Electron-Transfer Gated Ion Transport in Carbon Nanopipettes

Transcription

1 Supporting information for Electron-Transfer Gated Ion Transport in Carbon Nanopipettes Dengchao Wang and Michael V. Mirkin Department of Chemistry and Biochemistry, Queens College, City University of New York, Flushing, New York 11367, United States Table of contents: 1. Experimental section 2. Modeling and numerical simulations of ionic transport and bipolar electrochemistry in carbon nanopipettes Scheme S1. The 2D axisymmetric simulation model and boundary conditions. Figure S1. The TEM images and current-potential (i-v) responses of the glass and carbon nanopipettes. Figure S2. The multivalent anions effect on the i-v responses of carbon nanopipettes. Figure S3. Dependence of the OCP of the carbon nanopipette on [K3Fe(CN)6] and [Ru(NH3)6Cl3] Figure S4. Fitting the entire CNP i V curve to the theory. Figure S5. Additional example of the redox concentration effect on the CNP i-v curves in 10 mm KCl. Figure S6. Experimental i-v curves of the carbon nanopipettes at different ferrocene and ferrocenemethanol concertation. Figure S7. High redox concentration effect on CNP i-v curves. Figure S8. Carbon layer potential and ion concentration distributions at the carbon surface under different bias voltage polarities. S1

2 1. Experimental Chemicals and materials. KCl, potassium ferricyanide (K3Fe(CN)6), potassium ferrocyanide(k4fe(cn)6) and acetonitrile (CH3CN, gradient grade > 99.9%) were from Sigma-Aldrich; hexaammineruthenium (Ru(NH3)6Cl3) was purchased from Strem Chemicals; tetrabutylammonium perchlorate (TBAClO4) was from Fluka. Ferrocenemethanol (FcMeOH, 97%, Alfa Aesar) and ferrocene (Fc, 98%, Sigma-Aldrich) were sublimed before use. All other chemicals were used as received. Aqueous solutions were prepared using deionized water from the Milli-Q Advantage A10 system (Millipore) equipped with Q-Gard T2 Pak, a Quantum TEX cartridge and a VOC Pak with total organic carbon (TOC) 1 ppb. Fabrication of carbon nanopipettes. Nanopipettes with the tip radii from 50 to 100 nm were prepared by pulling quartz capillaries (1.0 mm o.d., 0.5 mm i.d.; Sutter Instrument Co.) with the laser pipette puller (P-2000, Sutter Instruments). The nanopipettes were pulled using a one-line protocol: (1) HEAT: 650; FIL: 3; VEL: 22; DEL: 135; PUL: 85. A layer of carbon was deposited on the interior surface of the glass nanopipette via chemical vapor deposition (CVD) at 950 C, using methane as carbon source and argon as the protector (methane/argon: 3/2), as described previously. S1 The thickness of the carbon layer is about 5- S1, S2 10 nm near the pore orifice. Instrumentation and Procedures. The i V curves were recorded with a CHI 760E bipotentiostat (CH Instruments, Inc.) in a two-electrode cell with the same solution inside and outside a CNP. Two homemade Ag/AgCl electrodes were used as the internal and external references. One of them was inserted into a CNP from the back, not touching the carbon surface, and the second one was placed in the external solution. To measure the OCP, a silver wire was used to connect the carbon layer to the CHI 760E instrument (Open Circuit Potential Time operating mode). A carbon nanopipette was centrifuged for 10 min after filling or replacing the inner solution. A JEOL JEM-2100 transmission electron microscope (TEM) was used to characterize the CNPs, as described previously. S2 The pipette was attached to the grid (PELCO Hole Grids, Copper) in such a way that its tip was shown in the grid center hole, and the rest of the pipette was cut off. A relatively low electron beam voltage of 120 kv was used to reduce charge/heat accumulating effects on the glass layer. S2

