Decoding Network Structure in On-Chip Integrated Flow Cells with Synchronization of Electrochemical Oscillators

Abstract

The analysis of network interactions among dynamical units and the impact of the coupling on self-organized structures is a challenging task with implications in many biological and engineered systems. We explore the coupling topology that arises through the potential drops in a flow channel in a lab-on-chip device that accommodates chemical reactions on electrode arrays. The networks are revealed by analysis of the synchronization patterns with the use of an oscillatory chemical reaction (nickel electrodissolution) and are further confirmed by direct decoding using phase model analysis. In dual electrode configuration, a variety coupling schemes, (uni- or bidirectional positive or negative) were identified depending on the relative placement of the reference and counter electrodes (e.g., placed at the same or the opposite ends of the flow channel). With three electrodes, the network consists of a superposition of a localized (upstream) and global (all-to-all) coupling. With six electrodes, the unique, position dependent coupling topology resulted spatially organized partial synchronization such that there was a synchrony gradient along the quasi-one-dimensional spatial coordinate. The networked, electrode potential (current) spike generating electrochemical reactions hold potential for construction of an in-situ information processing unit to be used in electrochemical devices in sensors and batteries.

Figure 1. Schematics of three commonly used dual-electrode configurations.

(a) Traditional (ipsilateral) placement of reference and counter electrodes. (b) Upstream (contralateral) reference and counter electrode placements. (c) Dual reference electrode configuration. WE_1,2: Ni working electrodes embedded in epoxy; RE and RE2: Ag/AgCl/3 M NaCl reference electrode; CE: Pt counter-electrode. RE1: Ni reference electrode for working electrode 1.

Figure 2. The effect of cell geometry on coupling topology obtained from equivalent circuit analysis of dual working electrodes.

RE: reference electrode. R₀: total cell resistance, R_C: collective resistance (resistance of electrolyte from working electrode 2 to the reservoir), R₁₂: solution resistance between two working electrodes, A: electrode surface area, R_ind,1: external resistance connected to working electrode 1, R_ind,2: external resistance connected to working electrode 2. K: coupling strength. (The derivations of these equations can be found as Supplementary Note).

Figure 3. Effects of cell geometry on synchronization of current oscillations between two working electrodes.

Top row: two electrodes with ipsilateral (traditional) placement of reference and counter electrodes. The distance from the downstream electrode to the reservoir D_2R = 5.0 mm, the distance between the two electrodes D₁₂ = 2.4 mm. V = 1.68 V. Middle row: Dual electrodes with reference and counter electrodes at opposite sides. D_2R = 6.0 mm, D₁₂ = 6.1 mm. V = 1.79 V. Bottom row: dual-reference electrode system. D_2R = 1.5 mm, D₁₂ = 12 mm. V = 1.74 V. (a–c) Current vs. time plots. (d–f) Phase interaction functions for electrode 1 (left) and 2 (right). (g–i) Schematics of coupling topologies. The open and shaded circles represent the electrodes (corresponding to the schematics in Fig. 1). Arrows and the +/− symbols represent the direction and sign of the coupling, respectively. For all experiments the total cell resistance R₀ = 20 kΩ.

Figure 4. Effect of placement of the middle working electrode on synchronization and network topology in switched dual reference electrode setup.

Top row: Distant WE2-RE1 placement (D₁₂ = 0.5 mm, D_2R = 15.5 mm). Middle row: medium placement (D₁₂ = 5.4 mm, D_2R = 5.8 mm). Bottom row: close placement (D₁₂ = 10.0 mm, D_2R = 0.7 mm). (a–c) Schematic diagram of dual electrode cell (top) and coupling topology (bottom). WE1,2: Ni working electrodes, RE1: Ag/AgCl/3 M NaCl reference electrode for WE1, RE2: Ni reference electrode for WE2, CE: Pt counter electrode. (d–g) current vs. time plots. R₀ = 20 kΩ. V = 1.61 V, 1.64 V, 1.62 V and 1.69 V respectively. (h–k) phase difference vs. time plot.

Figure 5. Three electrode networks with large distance to reservoir: dominating global coupling and partial synchronization without spatial organization.

Top: coupling topology. (a–c) Schematics of cells: shaded circles denote synchronized electrodes. (d–f) Synchronization matrices for the corresponding experiments. (a) D₁₂ = 2.9 mm, D₂₃ = 3.0 mm, D_3R = 11.9 mm, R₀ = 100 kΩ, V = 2.30 V. (b) D₁₂ = 3.7 mm, D₂₃ = 1.4 mm, D_3R = 12.4 mm, R₀ = 120 kΩ, V = 2.55 V. (c) Same parameters as in panel (b) except for V = 2.45 V.

Figure 6. Three electrode networks with close placement to reservoir: dominating upstream coupling and spatially organized partial synchronization.

Top: coupling topology. (a–c) Schematics of cells: Shaded circles denote synchronized electrodes. (d–f) Synchronization matrices for the corresponding experiments. (a) D₁₂ = 0.5 mm, D₂₃ = 5.8 mm, D_3R = 1.2 mm, R₀ = 50 kΩ, V = 1.93 V. (b) D₁₂ = 1.8 mm, D₂₃ = 4.2 mm, D_3R = 1.0 mm, R₀ = 20 kΩ, V = 1.68 V. (c) D₁₂ = 1.8 mm, D₂₃ = 2.9 mm, D_3R = 0.8 mm, R₀ = 20 kΩ, V = 1.6 V.

Figure 7. Spatially organized partially synchronized pattern with synchrony gradient in a six-electrode cell.

(a) Schematic of the cell (the spacing of the electrodes is approximately 2 mm). (b) Synchronization matrix. V = 1.95 V, R₀ = 50 kΩ.