# 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 | Read | From | |---|---| | Redox potentials E°′ ≈ (E_pa + E_pc)/2 | peak positions | | Reversibility | ΔE_p, i_pa/i_pc, E_p vs scan rate | | Diffusion- vs surface-controlled | **b-value** (log i_p vs log v) | | Diffusion coefficient D | **Randles–Ševčík** (i_p vs √v) | | Capacitive vs diffusive split at a potential | **Dunn** method | | Capacitance | area of the CV loop | | Stability / activation | change over cycles | --- ## 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.