Cyclic voltammetry: principles, diffusion, kinetics and battery electrodes

Shyma Sajeevan, Aswadh

Lab handbook · Lab 2

Cyclic voltammetry: principles, diffusion, kinetics and battery electrodes

What does a voltammogram tell us, and how do we read it?

Figure L2.1

Scan rate 100 mV/s

electrons in the leadsionic current in the solution supporting electrolyte

The experiment: three electrodes and a triangular sweep. Try this: press play and watch the current in the leads surge at each peak and reverse on the way back; tap each electrode for a close-up; then slow the sweep to 10 mV/s.

Source

Electrode roles and materials, the supporting electrolyte, argon sparging with the gas line lifted above the liquid during the scan, and ferrocene as an internal reference after Elgrishi et al. 2018; the linear sweep, switching and return after Elgrishi et al. 2018 and Kim et al. 2020, section 2.1. The current is simulated as in figure L2.2 (1 mM, 3 mm disc). Schematic; materials in their real colours; the animation runs at one pace, the display shows real time.

What a cyclic voltammogram is

In Lab 1 we held the current and watched the potential. Cyclic voltammetry does the opposite: it drives the potential of an electrode and records the current that flows. The potential is swept linearly in time from an initial value to a switching potential and back; the rate of the sweep, in mV/s or V/s, is the scan rate, and the plot of current against potential is the cyclic voltammogram.^1,2 A sweep in one direction only is linear sweep voltammetry.²

Why bother? A voltammogram shows at a glance where a material is oxidized and reduced and whether the reaction comes back; by changing the scan rate it separates fast from slow processes, diffusion from surface reactions, and it can estimate how fast ions diffuse.² That breadth is also the trap: the same review warns that interpretations of CV in battery research are often deficient or disputed, and that the technique should not be used without the basic electrochemistry behind it.² This page builds that basis, starting from a dissolved molecule and ending with battery electrodes and electrolytes.

The measurement needs three electrodes. The working electrode is where the reaction of interest happens: an inert disc of glassy carbon, platinum or gold, polished before each run, or, in battery work, the composite electrode itself. The reference electrode fixes the potential scale; the counter electrode, an inert platinum wire larger than the working electrode, carries the current so that the reference does not have to.¹ The solution holds the analyte in a large excess of supporting electrolyte, which carries the current and keeps the analyte from migrating in the field, so that it moves by diffusion alone; and dissolved oxygen, which gives peaks of its own, is removed by bubbling an inert gas through it first.¹

Figure L2.2

Time through the sweep

Red, the reduced formOx, the oxidized formwhere we are on the curve

The duck, step by step: the current and the concentration profiles behind it. Try this: press play and watch the flux arrow at the electrode: it is longest at the peaks, and it reverses with the sweep.

Source

Simulated with this page’s own finite-difference solution of the diffusion equation with the Nernst equation at the surface (assets/js/physics.js, cv.simulate): 1 mM, D = 10⁻⁵ cm²/s for both forms, a 3 mm disc, 100 mV/s, 25 °C, oxidation first and oxidation current positive. The simulation reproduces the Randles-Sevcik peak current to 0.1 % and a peak separation of 58 mV (tests). Points A to G, the role of the Nernst equation and the diffusion layer, and the 57 mV separation after Elgrishi et al. 2018, whose example runs the other way, reducing ferrocenium.

The duck

Let us follow one sweep of a solution that holds only the reduced form, Red, of a couple Red = Ox + e⁻. The curve has the shape known as the duck, and two things make it. The first is the Nernst equation: at every moment the potential sets the ratio of the two forms at the electrode surface,¹

E = E^{\circ'} + \frac{R T}{n F} \ln \frac{[O x]}{[R e d]}

so as the potential rises past the formal potential E°′, more and more of the Red at the surface must turn into Ox, and the current grows. The second is diffusion. The surface soon runs out of Red, and fresh Red has to diffuse in from the bulk. The region depleted of it, the diffusion layer, keeps growing through the sweep; the farther Red has to come, the slower it arrives, so past the peak the current falls although the potential keeps rising.¹

On the way back the Ox made on the way out is reduced again, and a negative peak appears. For an electrochemically reversible one-electron couple the two peaks are 57 mV apart at 25 °C (2.22 RT/F), and their midpoint, E½, is the usual estimate of E°′.¹ A caution on reading other people’s plots: two sign conventions are in use, for which way potential increases along the axis and for which current is positive, and papers seldom say which they follow.¹ In this course oxidation current is positive and potential increases to the right.

Figure L2.3

Double-layer capacitance 0 µF/cm²

Scan rate: the Randles-Sevcik equation, and the capacitive background. Try this: with no capacitance, read D from the slope; then add 60 µF/cm² and see what reading peaks from zero does to it.