3 2. Modeling and numerical simulations of ionic transport and bipolar electrochemistry in carbon nanopipettes Finite-element analysis of the charge transport in carbon nanopipettes was carried out using COMSOL Multiphysics 5.2a. A 2D-axisymmetric model was used to describe charge transport in the conical nanopipette with the carbon-coated inner wall. The variables z and r refer to the coordinates perpendicular and parallel to the carbon nanopipettes orifice, respectively. The geometric parameters a, r c, h and d represent the pore radius, carbon layer thickness, reservoir depth and the nanopipettes depth, respectively. Scheme S1. The 2D axisymmetric simulation model and parameters. The Transport of Diluted Species, Electrostatics and Electric Currents models of COMSOL were used. The solution contains the reduced redox form R, the oxidized form O, the cation K + and the anion Cl. The ionic transport flux, including diffusion and migration, in the solution reservoirs and carbon nanopipettes was described by the Nernst-Planck equation (S1), and the electric potential distribution in solution was calculated using the Poisson equation (S2): zf i Ji = Di ci Di ci φ RT (0 rr < aa, dd < zz < h;) (S1) S3

4 2 ( εεφ 0 r ) = F zc i i (0 rr < aa, dd < zz < h;) (S2) i where D i, C i, and z i are the diffusion coefficient, concentration, and charge of the ionic species i, F is the Faraday constant, R is the gas constant, T is the temperature, φ is the potential, ε 0 and ε r are the vacuum permittivity and medium dielectric constant, respectively. The bipolar electrochemical processes at the carbon layer was described by the Electronic Current mode. At the carbon layer surface, the flux of the redox molecules follows the Bulter-Volmer kinetics: R 0 0 c sol α c sol J = kce kc (r=a, h<z<0) (S3) 0 α f ( E E E ) 0 e (1 ) f ( E E E ) O R O 0 0 c sol α c sol J = kce + kc (r=a, h<z<0) (S4) 0 α f ( E E E ) 0 e (1 ) f ( E E E ) O R k 0 and E 0' are the standard rate constant and formal potential for the ET process. f = F/RT, and α is the transfer coefficient. The ionic transport current, i T, was calculated by integrating the total flux of the ionic species at either reference electrode: i = 2 π F ( J + J ) da T K Cl S S4

5 Figure S1. (A) TEM image of the glass nanopipette and (B) the corresponding i V curve. Solution contained 10 mm KCl. v = 0.1 V/s. Figure S2. Effect of multivalent anion (citrate, C6H5O7 3 ) concentration on the ion current. The background solution was 10 mm KCl. v = 0.1 V/s. a = 80 nm. S5

6 Figure S3. Dependence of OCP of the carbon nanopipette on concentration of redox species. (A) Experimental setup for OCP measurements. (B) OCP vs [K3Fe(CN)6]. (C) OCP vs. [Ru(NH3)6Cl3]. Modeling low-conductance state of CNPs. The conductive carbon layer in a CNP can be polarized by external voltage, and the non-uniformly distributed surface charge density is expected (Ref. 17). Therefore, the mean value of the charge density and its distribution can be different at different potentials. Previous simulations also showed that the shape of the low-conductance part of the i-v curve depends strongly on the spatial distribution of charge on the nanopore surface, and the non-uniform charge density distribution can lead to the higher degree of the ICR. S3 By contrast, in the high-conductance state, the i-v response is largely determined by the mean charge density value and essentially independent of its spatial distribution. Therefore, the high-conductance response can be simulated assuming the constant charge density on the carbon surface and using its value as an adjustable parameter (this is how we simulated the high-conductance parts of the i-v curves in Figure 4); but to accurately simulate the low-conductance part, one needs information about the surface charge distribution in a CNP, which is not currently available. Two possible approaches to simulating the low-conductance portion of the i-v curve are shown in Figure S4. In the first case, the entire curve was simulated with the constant charge density value extracted S6

7 from the high-conductance response (circles). Not surprisingly, the low-conductance portion of the curve cannot be fitted well with this simplifying assumption. By assuming an exponential distribution of the surface charge near the CNP tip (as suggested in ref. S3), one can fit well the entire i-v curve (squares). however, we are unaware of any technique suitable for validating the exponential charge distribution on the carbon surface. Figure S4. Fitting the entire CNP i V curve (solid line) recorded in 10 mm KCl to the theory with uniform (blue circles) and exponential (red squares) surface charge density distribution. a = 50 nm. Constant charge density (circles): σ = -23 mc/m 2 ; exponential charge density distribution (squares): σ(z) = x exp(z/0.15e-6) (mc/m 2 ). Figure S5. Additional example of the redox concentration effect on the CNP i-v curves in 10 mm KCl. S7

