Influence of Geometry on Thin Layer and Diffusion Processes at Carbon Electrodes

Abstract

Geometric structures of carbon electrodes affect their electrochemical behavior and large-scale surface roughness leads to thin layer electrochemistry when analyte is trapped in pores. However, the current response is always a mixture of both thin layer and diffusion processes. Here, we systematically explore the effects of thin layer electrochemistry and diffusion at carbon fiber (CF), carbon nanospike (CNS), and carbon nanotube yarn (CNTY) electrodes. The cyclic voltammetry (CV) response to surface-insensitive redox couple Ru(NH₃)₆^3+/2+ is tested, so the geometric structure is the only factor. At CFs, the reaction is diffusion-controlled because the surface is smooth. CNTY electrodes have gaps between nanotubes that are about 10 μm deep, comparable with the diffusion layer thickness. CNTY electrodes show clear thin layer behavior due to trapping effects, with more symmetrical peaks and ΔE_p closer to zero. CNS electrodes have submicron scale roughness, so their CV shape is mostly due to diffusion, not thin layer effects. However, even the 10% contribution of thin layer behavior reduces the peak separation by 30 mV, indicating ΔE_p is not only influenced by electron transfer kinetics but also surface geometry. A new simulation model is developed to quantitate the thin layer and diffusion contributions that explains the CV shape and peak separation for CNS and CNTY electrodes, providing insight on the impact of scan rate and surface structure size. Thus, this study provides key understanding of thin layer and diffusion processes at different surface structures and will enable rational design of electrodes with thin layer electrochemistry.

Graphical Abstract

INTRODUCTION

Carbon materials exhibit complex surface structures due to the type of carbon, its shape, the interfacial structures, and surface functional groups.^1,2 Most studies have explored the effects of surface chemical structure of carbon electrodes, aiming to promote electrocatalytic effects and adsorption.^1,2 But recently, more studies are addressing how three-dimensional geometric structure affects electrochemistry.^2–4 Kant et el. developed the theory regarding random surface roughness of electrodes, and demonstrated the surface roughness or morphology can affect amperometry,^5,6 voltammetry^7–10 and electrochemical impedance responses^11,12. In particular, when the size of the geometric structures match the thickness of the diffusion layer, the geometric structures confine the analyte within the rough surface, resulting in thin layer electrochemical behavior.^2,13 Thin layer electrochemistry affects the redox products observed; for example, under thin layer conditions, there is enhanced cyclization reactions of catecholamines.^4,14 The Compton group developed thin layer theory for several carbon geometric structures, including arrays^3,15 and porous structures.^16–19 Thin layer phenomena were observed in porous materials or those with cavities for solution confinement, such as vertically-aligned multiwall carbon nanotubes, carbon nanotube yarns, and carbon nanopipettes.^3,14,20–24 However, both diffusion and thin layer electrochemistry contribute to the electrode response, but results are often simplified to consider only one effect at a time.^3,20 Systematic experiments with simulations that explain the effects of various carbon electrode geometries would provide a comprehensive understanding of how surface structure affects the contributions of diffusion and thin layer processes to electrochemical behavior.

Carbon fibers (CFs) are the traditional electrodes material for neurochemical electrodes, and they have a relatively smooth surface without much geometric structure.^25,26 Carbon nanomaterials are often used to enhance surface roughness with different sizes and geometries.^27,28 Carbon nanospikes (CNSs) grown by plasma-enhanced chemical vapor deposition (PECVD) have surface structures of about 50 nm in length with tapered, spike-like features.^29–31 CNS electrodes have improved sensitivity for neurochemical detection due to their large electroactive surface area,³¹ but there have been no studies on whether their nanoscale geometric structures can exhibit thin layer electrochemical behavior. Carbon nanotubes (CNTs) are one of the most investigated carbon nanomaterials for electrochemistry, and they are made into electrodes with a variety of different formats, including dip coating onto an electrode,³² direct growth on a substrate,³³ or making electrodes from bundles spun into fibers or CNT-yarns (CNTYs).³⁴ CNTY electrodes trap analyte inside the gaps among the CNT bundles, so CNTYs exhibit a porous structure, which is dependent on the number of CNTs twisted together.^34,35 For neurochemical detection with fast-scan cyclic voltammetry (FSCV),^{14,21–23,36,37} the trapping effect at CNTY electrodes enables high temporal resolution measurements and affects the redox pathways of catecholamines.¹⁴ However, most of the research on CNTY electrodes is focused on FSCV applications, and there is little fundamental understanding of the thin layer electrochemical behavior.