Source

Simulated as in figure L2.2. Randles-Sevcik equation after Elgrishi et al. 2018, eq 3, and Kim et al. 2020, eqs 6, 18 and 19; the capacitive current C_dlA v after Kim et al. 2020, eq 10. The peak currents are read from zero, on purpose.

Scan rate and the Randles-Sevcik equation

Sweep faster and the current grows, because the diffusion layer has less time to spread and stays thinner.¹ For a reversible couple whose species diffuse freely in solution, the peak current follows the Randles-Sevcik equation,^1,2

i_{p} = 0.446 n F A C {(\frac{n F v D}{R T})}^{1 / 2}

with A the electrode area (usually the geometric one), C the bulk concentration and D the diffusion coefficient. The peak current is proportional to the square root of the scan rate, and a straight line of i_p against v^1/2 is the test that the species diffuses freely rather than sitting adsorbed on the electrode; its slope gives D.^1,2

Every voltammogram also carries a current that has nothing to do with the analyte: charging the electrical double layer of chapter 3. This capacitive current, C_dlA v, is proportional to the scan rate itself, so it grows faster with v than the diffusion peak does.^1,2 That is why a background scan of the electrolyte alone comes first: it tests the cell and measures the capacitive current that must be subtracted.¹

Worked example. At 25 °C the equation reads i_p = 2.69 × 10⁵ n^3/2A D^1/2C v^1/2, with i_p in A, A in cm², D in cm²/s, C in mol/cm³ and v in V/s.² Take 1 mM (10⁻⁶ mol/cm³), a 3 mm disc (0.0707 cm²), D = 10⁻⁵ cm²/s, 100 mV/s. i_p = 2.69 × 10⁵ × 0.0707 × (10⁻⁵)^1/2 × 10⁻⁶ × (0.1)^1/2 = 19.0 µA double layer, 20 µF/cm²: C_dlA v = 20 × 10⁻⁶ × 0.0707 × 0.1 = 0.14 µA At 100 V/s the peak would be 32 times larger and the capacitive current 1000 times: the background that was negligible becomes the signal.

Figure L2.4

Double-layer capacitance 20 µF/cm²Uncompensated resistance 0 Ω

Everything that can be read off one voltammogram, and the baselines the readings need. Try this: raise the capacitance to 1000 µF/cm², as on a porous electrode, and compare the peak current read from the baseline with the one read from zero; then add 300 Ω and watch the separation grow while E½ stays.

Source

Peak potentials, currents, separation, midpoint and the peak ratio after Elgrishi et al. 2018; the capacitive current as C A v and its subtraction, and the charge under a peak as the capacity of the reaction, after Kim et al. 2020, eqs 10 and 11; reading the double-layer current from the region before the redox reaction, where it is the same at every potential and scales with v, after Pu et al. 2021 (their eqs 9 to 11). Simulated as in figure 11.20, 1 mM, 100 mV/s; the baselines are linear fits to the first quarter of each sweep, and the capacitance is read from the forward foot alone, because the reverse sweep still carries the diffusion tail of the reduction peak there.

Extracting the parameters: what one curve gives

A voltammogram is a list of (E, i) pairs, and before any model it yields a set of numbers that should be written down for every curve. The peak potentials E_pa and E_pc, their separation ΔE_p, and their midpoint E½, the estimate of the formal potential.¹ The peak currents i_pa and i_pc, each measured from a baseline, not from zero: the flat foot of the sweep before the reaction, fitted by a line and extrapolated under the peak, because the current there is the capacitive current C_dlA v and whatever reaction is still tailing off from the previous sweep.^1,2 The ratio i_pc/i_pa, which is 1 for a reversible couple whose product survives and falls below 1 when the product is consumed by a chemical reaction.¹ The charge under a peak, the area between the curve and its baseline divided by the scan rate, is the capacity of that reaction, in coulombs or, per gram of active material, in mAh/g at that rate.² And the double-layer capacitance, read where nothing reacts: the flat current at the foot of the forward sweep divided by the scan rate and the area, or half the gap between the forward and reverse currents in a narrow window with no reaction in it (a separate scan in practice, because inside a full voltammogram the reverse sweep still carries the tail of the previous peak), is C_dl, a current that is the same at every potential and scales with v, so that i₁/v₁ = i₂/v₂ between two scan rates is the check that it has been read correctly.³

L2.4 reads all of these off a simulated curve, and shows the two commonest errors. Peaks read from zero rather than from the baseline carry the capacitive current with them, and the error grows with scan rate, because the capacitive current grows as v and the peak as v^1/2.² And a separation above 57 mV in a cell with an uncompensated resistance is the i R drop, which spreads the peaks in proportion to the current while leaving E½ almost where it was, since the two peaks move in opposite directions.¹

Figure L2.5

Rate constant k⁰ 1.0 cm/sScan rate 100 mV/s

How fast is the electron? Reversible, quasi-reversible and irreversible. Try this: set k⁰ to 10⁻² cm/s and sweep the scan rate from 10 mV/s to 10 V/s; watch where the separation leaves 57 mV.

