Cyclic Voltammetry

date2026-07-24tags:chem:

Cyclic voltammetry (CV) is the technique that most people mean when they say that they ran an electrochemistry experiment. You sweep the potential of the working electrode in a linear way. Then you reverse the sweep direction and sweep back. You then read a current versus potential trace. The trace can look like a duck. It can look like a wave. It can also look like a mess if something is wrong. This page is a deep-dive companion to Electrochemistry. That page covers the three-electrode cell and the Nernst equation. This technique relies on those concepts. This page also links to Potentiostat. That page covers iR drop and instrument control. This page focuses on CV specifically. It covers the waveform. It covers how to read the duck shape. It has the equations to turn a peak height into a diffusion coefficient. It also has a practical SOP to keep your data reliable.

The best next resource for everything on this page is Daniel Graham's SOP4CV. Standard Operating Procedures for Cyclic Voltammetry. The key paper is Elgrishi et al., "A Practical Beginner's Guide to Cyclic Voltammetry", J. Chem. Educ. 2018, 95, 197-206. This paper is open access. Every equation and figure reference below that is attributed to Elgrishi is checked directly against that paper. The references are not based on AI-drafted notes that used to sit in this file.

What CV actually measures

Cyclic voltammetry does one main task. It forces the working electrode potential through a triangular program over time. The program is written as $E(t)$. The instrument then records the resulting current $i(t)$. You plot those two values against each other. Current appears on the y axis. Potential appears on the x axis. You get the voltammogram.

$$ E(t) = E_i - vt \quad (\text{forward/cathodic segment}), \qquad E(t) = E_\lambda + v(t - t_\lambda) \quad (\text{reverse/anodic segment}) $$

The variable $E_i$ is the initial potential. The variable $E_\lambda$ is the switching potential. The scan reverses at that point. The variable $v$ equals the absolute value of $dE/dt$. This is the scan rate in V per s. The variable $t_\lambda$ is the time of the switch. That is the entire experimental input. The input is a linear ramp up followed by a linear ramp back down. You can repeat this for as many cycles as you need. Everything interesting in the output comes from how the electrochemistry responds to that ramp.

Why use a triangular shape instead of a single one-way sweep? A one-way sweep technique does exist. It is called linear sweep voltammetry or LSV. The reverse scan is what gives CV its diagnostic power. The reverse scan tells you whether the species that got reduced or oxidized on the forward scan is still present to react back. CV interrogates the same patch of solution twice. It goes forward and it comes back. It then compares the two answers.

Reading a voltammogram: the duck shape

Consider the simplest case. The case is a single reversible one-electron couple. The couple follows this pattern: $\mathrm{Ox} + e^- \rightleftharpoons \mathrm{Red}$. The species diffuses freely in solution. No stirring occurs. The potential sweeps toward more reducing values. Nothing happens until the potential $E$ nears the formal potential $E^{0\prime}$ of the couple. Then Ox starts converting to Red at the electrode surface. Current starts flowing. The Nernst equation pins the surface concentrations of Ox and Red to the instantaneous potential demand. See Corrosion for the full Nernst derivation. The electrode can only reduce the Ox that diffuses to the surface. The reaction creates a depletion layer of Ox. This layer grows outward from the electrode. Fresh Ox from the bulk now arrives more slowly. The diffusion flux falls as the concentration gradient flattens. Current rises while the potential pulls harder than the depletion layer throttles. Current peaks when the two effects balance. Current then decays as the depletion layer wins. The potential keeps getting more reducing even while current falls. That rise-peak-fall shape mirrors on the reverse scan. The accumulated Red gets reoxidized on the reverse scan. That mirrored shape is the duck. It reflects a competition between thermodynamic driving force via the Nernst equation and mass transport via diffusion. It is not a resonance or a kinetic artifact.

Four numbers get read from that duck for every couple you study:

Cathodic and anodic peak potentials, written $E_{p,c}$ and $E_{p,a}$.
Cathodic and anodic peak currents, written $i_{p,c}$ and $i_{p,a}$.
The half-wave potential $E_{1/2} \approx (E_{p,c}+E_{p,a})/2$. This value stands in for the formal potential $E^{0\prime}$ when the couple is reversible and Ox and Red have similar diffusion coefficients.
The peak-to-peak separation $\Delta E_p = E_{p,a} - E_{p,c}$. This is the most used reversibility diagnostic. The topic is covered below.