Here, we used CFs, CNSs, and CNTYs as carbon electrode materials to systematically compare how electrode geometry on different scales affects electrochemical behavior. CFs are smooth without much surface structure, CNSs have short and dense geometric structures on the submicron scale, and CNTYs are porous with cavities around 10 μm between bundles. Studying the outer-sphere, surface insensitive probe Ru(NH₃)₆^3+/2+, CNTY electrodes show predominantly thin layer electrochemical behavior, especially at high scan rates. The electrochemical processes of CF and CNS electrodes are mostly controlled by diffusion, but the nanostructured surface of CNSs causes some trapping, decreasing the peak separation in cyclic voltammetry. COMSOL modeling of CF, CNS and CNTY electrodes revealed changes in symmetry and peak separation with surface structure. New models were created to separate and quantify the contribution of thin layer and diffusion behavior. Thus, this study provides a systematic understanding of how thin layer and diffusion contribute to electrochemistry with different size surface structures, facilitating design of future electrode surface structures based on their expected electrochemical properties.

EXPERIMENTAL SECTION

Fabrication of CF, CNS, and CNTY electrodes.

To make microelectrodes, CFs were used with a 30 μm diameter (World Precision Instruments, Sarasota, FL) and CNTYs with 25 μm diameter (General Nano, LLC, Cincinnati, OH). By using a custom-built PECVD system, CNSs were grown on a piece of 25 μm diameter niobium wire (ESPI Metals, Ashland, OR), which was immobilized on a stainless-steel stage, and served as the cathode for the DC plasma.³⁸ The DC plasma discharge was operated at 250 mA and 480 – 550 V at 650°C. The pressure was 6 Torr, the flow was set to contain 100 sccm ammonia and 80 sccm acetylene, and the growing time was 6 min. CFs, CNSs or CNTYs were then directly inserted into a glass capillary and sealed with 5-min epoxy (J-B weld, Sulphur Springs, TX).

Surface characterization.

Scanning electron microscope (SEM) images were taken on Merlin field emission SEM (Zeiss, Thornwood, NY) and FEI Quanta 650 SEM (Thermo Fisher Scientific, Waltham, MA). Surface profiles along the diameter of the electrodes were obtained by Wyko NT9800 Optical Profilometer (Bruker Corporation, Billerica, MA) using Vertical shift interferometry (VSI) mode. A 50x optical lens was used and the sampling size was 96 nm. Cylinder tilt correction was applied.

Electrochemical methods.

Cyclic voltammetry and EIS experiments were performed with Reference 600 potentiostat (Gamry Instruments, Warminster, PA). A three-electrode system was built with CF, CNS, or CNTY electrodes as working electrodes, standard Ag/AgCl electrode as reference electrode, and a Pt wire as counter electrode. Cyclic voltammetry was performed in 5 mM Ru(NH₃)₆^3+/2+ solution in 1M KCl supporting electrolyte, with a linear voltage sweep from −0.4 V to 0 V and back at various scan rates. EIS experiments were performed in 5 mM Fe(CN)₆^3-/4- solution, the frequency range was 100 kHz to 1 Hz, and the amplitude of the AC voltage applied was 10 mV. The DC biased potential is 0.2 V.

Simulation of cyclic voltammetry and concentration.

The cyclic voltammetry and concentration simulation of three types of electrodes, including CFs, CNSs and CNTYs, for Ru(NH₃)₆^3+/2+ redox couple detection were performed in COMSOL Multiphysics (Burlington, MA). A 200 μm * 200 μm square was set up to represent the bulk solution with initial concentrations of 5 mM Ru(NH₃)₆²⁺ and 0 mM Ru(NH₃)₆³⁺. The solid electrode was assumed to have a uniform current distribution, and reaction only happens at the electrode surface. The structures of electrodes and reaction environment were simplified to a 2D axisymmetric model.