Source

Simulated as in figure L2.2 with Butler-Volmer kinetics at the surface (α = 0.5) and a ±0.6 V window. The three regimes and their tests after Kim et al. 2020, section 2.3, and Elgrishi et al. 2018; the labels in the right panel (below 63 mV reversible, below 200 mV quasi-reversible) are this figure’s rough guide, not a standard.

How fast is the electron?

The duck assumed that electron transfer at the surface is instantaneous, so that the Nernst equation holds at every moment. Such a couple is electrochemically reversible: the peak potentials do not depend on the scan rate, the peak separation stays at about 57 to 59 mV for one electron, and the two peak currents are equal.^1,2 When electron transfer is slower, extra overpotential is needed to drive it, the peaks move apart and the separation grows with scan rate: a quasi-reversible process. Slower still, the process is irreversible, with the peaks far apart.² The scan-rate dependence is the test, and lithium insertion reactions tend to be quasi-reversible.²

Keep two meanings apart. Electrochemical reversibility is about the speed of electron transfer; chemical reversibility asks whether the product survives to be converted back. A follow-up chemical reaction that destroys the product shrinks the return peak, and a faster sweep, which outruns the chemistry, can bring it back.¹

Molecules that take two electrons can show two waves. If the second electron is accepted more easily than the first, the two merge into one wave with a separation of 28.5 mV; if it is harder, the wave splits into two one-electron waves, each with 57 mV.¹ An organic electrode material from chapter 15 gives an example: dissolved at 5 mM and swept on platinum, Li₂-PDFSA shows two successive oxidation waves at 0.23 and 0.08 V against the ferrocene couple, 3.66 and 3.51 V against lithium.⁴ Ferrocene, added to the solution from the start, is the recommended reference in nonaqueous solvents, whose reference electrodes drift.¹

Figure L2.6

Uncompensated resistance 200 Ω

Uncompensated resistance makes a fast couple look slow. Try this: raise the resistance until the separation doubles, and compare that curve with the slow electron transfer of figure L2.5.

Source

Simulated as in figure L2.2 (5 mM, 1 V/s), the electrode feeling the applied potential minus i R_u, solved at each step. Symptoms and remedies after Elgrishi et al. 2018.

Ohmic drop

The potentiostat controls the potential between the working and reference electrodes, but part of the solution resistance lies between them, uncompensated. The electrode then feels the applied potential minus i R_u, and the voltammogram stretches: the tell-tale sign is a peak separation larger than it should be for a couple known to be reversible, such as ferrocene in the same cell.¹ Ohmic drop and slow electron transfer look alike, and the larger the current, the worse it gets.

The remedies follow from i R_u. Pass less current, with a smaller electrode or a slower sweep; lower the resistance, with more supporting electrolyte; bring the reference closer to the working electrode. Many potentiostats can also measure R_u and compensate for it.¹ In a battery half-cell, the resistance of the porous electrode and of the separator adds to that of the solution, which is one reason battery CVs are run slowly.

Worked example. A 5 mM solution swept at 1 V/s on a 3 mm disc gives a peak of about 300 µA (figure L2.3’s 19 µA, × 5 for the concentration, × 10^1/2 for the rate). i R_u = 300 µA × 200 Ω = 60 mV on each peak, in opposite directions The peak separation grows by tens of millivolts, enough to mistake a reversible couple for a quasi-reversible one.

Figure L2.7

Uncompensated resistance 150 Ω

De-polarization: the peak potentials against the peak currents give the resistance, and E − iR gives the curve back. Try this: set 300 Ω, read the resistance off the slope, then switch to the de-polarized view and compare the separations.

Source

Peak potential against peak current across scan rates as a straight line whose slope is the ohmic resistance, the two lines parallel, the nonlinear part of the resistance below about 7 percent of the total, and the correction V = V − R I, after Pu et al. 2021, eqs 2 and 12 to 17 and Table 1 (LiFePO4, LiMn2O4 and Na4Fe3(PO4)2P2O7 with R² of 0.991 to 0.999). Simulated, 5 mM, reversible couple, 20 to 500 mV/s; the slope of the simulated lines exceeds the resistance put in, as the readout states.

