Biosensor EIS (Electrochemical Impedance Spectroscopy) Simulator
Compute the Randles equivalent circuit response for a label-free biosensor and watch the Nyquist semicircle plus Warburg tail update in real time. Tune R_s, R_ct, C_dl and sigma for glucose, dopamine, cortisol, DNA hybridization or protein binding to see the detection limit (LoD) and Q factor instantly.
Parameters
Solution resistance R_s
Ω
Bulk electrolyte resistance (e.g. PBS)
Charge-transfer resistance R_ct
Ω
Electron-transfer resistance at the electrode/electrolyte interface
R_s = solution resistance, R_ct = charge-transfer resistance, C_dl = double-layer capacitance, ω_peak = frequency at the apex of the Nyquist semicircle.
Professor, an "EIS biosensor" is what we use to read blood glucose or COVID antigens electrically, right? How is it different from a fluorescent assay?
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Good question. Fluorescence or ELISA needs a labelled dye or enzyme, but EIS (electrochemical impedance spectroscopy) directly senses how a bound target blocks the electron pathway at the electrode. That makes it label-free — you don't need to add a reagent afterwards. When SARS-CoV-2 spike protein binds to an aptamer-modified gold electrode, the charge-transfer resistance R_ct jumps by several times. From that shift you can back-calculate the virus concentration.
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Impedance means AC, right? Why don't we just use DC?
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A DC technique like CV or DPV actually drives faradaic reactions, so proteins can get oxidised, protonated, even destroyed. EIS only applies a ±5-10 mV AC perturbation swept from 0.01 Hz to 100 kHz, so the biomolecules survive. And in the frequency domain you can separate R_s (bulk solution), R_ct (interfacial reaction), C_dl (double layer) and W (diffusion) into different peaks and slopes. On the Nyquist plot you read R_ct from the semicircle diameter, C_dl from the apex frequency, and σ from the 45° low-frequency tail — all at a glance.
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You mentioned the Randles equivalent circuit. Why can such a simple circuit model the real interface?
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Because the electrode/electrolyte interface really does decompose into a resistive part, a capacitive part and a diffusive part. R_s is the bulk salt water (PBS, serum) conducting current; C_dl is the Helmholtz layer of ions packed on the electrode; R_ct is the energy barrier to faradaic charge transfer; W is the slow diffusion of redox species from the bulk. Wire these four up in series-parallel and the model fits real spectra astonishingly well. When a target binds, only R_ct shifts strongly — that's the key to quantitative detection.
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So is fM- or pM-level detection really achievable? Could we screen patients with a phone someday?
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In research labs, aptamer-functionalised carbon nanotube electrodes have hit fM-level SARS-CoV-2 detection. The key is producing an R_ct change at least 3σ above the noise floor. That's exactly why the tool computes LoD = 10^(refLog + 3·noise/ΔR_ct_per_decade). Commercial potentiostats (PalmSens EmStat Pico, BioLogic, Metrohm Autolab) are already palm-sized and stream data to a phone over Bluetooth. Point-of-care diagnostics is no longer science fiction.
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In the Nyquist plot on the right, raising the concentration grows the semicircle. What dictates the length of the low-frequency tail?
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Exactly — the semicircle diameter equals R_ct, which is the binding signature. The low-frequency tail flattens to a 45° line as the Warburg coefficient σ grows; it represents how long it takes the redox probe to diffuse from the bulk to the electrode. Stirring shortens it, and microelectrodes give spherical diffusion that also drops σ. Without stirring σ rises, so always log the convection state — otherwise you'll never reproduce a paper.
Frequently Asked Questions
Electrochemical impedance spectroscopy (EIS) applies a small AC voltage (typically 5-10 mV) to a working electrode and sweeps frequency from 0.01 Hz to 100 kHz. The complex impedance Z(ω) is fitted to a Randles equivalent circuit R_s + (R_ct ∥ C_dl) + W to extract solution resistance R_s, charge-transfer resistance R_ct, double-layer capacitance C_dl and Warburg coefficient σ. For biosensors, binding of a target molecule (antigen, DNA, neurotransmitter) on the electrode surface causes R_ct to shift dramatically, enabling label-free quantification of concentration.
On the Nyquist plot (Z' on x-axis, -Z'' on y-axis), the high-frequency semicircle has a diameter equal to the charge-transfer resistance R_ct. The frequency at the apex, f_c = 1/(2π R_ct C_dl), simultaneously yields the double-layer capacitance C_dl. When target molecules adsorb on the electrode, electron transfer is impeded and the semicircle grows in diameter. The relationship ΔR_ct ∝ log[analyte] forms the calibration curve used to back-calculate unknown concentrations.
Below ~1 Hz the Nyquist plot extends toward the origin as a 45° line. This is the Warburg impedance W = σ/√(ω) · (1-j), which represents diffusion-limited transport of electroactive species to the electrode. A larger Warburg coefficient σ means slower diffusion and a longer low-frequency tail. Stirring or shrinking to microelectrodes can reduce σ and shorten measurement time, but some information about bulk concentration is also lost.
