Materials and Methods

3.3.1 Reagents and Materials

All reagents such as K3Fe(CN)6, K4Fe(CN)6 and KCl are purchased from Sigma-Aldrich. Other organic solvents like ethanol, acetone, and isopropyl alcohol are obtained from HSIN MING chemical instruments co., LTD (Taipei, Taiwan). The materials and reagents used for the device construction are obtained from commercial sources as follows: glass slide (FEA, 1“×3“, 1–1.2mm thickness); Au slugs, Cr pieces and crucible (Guv Team International, Taiwan); S1813 photoresist (SHIPLEY); glass photomask (NCHU, Taiwan); TMAH (Sigma); PDMS (BingBond, Taiwan).

3.3.2 Design and Fabrication

9 types of IDA electrode configurations: wg-we = (1) 100, (2) 50, (3) 100-25, (4) 50-100, (5) 50-50, (6) 50-100-25, (7) 25-50, (8) 5-100 and (9) 2-100(μm) are designed.

The electrodes are fabricated on a glass slide by a standard photolithography and deposition process. First, the glass slides are cleaned with acetone, isopropyl alcohol, ddH2O sonication, and dried by N2 and 120℃ hotplate. Second, the positive photoresist

S1813 is coated on the cleaned glass slides by spin coating at 1000rpm for 20s and 4000rpm for 60s then soft baked at 115℃ for 2min. Third, the cured photoresist is

exposed to UV light (15mW/cm²) for 10s and immediately developed in TMAH for 1min.

Fourth, the developed chips are put into an E-beam evaporator (FULINTEC) then an adhesive layer of Cr (20nm) and electrode material Au (80nm) is deposited. At last, the chips are immersed in acetone overnight, sonicated in acetone for full lift-off of photoresist, washed with ddH2O and dried by a stream of N2. In order to restrict the working area of the IDA electrode, microwells of 4mm thickness with an inner empty rectangular shape are designed and fabricated. The empty rectangular shape has a length of 3mm parallel to the electrode bands and a variable width perpendicular to them to contain all the electrode area. For microwell fabrication, PDMS with a standard mixing

ratio of 10:1 is poured into its aluminum mold (fabricated by a CNC machine), cured at 150℃ for 10 min, cooled then peeled off. Finally, for bonding of the microwell to the

IDA electrode glass chip, a reusable PLA fixture for clipping them together is designed and fabricated by a 3D printer. Several specifications of fixtures are designed for different microwells to balance between firmness and elasticity and one can be confident that the it doesn’t cause deformation of the microwell or leakage. The illustration of the clipped microwell on IDA electrode chip is in Figure 3-7a and a photograph is shown in Figure 3-7b.

Figure 3-7 (a) Illustration and (b) photograph of the IDA electrode chip clipped with a microwell.

3.3.3 Electrochemical Characterization

The chips are immersed in a piranha solution (H2SO4:H2O2 = 3:1(v/v)) for 5min, rinsed by ddH2O, dried by N2, clipped with microwells and the two electrode pads at the side are pasted with copper tape prior to electrochemical measurements. The solution including the redox species for EIS, CV and CA measurements is 5mM K3Fe(CN)6, 5mM K4Fe(CN)6 and 0.1M KCl in 40μL ddH2O. CA measurements with no K4Fe(CN)6

are also performed. A two-electrode configuration is used throughout these methods with one side of the electrode connecting to the CE/RE and the other connecting to the WE.