8 Figure S6. Effect of concentration of neural redox species on the shape of the CNP i-v curves. a = 90 nm. (A) Aqueous 10 mm KCl solution contained: 0 M (black curve), 1 nm (red), 2 nm (blue), and 3 nm (green) ferrocenemethanol. (B) Acetonitrile solution contained 10 mm tetraethylammonium perchlorate and: 0 nm (red curve) or 0.2 nm (black) ferrocene. Figure S7. Effect of high K3Fe(CN)6 concentration on CNP i-v curves. a = 30 nm. S8

9 Figure S8. The distributions of (A) Carbon layer potential, (B) solution potential along the CNP axis, (C) electronic current density at the carbon surface, (D) concentration of K +, and (E) concentration of Cl near the pore orifice at different values of applied voltage. The pore orifice coordinate is z = 0. The bulk concentration of the cations and anions is 10 mm, and the bulk concentration of the redox species is 10 μm. S9

10 COMSOL REPORT 1.1 PARAMETERS 1 Name Expression a 50e-9[m] 5E 8 m pore radius SCD [C/m^2] C/m² surface charge density zk 1 1 zcl -1 1 DK 1.92e-9[m^2/s] 1.92E 9 m²/s DCl 1.99e-9[m^2/s] 1.99E 9 m²/s Vapp 0.5[V] 0.5 V c0 10[mol/m^3] 10 mol/m³ c1 10[uM] 0.01 mol/m³ E0 0.15[V] 0.15 V k0 20[cm/s] 0.2 m/s F 96500[C/mol] C/mol S10

11 2 Component 1 COMPONENT SETTINGS Unit system SI 2.1 DEFINITIONS Component Couplings Integration 1 Coupling type Operator name Integration intop1 SOURCE Geometric entity level Boundary Selection Boundary Coordinate Systems Boundary System 1 Coordinate system type Tag Boundary system sys1 COORDINATE NAMES First Second Third t1 to n S11

12 2.2 GEOMETRY 1 Geometry 1 UNITS Length unit Angular unit m deg GEOMETRY STATISTICS Space dimension 2 Number of domains 2 Number of boundaries 11 Number of vertices Bézier Polygon 1 (b1) POLYGON SEGMENTS Control points {{0, 2e-6, 2e-6, 1e-7, 50e-9, 2e-6, 2e-6, 0, 0}, {2e-6, 2e-6, 0, 0, 0, -10e-6, - 12e-6, -12e-6, 2e-6}} Degree {1, 1, 1, 1, 1, 1, 1, 1} Weights {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} Type Solid Bézier Polygon 2 (b2) POLYGON SEGMENTS S12

13 Control points {{50e-9, 55e-9, 2.005e-6, 2e-6, 50e-9}, {0, 0, -10e-6, -10e-6, 0}} Degree {1, 1, 1, 1} Weights {1, 1, 1, 1, 1, 1, 1, 1} Type Solid 2.3 TRANSPORT OF DILUTED SPECIES USED PRODUCTS COMSOL Multiphysics Chemical Reaction Engineering Module Transport of Diluted Species Geometric entity level Domain Selection Domain 1 EQUATIONS S13

14 2.3.1 Diffusion and Migration Diffusion and Migration Geometric entity level Domain Selection Domain 1 EQUATIONS SETTINGS Electric potential Electric potential (es) Charge number {1, -1, 0, 0} Mobility Nernst - Einstein relation Material None Temperature User defined Temperature [K] Diffusion coefficient {{DK, 0, 0}, {0, DK, 0}, {0, 0, DK}} Diffusion coefficient User defined Diffusion coefficient {{DCl, 0, 0}, {0, DCl, 0}, {0, 0, DCl}} Diffusion coefficient User defined Diffusion coefficient {{1e-9[m^2/s], 0, 0}, {0, 1e-9[m^2/s], 0}, {0, 0, 1e-9[m^2/s]}} Diffusion coefficient User defined S14