The Randlesevekik equation

For a reversible diffusion controlled one electron couple, the peak current scales with the square root of the scan rate. This is the Randlesevekik equation. This page does not trust any previous AI draft that was never checked against a primary source. This page pulls the equation directly from Elgrishi et al. eq. 3.

$$ i_p = (0.446)\, n F A C^0 \left( \frac{n F v D_O}{RT} \right)^{1/2} $$

The variable $i_p$ is in A. The variable $n$ is the number of electrons transferred. The variable $F$ is Faraday's constant at 96,485 C per mol. The variable $A$ is the electrode area in cm$^2$. The variable $C^0$ is the bulk concentration of the analyte in mol per cm$^3$. Use cm$^3$ not L if you plug numbers in directly. The variable $D_O$ is the diffusion coefficient of the oxidized species in cm$^2$/s. The variable $v$ is the scan rate in V/s. The variable $R$ is the gas constant. The variable $T$ is the temperature in K. The prefactor is 0.446. This value is confirmed against the peer reviewed source. The more precise value carried in Bard and Faulkner Electrochemical Methods is 0.4463. Elgrishi rounds this to three figures. That book is the standard graduate reference and Elgrishi cites it for this equation.

You can use a collapsed form at 25 C. You will see this form in most lab manuals. The form folds the constants together:

$$ i_p = (2.69\times10^5)\, n^{3/2} A C^0 D_O^{1/2} v^{1/2} $$

Here $i_p$ is in A, $A$ is in cm$^2$, $C^0$ is in mol per cm$^3$, $D_O$ is in cm$^2$/s, and $v$ is in V/s. The value $2.69\times10^5$ comes from $0.4463$ times $F$ times $\sqrt{F/(RT)}$ at 298.15 K. That product gives about $2.687\times10^5$. Some lecture notes show $2.72\times10^5$. That value uses 298 K instead of 298.15 K. The difference is 0.5 percent. It is not worth worrying about. The two forms are algebraically identical. Pick whichever fits your units.

The equation comes from solving Fick's second law for Ox and Red. The boundary condition pins their surface concentrations to the Nernst equation at every instant. This is the reversible assumption. The potential is a linear function of time. This is a semi-infinite linear diffusion problem. Randlesevekik solved it independently in 1948. Nicholson and Shain later generalized it to quasi-reversible and irreversible cases. See Nicholson, R. S. Anal. Chem. 1965, 37, 1351. That paper underlies almost every reversibility criterion below. I do not reproduce the full boundary value solution here. You do not need it to use this equation. The peak current comes from numerically inverting a Laplace transform. That is why the prefactor 0.4463 looks like an odd number.

Scan rate dependence as a diagnostic

The peak current scales as the square root of scan rate for a freely diffusing reversible species. A plot of $i_p$ against $\sqrt{v}$ should be a straight line through the origin. This is one of the cheapest checks in CV. It serves two purposes:

If $i_p$ vs $v^{1/2}$ is linear. The species diffuses freely to a planar electrode. This matches the Randlesevekik derivation. You can use the slope of that line with a known $n$, $A$, and $C^0$. You can then calculate the diffusion coefficient $D_O$. This is exactly what Elgrishi does in his training module on ferrocene.
If $i_p$ vs $v$ is linear instead of linear with $\sqrt{v}$. The current comes from a species stuck to the electrode surface. The species is adsorbed. It does not diffuse from bulk solution. The current versus scan rate law for a surface confined redox couple is $i_p = n^2F^2 v A \Gamma^* / 4RT$. This law is linear in $v$. It is not linear in $\sqrt{v}$. This is a different physical picture. The variable $\Gamma^*$ is surface coverage. Confusing this case with bulk diffusion is a classic beginner mistake. Elgrishi calls this out in Box 2.
The peak-to-peak separation resolves the ambiguity. An adsorbed species shows no peak-to-peak separation at any scan rate. A diffusing species that only looks irreversible because of a fast scan will show $\Delta E_p$ growing with scan rate.