“Cyclic Voltammetry” sub-module under “Electroanalysis” module was used to simulate the cyclic voltammograms. In parameter setting, the reference exchange current density i_0,ref was set to 15,000 A/m² to best simulate the reaction rate of a carbon electrode. Using the relationship between exchange current density and electron transfer kinetics, the electron transfer rate constant k⁰ is calculated as 3 cm/s, which is at the same magnitude with the experimental value published for Ru(NH₃)₆^3+/2+.¹ A smaller i_0,ref, 1500 A/m² was used to fit the CNTY electrodes due to slower electron transfer kinetics at basal-plane carbon, and then k⁰ is calculated as 0.3 cm/s, which is also a valid value matches the experimental results.¹ The one electron reversible redox reaction of Ru(NH₃)₆^3+/2+ couple has a equilibrim potential E_{eq, ref} = −0.175 V, and diffusion coefficient of 10⁻⁹ m²/s at room temperature. The start and vertex voltage of cyclic voltammetry was set to be −0.4 V and 0 V. Cyclic voltammograms obtained from multiple scan rates varying from 20 mV/s to 1000 mV/s were achieved by the Parametric Sweep study. All parameters were the same for CF, CNS and CNTY electrodes, and the only difference among their simulation models was the geometries. More theory and background information can be found in supporting information.

RESULTS AND DISCUSSION

CF, CNS, and CNTY cylinder microelectrodes were fabricated in similar diameters to enable direct comparison of their behaviors. CFs with 30 μm diameter and CNTYs with 25 μm diameter were used, and CNSs were grown on niobium wires with 25 μm diameter. SEM images show the surface of the cylinder microelectrodes, and the zoomed in images display their geometric structure on a finer scale. Using SEM, the diameter of the CF, CNS and CNTY cylinder electrodes were measured at 34 μm, 32 μm, and 27 μm respectively. In Figure 1, the left column shows overall profiles of the electrodes, and the right column shows zoomed in images from the side wall of the cylinder, showing their surface morphologies on the micron scale. Figures 1a and 1b illustrate that CF electrodes have a flat and smooth surface without much surface roughness. Figures 1c and 1d show CNSs form short and dense clusters on the submicron scale, and each cluster is composed of numerous spike-like structures. Figure S1 shows a more zoomed in SEM image of CNSs, displaying individual spike-like features about 50 nm in length. Figures 1e and 1f show the twisted bundle of CNT fibrils in CNTY electrodes. CNT fibrils are dense and parallel aligned, providing a porous structure with gaps enabling the solution to be trapped inside.

Figure 1.

SEM images of a-b) CF, c-d) CNS and e-f) CNTY microelectrodes. Left column: zoomed out CF, CNS and CNTY cylindrical microelectrodes; and right column: zoomed in images to see the geometric structures of the CF, CNS and CNTY electrode surface.

Optical profilometry was used to measure the surface roughness of the electrodes. Figures 2a–c show the surface profile of CF, CNS, and CNTY electrodes along a crossline and Table 1 lists the measured average roughness (R_a) and maximum peak to valley height (R_z). The R_a value of CF electrode is at nanometer scale and much smaller than that of CNS or CNTY electrodes, indicating a very smooth surface. The R_a value for CNS electrodes is 0.64 ± 0.11 μm, with short geometric structure on the submicron scale (Figure 1d). The R_a value for CNTY electrodes is 1.21 ± 0.29 μm, indicating a rougher surface on the micrometer scale. The R_z values are larger, but have a similar trend. While the optical profilometer measured roughness on the apparent surface, these values might not reflect the electroactive surface area, because solution can penetrate the CNTY electrodes into the porous structures and be trapped inside.

Figure 2.

Surface structure and background capacitance. a-c) Optical Profilometry measurements of surface roughness profile of a) CF, b) CNS and c) CNTY microelectrodes along a cross line with cylinder tilt correction applied; d-e) Background charging current for d) CF, CNS and e) CNTY microelectrodes (scan rate is 200 mV/s, note scale difference from d). f) Nyquist plot of EIS.

Table 1.

Surface area and roughness measurements of the microelectrodes.

	Ra (μm)	Rz (μm)	Capacitance (μF cm−2)	surface area ratio (to CF)
CF	0.025 ± 0.005	0.43 ± 0.28	22 ± 2	1
CNS	0.64 ± 0.11	1.97 ± 0.38	118 ± 13	5.4
CNTY	1.21 ± 0.29	3.63 ± 1.27	3325 ± 227	151

Values are mean ± standard deviation, n = 5.