15 Diffusion coefficient Diffusion coefficient {{1e-9[m^2/s], 0, 0}, {0, 1e-9[m^2/s], 0}, {0, 0, 1e-9[m^2/s]}} User defined Axial Symmetry 1 Axial Symmetry 1 Geometric entity level Boundary Selection Boundary 1 S15

16 2.3.3 No Flux 1 No Flux 1 Geometric entity level Boundary Selection Boundaries 4, 6, 8 9, 11 EQUATIONS Initial s 1 Initial s 1 S16

17 Geometric entity level Domain Selection Domain 1 SETTINGS Concentration {c0, c0, c1, c1} Concentration 1 Concentration 1 Geometric entity level Boundary Selection Boundaries 2 3 EQUATIONS SETTINGS Concentration {c0, c0, c1, c1} Species ck On Species ccl On Species co On Species cr On Apply reaction terms on All physics (symmetric) S17

18 Use weak constraints Constraint method Off Elemental Flux 1 Flux 1 Geometric entity level Boundary Selection Boundary 5 EQUATIONS SETTINGS Species ck Species ccl Species co Species cr Flux type Off Off On On General inward flux 2.4 ELECTROSTATICS USED PRODUCTS S18

19 COMSOL Multiphysics Electrostatics Geometric entity level Domain Selection Domain 1 EQUATIONS SETTINGS Electric potential type when using splitting of complex variables Activate terminal sweep Reference impedance Quadratic Complex Off 50[ohm] S19

20 2.4.1 Charge Conservation 1 Charge Conservation 1 Geometric entity level Domain Selection Domain 1 EQUATIONS SETTINGS Constitutive relation Relative permittivity Relative permittivity User defined Relative permittivity {{80, 0, 0}, {0, 80, 0}, {0, 0, 80}} S20

21 2.4.2 Axial Symmetry 1 Axial Symmetry 1 Geometric entity level Boundary Selection Boundary Zero Charge 1 Zero Charge 1 Geometric entity level Boundary S21

22 Selection Boundaries 6, 8 9, 11 EQUATIONS Variables Name Expression Unit Selection es.nd 0 C/m² Surface charge density Boundaries 6, 8 9, Initial s 1 Initial s 1 Geometric entity level Domain Selection Domain 1 SETTINGS Electric potential 0 S22

23 2.4.5 Ground 1 Ground 1 Geometric entity level Boundary Selection Boundary 2 EQUATIONS SETTINGS Apply reaction terms on Use weak constraints Constraint method All physics (symmetric) Off Elemental S23

24 2.4.6 Electric Potential 1 Electric Potential 1 Geometric entity level Boundary Selection Boundary 3 EQUATIONS SETTINGS Electric potential Apply reaction terms on Use weak constraints Constraint method Vapp All physics (symmetric) Off Elemental S24

25 2.4.7 Space Charge Density 1 Space Charge Density 1 Geometric entity level Domain Selection Domain 1 EQUATIONS Variables Name Expression Unit Selection es.scd1.rhoq (ck-ccl)*96500[c/mol] C/m³ Space charge density Domain 1 es.rhoq es.scd1.rhoq C/m³ Space charge density Domain 1 S25

26 2.4.8 Surface Charge Density 1 Surface Charge Density 1 Geometric entity level Boundary Selection Boundaries 4 5 EQUATIONS SETTINGS Surface charge density *exp(z/1.2e-6[m]) ELECTRIC CURRENTS USED PRODUCTS COMSOL Multiphysics S26

27 Electric Currents Geometric entity level Domain Selection Domain 2 EQUATIONS SETTINGS Electric potential type when using splitting of complex variables Activate terminal sweep Reference impedance Quadratic Complex Off 50[ohm] S27

28 2.5.1 Current Conservation 1 Current Conservation 1 Geometric entity level Domain Selection Domain 2 EQUATIONS SETTINGS Electrical conductivity User defined Electrical conductivity {{1e3, 0, 0}, {0, 1e3, 0}, {0, 0, 1e3}} Constitutive relation Relative permittivity Relative permittivity User defined Relative permittivity {{10, 0, 0}, {0, 10, 0}, {0, 0, 10}} S28