Correct before you fit: de-polarization, de-residual, de-background

The scan-rate methods that follow assume the potential axis is the electrode’s own. In a battery electrode it rarely is: as the scan rate rises, the oxidation peaks drift positive and the reduction peaks negative, and if that drift were kinetic the plot of peak potential against peak current would curve. In LiFePO₄, LiMn₂O₄ and Na₄Fe₃(PO₄)₂P₂O₇ it is a straight line, with R² from 0.991 to 0.999, and the lines for the two peaks are parallel: the drift is an ohmic drop, the same resistance acting on both peaks, with the nonlinear kinetic and diffusional parts amounting to less than about 7 % of the total.³ The slope is the resistance, read without an impedance measurement, and the correction is simply V′ = V − R i at every point, after which the curves are symmetric about their peaks whatever the rate and the number of peaks.³ This is the first of three corrections that Pu and co-workers apply before any fit.³ One caution from our own simulation in L2.7: for a diffusion-controlled couple in solution the slope comes out above the resistance put in, because the drop also lowers the sweep rate the electrode feels near the peak, so we treat the slope as an upper estimate and the intercepts, the peak potentials at zero current, as the robust part of the result.

The second is de-residual. When the sweep reverses, the reaction of the previous sweep is still running: an oxidation current at the start of the reduction sweep and vice versa, larger at faster rates because more material has been left unreacted. Fitting these tails as exponentials from the first and last points of each segment and subtracting them makes each sweep start from zero, and raises the correlation of the scan-rate fits from poor, or even of the wrong sign, to above 0.95.³ The third is de-background: the double-layer current, read from the flat region before the reaction and checked between rates by i₁/v₁ = i₂/v₂, is subtracted, because otherwise it is counted as pseudocapacitance and inflates it.³ Only the corrected current is then fitted, in one matrix least-squares step for every potential at once, into a term in v^1/2 and a term in v.³ In LiMn₂O₄ the result returned apparent diffusion coefficients of 9.5 × 10⁻¹¹ cm²/s on oxidation and 7.0 × 10⁻¹¹ on reduction, and a surface share that grows with scan rate because the diffusion length r² = D t shrinks as the sweep gets faster.³

Subtract the i R, the tail of the last sweep and the double layer first; a fit to raw current fits the instrument as much as the electrode.

Figure L2.8

Scan rate 1.0 mV/sCapacitive share at 1 mV/s 30 %

Diffusion or surface? The b-value and the k₁v + k₂v^1/2 split. Try this: at a 30 % share, sweep from 0.1 to 100 mV/s and watch b rise from near 0.5 towards 1 as the capacitive term takes over.

Source

The power law, the split and their limits after Kim et al. 2020, sections 2.4 and 4.1, and Fleischmann et al. 2020. The electrode is this figure’s illustration, built so that both terms are exact; real voltammograms add peak shifts from ohmic losses that the split ignores.

Diffusion or surface? The b-value

Battery electrodes rarely store charge in one way only. Some current comes from diffusion into the bulk of the particles, which scales with v^1/2; some from processes at the surface, double-layer charging or fast surface redox, which scale with v. Writing the peak current as a power law,^2,5

i = a v^{b}

b is the slope of log i against log v: 0.5 for semi-infinite diffusion, 1 for a surface-controlled process, and between them mixed control or diffusion over a finite length.^2,5 A finer split works potential by potential: i(V) = k₁v + k₂v^1/2, where a plot of i/v^1/2 against v^1/2 gives k₁ as slope and k₂ as intercept, and so the capacitive and diffusion-controlled fractions of the current.^2,5

These tools are popular and easily abused. The split ignores the shift of the peaks caused by ohmic losses, which becomes significant above about 10 mV/s; a b of 1 cannot tell double-layer charging from fast surface redox without other evidence; and electrochemical signatures alone cannot establish a mechanism.⁵ In Nb₂O₅, b is close to 1 below 20 mV/s but falls to about 0.7 above it, which Kim and co-workers attribute to ohmic contributions of the active material and the SEI, and to diffusion.² Used carefully, the method shows, for instance, that smaller TiO₂ particles store more of their charge at the surface, and that a LiF–MnO composite stores about 94 % of its capacity in surface-controlled reactions.² Pseudocapacitive materials have a recognizable voltammogram: broad peaks whose anodic and cathodic branches are mirror images, barely moving with scan rate over some range; nearly all battery-type materials fail that test (chapter 6).⁵

Figure L2.9

Diffusion-limited share at 1 mV/s 60 %Capacitive share at 1 mV/s 20 %

Three mechanisms, three powers of the scan rate. Try this: give the non-diffusion-limited share most of the charge, then switch on the decomposition and watch where the fit puts it.

Source

The three-term fit |i| = a v^1/2 + b v + c v^3/2 with non-negative coefficients at every potential, from at least four scan rates, oxidation and reduction fitted separately, the charge of each mechanism by integration, the R² threshold of 0.99 and the misclassification of decomposition at the window limits, after Ghasemiahangarani et al. 2026, eq 3 and section 2; their validation on silver (73 percent diffusion-limited), activated carbon (70 percent capacitive) and MnO2 (96 percent non-diffusion-limited). The electrode here is illustrative: three shapes with exact power laws, fitted with this page’s non-negative least squares.