An electrochemical workstation is used (CH Instruments). In EIS experiments, an AC

voltage amplitude of 5mV with no DC voltage is applied and the frequency range is 10

-2~10⁵Hz. In CV experiments, a scan window of -0.5~0.5V (vs CE/RE) is set and the scan rates are 20mV/s, 100mV/s and 500mV/s. In CA experiments, a potential step of -0.2V is

3.3.4 Simulation of Concentration Profile

Simulation for the 2D time-dependent concentration profile of the unit cell defined in theory is carried out using COMSOL Multiphysics. Electroanalysis of both redox species are performed. The time-dependent concentration profile for species i can be calculated using finite difference method of the equation below:

𝜕𝜕𝐶𝐶_𝑑𝑑

𝜕𝜕𝑡𝑡 + ∇ ∙(−𝐷𝐷_𝑑𝑑∇𝐶𝐶_𝑑𝑑) = 𝑅𝑅_𝑑𝑑

where Ci is the concentration of species i, Di is its diffusion coefficient and Ri is its

generation rate. The flux of species i can be calculated as:

𝑵𝑵_𝑑𝑑 = −𝐷𝐷_𝑑𝑑𝛻𝛻𝐶𝐶_𝑑𝑑

For redox reactions at the electrode, an electroanalytical Butler-Volmer equation is

applied:

𝛽𝛽_{𝑐𝑐𝑙𝑙𝑐𝑐} = 𝑛𝑛𝐹𝐹𝑘𝑘₀�𝐶𝐶_𝑅𝑅𝑒𝑒^{(𝑢𝑢−𝛼𝛼𝑅𝑅𝑅𝑅𝑐𝑐)𝐹𝐹𝐹𝐹}− 𝐶𝐶_𝑂𝑂𝑒𝑒^{−𝛼𝛼𝑅𝑅𝑅𝑅𝑐𝑐𝐹𝐹𝐹𝐹}�

where iloc is the current density, k0 is the heterogeneous rate constant, α^c is the cathodic transfer coefficient and η is the overpotential. It is already known that n = 1, and α^c = 0.5 is set. Global constant parameters l = 3mm (electrode length), 𝐶𝐶𝑑𝑑𝑢𝑢𝑑𝑑𝑢𝑢𝑑𝑑𝑖𝑖𝑐𝑐∗ = 5mM (initial bulk concentration), D = DO = DR = 6×10^-10m²/s, Vamp = 5mV (applied AC voltage), k0 = 0.01m/s and T = 298K are set. The reason of k0 being so high is because a diffusion controlled reaction with redox species rapidly reacting at the electrode is assumed. The height of the unit cell is set as 2w for computational needs, and this study has proven in (33)

(34)

(35)

supplementary material that this height is large enough to keep simulations accurate (section 3.4.2). The other parameters: wg, we and f (frequency) are being given different values for required experiments. The geometry of the unit cell is set using the same definition in the theory. Boundaries with no flux are set at the top and electrode gap of the unit cell. Symmetry boundaries are set at the left and right. The electrode surface at the left is set as the WE with a start potential of 0V, linear voltage sweep rate of 4Vampf, lower vertex potential of –Vamp and upper vertex potential of Vamp. The electrode surface at the right is set as the CE with an initial potential value of 0V. For keeping an acceptable

computational time, a predefined value of “Finer” is used as the element size. However, to make simulations accurate enough, a “Free Triangle → Distribution” with an element

number of 20 and an element ratio of 2 on the two electrode surfaces are set. All other parameters are as of system default. At last, time-dependent studies with a time step of 0.1s and overall periods of at least 2s are computed.

3.3.5 Impedance Calculation and Circuit Fitting Program

For preliminary implementation of necessary calculations, a MATLAB software (R2018b) is used to tackle with complicated functions such as complete, incomplete elliptic integrals and modified Bessel functions that mostly take complex numbers as the input parameter. However, this software is used only for figure drawing and some part of theory confirmation but not the calculation of impedance due to the fact that numerical integrations are needed for calculating the IDA diffusion impedance which may cause comparatively longer computational time.

A program written in C language is designed using the open-source numerical analysis library ALGLIB^® to implement numerical integrations and calculations of the equations in the theory. Bessel functions and the complete elliptic integral of the second kind are pre-calculated and saved in a 1D array. Faster numerical integration can therefore be carried out. A program for calculating the IDA diffusion impedance is designed according to the theory. ALGLIB is also used for non-linear least squares fitting of EIS data using Levenberg-Marquardt method. A program for fitting any user-defined equivalent circuit is designed with several elements available including the IDA diffusion element derived in the theory.