modeled as a 5 mM KCl aqueous solution and the external as a 5 mM KCl in DMSO/H2O mixture (volume fraction of DMSO = 0.8). DMSO is treated as a solute that is transported from the external DMSO/H2O solution to the internal aqueous solution. The 2D axial-symmetric geometry and boundary conditions are provided in 2.5 Appendix. The radius of the nanopore opening was set as 400 nm and the thickness of the GNM as 20 |im, corresponding approximately to the nanopore geometry used in the experiments. A surface charge of -26 mC/m2 was assumed (see 2.5 Appendix for details).41, 50 A description of ion and solvent transport in the nanopore begins with the Navier- Stokes equation, describing pressure and electric force driven flow. 33 uVu = - (-Vp + /7V2 u - F ( V z.c. )VO) P i (2.1) 34 In eq 2.1, u and O are the local position-dependent fluid velocity and potential, p and n are the density and viscosity of the fluid, respectively, c and zt are concentration and charge of species i in solution, p is the pressure and F is the Faraday's constant. For computational simplicity, we assume a constant value for p of 1000 kg/m3. However, ion diffusivities and mobilities are strongly dependent on n; thus, literature values of n for DMSO/H2O mixtures 53 were used in the simulation, as detailed in 2.5 Appendix. The ion fluxes are modeled by the Nernst-Planck equation, including the diffusion, migration and convection terms. Fz. J = ~D1Vc1 - R T DC V®+Cu (2 2 ) In eq 2.2, J and Dt, are, respectively, the ion flux vector and diffusion coefficient of species i in solution and T is the absolute temperature. The ion diffusion coefficients Dt in DMSO/water mixtures were estimated by Stokes-Einstein equation, eq 2.3, using the composition-dependent value of n (see 2.5 Appendix). Dr* 6k-B--T--- (2.3) 6 n 7 r In eq 2.3, kB is Boltzmann's constant and r is the solvated radius of the species i. A value of r = 1.5 x 10-10 m was employed for both K+ and Cl-. The relationship between the local ion distributions and potential is described by Poisson's equation, eq 2.4, 2 F V O = ---- \ z , c , (2 .4) £ i Here, e is the dielectric constant of medium, which is also dependent on the molar fraction of DMSO in the DMSO/water mixture (see 2.5 Appendix).54 Eqs 2.1 to 2.4 are coupled with an additional equation describing the flux of DMSO. J DMSO = DdMSoVCdMSO + CDMSOu (2.5) In this model, to simplify the computations, we assumed DDMSo to be independent of the solution composition (1.25 x 10-9 m2/s), and the interfacial tension55 between the external and internal solution was not taken into consideration. The interface between the external and internal solutions was initially set at the nanopore orifice. Figure 2.3a shows the simulated i-V response of the nanopore in absence of an applied pressure across the GNM. The simulation captures the electro-osmosis-induced enhancement of ICR, first reported by Yusko and Mayer et al.49 (We also verified the experimental results of Yusko and Mayer, see 2.5 Appendix) As seen in Figure 2.3a, at 35 36 Figure 2.3. Simulation of electro-osmosis induced ICR behavior. (a) Simulated steady-state i-V response of a 400 nm radius GNM in the absence of an applied pressure. In the simulation, the external solution (z > 0) initially contained a solution of 5 mM KCl in DMSO/water mixture (volume fraction of DMSO = 0.8), while the internal aqueous solution (z < 0) initially contained 5 mM KCl. The surface of nanopore is negatively charged (-26 mC/m ). (b) is simulated steady-state volume fraction distributions of DMSO at -1 V and 1 V (internal vs. external). r = 0 is the symmetry axis of the GNM geometry, while z = 0 corresponds to the nanopore orifice. potentials more positive than -0.2 V and at negative potentials, the i-V responses are approximately ohmic. Between these two zones, there is a short transition range where nonlinear i-V behavior is observed. Figure 2.3b shows plots of the simulated DMSO volume fraction distribution at 1 V and -1 V. At V = 1 V, the DMSO distribution gradient is pushed out of the nanopore, resulting in the high conductivity internal solution occupying the sensing zone of nanopore. At V = -1 V, the DMSO/H2O solution is driven into the nanopore by electro-osmosis, forming an interfacial zone below the orifice; the solution at the sensing zone has essentially the same composition as the external bulk solution, resulting