Cyclic Voltammetry

The triangular sweep and the current it draws out

Drop a small electrode into a solution containing a dissolved redox-active molecule, then march its potential along a triangle: ramp it up at a steady scan rate, hit a switching potential, and ramp it straight back down to where you started. The y-axis records the current that flows. That current is the story.

When the potential becomes positive enough, the molecule starts giving up electrons at the electrode surface — oxidation. Current climbs. But the molecules sitting right at the surface get consumed faster than fresh ones can diffuse in from the bulk solution, so after a brief surge the current peaks and then sags as the diffusion layer thickens. On the return sweep, the freshly-made oxidized form gets electrons handed back to it — reduction — and a mirror-image peak appears below the axis. Two peaks, two trailing tails. The shape is famously called a "duck."

  current i
    │            anodic (oxidation) peak  ip,a
    │                  ╱‾╲
    │                ╱     ╲___          ← forward sweep
    │              ╱           ‾‾‾──
  0 ┼────────────────────────────────────── potential E →
    │      ___───‾‾‾           ╱
    │   ──‾          ╲       ╱            ← reverse sweep
    │                  ╲___╱
    │            cathodic (reduction) peak  ip,c
                 |←  ΔEp  →|

The horizontal axis is potential, swept linearly in time, so a CV is really a current-vs-time curve folded back on itself — the forward and reverse legs share the same potential window. The two peaks, their separation, their relative heights, and how all of that changes when you scan faster are the four levers chemists read to fingerprint the species.

Why it takes three electrodes and a potentiostat

A CV is run in a three-electrode cell driven by a potentiostat. The jobs are deliberately split:

• Working electrode (WE) — the small electrode where the reaction you care about happens (glassy carbon, platinum, or gold, typically 1–3 mm diameter).
• Reference electrode (RE) — holds a fixed, known potential (Ag/AgCl, saturated calomel, or a Ag wire pseudo-reference) and carries essentially no current, so it never polarizes.
• Counter electrode (CE) — a Pt wire or coil that completes the circuit; all the current flows between WE and CE.

If you tried to both pass current and measure potential through the same two electrodes, the reference would drift the instant current flowed. By measuring potential against a current-free reference while pushing current through a separate counter, the potentiostat keeps the working-vs-reference potential locked to your commanded triangle. A supporting electrolyte (e.g. 0.1 M KCl in water, or 0.1 M tetrabutylammonium hexafluorophosphate in acetonitrile) is added at ~100× the analyte concentration so that ions, not your analyte, carry the bulk current and the diffusion layer stays thin.

Reading the duck: the reversibility diagnostics

An electrochemically reversible couple is one where electron transfer is so fast that the surface concentrations always obey the Nernst equation. Such a couple leaves four telltale signatures at 25 °C:

Peak separation:        ΔEp = Ep,a − Ep,c = 59/n  mV     (≈ 57–59 mV for n = 1)
Formal potential:       E°' ≈ (Ep,a + Ep,c) / 2          (the midpoint)
Peak-current ratio:     ip,a / ip,c = 1
Peak position:          independent of scan rate v
Peak height scaling:    ip ∝ √v   (Randles–Ševčík)

Each one is a separate, falsifiable test. If ΔEp comes out near 59 mV and stays there as you change the scan rate, electron transfer is fast and the couple is reversible. If ΔEp is 150 mV and balloons to 300 mV when you scan ten times faster, the electron transfer is quasi-reversible or irreversible — kinetically sluggish, so the electrode has to be over-driven past the thermodynamic potential before the reaction will keep up. (One honest caveat: uncompensated solution resistance also inflates ΔEp by iR, so reversibility is only confirmed when ΔEp is near-ideal and roughly scan-rate-independent.)

The relationship between the kinetic rate constant k° and the observed ΔEp is captured by the Nicholson method: a dimensionless parameter ψ = k°·[π·D·n·F·v/(RT)]^(−1/2) maps onto the measured ΔEp through a published working curve. Larger ψ (faster k°) means smaller ΔEp; for k° below ~10⁻³ cm/s a one-electron couple looks fully irreversible.

