Cyclic Voltammetry (CV) — run it, calculate it, report it

CV sweeps the potential up and back at a constant scan rate v and records the current. From the peak positions, peak currents, and how they change with v you get: redox potentials, reversibility, the mechanism (diffusion- vs surface-controlled), a diffusion coefficient, capacitance, and how all of these evolve over cycles.

Do the b-value check first. Randles–Ševčík (and a “diffusion coefficient”) only make sense if the current is actually diffusion-controlled. If b ≈ 1 the process is surface/capacitive and you should report capacitance, not D.

What CV tells you

How to run it — choosing parameters

• Reference electrode — state it (Ag/AgCl, SCE, Li/Li⁺, Hg/HgO…) and quote all potentials against it.
• Potential window — inside the electrolyte’s stability; extend only far enough to capture the peaks. Going too far adds side reactions and irreversible damage.
• Scan-rate range — cover at least a decade, e.g. 5, 10, 20, 50, 100 (mV/s), so slopes (i_p vs √v, log–log) are well defined. Low rates → near-equilibrium; high rates → kinetics + more iR.
• Start potential & equilibration — start at OCV (or a defined potential) and let the cell settle.
• Number of cycles — run several and report a stabilised cycle (often the 3rd–5th), not the first (formation/activation). Show cycle 1 vs stabilised if they differ.
• iR compensation — correct or report the uncompensated resistance; iR drop distorts peaks at high v.
• Cell — usually 3-electrode (working / counter / reference); state area and (for gravimetric metrics) active mass. Temperature too.

Calculations

Diffusion coefficient — Randles–Ševčík (reversible, 25 °C)

i_p = 2.69e5 · n^(3/2) · A · D^(1/2) · C · v^(1/2)

Plot i_p vs √v (a straight line through ~0 confirms diffusion control) and take the slope:

D = ( slope / (2.69e5 · n^(3/2) · A · C) )²

n electrons, A electrode area (cm²), C bulk concentration (mol cm⁻³; 1 mM = 1e-6), v (V s⁻¹). For quasi-reversible/irreversible systems this constant changes (use the α-dependent form).

Reversibility diagnostics

• ΔE_p = |E_pa − E_pc| ≈ 59/n mV at 25 °C (reversible; grows with v if sluggish).
• i_pa / i_pc ≈ 1.
• E_p independent of scan rate (reversible) vs shifting (irreversible).

What controls the current — the b-value

i_p = a · v^b     → plot log(i_p) vs log(v);  b = slope

b ≈ 0.5 diffusion-controlled · b ≈ 1.0 surface / capacitive · in between = mixed.

Capacitive vs diffusive split — Dunn method

At a fixed potential, across scan rates:

i(V) = k1·v + k2·√v      (k1·v = capacitive,  k2·√v = diffusion)
i(V)/√v = k1·√v + k2      → fit vs √v to get k1, k2 ; integrate the capacitive part over the sweep

Capacitance from the CV loop

C = (∮ i dV) / (2 · v · ΔV)          C_specific = C / m

∮ i dV = area enclosed by one full loop; ΔV = window; m = active mass. (Factor 2 = charge+discharge.)

Running several cycles

• Report which cycle you show, and why. Use a stabilised cycle for quantitative reads; show cycle 1 separately if activation/formation matters.
• Overlay cycle 1 → N to show stabilisation; don’t average across non-equivalent cycles.

Running several samples

• Fix everything: window, scan-rate set, reference, cycle number, equilibration, temperature.
• Normalise the current — per area (mA cm⁻²) or per active mass (A g⁻¹) — before comparing.
• Fit each sample, then report the numbers (E_p, ΔE_p, i_p, D, C, b) as mean ± SD with n.
• Overlay the CVs as thin lines with a representative one bold; state n in the caption.
• Account for every cell (how many measured vs included, and why any were excluded).

Presentation

• Overlay scan rates on one set of axes; mark the scan direction.
• Normalise current (mA cm⁻² or A g⁻¹) so samples are comparable.
• Show the pair: the CV overlay and the analysis plot (i_p vs √v, or the log–log b-value plot).
• Caption must give scan rate(s), window, reference electrode, cycle number, temperature, and iR status.

Caveats

• b-value first. Randles–Ševčík is for diffusion-controlled, reversible couples with known A and C. On porous/insertion electrodes it gives only an apparent D, and a capacitive contribution inflates i_p.
• Don’t apply Randles–Ševčík to a surface/capacitive system (b ≈ 1).
• iR drop distorts peaks and inflates ΔE_p at high v — compensate or report R_u.
• Area matters: geometric vs real (BET) area shifts D; state which.
• First cycle differs from later ones — never quote formation-cycle numbers as steady state.

References to read (start with 1–2)

1. N. Elgrishi et al., “A Practical Beginner’s Guide to Cyclic Voltammetry,” J. Chem. Educ. 95, 197–206 (2018). The clearest student introduction. https://doi.org/10.1021/acs.jchemed.7b00361
2. A. J. Bard & L. R. Faulkner, Electrochemical Methods: Fundamentals and Applications, Wiley. The reference text — CV theory, Randles–Ševčík, reversibility.
3. J. Wang, B. Dunn et al., “Pseudocapacitive contributions to electrochemical energy storage in TiO₂ (anatase) nanoparticles,” J. Phys. Chem. C 111, 14925 (2007). The k1·v + k2·√v separation.
4. The Randles–Ševčík equation — overview and the exact constant/derivation: https://en.wikipedia.org/wiki/Randles%E2%80%93Sevcik_equation
5. For pseudocapacitance vs battery behaviour: T. Brousse, D. Bélanger, J. W. Long, “To Be or Not To Be Pseudocapacitive?” J. Electrochem. Soc. 162, A5185 (2015).

Script: cv.py (in the Resources downloads) computes D (Randles–Ševčík), the b-value, the Dunn split, and capacitance, and plots the CV overlay + i_p-vs-√v fit. Run python cv.py for a demo.