in a low conductivity state. In summary, the finite-element simulations are in good agreement with the experimental results of Yusko and Mayer and indicate that the enhanced ICR results from electro-osmosis driven positioning of the interfacial zone below (negative potentials) or above (positive potentials) the nanopore orifice. Figure 2.4a shows the numerically simulated i-V response in the absence (blue line) and presence of 5 mmHg applied pressure (red line), for the same GNM as described above. The simulation qualitatively captures the existence of the nanopore NDR phenomenon at negative potentials when a pressure is applied across the GNM. A sudden decrease in the current is observed between -0.770 and -0.778 V, similar in shape, albeit smaller, than that observed in the experiments. Given the several approximations employed in the simulation, e.g., the surface tension between the two solutions not taken into account and the immediate mixing of two solutions, the qualitative agreement between these preliminary simulations and experiment is considered to be reasonable. Figure 2.4b shows the distribution of DMSO across the nanopore as a function of the applied potential. Similar to the results presented in the preceding section, the interfacial 37 38 Figure 2.4. Simulation of NDR behavior in a nanopore. (a) Simulated i-V curves of a 400 nm radius nanopore at 5 mmHg pressure (red line) and in the absence of pressure (blue line).The other initial settings are the same as Figure 2.3. (b) The volume fraction distributions of DMSO at selected voltages ranging from -0.2 to -1 V. zone between the external DMSO/H2O and internal H2O solutions is a function of the applied potential, a consequence of the electro-osmotic forces driving the external solution inward through the nanopore. However, as the potential is varied from -0.770 to -0.778 V in the simulated i-V curve (Figure 2.4a), the results in Figure 2.4b show that the onset of NDR is accompanied by a discontinuous jump due to the positioning of the interfacial zone from the external solution to a position within the nanopore. This abrupt change in position results in the nanopore switching from a high conductivity state to a low conductivity state. Ion and solvent diffusion, electro-osmosis and pressure driven flow each contribute to the position of the interfacial zone. A complete understanding of how these highly coupled factors lead to the NDR behavior is beyond the scope of this report. However, the following discussion presents our preliminary understanding of the phenomenon. Figure 2.5 shows the simulated steady-state DMSO convective and diffusive flux vectors at the orifice of the nanopore at -0.770 V, just prior to the nanopore entering the low conductivity state. This figure shows that the convective flux (black arrows) due to the applied pressure engendered force is largest across the central region of the nanopore orifice and is directed outward, while the diffusive flux of DMSO (red arrows) and the convective flux due to electro-osmosis is directed inward along the circumference of the orifice. At steady-state, the outward directed pressure-driven convective flux must balance the inward directed diffusive flux and electro-osmosis-driven convective flux, resulting in a stationary interfacial zone that is located external to the nanopore (Figure 2.4b, -0.770 V). As the voltage is shifted to a slightly more negative value, the electro-osmotic force increases resulting in a larger inward electro- 39 40 Figure 2.5. Simulated steady-state DMSO flux in the 400 nm radius GNM at an applied voltage of -0.77 V (internal vs. external). The color surface indicates the net DMSO flux magnitude. The flux vectors at the opening of nanopore indicate the directions and relative magnitudes of the convective (black arrows) and diffusive DMSO fluxes (red arrows). osmosis-driven convective DMSO flux and the movement of the interfacial zone towards the nanopore interior. We speculate that the very nonlinear NDR behavior results from the increase in the viscosity of the solution as the DMSO concentration increases at the orifice, resulting in a further decrease in the outward convective flow. The resulting decrease in outward flow would result in even higher DMSO concentrations within the nanopore, and the process would continue until the nanopore entered the low conducting state; at