LoD is set by the 3σ rule: any signal exceeding three times the baseline noise (typically ~100 Ω) is considered significant. This tool uses LoD = 10^(refLog + 3·noise/ΔR_ct_per_decade). Electrodes with higher ΔR_ct per decade (carbon, gold-nanoparticle modified, aptamer functionalised) achieve fM-pM detection limits. To lower the LoD, optimise the electrode material, ensure uniform self-assembled monolayers (SAMs) and use a low-noise potentiostat (PalmSens, BioLogic, Metrohm Autolab, etc.).
Real-world Applications
Blood glucose and diabetes management: Some Abbott FreeStyle Libre and Dexcom G7 continuous glucose monitors (CGMs) combine glucose-oxidase modified electrodes with impedance measurements to track interstitial glucose in a label-free way. Back-calculating concentration from the change in charge-transfer resistance is exactly the ΔR_ct ∝ log[analyte] relationship used in this tool.
Neuroscience and dopamine detection: Carbon-fibre microelectrodes combined with EIS are used in Parkinson's and depression research to track dopamine concentration (nM-μM) in the synaptic cleft in real time. Dopamine adsorption shifts R_ct strongly, which is reproduced here by the "Dopamine x 2.5" preset. Combined with fast-scan cyclic voltammetry (FSCV), millisecond-scale neural activity becomes accessible.
Infectious disease and pandemic response: Since 2020, aptamer-functionalised gold electrodes for SARS-CoV-2 spike protein detection at the fM level using ΔR_ct have advanced rapidly. They are faster than PCR (minutes) and run on miniaturised hardware, making them strong candidates for point-of-care (POC) diagnostics. Wearable cortisol, CRP and troponin sensors for sweat and saliva are also reaching the market.
Food and environmental monitoring: EIS biosensors are deployed for food allergens (peanut protein, gluten), pesticide residues (parathion, glyphosate) and heavy metals (Pb²⁺, Cd²⁺). Selectivity comes from aptamers or molecularly imprinted polymers (MIPs), and the devices are typically hand-held potentiostats for on-site rapid screening.
Common Misconceptions and Pitfalls
First, do not judge concentration from absolute R_ct alone. R_ct drifts by ±30 % depending on electrode pre-treatment (polish, UV/ozone), SAM lot variation, temperature (about 10 % per ±2 °C around 25 °C) and reference electrode drift. Always measure the same electrode before and after binding and use ΔR_ct, paired with day-to-day calibration and an internal redox probe (ferrocene, ferri/ferrocyanide).
Second, a depressed semicircle does not mean a failed measurement. Real interfaces behave like a Constant Phase Element (CPE) rather than an ideal capacitor, so the semicircle looks flattened (depression angle). Introducing α (0.7-0.95) in the fit captures this physics. This tool uses α = 1; in the lab, CPE is the norm.
Third, the theoretical LoD is rarely matched in practice. The 3σ rule here gives a theoretical floor; in real instruments mains noise, poor shielding, temperature drift and non-specific binding (BSA, interferents in serum) can inflate noise 5-10×. The dynamic range with a linear calibration tops out around 3-4 decades. If you target fM detection, Faraday cages, frequent Ag/AgCl reference exchange and optimised blockers (casein, BSA) decide whether you reach paper-grade reproducibility.
How to Use
Enter solution resistance (Rs, typically 100–500 Ω for aqueous buffer) and charge-transfer resistance (Rct, 1 kΩ–100 kΩ depending on electrode kinetics and surface coverage).
Set double-layer capacitance (Cdl, 10–100 µF/cm² scaled to electrode area) and Warburg coefficient (σ, 10–1000 Ω·s⁻⁰·⁵ for diffusion-limited steps).
Simulate across frequency range (0.1 Hz–100 kHz); observe Nyquist arc diameter, peak −Z″ height, and characteristic frequency fc = 1/(2πRctCdl).
Worked Example
Gold SPR biosensor with target DNA hybridization: Rs = 250 Ω (PBS buffer), initial Rct = 5 kΩ (bare gold), Cdl = 35 µF, σ = 250 Ω·s⁻⁰·⁵. After target binding: Rct increases to 8.5 kΩ (ΔRct = 3.5 kΩ response). Nyquist peak −Z″ ≈ 2650 Ω at fc ≈ 0.91 Hz. Q factor = 8.5/0.25 = 34, indicating sensitive charge-transfer limitation. Detection limit LoD ≈ 10 pM for 10 µL sample.
Practical Notes
Warburg impedance dominates at low frequency; increase σ for surface-bound redox probes (e.g., [Fe(CN)6]³⁻/⁴⁻) versus freely diffusing analytes.
Rct is label-free readout; track ΔRct shifts >500 Ω above noise floor (typically ±50 Ω in potentiostat) for reliable detection.
High Q factor (>10) ensures Nyquist arc separation from axes; poor arc definition indicates Rs dominance or instrumental drift—recalibrate electrolyte conductivity.