Double layer capacitance measured by cyclic voltammetry background current was used to estimate the electroactive surface area and the relative surface roughness ratio (Figure 2d–e). We used anodic and cathodic current response at 0.5 V to estimate the electrode capacitance and the roughness ratio to CFs (see supplemental theory section). As shown in Table 1, the specific capacitance (capacitance per area) for CF electrodes was 22 ± 2 μF cm⁻², for CNS electrodes was 132 ± 21 μF cm⁻², and for CNTY electrodes was 3325 ± 227 μF cm⁻², comparable to published works.^31,35 The specific capacitance for CNTY electrodes is much larger due to the porous geometric structure. To estimate surface roughness ratio of CNS and CNTY electrodes, we divided their capacitance values with the capacitance of CF electrodes, which is considered to be flat. CNS electrodes have 5-fold larger surface area than CFs, while CNTY electrodes are about 150 times larger.

Electrochemical impedance spectroscopy (EIS) is a powerful tool to characterize both electron transfer and mass transfer properties of the electrodes.³⁹ Figure 2f shows the Nyquist plot of EIS. Both CF and CNS electrodes exhibit a semicircle indicating electron transfer with a line indicating diffusion. A smaller semicircle for CNS proves a faster electron transfer rate.³¹ However, CNTY electrodes have linear relation between imaginary and real impedance in the high frequency region, and a near vertical line in the low frequency region, which is characteristic of porous electrode surfaces.⁴⁰ The EIS Nyquist plots indicate that diffusion happens at CF and CNS electrode surfaces, while mass transfer is confined by the porous surface structure of CNTY electrodes. Figure S2 shows the Bode plot of the three electrodes. CF electrodes show smaller solution resistance than CNS electrodes, which shifts the phase vs. log of frequency plot to the lower frequency. The phase plot of CNS electrodes also shows a deviation from planar response due to surface roughness. The CNTY electrodes have much larger surface roughness and show larger solution resistance, which shifts the Bode plot more to the lower frequencies.^12,35,41

To investigate how the surface geometric structures affect electrochemical behavior, we performed cyclic voltammetry (CV) on CF, CNS and CNTY electrodes. The outer sphere redox couple Ru(NH₃)₆³⁺/²⁺ insensitive to surface chemical structures was used;¹ therefore, surface effects on electron transfer are minimized and the geometric structure is the main factor influencing the electrochemical behavior. As shown in Figure 3a–c, although CNTY electrodes have much larger electroactive areas than CNS or CF electrodes, their peak current in the cyclic voltammogram is only about twice as much as CF and CNS electrodes. This result indicates that only limited analyte solution is trapped inside the surface structure, and the current contribution from thin layer electrochemistry and diffusion is about the same, which will be further quantified in the simulation part of this work (vide infra). Scan rate is an important factor to discriminate diffusion-controlled electrochemistry and thin layer electrochemistry with confined mass transfer. On a flat electrode surface with linear diffusion, the peak current in the cyclic voltammogram is proportional to square root of scan rate (v^0.5), following the Randles-Ševčík equation. On a porous electrode surface where diffusion is confined, thin-layer electrochemistry would govern the process and the peak current is proportional to scan rate (v).⁴² Figures 3a–c show the cyclic voltammograms for CF, CNS, and CNTY electrodes at scan rates from 20 mV s⁻¹ to 1000 mV s⁻¹. CF and CNS electrodes show similar CV shapes which are characteristic of diffusion-controlled electrochemical reactions, while the CV shape of CNTY is more symmetrical and the peak almost returns to the x-axis, which is a feature of thin layer electrochemistry. The relationship of peak current vs. scan rate provides more evidence of the thin layer effect, where peak current is proportional to scan rate for CNTY electrodes (Figure 3d). The slope plot of log i vs. log v curve indicates the extent to which the electrochemistry is governed by diffusion (expected slope 0.5) or thin layer electrochemistry (expected slope 1.0) (Figure 3e). The slope for CF electrodes is 0.56, which is close to the 0.5 value for diffusion-controlled process according to Randles-Ševčík equation. The slope for CNS electrodes is 0.66, which is higher than 0.5 because the surface roughness results in anomalous Randles-Ševčík behavior.⁷ Although CNS electrodes have surface nanostructures, the scale is much smaller than the thickness of the diffusion layer. Thus, at normal scan rates, the nanoscale geometric structures cannot provide much confinement of solution, and the contribution to the current of thin layer electrochemistry is less than diffusion. The slope for CNTY electrodes is 0.92, which is close to 1.0, indicating majority of current contribution is from the thin layer electrochemistry rather than diffusion.