that point, the electro-osmotic forces would decrease and a new steady state interfacial zone between the external and internal solutions would be established. Additional numerical simulations of this system are required to better understand the positive feedback process that leads to NDR. The computational results indicate that the transition between high and low conductivity states in the nanopore can occur over a very narrow potential range (< 8 mV). This behavior corresponds to a nanopore electrical switch and has potentially interesting applications in chemical sensing. For instance, because the NDR behavior is a function of the electro-osmotic force generated within the nanopore, the potential at which the turning point is observed will be a function of the electrical charge density on the nanopore surface. Thus, by modifying the nanopore surface with receptors that bind charged analytes, it appears plausible to build a nanopore "on/off' switch that allows detection of the presence of a small amount of analyte. In a preliminary experiment, we constructed a GNM with a smaller orifice (230 nm radius) and measured the i-V response at a slow scan rate (10 mV/s) to estimate how sharp of a conductivity transition can be realized, and whether or not the simulated prediction of an 8 mV wide transition window is reasonable. Figure 2.6 shows the i-V response for this experiment, recorded under the 41 42 Figure 2.6. Experimental NDR behavior for a 230 nm radius GNM with a scan rate of 10 mV/s and 20 mmHg pressure applied across the membrane. NDR behavior occurs over a potential difference of ~7 mV (from -0.852 to -0.859 V). Internal and external solutions were an aqueous 5 mM KCl solution and a DMSO/water (v:v 3:1) mixture containing 5 mM KCl, respectively. The volume fraction distributions of DMSO before and after the NDR point are taken from Figure 2.4 (-0.770 and -0.778V) to reiterate the origin of the NDR behavior. same conditions as in previous experiments. The current decreases by -80% over a 7 mV range, demonstrating that very sharp NDR transitions can be obtained using smaller nanopores and slow scan rates. Finally, we note that the NDR behavior reported here can, in principle, be realized using solvents other than DMSO and water. The only requirements of our proposed mechanism are that the external and internal solutions are miscible, and that they have significantly different ionic conductivities. Thus, it is likely that charged nanopores employed with other appropriate solution compositions will also exhibit NDR behavior. 2.4 Conclusions We have demonstrated that liquid-phase NDR was observed in the i-V behavior of a negatively charged conical nanopore in a glass membrane that separates an external low-conductivity solution from an internal high-conductivity aqueous solution. NDR results from the voltage-dependent electro-osmotic force opposing an externally applied pressure force, continuously moving the location of the interfacial zone between the two miscible solutions through the nanopore orifice until a potential of interfacial instability is reached. The NDR curve is reversible and can be tuned by adjusting the pressure across the GNM. Preliminary numerical simulations support the proposed mechanism and are able to semiquantitatively capture the NDR response. Current work is being directed towards developing a better understanding of the NDR behavior, as well as applying this phenomenon in chemical analyses. 43 2.5 Appendix In this appendix, optical microscopy images of the GNM during polishing, i-V response of 330 and 800 nm radii GNM, simulated potential profile in a 400 nm GNM, details of the finite-element simulation (parameters setting, geometry, mesh, etc.), the value of diffusion coefficient, viscosity and relative permittivity for DMSO/H2O mixture, and electro-osmosis-induced ICR curve for 380 nm radius GNM are shown in Figure 2.7­2.14, respectively. Figure 2.7 shows optical microscope images of a sharpened Pt wire sealed at the end of a glass capillary at different stages during the polishing process to expose a Pt disk. After removal of the Pt, the size of the nanopore was measure from the nanopore i-V response in an aqueous 1 M KCl solution. The relationship between the membrane resistance Rp and the small orifice radius is given by: 44 1 , 1 \ R p ~ -K-U--p- (~;rtt-an99 + 44) (2 6) where 9 is half cone angle of the nanopore, K is conductivity of the aqueous 1 M KCl solution, Rp is the resistance of the nanopore and ap is the radius of the orifice of nanopore. 