The Randles–Ševčík equation

The single most-used equation in CV predicts the peak current of a reversible, freely-diffusing species:

ip = 0.4463 · n · F · A · C · (n · F · v · D / (R · T))^(1/2)

At 25 °C this collapses to the working form:

ip = (2.69 × 10⁵) · n^(3/2) · A · D^(1/2) · C · v^(1/2)

   ip = peak current               (amperes, A)
   n  = electrons transferred       (dimensionless)
   A  = electrode area              (cm²)
   D  = diffusion coefficient       (cm²/s)
   C  = bulk concentration          (mol/cm³)   ← note: per cm³, not per L
   v  = scan rate                   (V/s)

The killer feature is the √v dependence. Plot ip against √v and a diffusion-controlled species gives a straight line through the origin. If instead ip scales linearly with v (not its square root), the current is coming from a species bound to the electrode surface as a thin film — a completely different regime used to quantify monolayers and electroactive coatings. That single plot tells you whether your signal is from solution diffusion or a surface layer.

Worked example: how many electrons and how much is there?

Suppose you run 1.0 mM of a complex in 0.1 M electrolyte at a 3.0 mm diameter glassy-carbon disk (A = π·(0.15 cm)² = 0.0707 cm²), scan rate 0.100 V/s, and the diffusion coefficient is D = 6.0 × 10⁻⁶ cm²/s. First convert concentration to mol/cm³: 1.0 mM = 1.0 × 10⁻⁶ mol/cm³. Assume a one-electron transfer (n = 1):

ip = 2.69×10⁵ · (1)^(3/2) · 0.0707 · (6.0×10⁻⁶)^(1/2) · 1.0×10⁻⁶ · (0.100)^(1/2)
   = 2.69×10⁵ · 0.0707 · 2.449×10⁻³ · 1.0×10⁻⁶ · 0.3162
   = 1.47×10⁻⁵ A
   ≈ 14.7 µA

Measure ~15 µA and n = 1 is confirmed; measure ~42 µA and the n^(3/2) factor points to a two-electron process (2^(3/2) = 2.83×, so 14.7 → 41.6 µA). Run a fast diagnostic the other direction: take the same compound at a known concentration, measure ip, and back out D — CV is one of the standard ways to get diffusion coefficients of new compounds. And if the analyte concentration is the unknown, ip is linear in C, so a calibration line turns CV into a quantitation tool.

Cyclic voltammetry vs other electroanalytical methods

	Cyclic voltammetry (CV)	Differential pulse (DPV)	Chronoamperometry
Applied signal	Triangular ramp, up and back	Staircase + small pulses	Single potential step, held
What you read	i–E peaks both directions	Differential current peaks	i vs t decay (Cottrell)
Reversibility info	Yes — directly from ΔEp and return peak	Indirect	No
Detection limit	~10⁻⁵ M (background-limited)	~10⁻⁸ M (pulse subtracts charging current)	~10⁻⁵ M
Mechanism diagnosis	Excellent (scan-rate study)	Limited	Limited
Typical scan rates	10 mV/s – 1000 V/s	1–50 mV/s effective	n/a (step)
Best for	First-look characterization, mechanism, E°'	Trace quantitation	Diffusion coefficients, kinetics

CV is the reconnaissance tool: you run it first on any new redox system because in 30 seconds it tells you where the redox events are, how many there are, whether they're reversible, and roughly how concentrated the species is. DPV then squeezes out trace sensitivity by chopping out the capacitive charging current; chronoamperometry pins down kinetics once you know where to step.

The charging current — CV's built-in noise floor

Every electrode/solution interface behaves like a capacitor (the electrochemical double layer). Sweeping the potential at rate v forces a non-Faradaic charging current i_c = C_dl · A · v, where C_dl ≈ 10–40 µF/cm² for typical electrodes. This current flows whether or not anything reacts, and it grows linearly with scan rate.

Here is the tension built into CV: the useful Faradaic peak grows as √v, but the useless charging background grows as v. So fast scans (good for outrunning slow follow-up chemistry) bury small redox peaks under a fat rectangular charging box. That trade-off — Faradaic √v vs capacitive v — is why dilute analytes are run slowly, why DPV exists to subtract the charging term, and why CV's practical detection limit sits around 10⁻⁵–10⁻⁶ M.