29 2.5.2 Axial Symmetry 1 Axial Symmetry 1 Geometric entity level Selection Boundary No boundaries Electric Insulation 1 Electric Insulation 1 Geometric entity level Boundary S29

30 Selection Boundaries 7, 10 EQUATIONS Initial s 1 Initial s 1 Geometric entity level Domain Selection Domain 2 SETTINGS Electric potential 0 S30

31 2.5.5 Normal Current Density 1 Normal Current Density 1 Geometric entity level Boundary Selection Boundaries 4 5 EQUATIONS SETTINGS Type Normal current density Inward current density chds.ntflux_co*96500[c/mol] S31

32 2.6 MESH 1 Mesh Size (size) SETTINGS Maximum element size 4.6E-7 Minimum element size 1.73E-9 Curvature factor 0.25 Maximum element growth rate 1.2 Predefined size Extra fine Size 1 (size1) Geometric entity level Boundary Selection Boundaries 4 6, 9 10 S32

33 Size 1 SETTINGS Maximum element size 1e-9 Minimum element size 3.9E-9 Minimum element size Off Curvature factor 0.3 Curvature factor Off Resolution of narrow regions Off Maximum element growth rate 1.3 Maximum element growth rate Off Custom element size Custom Size 2 (size2) Geometric entity level Point Selection Points 3, 7 S33

34 Size 2 SETTINGS Maximum element size 1e-10 Minimum element size 3.9E-9 Minimum element size Off Curvature factor 0.3 Curvature factor Off Resolution of narrow regions Off Maximum element growth rate 1.3 Maximum element growth rate Off Custom element size Custom Size 3 (size3) Geometric entity level Boundary Selection Boundaries 2 3, 8 9 S34

35 Size 3 SETTINGS Maximum element size 5E-8 Minimum element size 3.9E-9 Minimum element size Off Curvature factor 0.3 Curvature factor Off Resolution of narrow regions Off Maximum element growth rate 1.3 Maximum element growth rate Off Custom element size Custom Free Triangular 1 (ftri1) Geometric entity level Selection Domain Remaining S35

36 Free Triangular 1 S36

37 3 Study 1 COMPUTATION INFORMATION Computation time 49 min 59 s CPU Intel(R) Core(TM) i7 CPU 2.80GHz, 4 cores Operating system Windows PARAMETRIC SWEEP Parameter name Parameter value list Vapp 0.5,0.2,0.1,-0.2, STATIONARY STUDY SETTINGS Include geometric nonlinearity Off PHYSICS AND VARIABLES Physics interface Transport of Diluted Species (chds) Electrostatics (es) Electric Currents (ec) Discretization physics physics physics MESH Geometry Geometry 1 (geom1) Mesh mesh1 3.3 SOLVER CONFIGURATIONS Solver 1 Compile Equations: Stationary (st1) STUDY AND STEP Use study Study 1 Use study step Stationary Defined by study step Stationary S37

38 RESULTS WHILE SOLVING Probes None Parametric 1 (p1) GENERAL Defined by study step Parametric Sweep Sweep type All combinations Parameter value list Run continuation for No parameter Fully Coupled 1 (fc1) GENERAL Linear solver Direct 1 METHOD AND TERMINATION Initial damping factor 0.01 Minimum damping factor 1.0E-6 Maximum number of iterations 50 S38

39 Supplementary References S1. Hu, K.; Wang, Y.; Cai, H.; Mirkin, M. V.; Gao, Y.; Friedman, G.; Gogotsi, Y. Anal. Chem. 2014, 86, S2. Yu, Y.; Noël, J.-M.; Mirkin, M. V.; Gao, Y.; Mashtalir, O.; Friedman, G.; Gogotsi, Y. Anal. Chem. 2014, 86, S3. Liu, J., Wang, D., Kvetny, M., Brown, W., Li, Y.; Wang, G. Langmuir 2013, 29, S39