56 Herein, K= 0.1119 Q-1cm-1, 9 is ~ 10o and Rp is obtained from the slope of i-V response (Figure 2.8). The radius of the nanopore in Figure 2.8 was calculated to be 379 nm with a relative uncertainty of -10%. i-V response for an 857 nm radius GNM (Figure 2.9) using the same experimental conditions as in Figure 2.1. NDR is not observed for the larger nanopore, most likely due to the larger pressure driven flow. Thus, Figure 2.7. Optical microscope images of a sharpened Pt wire sealed at the end of a glass capillary at different stages during the polishing process to expose a Pt disk. (Note: the "two wires" in the third photo corresponds to a single folded wire.) 46 Figure 2.8. i-V response of the nanopore filled with and immersed in an aqueous 1 M KCl solution. The i-V response exhibits ohmic behavior in the 1 M KCl solution. 47 Figure 2.9. Experimental i-V responses of an 857 nm radius nanopore using an internal aqueous 5 mM KCl solution and an external DMSO/H2O mixture (v:v 3:1) containing 5 mM KCl. Positive pressures were applied from 0 mmHg to 280 mmHg. 48 Figure 2.10. Experimental i-V responses of a 330 nm radius GNM with an internal aqueous 5 mM KCl solution and an external DMSO/water mixture (v:v 3:1) containing 5 mM KCl. A positive pressure (internal vs. external) ranging from 20 mmHg to 80 mmHg was applied across the GNM. Scan rate = 200 mV/s. The i-V curves show the forward and reverse scan responses at each pressure. 49 Potential profile on the central line Figure 2.11. The steady-state potential profile along the center axis (left) and potential distribution (right) when -0.77 V is applied across a 400 nm radius GNM. Internal solution: 5 mM KCl in H2O; external solution: 5 mM KCl in DMSO/H2O. 50 Figure 2.12. The 2D axial-symmetric geometry of the GNM and the mesh for the finite-element simulation (red dash line: the symmetry axis). The initial interface between the internal 5 mM KCl aqueous solution and the 5 mM KCl external DMSO/H2O solution is located at the pore orifice, z = 0 . 51 Figure 2.13. (a) Viscosity and (b) diffusion coefficients of K+ and Cl' in DMSO/H2O mixtures. The diffusion coefficients of K+ and Cl' were calculated based on Stokes' Einstein equation (eq 2.3) using the values of viscosity reported in ref. 53 and are plotted. The polynomial fittings of data points shown on the graphs were used in the finite element simulation. 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Langmuir 2006, 22, 10777. 56 CHAPTER 3 CHEMICAL SENSING BASED ON NEGATIVE DIFFERENTIAL ELECTROLYTE RESISTANCE IN A SOLID-STATE NANOPORE 3.1 Introduction Negative differential resistance (NDR) is used to describe electrical behavior where current decreases with an increasing applied voltage. One well-known NDR device is the Esaki or tunnel diode, where electron tunneling between the valence and conduction bands of a heavily doped p-n junction leads to a decrease of conductivity as the voltage is increased.1 In this report, we describe NDR associated with a solid-state nanopore immersed in an aqueous solution. We describe the mechanism for this unusual electrolyte behavior, and demonstrated how NDR can be applied in chemical sensing. The nonlinear current-voltage (i-V) behavior of geometrically asymmetric and electrically charged nanopores has been extensively investigated since the initial report of ion current rectification in glass pipettes by Wei, Bard and Feldberg.2-1620 More recently, electro-osmotic and pressure-driven flows have been used to control electrolyte 21-24 or solvent flux9,25 and, thus, alter the nanopore conductance, with applications in the resistive-pulse detection of nanoparticles or macromolecules. 