Peak separation and the reversibility ladder

The value $\Delta E_p = 59/n$ mV appears all over the internet as a rule. The actual value in the peer reviewed source is not 59. Elgrishi et al. state that for a chemically and electrochemically reversible one electron couple at 25 C, the peak-to-peak separation is 57 mV. This equals $2.22\,RT/F$. The width at half maximum of the forward peak is 59 mV. This is a related but distinct value. It describes peak shape not peak position. The two numbers are close enough that they get confused in secondary sources. You can also see 56.5 mV or the round value of 60 mV in various textbooks. Those variants come from using $2.303RT/F$ which is the Nernst slope constant at 59.16 mV. Some sources use the more careful Nicholson and Shain diffusion controlled derivation which gives 2.22 $RT/F$ or 57 mV. The important takeaway for this page is the order of magnitude and the diagnostic use. Do not focus on the third significant figure. If you cite a specific number, cite 57 mV per n for peak separation. Attribute it to Elgrishi or to Nicholson and Shain. Do not cite an unsourced 59 mV rule.

For an $n$ electron reversible couple the separation is about $57/n$ mV. The separation is smaller for more electrons with all else equal. This is itself a diagnostic. A two electron process with strongly separated formal potentials for its two steps shows $\Delta E_p$ of 57 mV per resolvable wave. This looks like two one electron couples. Two steps close together collapse into a single wave. The second reduction can be thermodynamically favored over the first. The wave then shows $\Delta E_p$ as low as about 28.5 mV. Steps of decreasing favorability spread out toward a broad 140 mV hump before they separate into two waves.

The reversibility ladder

CV sorts a redox couple into one of three buckets:

Reversible (Nernstian). Electron transfer is fast relative to the scan rate at every point. The Nernst equation holds at the electrode surface at all times. The signature values are: $\Delta E_p$ is about 57 per n mV and is independent of scan rate. The peak potential $E_p$ is independent of scan rate. The ratio of peak currents $|i_{p,a}/i_{p,c}|$ is about 1. Equal peak heights appear if no following chemical reaction exists. The peak current scales as the square root of scan rate $v$.
Quasi-reversible. Electron transfer kinetics match the experiment timescale. The peak separation $\Delta E_p$ grows with scan rate. Sluggish electron transfer cannot keep up at faster sweeps. Peak currents drop below the reversible prediction. Peak shapes broaden. Whether a couple looks reversible or quasi reversible depends on the scan rate and electrode you chose. Slow the scan down enough and a sluggish couple looks reversible. Speed it up and a fast couple can look quasi reversible.
Irreversible. Electron transfer is the rate limiting step across the whole potential window. No return peak appears or it is small. The peak potential $E_p$ shifts with $\ln v$ instead of staying fixed. The single peak that remains resembles linear sweep voltammetry. The reverse sweep does not recheck anything. The forward reaction goes to completion irreversibly.

None of this behavior is exclusive to electron transfer speed. A chemically reversible electron transfer can couple to a fast follow up chemical reaction. This is an $E_rC_i$ mechanism in the E C notation from Elgrishi. E means electrochemical step. C means chemical step. The subscript r or i means reversible or irreversible. The reduced species can get consumed by a homogeneous reaction before the reverse scan reaches it. This happens for a different reason than slow electron transfer. The tell is that speeding up the scan rate on an $E_rC_i$ system can restore the return peak. The chemical step does not get time to consume the intermediate. A genuinely slow electron transfer process gets more irreversible at faster scan rates. If your irreversible wave becomes reversible at high scan rate, you have a coupled chemical reaction not slow kinetics. This is one of the real mechanistic powers of CV.

Capacitive vs faradaic current

Every CV trace has two currents. You separate them to get a clean voltammogram instead of a sloping mess:

Faradaic current. This is electrons crossing the electrode solution interface via a redox reaction. This is the signal you want. It scales as $v^{1/2}$ for a diffusing species.
Capacitive current. This is also called non Faradaic or double layer current. It comes from charging the electrical double layer at any electrode electrolyte interface. This current appears even without a redox reaction. It scales linearly with scan rate. The formula is $i_C = C_{dl}\,v$ where $C_{dl}$ is the double layer capacitance. This current exists even in a blank electrolyte with no analyte.