Three mechanisms, three powers of v

The k₁v + k₂v^1/2 split of L2.8 knows two mechanisms. A tutorial from 2026 adds the third. A faradaic reaction that is not limited by diffusion, because the migrating electrolyte keeps the surface supplied, scales with neither v^1/2 nor v; written against the time of the sweep, its current goes as v^3/2, and the full regression becomes |i| = a v^1/2 + b v + c v^3/2 at every potential.⁶ It needs at least four scan rates, the coefficients are held non-negative, oxidation and reduction are fitted separately, and a coefficient of determination below 0.99 says the three-term model does not describe the data.⁶ The current of each term, integrated over the sweep, is the charge stored by that mechanism; the coefficients do not change with scan rate, but the shares do, because the three terms scale differently.⁶

Tested on electrodes whose mechanism is known, the method returned 73 % diffusion-limited charge for silver plating and stripping, 70 % capacitive for activated carbon, and 96 % non-diffusion-limited for MnO₂ in lithium chloride, with the rest in each case a measurable deviation from the ideal.⁶ The same graphite stored its charge by a diffusion-limited route in sulfuric acid, by a larger non-diffusion-limited share in a carbonate lithium electrolyte, and by a predominantly non-diffusion-limited route in an ionic liquid: the mechanism belongs to the interface, not to the material alone.⁶ Two warnings come with the tool. It classifies by scaling, not by chemistry, so it is a phenomenological regression rather than a kinetic model; and decomposition of the electrolyte at the limits of the window is booked as a non-diffusion-limited faradaic current, so the window must stop before it.⁶ Both groups publish their code: a MATLAB interface and a Python notebook called deConV for the three-term fit,⁶ and the matrix least squares of the two-term fit.³

Fit the powers of v at every potential, integrate each term, and read the shares with their R²; the shares are properties of the rate as much as of the electrode.

Figure L2.10

Scan rate 0.05 mV/sResistance 5 Ω

A battery electrode under a slow sweep. Try this: for graphite, compare 0.02 and 0.2 mV/s; then switch to LiFePO₄ and find the rate at which its peaks are 100 mV apart.

Source

Relation dQ/dV = I/v, the difference between a CV and a dQ/dV plot, and the factors that shift battery CV peaks after Kim et al. 2020, sections 2.2 and 3. The electrode model is this page’s illustration (assets/js/physics.js, cv.electrode): the open-circuit curve of the illustrative graphite of chapter 12, or of LiFePO₄ after Safari and Delacourt 2011, behind one resistance. Not measured data.

Battery electrodes

A battery electrode is a solid that takes up lithium, not a dissolved couple, but the voltammogram follows from the same bookkeeping. With the potential rising at v = dV/dt and the current being I = dQ/dt, the two combine into²

\frac{d Q}{d V} = \frac{I}{v}

so the current at each potential is the scan rate times the charge the electrode stores per volt there. At slow enough rates, a battery CV is the differential capacity of Lab 1 turned on its side. It is not the same thing: a CV contains rate information that the dQ/dV plot of a galvanostatic test does not, it forces the potential rather than the current, and its i R drop changes along the sweep, so peak positions and shapes can shift.²

What shifts the peaks of a battery electrode? Smaller particles shorten the diffusion paths and raise the peak current; in silicon, the alloying peak that is barely visible with large particles becomes clear with small ones. Thick electrodes show peaks that split faster with scan rate than thin ones, because lithium has farther to go from the surface into the bulk. Higher temperature brings the peaks closer together and earlier.² So report the scan rate, the loading and the temperature with every battery CV, and compare voltammograms only at matching conditions. A slow example from the review: a LiₓMn₂O₄₊δ electrode swept at 0.04 mV/s against lithium, a full sweep up and down taking 6.9 hours.²

Figure L2.11

from CV (Randles-Sevcik)from GITT or EIS

Diffusion coefficients from CV, and from the other methods. Try this: find the material for which the methods disagree by the most orders of magnitude.

Source

Values from Kim et al. 2020, Table 1 and section 4.2, which collect them from the original studies.

A diffusion coefficient from a voltammogram

The Randles-Sevcik slope is widely used to estimate an apparent diffusion coefficient of lithium in an electrode: plot the peak current against v^1/2, and D follows from the slope, the area and the lithium concentration in the solid.² The conditions are strict. The analysis assumes semi-infinite diffusion in a single phase, so for a material that changes phase as it charges, such as LiMn₂O₄ with its two transitions, the numbers must be treated with care; the slope of log i_p against log v should be 0.5, and when the resistance of the cell rather than diffusion limits the current, the relation breaks down.² At slow sweeps a thin electrode is filled throughout and its peak current grows with v, not v^1/2.²

Figure L2.11 shows what follows in practice: CV and GITT or impedance (Lab 3, Lab 4) give values that agree within a factor of a few for some materials and span orders of magnitude for others.² Quote an apparent D from CV with its method, its assumptions and its area, and compare trends rather than absolute numbers.