26 - 34 A solution flow-engendered NDR response in a conical shaped glass nanopore separating aqueous and dimethylsulfoxide (DMSO) solutions containing equal concentrations of dissolved KCl was previously demonstrated by our laboratory.35 A decrease in the electrical current in the nanopore was observed with increased applied voltage, a result of the voltage-dependent electro-osmotic flow (EOF) driving the external DMSO solution into the nanopore; the ion mobilities are lower in DMSO than water due to the much higher viscosity of DMSO. By varying the applied pressure across the nanopore, the voltage where NDR occurs was found tunable over a ~1 V range. An NDR-like response with ion current fluctuations was also reported by Siwy and coworkers for a polymer nanopore when a divalent cation (Ca2+, Mn2+) was present in solution and adsorbed to the interior nanopore surface. In contrast to EOF flow-induced NDR phenomenon described herein, this latter behavior was tentatively ascribed to voltage-dependent fluctuations in the local electrostatic potential resulting from transient binding of the dication.36, 37 In the chapter, NDR in a purely aqueous system is reported. A conical nanopore in a ~25 ^m-thick glass membrane was used to separate aqueous solutions with two different KCl concentrations. In a typical experiment, the radius of the small orifice of the nanopore is ~300 nm; the internal solution within the nanopore contains 50 mM KCl and the external solution contains 5 mM KCl, as shown schematically in Figure 3.1a. After a pressure and a negative voltage are applied across the nanopore, a force balance is established, resulting in a steady-state electro-osmotic flow (white arrow) driving the lower concentration KCl solution into the nanopore while the pressure-driven flow (red arrow) pushes the higher concentration KCl solution out of the nanopore. At steady-state, the opposing pressure and electro-osmotic forces, along with the nanopore surface charge, determine the distribution of K+ and Cl- within the nanopore and, thus, the nanopore 58 59 Figure 3.1.(a) Illustration of pressure-driven and voltage-engendered electro-osmotic flows that give rise to negative differential resistance (NDR) in the i-V response of a negatively charged, conical nanopore that separates high and low ionic strength solutions. The color surface indicates the magnitude of the net flow velocity; red and blue denote higher and lower velocities, respectively. Pressure-driven flow out of the pore occurs along the central axis of the nanopore (red arrow), while an opposing electro-osmotic flow (EOF) into the pore occurs along the negatively charged nanopore surface (white arrows). NDR observed in the i-V response of the nanopore results from positive feedback associated with an increase in EOF as the voltage is increased: an increased flux of the external low-conductivity solution into the nanopore orifice results in a decreased ionic conductivity of solution in the nanopore causing a further increase in EOF and a sudden drop in the nanopore conductivity at a critical voltage, V*. (b) Profiles of the total ion concentration (K+ plus Cl-) in the nanopore for applied voltages above (V > V*,, high conductivity state) and below (V < V*, low conductivity state) the conductivity switching potential, V*. conductivity. Qualitatively, and as shown in Figure 3.1b, by holding the pressure constant while increasing the applied voltage, the balance in flow within the nanopore shifts from an outward pressure-driven dominated flow at low voltages to an inward electro-osmotic dominated flow at high voltages. The change in flow direction results in a decrease of total ion (K+ and Cl-) concentration near the nanopore orifice, which further enhances the electro-osmotic flow into the pore. We demonstrate that the dependence of EOF on ion concentration creates a strong positive feedback mechanism between the nanopore flow and ion distributions, generating a bistability in the nanpore conductace. The switch from a high-conductance to low-conductance state at a critical potential, V\, occurs over a very narrow voltage range (< 2 mV) as demonstrated by the experimental results and finite element simulations described below. Because electro-osmotic flow depends strongly on the surface electrical charge density, V is also very sensitive to the binding of charged analytes to the nanopore. This property of nanopore-based NDR is used to develop a new method of chemical detection. 3.2 Experimental section 3.2.1 Chemicals and materials KCl, K2HPO4, KH2PO4, and CaCl2 (all from Mallinckrodt chemicals) were used as received. All aqueous solutions were prepared using water (18 MQ cm) from a Barnstead E-pure H2O purification system. Solution pH was buffered to a selected value with an appropriate ratio of K2HPO4 and KH2PO4, present at a combined concentration equal to 10% of the KCl concentration. For example, 100 mM KCl contains 10 mM K2HPO4 and KH2PO4 in total. All solution pHs were measured using a pH meter. 