Figure 3.

Scan rate study of CF, CNS and CNTY microelectrodes. a) Cyclic voltammograms of CF, b) Cyclic voltammograms CNS and c) Cyclic voltammograms CNTY at different scan rates (The CV for CNTY electrodes are background-subtracted), d) Normalized anodic peak current vs. scan rate, e) log i vs log v plots and f) Anodic and cathodic peak separation vs. scan rate.

The peak-to peak separation (ΔE_p) obtained from the CV curves also indicates the electrochemical process. For a diffusion-controlled process, the ΔE_p is 57–59 mV/n for an ideal reversible reaction at room temperature. However, in thin layer electrochemistry where the solution is confined, the ideal ΔE_p is 0, because the electroanalyte is adjacent to the electrode surface and the diffusion time is very short.⁴² Figure 3f shows the ΔE_p vs. scan rate of CF, CNS, and CNTY electrodes. At slower scan rates (20–200 mV/s), the ΔE_p values of all three electrodes are larger due to the microelectrode behavior, and a plateau is observed due to the steady-state currents instead of obvious CV peaks.⁴³ From 200 – 1000 mV/s, the peak separation is nearly constant for CF and CNS electrodes, with a ΔE_p value around 100 mV for CF and 70 mV for CNS. This result indicates that the nanostructured surface of CNSs lowers the ΔE_p value. Although the thin layer electrochemistry makes little contribution to the total current and CV shape, it decreases ΔE_p.

The ΔE_p value of CNTY electrodes is smaller than CNSs in the slower scan rate range, because their porous structures trap more solution and the thin layer effects contribute to the CV shape. But at faster scan rates, the ΔE_p increases with scan rate, likely due the slower electron transfer kinetics of CNTY electrodes. The electroactive surface of CNTY electrodes is mostly from side walls of CNTs, which is rich in basal-plane carbon that has slower electron transfer rates than edge-plane carbon.^2,44

To further understand the effects of diffusion and thin layer electrochemical process on the electrodes surface, we made numerical simulations on the CVs of CF, CNS, and CNTY electrodes. Figure 4 illustrates the 2D axisymmetric models of CF, CNS, and CNTY electrodes and the comparison of simulated and experimental CVs at different scan rates. The model for CFs was a simple line, reflecting the flat and smooth surface. To simulate the thin layer structures of CNS and CNTY electrodes, a series of parallel line segments were added to the CF model. Analyte can diffuse into the porous surface structure in a relatively random manner. The thickness of the paralleled line segments was 1 μm for CNSs (0.25μm *4 layers) according to the surface roughness measurement (Figure 2b and Table 1), and 12 μm for CNTYs because CNTY has ~12 μm radius (Figure 1e). All other simulation conditions were the same including electrode size, analyte concentration, electron transfer kinetics, and diffusion as the only mass transport component. Under those simulation conditions, the different surface geometry of the CF, CNS, and CNTY microelectrodes will be the only factor to influence the electrochemical behavior.

Figure 4.

Simulation models (Blue color represents electrode area, the lines in actual models are denser) and cyclic voltammograms for experiment (Red) and simulation (Black) at different scan rates; a) CF electrodes, b) CNS electrodes and c) CNTY electrodes. The experimental CVs for CNTY electrodes are background-subtracted. A 200 μm * 200 μm square was set up to represent the bulk solution with initial concentrations of 5 mM Ru(NH₃)₆²⁺. Model parameters: reference exchange current density i_0,ref = 15,000 A/m², equilibrium potential E_{eq, ref} = −0.175 V, diffusion coefficient = 10⁻⁹ m²/s, potential scan range −0.4 V to 0.

