SECM Study of Permeability of a Thiolated Aryl Multilayer and Imaging of Single Nanocubes Anchored to It

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1 Supporting Information SECM Study of Permeability of a Thiolated Aryl Multilayer and Imaging of Single Nanocubes Anchored to It Pierre-Yves Blanchard, Tong Sun, Yun Yu, Zengyan Wei, Hiroshi Matsui, # * and Michael V. Mirkin * Department of Chemistry and Biochemistry, Queens College and the Graduate Center, CUNY, Flushing, NY Department of Chemistry and Biochemistry, Hunter College and the Graduate Center, CUNY, New York, NY # Department of Biochemistry, Weill Medical College of Cornell University, New York, NY s-1

2 Figure S1. Simulated feedback-mode 3-D SECM image of an individual nanocube. The tip current is normalized by it, ; and x and y are normalized by the tip radius, a. The edge length of the cube is 1.3a. The tip/cube vertical separation distance, d = 0.5a. Figure S2. Simulated 2-D SECM image of a nanocube corresponding to the 3-D image in Fig. S1. s-2

supporting electrolyte initially present in solution.

3 Figure S3. Parameters defining the diffusion problem and the geometry of the simulation space. Steady-state Diffusion Problem for the SECM of an individual nanocube The three-dimensional SECM diffusion problem is formulated here for the reduced form of the redox mediator (R) and excess supporting electrolyte initially present in solution. The corresponding differential equations are as follows: 2 cc RR cc RR + 2 cc RR 2 2 = 0; (S1) 2 cc OO cc OO cc OO 2 = 0; (S2) where cr and co are the concentrations of R and O species, respectively. The SECM tip is biased at a potential where the oxidation of R takes place at a diffusion-limited rate: cc OO = cc, cc RR = 0; xx 2 + yy 2 aa 2, zz = dd + 2rr pp (tip) (S3) where c * is the bulk concentration of R, d is the vertical distance from the tip to the top plane of the nanocube, and rp is half-width of the nanocube. The reduction of O at the nanocube surface is s-3

4 diffusion controlled: cc OO = 0, cc RR = cc ; rr pp xx xx 0 rr pp, rr pp yy yy 0 rr pp, zz = 2rr pp ; rr pp xx xx 0 rr pp, 0 zz 2rr pp, yy yy 0 = ±rr pp ; rr pp yy yy 0 rr pp, 0 zz 2rr pp, xx xx 0 = ±rr pp (cube surface) (S4) where x0 and y0 are the coordinates of the nanocube center. The rest of the boundary conditions are as follows: cc RR = cc OO = 0 ; dd + 2rr pp zz ll, xx 2 + yy 2 = rr gg 2 ; aa 2 < xx 2 + yy 2 rr gg 2, zz = dd + 2rr pp ; zz = 0; (insulating glass and substrate surface) (S5) cc OO = 0, cc RR = cc ; rr gg 2 < xx 2 + yy 2 < rr ss 2, zz = ll + dd + 2rr pp ; 0 < zz < ll + dd + 2rr pp, xx 2 + yy 2 = rr ss 2 (simulation space limits) (S6) where is the normal derivative of the concentration, rs is the simulation space limit in x and y directions, and l is the space limit in z direction. The tip current was obtained by integrating the diffusion flux over the tip electrode surface. s-4

5 COMSOL Simulation Report 1. Global Definitions 1.1 Parameters 1 Parameters Name Expression d tip-cube distance RP cube half width RG RG X X offset Y Y offset 2. Component Geometry 1 Geometry 1 Units Length unit m s-5

6 Angular unit deg Geometry statistics Space dimension 3 Number of domains 3 Number of boundaries 19 Number of edges 40 Number of vertices Cylinder 1 (cyl1) Position Position {0, 0, 0} Axis Axis type Cartesian Size and shape Radius 50 Height Cylinder 2 (cyl2) Position Position {0, 0, 2*RP + d} Axis Axis type Cartesian Size and shape Radius Height RG 50-2*RP - d s-6

7 2.1.3 Block 1 (blk1) Position Position Base {X, Y, RP} Center Axis Axis type z - axis Size and shape Width Depth Height 2*RP 2*RP 2*RP Work Plane 1 (wp1) Unite objects Unite objects Plane Geometry (wp1) Circle 1 (c1) Position Position {0, 0} Size and shape Radius 1 s-7

8 2.2 Transport of Diluted Species Transport of Diluted Species Domain Domain 1 Equations Settings Concentration Compute boundary fluxes Apply smoothing to boundary fluxes type when using splitting of complex variables Streamline diffusion Crosswind diffusion Crosswind diffusion type for free flow Equation residual Convective term Convection Linear Real Do Carmo and Galeão Approximate residual Non - conservative form s-8

9 Migration in electric field Adsorption in porous media Dispersion in porous media Volatilization in partially saturated porous media Diffusion Diffusion Domain Domain 1 Equations Settings Material None Diffusion coefficient {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}} Diffusion coefficient User defined s-9

10 2.2.2 No Flux 1 No Flux 1 Boundary Boundaries 3, 5 7, Equations Initial s 1 Initial s 1 s-10

Domain Domain 1 Settings Concentration 1 2.

11 Domain Domain 1 Settings Concentration Concentration 1 Concentration 1 Boundary Boundary 9 Equations Settings Concentration 0 Species c Apply reaction terms on Use weak constraints Constraint method All physics (symmetric) Elemental s-11

12 2.2.5 Concentration 2 Concentration 2 Boundary Boundaries 1 2, 4, 10, 13 Equations Settings Concentration 1 Species c Apply reaction terms on Use weak constraints Constraint method All physics (symmetric) Elemental s-12

2.2.6 Concentration 3 Concentration 3 Boundary Boundaries 14 15, 17 19 Equations Settings Concentration 1

13 2.2.6 Concentration 3 Concentration 3 Boundary Boundaries 14 15, Equations Settings Concentration 1 Species c Apply reaction terms on Use weak constraints Constraint method All physics (symmetric) Elemental s-13

14 2.3 Mesh 1 Mesh 1 3. Study Stationary Study settings Include geometric nonlinearity Physics and variables selection Physics interface Transport of Diluted Species (chds) Discretization physics Mesh selection Geometry Geometry 1 (geom1) Mesh mesh1 4. Results 4.1 Derived s Surface Integration 1 Boundary Boundary 9 s-14

15 Data Data set Study 1/Solver 1 Expression Expression Unit chds.ndflux_c mol/s Normal diffusive flux Settings Integration order 4.2 Plot Groups Concentration (chds) 1 Surface: Concentration (mol/m 3 ) s-15

The Dynamic Steady State of an Electrochemically Generated Nanobubble

Supporting Information. Part 2 The Dynamic Steady State of an Electrochemically Generated Nanobubble Yuwen Liu, Martin A. Edwards, Sean R. German, Qianjin Chen and Henry S. White * The following is a detailed