60 3.2.2 Glass nanopore membrane (GNM) GNM preparation and sizing followed the procedures reported in Chapter 2. Four GNMs with orifice radii ranging from 260 to 470 nm were used in the experiments described herein. 3.2.3 Experimental set-up and data acquisition A schematic diagram of the experimental set-up is presented in Figure 3.2. A glass capillary containing a glass nanopore membrane (GNM) at one end was used, as illustrated in the insert of Figure 3.2. The fabrication and sizing of GNMs followed procedures previously reported.38 Four GNMs with orifice radii ranging from 260 to 470 nm were used in the experiments described herein. Pressure was applied across the nanopore using an airtight syringe connected to the capillary. A voltage was applied across the nanopore using two Ag/AgCl electrodes; one electrode is placed in the internal solution of the capillary, and the other in the external solution. The voltage between the two electrodes was scanned at a constant rate (10 mV/s) while measuring the current using a Dagan 2-electrode Voltammeter/Amperometer with a 10 kHz bandpass. A LabVIEW program was used to sample the current at a frequency of 10 kHz, and every 500 data points were averaged and used to construct D.C. i-V curves. For A.C. conductance measurements, a 1 kHz small-amplitude (10 mV) sine wave was superimposed on the slowly-varying D.C. voltage, and a Stanford Research Systems SR830 lock-in amplifier was used to separate the A.C. component from the total current. The root mean square (RMS) amplitude of the A.C. component was simultaneously recorded by the same LabVIEW program described above. 61 62 Figure 3.2. Schematic drawing of the experimental set-up. A glass nanopore membrane (GNM) at the end of a glass capillary separates the high (internal) and low (external) concentration KCl solutions. A positive pressure (inside vs. outside nanopore) is applied across the GNM to generate an outward pressure-driven flow. A 1 kHz, 10 mV (rms) sine wave superimposed on a slowly varying voltage (10 mV/s) is applied between the two Ag/AgCl electrodes located on opposite sides of the nanopore. The lock-in amplifier is used to analyze the A.C. component of the current. 3.2.4 Finite-element simulations The finite-element simulations were performed using COMSOL Multiphysics 4.1 (Comsol, Inc.) to study the mechanism of NDR response as well as its sensitivity to surface charge density. Simulation details are provided in 3.5 Appendix. 3.3 Results and discussion 3.3.1 Negative Differential Resistance (NDR) in aqueous solutions Glass membranes, ~25 ^m-thick and containing a single conical nanopore with a half-cone angle of ~10o, as schematically shown in Figure 3.2, were synthesized at the end of a glass capillary. Aqueous solutions with different KCl concentrations were placed inside and outside the capillary, and a constant positive pressure and varying negative voltage were applied across the glass membrane. All values of applied pressure and applied voltage reported herein correspond to the values measured within the capillary relative to the external solution and are designated below as "internal vs. external." A lock-in amplifier interfaced to the potentiostat enables simultaneous recording of the A.C. and D.C. currents while slowly scanning the voltage across the nanopore, as discussed in a later section. Details of nanopore synthesis, instrumentation and data acquisition are provided in the Experimental section. Figure 3.3a shows a series of typical i-V curves exhibiting NDR for a 260-nm-radius nanopore containing a 50 mM KCl internal solution while varying the KCl concentration in the external solution between 5 and 25 mM. A constant pressure of 10 mmHg was applied across the nanopore while the voltage was scanned slowly in the negative direction at a rate of 10 mV/s. In general, the NDR switching potential is a strong function of the solution pH (vide infra); thus, the solutions 63 64 Figure 3.3. NDR behaviors in a nanopore. (a) A series of NDR curves as a function of the external KCl concentration measured using a 260-nm-radius nanopore. The KCl concentration of the external solution was varied between 5 and 25 mM KCl, while the internal KCl concentration (50 mM) was held constant; pH = 7.0. A 10 mmHg pressure (internal vs. external) was