Figure 4 also shows simulated CV curves at various scan rates. The simulated CV curves match well in shape with experiment results, especially for CF and CNS electrodes. The experimental CV of CNTY electrodes at 1000 mV/s has a larger peak separation than the simulation result, because the electron transfer kinetics are slower at CNTY electrodes. If a smaller electron transfer rate constant is applied to the same simulation model, the simulated CV curves as well as the peak separation values match well with the CNTY experiment result (Figure S3). Also, CNTY electrodes exhibit large uncompensated solution resistance according to the EIS Bode plot (Figure S2), which also has pronounced effects to increase peak separation for porous electrodes at high scan rate.^45,46 The models successfully predicted the electrochemical process, for all three geometries and at different scan rates. The CVs of smooth CF electrodes have only a diffusion contribution, and the CVs of nanostructured CNS electrodes are not distinct from CFs, because the diffusion layer is much thicker than the nanostructures. The porous CNTY electrodes show more symmetric anodic and cathodic peaks and smaller peak separation, because thin layer electrochemistry contributes to the current.

Simulated concentration profiles provide information about the diffusion layer during the CV process. For CF and CNS electrodes, the diffusion-controlled concentration profile appears similar to CNTY electrodes, excluding the thin layer electrode area (Figure S4). Figure 5 shows a simulated concentration profile of the CNTY electrode. The concentration profile is shown at several time points, marked on the CV in Figure 5a. The red color represents the concentration of reduced form Ru(NH₃)₆²⁺ and the blue color represents the depletion of Ru(NH₃)₆²⁺ and the formation of oxidized form Ru(NH₃)₆³⁺. At initial conditions when no reaction happened, the concentration profile is uniform in red color (Figure 5b). When the potential is close to the equilibrium potential of Ru(NH₃)₆²⁺, the concentration of the reduced form inside the CNTY structure quickly depletes and the diffusion layer starts to build (Figure 5c). At the vertex potential where the potential is reversed (0 V), the concentration of reduced form inside the CNTY structure is zero, and a concentration gradient outside the structure is built (Figure 5d). When the potential scan reverses to near the equilibrium potential, the reduced form reappears (Figure 5e). As the full scan cycle finishes, the concentration of the reduced form is back to initial concentration inside the CNTY structure and around the electrode surface (Figure 5f).

Figure 5.

Concentration profile of 5 mM Ru(NH₃)₆²⁺ simulated at a CNTY electrode surface (Red color represents concentration of the reduced form, and blue color represents the depletion of reduced form. concentration varies from 0 to 5 mM.). a) The CV curve shows the time points used to illustrate concentration profile. b-e) Simulated concentration profile at CNTY electrode surface. The potential scan range is −0.4 V to 0 and the scan rate is 1000 mV/s.

The concentration profile clearly shows how the scale of the diffusion layer compares with the modeled size of CNTY electrodes. The diffusion layer thickness is only dependent on time, while the thin layer effect is dependent on the volume of analyte solution trapped inside the geometric structure of electrode. Thus, electrodes with an overall larger size of porous or cavity geometries, such as CNTY electrodes, would demonstrate more thin layer electrochemical process. The CNTY electrode is 12 μm in radius, which is comparable with ~20 μm diffusion layer thickness, thus the thin layer electrochemistry is evident. For the CNS electrodes, although the rough surface structures can trap the analyte solution, the submicron geometry size is too small compared with ~20 μm diffusion layer thickness to trap much analyte. Thus, to exhibit thin layer electrochemistry, the overall geometric structure size should match the scale of the diffusion layer. On the other hand, when diffusion-based methods, such as CV and amperometry, are used to study geometric structures, the time scale should be short enough so that the diffusion layer is not too thick.

Since thin layer electrochemistry happens inside the geometric structure while diffusion builds a concentration gradient outside the electrodes (Figure 6a), we further split the simulation model of CNTY electrodes into two models separately representing diffusion-controlled and thin layer electrochemistry, to quantify the contribution of each to the total current. Figure 6b displays the two separated models where the blue lines are the electrode surface. The thin layer part of the model was created by insulating the area outside the electrode, and only an initial concentration was applied. The diffusion model erased the all geometric structures of CNTY, leaving only the outer surface for linear diffusion (Figure 6b and S4c). All other parameters were the same. Figure 6c shows the CV calculated from the two separate simulation models and their superimposition at the scan rate of 1000 mV. The thin layer portion shows a symmetrical CV, with zero ΔE_p and the oxidation and reduction peaks with identical heights, indicating perfect thin layer electrochemistry. The CV of the diffusion portion is the same as the simulation of a CF electrode, a “duck-shape” with peak separation approximately 100 mV, which is a quasi-reversible process governed by diffusion. The total current was obtained by simply superimposing the CV of the thin layer portion and the diffusion portion, and the added CV shape is identical to the original CV (Figure 6d). This result proves it is valid to split the models into thin layer part and diffusion part and calculate the current contribution separately.