Where cyclic voltammetry shows up

• The ferrocene benchmark. Ferrocene oxidizes cleanly and reversibly to ferrocenium, Fc → Fc⁺ + e⁻, with ΔEp ≈ 59–70 mV on a good day. IUPAC recommends reporting non-aqueous redox potentials versus the Fc/Fc⁺ couple, so it is the universal internal standard — a pinch added to the cell calibrates everyone's different reference electrode onto a common scale. In aqueous work, the analogous reversible test is ferri/ferrocyanide, [Fe(CN)₆]³⁻/⁴⁻.
• Battery and supercapacitor R&D. A CV of a Li-ion cathode like LiFePO₄ or a supercapacitor electrode reveals the redox potentials of the active material and, from the area under the curve (charge = ∫i dt), the capacity. A rectangular "box" CV with no peaks is the signature of pure double-layer capacitance; sharp peaks signal pseudocapacitance or battery-like faradaic storage.
• Glucose sensors and bioelectrochemistry. The first-generation glucose meter chemistry was characterized by CV: glucose oxidase shuttles electrons to a mediator (often a ferrocene derivative), and the catalytic CV wave — where the oxidation peak grows and the return peak disappears as substrate is consumed — is the diagnostic of an EC' catalytic mechanism.
• Organometallic and inorganic chemistry. Each accessible oxidation state of a metal complex shows up as its own peak pair, so a CV maps the redox ladder of a catalyst in one experiment — essential for water-splitting catalysts, CO₂-reduction complexes, and metalloenzyme models.

Coupled chemistry: EC, CE, and catalytic waves

The reverse sweep is where mechanism hides. If the species you generate on the forward sweep is chemically stable, it waits patiently to be converted back and the return peak is full-sized (ip,a/ip,c = 1). But if it reacts before the reverse sweep reaches it, the return peak shrinks or vanishes:

EC mechanism:   O + e⁻ ⇌ R          (electron transfer)
                R → P                (irreversible follow-up chemistry)
                → return peak shrinks as scan slows (more time to react)

CE mechanism:   Y → O                (chemistry feeds the electroactive form)
                O + e⁻ ⇌ R
                → forward peak grows as scan slows

EC' (catalytic): O + e⁻ ⇌ R
                R + S → O + product  (substrate regenerates O)
                → huge forward wave, return peak gone

The diagnostic is the scan-rate study. In an EC mechanism, scanning faster outruns the follow-up reaction and restores the return peak; the scan rate at which the return-to-forward peak ratio climbs back toward 1 gives the rate constant of the coupled chemical step. This is how CV measures the lifetime of reactive intermediates — radical cations, unstable oxidation states — that exist for microseconds to milliseconds. Ultramicroelectrodes pushed to 10⁶ V/s have captured intermediates living mere nanoseconds.

Common pitfalls and misconceptions

• Confusing kinetic reversibility with chemical reversibility. "Reversible" in CV means electron transfer is fast (ΔEp ≈ 59/n mV), a kinetic statement about the electrode. It does not mean the product is chemically stable — a couple can be electrochemically reversible yet have a vanishing return peak because the product reacts. Read both ΔEp and the peak ratio.
• Forgetting iR drop. Uncompensated resistance between WE and RE adds iR to the measured potential, inflating ΔEp and making a fast couple look sluggish. It's worst in resistive non-aqueous solvents and at high currents. Use enough supporting electrolyte and the potentiostat's iR compensation before declaring a couple irreversible.
• Quoting potentials without a calibrated reference. A pseudo-reference Ag wire drifts. Reporting "Epc = −1.8 V" without specifying the reference (and ideally referencing to Fc/Fc⁺) makes the number useless to anyone else.
• Wrong concentration units in Randles–Ševčík. The classic constant 2.69 × 10⁵ requires C in mol/cm³, not mol/L. Plugging in molarity directly gives an ip wrong by 1000×. (Use 2.69 × 10² as the prefactor if you keep C in mol/L and A in cm².)
• Ignoring oxygen. Dissolved O₂ is electroactive and reduces around −0.3 to −0.9 V vs SCE in two broad waves, dumping a large background into any cathodic scan. Purge with N₂ or Ar before reductive CV, and blanket the headspace during it.
• Assuming peak height equals concentration without checking the regime. ip ∝ C only holds for diffusion control. If the species adsorbs onto the electrode, ip scales with v and a different (surface) calibration applies — verify with the ip-vs-√v plot first.