Figure L2.12

Hydrostatic stress in the host 2.0 GPa

A mechanical artefact: stress in the lattice shifts the peak and inflates the apparent diffusion coefficient. Try this: set 2 GPa and read the shift; then compare its flat line with the ohmic curve that grows with scan rate.

Source

The stress-dependent chemical potential and the shift of the insertion potential by sigma Omega over F, tens of millivolts for stresses near 2 GPa, the Randles-Sevcik diffusivity of 0.826 × 10⁻¹⁶ cm²/s for the dislocation-free olivine particle rising to 2.72 × 10⁻¹⁶, a factor of 3.3, at the highest dislocation density and the most effective orientation, the asymmetric broadening, and the scan-rate test that separates a stress shift (constant, preserving the square-root law) from an ohmic one (growing with scan rate), after Chen, Dhiman and Huang 2026, sections 2, 3 and 5. The curves are illustrative: the shift uses a partial molar volume of 3 cm³/mol, and the inflation curve passes through the two modelled points.

When the lattice is stressed: artefacts that look like kinetics

One more thing can move a peak, and it is neither chemistry nor the instrument. The chemical potential of lithium in a stressed solid carries a mechanical term, μ = μ⁰ − σ_HΩ, with σ_H the hydrostatic stress and Ω the partial molar volume of lithium; the insertion potential shifts by σ_HΩ/F, tensile stress raising it and compressive stress lowering it, and the stresses near 2 GPa that coherency strain produces in nanoparticles shift open-circuit voltages by tens of millivolts.⁷ Dislocations are the usual source: the 7 % volume mismatch between FePO₄ and LiFePO₄ generates them as the phase boundary sweeps through a particle, faster cycling makes more, and cycled layered oxides carry densities of order 10¹⁰ cm⁻².⁷

In a modelled olivine particle, the stress enters the Butler-Volmer boundary condition as an effective overpotential η − σ_HΩ/F. With a fixed Ω the voltammogram simply translates; with Ω varying with lithium content, as it does in staged graphite and in spinels, the peak also deforms, with a higher peak current and asymmetric broadening on the high-overpotential flank.⁷ The Randles-Sevcik diffusivity read from five scan rates then rose from 0.83 × 10⁻¹⁶ cm²/s for the dislocation-free particle to 2.72 × 10⁻¹⁶ at the highest dislocation density and the most effective orientation, a factor of 3.3 that is a mechanical artefact, not better transport.⁷ The review’s own test is the scan rate: a stress shift is the same at every rate and preserves the v^1/2 law, where an ohmic shift grows with scan rate; the asymmetric broadening is distinguishable from diffusional broadening; and a diffusion coefficient from CV should be checked against GITT (L2.11).⁷ For lithium-rich layered oxides the decisive proof is thermal: heating above 150 °C annihilates the dislocation network and recovers the lost voltage plateau, which no chemical degradation would do.⁷ The authors are careful to say that no experiment has yet measured a voltammogram on a particle of known dislocation content, and that the orientation hierarchy is established only for the olivine lattice; the framework is a warning and a test, not yet a correction.⁷

The parameter sheet

What to extract from a set of voltammograms, and how
Parameter	From	How	What it says, and the trap
E_pa, E_pc, ΔE_p, E½	one curve	peak positions; E½ = (E_pa + E_pc)/2	E½ estimates E°′; ΔE_p of 57 mV is reversible; a larger one is slow kinetics or i R, settled by the scan-rate test¹
i_pa, i_pc, their ratio	one curve	from the extrapolated foot of each sweep, never from zero	a ratio of 1 means the product survives; the capacitive background inflates peaks read from zero^1,2
Q, capacity	one curve	area between curve and baseline, divided by v; per active mass for mAh/g	the capacity at that rate; compare with the galvanostatic value at the same rate²
C_dl	one curve, checked at two rates	the flat foot current divided by v and the area, or half the forward-to-reverse gap in a window with no reaction	i/v must be the same at every rate; subtract it before any fit³
R, uncompensated	peaks at several rates	slope of E_p against i_p; two parallel lines	then de-polarize, V′ = V − R i, before fitting; a curved plot means kinetics, not resistance³
b-value	peaks at several rates	slope of log i_p against log v	0.5 diffusion, 1 surface; the same b for double-layer and surface redox; ohmic shifts bend it above about 10 mV/s^2,5
D, apparent	peaks at several rates	Randles-Sevcik slope of i_p against v^1/2, with A, C, n	single phase and semi-infinite diffusion assumed; quote with its assumptions; check against GITT; stress inflates it^2,7
k⁰, reversibility	ΔE_p at several rates	constant: reversible; growing with rate after de-polarization: quasi-reversible	lithium insertion electrodes are usually quasi-reversible²
mechanism shares	whole curves at four or more rates	\|i\| = a v^1/2 + b v + c v^3/2 at every potential, non-negative, then integrate	shares depend on the rate; R² at least 0.99; decomposition at the edge is misread as faradaic⁶
stability limit	a linear sweep	potential at a chosen cut-off current	the cut-off, the rate and the electrode are part of the number⁸

One curve gives the peaks, the charge and the double layer; several rates give the resistance, the b-value, the diffusion coefficient and the mechanism shares; and every number carries the rate, the window and the corrections it was made with.