Faradaic current grows as the square root of scan rate. Capacitive current grows linearly with scan rate. The ratio of the two gets worse at higher scan rates. Push the scan rate high enough on a dilute sample and your peak comes mostly from double layer charging instead of chemistry. Elgrishi suggests a practical fix that everyone uses. Record a background scan in supporting electrolyte alone before adding analyte. This also confirms your solvent window and checks that nothing in the cell malfunctions. Treat any current above the blank trace as your faradaic signal. A baseline subtraction fits and subtracts an extrapolated pre peak baseline under the peak itself. This practice is standard but has no rigorous theoretical basis for the exact baseline position. Different people draw slightly different lines under the same peak. Do not over trust the third significant figure of a peak current from a hand drawn baseline.

Practical SOP

The procedure below leans on SOP4CV and on Elgrishi experimental sections. Where this page overlaps with Potentiostat or Reference Electrodes, I link instead of repeating.

Electrode polishing

The working electrode surface must be clean before you trust any measurement. The surface area must also be well defined. Elgrishi Box 4 describes the standard wet polish for glassy carbon or platinum disks. Use a water or alumina slurry on a polishing pad. Work in figure eight motions instead of circles. Circular motion polishes unevenly and can slant the disk face. Sonicate the electrode in ultrapure water after polishing. This knocks off residual alumina particles. Run several CV scans in blank electrolyte across a wide potential window. Stop when successive scans overlap with no residual peaks. This pretreatment step removes anything adsorbed from the polishing slurry. Keep separate polishing pads for before and after experiment use. This avoids cross contamination from your analyte.

Degassing and sparging

Dissolved oxygen undergoes its own reduction in most solvents. This reduction can look reversible. Dissolved oxygen can also chemically intercept a reduced analyte before the reverse scan reoxidizes it. The result is a couple that looks irreversible for extraneous reasons. Spurge every electrolyte solution with an inert gas like nitrogen or argon before recording data. A bare gas stream evaporates your solvent slowly. Bubble the inert gas through a solvent matched pre bubbler first. The gas then arrives at the cell saturated with solvent vapor. This prevents drying of your electrolyte over the experiment. Once the bulk solution is degassed, move the sparge tubing above the liquid surface. Blanket the headspace this way. Do not continue bubbling through the solution. Bubbles at the electrode introduce noise.

iR drop or ohmic drop

See Potentiostat for the full treatment. The short version for CV is that ohmic drop shows itself as an increased $\Delta E_p$. This happens for a couple that you know is electrochemically reversible by other evidence. If your peak separation exceeds about 60 to 70 mV per n, suspect uncompensated resistance before suspecting the chemistry. Fix the issue by increasing supporting electrolyte concentration. You can also shrink the working electrode to reference distance. Slow the scan rate helps too. You can engage the potentiostat iR compensation routine.

Reference electrode choice

See Reference Electrodes for construction and maintenance. The CV specific issue appears in non aqueous work. A silver wire pseudo reference drifts. Its potential depends on the silver salt, concentration, and solvent. The potential is not directly comparable between labs or between runs. Elgrishi suggests a fix now close to universal in molecular electrochemistry. Add a known internal standard to every solution. Ferrocene is the default choice. Report all potentials versus the ferrocene ferrocenium couple. Use 0 V vs Fc/Fc+. This sidesteps reference electrode drift entirely. This works if the internal standard redox window does not overlap the analyte window and the two do not interact.

Baseline or background subtraction

Record and keep a background scan in supporting electrolyte alone. Use the same electrodes, scan rate, and potential window as your analyte experiment. Record the background before adding your analyte. This blank confirms your solvent window. See Potentiostat and Electrochemistry for more. The blank is what you subtract to separate faradaic signal from capacitive background. See the discussion above. There is no substitute for running the blank. Extrapolating a baseline from the analyte scan alone without a blank is guesswork.