Figure 6.

a) The separation of thin layer contribution and diffusion contribution of total current in concentration profile. (Color represents concentration of the reduced form in different areas, from blue to red concentration varies from 0 to 5 mM.) b) Two separate simulation models representing thin layer portion and diffusion portion. c) The simulated CV from two separate models and the added CV of the two portions. Scan rate is 1000 mV/s. d) The added CV from two separate models is identical with the CV from the original integrated model. e) The current of thin layer model and diffusion model at different scan rates. f) The contribution of thin layer electrochemistry and diffusion to total current. The model was split into thin layer area and diffusion area by separating the electrode (30.5 μm*12.5 μm) from the bulk solution (200 μm*200 μm). Diffusion coefficients of analytes were set to be 10⁻⁹ m²/s, reference exchange current density = 15000 A/m², equilibium potential E_eq,ref = −0.175 V, diffusion coefficient = 10⁻⁹ m²/s, and potential scan range was −0.4 V to 0.

Figure 6e shows the thin layer and diffusion contribution for more scan rates. At 200 mV/s, the current contribution from diffusion is much larger than for thin layer, while at 1000 mV/s, the thin layer contributes more to the total current. Figure 6f illustrates the relationship of current contribution from thin layer or diffusion vs. scan rate. At faster scan rates, time is shorter to build the diffusion layer, so the current from thin layer diffusion increases faster than that of diffusion. In this work, we used traditional CV and the scan rate applied was up to 1 V/s, but in fast-scan cyclic voltammetry the scan rate can be as fast as 1000 V/s.^24,44 In FSCV, the diffusion layer is short and the thin layer contribution is more pronounced. The study of CNTY disk electrodes and carbon nanopipette has shown that <1 μm surface roughness or submicron cavity could also result in thin layer electrochemistry.¹⁴

We also used the separated models to quantitatively study the effects of surface roughness, which is the depth of surface geometric structure trapping analytes. Figure 7 displays the current contribution of thin layer electrochemistry and diffusion at the scan rate of 1000 mV/s, and the surface roughness was adjusted by varying the layers of line segments in the simulation model. Figure 7a shows the CV of the thin layer model and Figure 7b shows the diffusion portion. With increased thin layer surface size, the current from thin layer electrochemistry increases proportionally while the current from diffusion has much less increase. Therefore, the CV shape switches from “duck shape” characteristic for diffusion, to a more symmetrical shape for thin layer electrochemistry (Figure 7c).

Figure 7.

Study of surface structure size. a) The current of thin layer model (Blue) and diffusion model (Red), b) total current of the models added together, c) the contribution of thin layer electrochemistry and diffusion to total current at different surface roughness, and d) peak separation at different surface roughness.

Figure 7d illustrates the current contribution from thin layer or diffusion, where the thin layer contribution to the total current increases with surface roughness. These results indicate that, if the surface roughness is at submicron scale, such as CNSs, the current contribution from thin layer electrochemistry is less than 10 percent and the CV shape is not dominated by thin layer electrochemistry. When the surface structure is larger than 10 μm, such as CNTY electrodes, it can trap solution, and thin layer electrochemistry contributes to more than half of the total current. When the surface roughness is 2 μm, the thin layer contribution to the total current rises to about 25 percent. Since the estimated diffusion layer thickness is 28 μm (estimated by $\delta =\sqrt{2Dt}$, D = 10⁻⁵ cm²/s, t = 0.4 s), the result indicates the thin layer electrochemical behavior emerges when the surface roughness scale is about 10% of the diffusion layer thickness, while it dominates when the surface roughness scale is 50% that of the diffusion layer thickness.