Figure L2.13

Sweep rate 5 mV/s

The stability window of an electrolyte, and why its edge is a choice. Try this: change the cut-off from 1 to 0.01 mA/cm² and read how far the “limit” moves.

Source

Oxidation limits of EC, PC, DMC, EMC and DEC (6.2, 6.6, 6.5, 6.7 and 6.7 V vs Li⁺/Li) from Ue et al. 2014, Table 2.1, measured in 1 mol/dm³ Et₄NBF₄ (0.65 mol/dm³ Bu₄NBF₄ for the linear carbonates) on glassy carbon at 5 mV/s with a cut-off of 1 mA/cm². The effect of cut-off, sweep rate and electrode choice after Scheers and Johansson 2014, section 9.2.2. The curve itself is illustrative.

The stability window of an electrolyte

Voltammetry is also how the electrochemical stability of an electrolyte is measured, the window of chapter 3. A linear sweep runs the potential until one of the components starts to be oxidized or reduced and a current flows; the potential at which that current reaches a chosen cut-off is reported as the stability limit.⁸ Single carbonate solvents measured this way, in a tetraalkylammonium salt on glassy carbon at 5 mV/s with a cut-off of 1 mA/cm², reach their oxidation limits between 6.2 V (EC) and 6.7 V (EMC, DEC) vs Li⁺/Li.⁹

Those numbers sit far above the 4.2 to 4.4 V at which carbonate electrolytes run in real cells, and the reasons are in the method. The cut-off current and the sweep rate are arbitrary choices that change the reported limit, as do the electrode, the electrolyte composition and whether a sweep or a step is used.⁸ An inert, non-porous electrode such as platinum or glassy carbon measures the intrinsic stability of the liquid, but excludes the catalytic activity of porous transition-metal oxides, which a real positive electrode brings; Scheers and Johansson advise taking stability values from one source rather than mixing studies, and testing as close to the real cell as possible when the cell is the question.⁸

Before you press start

Most bad voltammograms are made before the first sweep. Polish the working electrode, and polish it again after each experiment, because analytes adsorb. Use a large excess of dry, pure supporting electrolyte. Remove oxygen by bubbling inert gas, then lift the gas line above the liquid. Run a background scan without the analyte. In nonaqueous solvents, add ferrocene from the start and quote potentials against it. Check the uncompensated resistance on a reversible couple, and compensate it if the instrument can. And say which sign convention the plot follows.¹ For a battery electrode, add the scan rate, the loading, the temperature and the cell format to that list.²

References for this page

Numbers in the text refer to this list. All references of the course, with the chapters that use each one.

1 N. Elgrishi, K. J. Rountree, B. D. McCarthy, E. S. Rountree, T. T. Eisenhart, J. L. Dempsey, "A Practical Beginner's Guide to Cyclic Voltammetry", Journal of Chemical Education 95, 2018, 197-206. doi:10.1021/acs.jchemed.7b00361
2 T. Kim, W. Choi, H.-C. Shin, J.-Y. Choi, J. M. Kim, M.-S. Park, W.-S. Yoon, "Applications of Voltammetry in Lithium Ion Battery Research", Journal of Electrochemical Science and Technology 11, 2020, 14-25. doi:10.33961/jecst.2019.00619
3 X. Pu, D. Zhao, C. Fu, Z. Chen, S. Cao, C. Wang, Y. Cao, "Understanding and Calibration of Charge Storage Mechanism in Cyclic Voltammetry Curves", Angewandte Chemie International Edition 60, 2021, 21310-21318. doi:10.1002/anie.202104167
4 X. Guo, P. Apostol, X. Zhou, J. Wang, X. Lin, D. Rambabu, M. Du, S. Er, A. Vlad, "Towards the 4 V-class n-type organic lithium-ion positive electrode materials: the case of conjugated triflimides and cyanamides", Energy & Environmental Science 17, 2024, 173–182. doi:10.1039/d3ee02897f
5 S. Fleischmann, J. B. Mitchell, R. Wang, C. Zhan, D. Jiang, V. Presser, V. Augustyn, "Pseudocapacitance: From Fundamental Understanding to High Power Energy Storage Materials", Chemical Reviews 120, 2020, 6738-6782. doi:10.1021/acs.chemrev.0c00170
6 P. Ghasemiahangarani, D. del Mundo, R. C. Chow, G. Farhan, L. W. Gordon, T. Schoetz, "A tutorial for the identification and quantitative disentangling of charge storage mechanisms by variable-rate cyclic voltammetry", Electrochimica Acta 551, 2026, 148127. doi:10.1016/j.electacta.2026.148127
7 H. Chen, P. Dhiman, H.-Y. S. Huang, "Dislocation-induced artifacts in cyclic voltammetry of battery materials", Journal of Solid State Electrochemistry, 2026. doi:10.1007/s10008-026-06729-3
8 J. Scheers, P. Johansson, "Prediction of Electrolyte and Additive Electrochemical Stabilities", in T. R. Jow, K. Xu, O. Borodin, M. Ue (eds.), Electrolytes for Lithium and Lithium-Ion Batteries, Modern Aspects of Electrochemistry 58, Springer, New York, 2014, 403-443. doi:10.1007/978-1-4939-0302-3_9
9 M. Ue, Y. Sasaki, Y. Tanaka, M. Morita, "Nonaqueous Electrolytes with Advances in Solvents", in T. R. Jow, K. Xu, O. Borodin, M. Ue (eds.), Electrolytes for Lithium and Lithium-Ion Batteries, Modern Aspects of Electrochemistry 58, Springer, New York, 2014, 93-165. doi:10.1007/978-1-4939-0302-3_2