Worked example: a generic reversible one electron couple

Take a textbook standard reversible couple as the example. The couple is the hexacyanoferrate three two pair. This is $\mathrm{[Fe(CN)_6]^{3-}}$ with an electron forming $\mathrm{[Fe(CN)_6]^{4-}}$. This is ferricyanide forming ferrocyanide. Run it in aqueous KCl at a platinum or glassy carbon disk. This choice is deliberate. It is a one electron aqueous couple with no link to any specific alloy system. It illustrates the diagnostics above.

Reading the trace:

A proper run shows a cathodic peak for Fe three plus to Fe two plus. The reverse scan shows an anodic peak of comparable height for Fe two plus to Fe three plus. The ratio $|i_{p,a}/i_{p,c}|$ close to 1 is your first reversibility check.
The peak separation $\Delta E_p$ close to the 57 to 65 mV range tells you electron transfer is fast relative to your scan rate. Some excess above 57 mV is normal with a small uncompensated resistance.
Run the same solution at several scan rates. Plot $i_p$ against $\sqrt{v}$. The plot should give a straight line through the origin. This confirms diffusion control per the Randlesek vik equation. You can also fit the slope for $D_O$.

To see the equation produce a number, consider these illustrative round figures. These are not a specific literature measurement. Let $n=1$. Let the electrode be a 3 mm diameter disk. The area is $\pi r^2$ which is about 0.0707 cm squared. Let $C^0 = 1$ mM or $1\times10^{-6}$ mol per cm$^3$. Let $D_O \approx 1\times10^{-5}$ cm$^2$/s. This is a typical order of magnitude for a small diffusing ion in aqueous solution. Let the scan rate $v = 0.1$ V/s at 25 C. Plugging into $i_p = 0.446\,nFAC^0\sqrt{nFvD_O/RT}$:

$$ \sqrt{\frac{nFvD_O}{RT}} = \sqrt{\frac{(96485)(0.1)(1\times10^{-5})}{(8.314)(298.15)}} \approx 6.2\times10^{-3}\ \mathrm{s^{-1/2}} $$

$$ i_p \approx 0.446 \times (96485) \times (0.0707) \times (1\times10^{-6}) \times (6.2\times10^{-3}) \approx 1.9\times10^{-5}\ \mathrm{A} \approx 19\ \mu\mathrm{A} $$

This gives a peak current in the tens of microamps. This is the right scale for a millimolar solution on a small disk at a modest scan rate. You can use this number to sanity check a real measurement before trusting it.

Sources and further reading

SOP4CV. Standard Operating Procedures for Cyclic Voltammetry (Daniel J. Graham): the practical reference for cell setup, electrode polishing, reversibility evaluation, and diffusion coefficient or adsorption testing. It organizes a full lesson sequence from the potentiostat and cell through Nernst equation theory to individual wave analysis. Read it start to finish once. Then bookmark it as a reference.
Elgrishi, N.; Rountree, K. J.; McCarthy, B. D.; Rountree, E. S.; Eisenhart, T. T.; Dempsey, J. L. "A Practical Beginner's Guide to Cyclic Voltammetry." J. Chem. Educ. 2018, 95, 197-206. This paper is open access. Every equation and constant attributed to Elgrishi was checked against that PDF.
BYU PyRO. Electrochemistry Lessons: video lessons with an online CV simulator. It has dedicated modules on soluble soluble and soluble insoluble electrodeposition CV systems. It includes a practical ohmic drop compensation tutorial.
Fuller, A.; Rappleye, D. "The Open Wiki of Electrochemical Methods (OWEM): A community-driven educational resource." RAISE 2026, 3(1), article 5. This peer reviewed paper introduces an open community maintained electrochemistry wiki. It uses cyclic voltammetry as a case study.
Pine Research Instrumentation. YouTube channel: the instrument maker video library includes a multi part Voltammetry Series webinar on CV. It also has Q&A livestream episodes on reading voltammograms.

A note on two sources the original brief asked for

Two links in the original research brief were not what they were assumed to be. I note this here:

The BYU ScholarsArchive article RAISE article 1009 is on topic. It is the OWEM paper above. It is cited in the list.
The YouTube video at id teTkvUtW4SA is an introduction to electrochemistry by Tyler DeWitt. It is a general audience intro level video. It is not a CV specific video. It is suitable for the Electrochemistry hub page as a gentle on-ramp. It does not carry enough CV specific content for this page. So I left it off.