The study of thin layer structure size also explains the peak separation. Since the ΔE_p is zero for thin layer electrochemistry and >59 mV for the quasi-reversible diffusion-controlled process, the total CV shape exhibits a ΔE_p value in between the two values. For example, CNTY electrodes at scan rate of 1000 mV/s have zero ΔE_p for thin layer portion and 110 mV for diffusion portion, and the combined CV has a ΔE_p of 28 mV. Figure 7d shows peak separation at different surface roughness, where the ΔE_p value decreases dramatically with increasing surface roughness due to more thin layer effects. Figure S5 shows simulated CVs of CNS electrodes using separate thin layer and diffusion models. Under these conditions (1 μm surface roughness, 1000 mV/s), the current contribution from thin layer electrochemistry is less than 10 percent, but the thin layer contribution decreases ΔE_p in the model from 110 mV at a flat electrode surface to 80 mV with 1 μm surface structure. These values match the experimental ΔE_p value of CNS (~70 mV) and CF (~110 mV) electrodes. Thus, even a small thin layer contribution decreases ΔE_p fairly substantially.

Changes in ΔE_p are often attributed to electrocatalytic effects of carbon nanomaterials,^1,47 but the results here indicate that even a small increase in surface roughness will add a contribution of thin layer electrochemistry that will lower ΔE_p. This is not an effect of increased electron transfer rate, but an effect of the geometry. Peak separation in cyclic voltammograms has been primarily used to study electron transfer kinetics,^47,48 but this study informs us that geometry is also a key consideration and not all decreases in ΔE_p should be attributed to electrocatalytic effects. These experiments and simulations demonstrate that surface geometric structures must be taken into consideration, even if the surface roughness is at submicron scale.

Three-dimensional surface geometric structures of carbon electrodes influence the electrochemical behavior by introducing thin layer electrochemistry, and its contribution to the total current can be quantitatively studied using separate models. Table 2 summarizes the estimated diffusion layer thickness at different carbon electrode materials with surface geometry ranging from submicron to micron scale. At scan rates of 100 mV/s, the diffusion layer thickness is 100 mm, so there are no materials exhibiting thin layer effects. At CV scan rates around 1 V/s, the diffusion layer thickness is around tens of microns, so the thin layer electrochemical behavior is noticeable only at carbon materials exhibiting porous or cavity structure in the scale of microns, such as long CNT arrays and CNTY cylinder electrodes.^3,4 However, in FSCV the scan rate can be as fast as 1000 V/s.^24,44 With the much faster scan rate, the reaction time is very short so the diffusion layer shorter, and submicron scale surface geometry can result in thin layer electrochemical behavior. For example, CNTY disk electrodes and carbon nanopipette electrodes have a cavity enhanced FSCV detection of catecholamines due to the trapping effect.^14,21,23,37 Future electrode geometries can be designed to take advantage of thin layer cell effects and their expected electrochemical properties. 3D printing enables fully controlled size and geometry with submicron resolution,^49,50 future works can take advantage of the thin layer effects by designing the pores between printed spikes to achieve a desired thin layer electrochemistry effect. Thus, these experiments and simulations enable more rational microelectrode design.

Table 2.

Carbon nanomaterials that exhibit thin layer effects at different scan rates and diffusion layer thicknesses

Technique	Scan rate (V/s)	Diffusion layer thickness (μm)	Carbon electrode materials that exhibit thin layer effects	References
CV	0.1	100	None	-
	1	30	CNTY cylinder electrodes	This work
			Long vertically aligned CNT	3,4
			Carbon pillar array	15,51
FSCV	100	3.2	CNTY disk electrodes	14,21,23,37
	400	1.6	Carbon nanopipette	14,52
	1000	1.0	Nano 3D-printing	49,50

Diffusion layer thickness is estimated by $\delta =\sqrt{2Dt}$, where scan range is 1 V and diffusion coefficient is 5 × 10⁻⁶ cm²/s.

CONCLUSIONS

We used both experiments and simulations to study the geometric effects of carbon surface on electrochemistry. CF, CNS and CNTY electrodes were used to systematically explore the effects of geometric structure on different scales. CFs have smooth surface, CNSs have short and dense surface geometry on the submicron scale, and CNTYs are porous with overall micrometer scale structure. The experiments demonstrate that the increas of geometric structure size, and the increase of scan rate leads to more current contribution from thin layer electrochemistry. The simulation models match well with the experiment results, both in surface geometry size and scan rate. We further spilt the simulation models and for the first time extracted the CV shapes of diffusion and thin layer chemistry separately. Thus, we now quantitatively understand the current contributions from diffusion and thin layer cell effects under various scan rates and surface structure sizes. This systematic study provides a comprehensive understanding on the electrochemical effects of electrode surface geometries. In the future, the simulation model can provide guidance for the design of functional electrochemical sensors based on the geometric effects.