Cite this page

Using this page in teaching, a thesis or an article? Cite it as follows; the date is the last update of the course.

Shyma Sajeevan, A. (2026). Cyclic voltammetry: principles, diffusion, kinetics and battery electrodes. How batteries work. https://asajeevan.github.io/batteries/lab/cyclic-voltammetry/

↑

[ref-1] 1 N. Elgrishi, K. J. Rountree, B. D. McCarthy, E. S. Rountree, T. T. Eisenhart, J. L. Dempsey, "A Practical Beginner's Guide to Cyclic Voltammetry", Journal of Chemical Education 95, 2018, 197-206. doi:10.1021/acs.jchemed.7b00361

[ref-2] 2 T. Kim, W. Choi, H.-C. Shin, J.-Y. Choi, J. M. Kim, M.-S. Park, W.-S. Yoon, "Applications of Voltammetry in Lithium Ion Battery Research", Journal of Electrochemical Science and Technology 11, 2020, 14-25. doi:10.33961/jecst.2019.00619

[ref-3] 3 X. Pu, D. Zhao, C. Fu, Z. Chen, S. Cao, C. Wang, Y. Cao, "Understanding and Calibration of Charge Storage Mechanism in Cyclic Voltammetry Curves", Angewandte Chemie International Edition 60, 2021, 21310-21318. doi:10.1002/anie.202104167

[ref-4] 4 X. Guo, P. Apostol, X. Zhou, J. Wang, X. Lin, D. Rambabu, M. Du, S. Er, A. Vlad, "Towards the 4 V-class n-type organic lithium-ion positive electrode materials: the case of conjugated triflimides and cyanamides", Energy & Environmental Science 17, 2024, 173–182. doi:10.1039/d3ee02897f

[ref-5] 5 S. Fleischmann, J. B. Mitchell, R. Wang, C. Zhan, D. Jiang, V. Presser, V. Augustyn, "Pseudocapacitance: From Fundamental Understanding to High Power Energy Storage Materials", Chemical Reviews 120, 2020, 6738-6782. doi:10.1021/acs.chemrev.0c00170

[ref-6] 6 P. Ghasemiahangarani, D. del Mundo, R. C. Chow, G. Farhan, L. W. Gordon, T. Schoetz, "A tutorial for the identification and quantitative disentangling of charge storage mechanisms by variable-rate cyclic voltammetry", Electrochimica Acta 551, 2026, 148127. doi:10.1016/j.electacta.2026.148127

[ref-7] 7 H. Chen, P. Dhiman, H.-Y. S. Huang, "Dislocation-induced artifacts in cyclic voltammetry of battery materials", Journal of Solid State Electrochemistry, 2026. doi:10.1007/s10008-026-06729-3

[ref-8] 8 J. Scheers, P. Johansson, "Prediction of Electrolyte and Additive Electrochemical Stabilities", in T. R. Jow, K. Xu, O. Borodin, M. Ue (eds.), Electrolytes for Lithium and Lithium-Ion Batteries, Modern Aspects of Electrochemistry 58, Springer, New York, 2014, 403-443. doi:10.1007/978-1-4939-0302-3_9

[ref-9] 9 M. Ue, Y. Sasaki, Y. Tanaka, M. Morita, "Nonaqueous Electrolytes with Advances in Solvents", in T. R. Jow, K. Xu, O. Borodin, M. Ue (eds.), Electrolytes for Lithium and Lithium-Ion Batteries, Modern Aspects of Electrochemistry 58, Springer, New York, 2014, 93-165. doi:10.1007/978-1-4939-0302-3_2