applied. (b) Conductance values measured from the slopes of i- V responses at voltages positive and negative of the NDR switching potential as a function of the external solution KCl concentration. were buffered to 7.0 with an appropriate ratio of K2HPO4 and KH2PO4, present at a combined concentration equal to 10% of the KCl concentration. For example, the 50 mM KCl solution contains 5 mM K2HPO4 and KH2PO4 in total. All solution pHs were measured using a pH meter. As shown in Figure 3.3a, NDR behavior in the i-V response occurs between -1.0 and -1.1 V, approximately independent of the KCl concentration in the external solution. However, the width of the potential range of the transition between high and low conductance states increases from less than 10 mV when the external solution contained 5 mM KCl, to ~100 mV at 20 mM, and to ~200 mV at 25 mM. The conductance of the nanopore, as measured from the slopes of the i-V curves in the high (V > Va) and low conductance states (V < Va) (abbreviated hereafter as HCS and LCS, respectively) is plotted in Figure 3.3b. The data indicate a HCS conductance of ~90 nA/V, approximately independent of the external KCl concentration. Conversely, the conductance of the LCS increases linearly with the concentration of external KCl bulk solution with a proportionality constant of ~1.8 nA/(VmM). Steady-state finite element simulations were performed in order to explore and understand the mechanism of NDR and its dependence on the KCl concentrations in the internal and external solutions, pore geometry, and nanopore surface charge density. The Nernst-Planck equation governing the diffusional, migrational and convective fluxes of K+ and Cl", the Navier-Stokes equation for low-Reynolds number flow engendered by the external pressure and electro-osmosis, and Poisson's equation relating the ion distributions to the local electric field were simultaneously solved to obtain local values of the fluid velocity, ion concentrations, electric potential, and ion fluxes. The electrical current in the nanopore was obtained by integrating the ion fluxes over a cross-sectional 65 area of the nanopore. Simulation details including boundary conditions, mesh, parameter and constant setting are provided in 3.5 Appendix. A simulated i-V response for a 260-nm-radius nanopore is shown in Figure 3.4, along with the volumetric flow rate (m3/s) at the orifice and the total ion concentration profiles (CK+ + CCl-) for applied voltages between -0.4 and -1.4 V, while holding the pressure constant at 10 mmHg. The internal and external solution KCl concentrations were initially set to 50 mM and 5 mM, corresponding to the experimental i-V result (gray line) shown in Figure 3.3a. The simulation predicts an NDR switch at -1.256 V for a 5 mM KCl external solution, in a reasonable agreement with the experimental measurement (Vx = -1.11 V). Figure 3.4c shows that the total ion concentration in the nanopore decreases from ~70 mM at -0.4 V to ~35 mM at -1.4 V, dropping suddenly within a narrow potential range between -1.256 and -1.258 V. Finite-element simulations of the nanopore system failed to converge within this narrow voltage window, suggesting that a stable fluid-flow and conductance state does not exist between the HCS and LCS. The simulated i-V curve suggests that NDR represents a sudden transition between high and low conductance states that is associated with a bistability in the electrolyte flow within the nanopore. As schematically illustrated in Figure 3.1, the ion concentration distribution is determined by the combination of the constant outward pressure-driven flow and the voltage-dependent inward electro-osmotic flow. The simulated flow rate at the orifice shown in Figure 3.4b provides a more quantitative view of the voltage dependent flow within the nanopore. At potentials positive of ~-1.1 V, the flow is directed outward from the nanopore (represented by a positive sign) and its magnitude is linearly correlated with the potential, a consequence of increasing electro- 66 67 Figure 3.4. Simulation of NDR behavior in a nanopore. (a) Simulated i-V curve of the 260-nm-radius nanopore with an external KCl concentration of 5 mM and an internal KCl concentration of 50 mM (corresponding to the experimental data (gray line) in Figure 3.3a). A pressure of 10 mmHg and a surface charge density of -12.5 mC/m2 were used in the<