Voltammetric and Chrono-techniques

Excitation and response

In CV the potential is scanned as a triangular wave between two limits at constant rate (v, V/s) and the current is recorded. For a reversible couple, during the forward scan the species at the surface is depleted while the diffusion layer grows; the current first rises, then decreases under transport limitation — this is how the peak forms. On the reverse scan the product is converted back and a peak in the opposite direction is seen.

Diagnostic criteria

In a reversible (Nernstian) system: ΔE_p = E_pa − E_pc ≈ 59/n mV (25 °C), peak-current ratio i_pa/i_pc ≈ 1, peak potentials independent of scan rate and peak current proportional to v^(1/2) according to the Randles–Ševčík equation: i_p = 2.69×10⁵·n^(3/2)·A·D^(1/2)·c·v^(1/2). In a quasi-reversible system ΔE_p grows with scan rate (k⁰ is calculated by the Nicholson method); in an irreversible system the reverse peak disappears. For surface-attached (adsorbed) species the peak current is directly proportional to v and ideally ΔE_p = 0 — this criterion separates a diffusion-controlled process from a surface-controlled one.

Mechanism diagnosis

Coupled chemical reactions (EC, ECE, catalytic EC′) change the peak ratios and potential shifts in characteristic ways; a scan-rate series is the basic tool for distinguishing these mechanisms. Overlaying experimental curves with digital simulation (finite differences) allows quantitative determination of k⁰, α and chemical rate constants.

Practical settings

Scan rates range from 1 mV/s (solid state, batteries) to 100 V/s+ (microelectrodes, fast kinetics); at high rates the capacitive current (i_C ∝ v) swamps the Faradaic current (∝ v^(1/2)) and the signal-to-background ratio falls. Potential step (resolution), filters and ohmic-drop compensation directly affect the peak shape. On battery electrodes CV is a fast map of redox potentials and phase transformations; on supercapacitors a near-rectangular curve indicates ideal capacitive behaviour.

Chronoamperometry (CA)

The potential is stepped suddenly from one value to another and the time-dependent decay of the current is recorded. In a diffusion-controlled step the current obeys the Cottrell equation: i·√t is constant. The linearity of the i vs t^(−1/2) plot is the measure of diffusion control, its slope the measure of the product n·A·√D·c. The exponential decay in the first microseconds–milliseconds is the charging of the double layer (τ = R_u·C_dl); this region is excluded. In nucleation and growth studies (electroplating, metal deposition) the shape of the current–time curve is compared with instantaneous/progressive nucleation models.

Chronopotentiometry (CP)

A constant current is applied and the potential is followed against time. When the species at the surface is depleted the potential jumps to the next reaction; this transition time τ depends on concentration through the Sand equation: i·τ^(1/2) = nFAc√(πD)/2. In the battery world the counterpart of CP is galvanostatic charge/discharge; potential plateaus correspond to phase transformations, sloping regions to single-phase solid solutions.

Pulse and relaxation measurements

When short current pulses are combined with subsequent rest (relaxation), the ohmic, charge-transfer and diffusion contributions separate by time scale: the first instantaneous jump is R_u, the millisecond–second region charge transfer, longer times diffusion. In batteries HPPC and GITT rest on this principle; the result is the time-domain counterpart of the frequency-domain behaviour measured by EIS (they are linked by the Laplace transform).

Why pulses?

In a linear sweep the capacitive current flows continuously together with the Faradaic current and keeps the detection limit around 10⁻⁵ M. After a potential step the capacitive current decays exponentially (τ = R_u·C_dl, of the order of ms) while the Faradaic current decreases more slowly as t^(−1/2). If the current is sampled at the end of the pulse the capacitive component is largely eliminated; the 10⁻⁷–10⁻⁹ M sensitivity of pulsed techniques comes from this.

Techniques

Normal pulse voltammetry (NPV) applies pulses of increasing amplitude from a base potential; it gives a sigmoid wave. Differential pulse voltammetry (DPV) superimposes constant-amplitude pulses on a slow ramp and plots the difference between the currents before and after the pulse; the result is a derivative-like peak centred on E₁/₂ with a width of 90.4/n mV. Square-wave voltammetry (SWV) applies a forward–reverse pulse pair at each staircase step and takes the difference of the forward and reverse currents; in reversible systems it gives the highest sensitivity and the fastest scan (seconds). The peak current is linear with concentration; peak height and width carry information about reversibility and n.

Stripping voltammetry

In trace-metal analysis the analyte is first deposited on the electrode by reduction during a long preconcentration step (minutes), then 'stripped' by a scan in the positive direction (anodic stripping, ASV). The preconcentration factor gains 10²–10³-fold sensitivity; ng/L levels are attainable. Mercury-film, bismuth-film and boron-doped diamond electrodes are common; adsorptive stripping (AdSV) extends the method to organic and complexing species.

Polarography and the dropping mercury electrode

Heyrovský's polarography is voltammetry performed with the dropping mercury electrode (DME); each drop provides a fresh, reproducible surface and the hydrogen overpotential allows very negative potentials to be reached. Static/hanging mercury drop electrodes (SMDE/HMDE) combined with modern pulsed techniques are still the reference method in heavy-metal analysis; the use of mercury is subject to laboratory safety rules.

Hydrodynamic principle

The rotating disk draws solution in at the centre and throws it out radially; a time-independent diffusion layer whose thickness is set by the rotation rate forms at the disk surface. This is one of the rare experimental geometries in which transport is exactly calculable. The Levich equation gives the limiting current: i_L = 0.620·n·F·A·D^(2/3)·ν^(−1/6)·ω^(1/2)·c. The practical range for laminar flow is roughly 100–10 000 rpm; disk eccentricity and vibration corrupt the results.

Koutecký–Levich analysis

Under mixed control 1/i = 1/i_k + 1/(B·ω^(1/2)) is written. The plot of 1/i vs ω^(−1/2) of currents measured at different rotation rates is linear; the intercept gives the kinetic current (i_k = nFAk·c), the slope n·D^(2/3). In the oxygen reduction reaction (ORR) this analysis determines whether n is close to 4 (water) or 2 (peroxide).

Ring-disk electrode (RRDE)

A concentric ring is added around the disk and the two electrodes are held at independent potentials with a bipotentiostat. The intermediate generated at the disk (e.g. H₂O₂) is carried by the flow to the ring and detected there; the collection efficiency N is set by the geometry (typically 0.2–0.4) and calibrated with a standard couple such as ferricyanide. Peroxide yield and electron number: n = 4·i_D/(i_D + i_R/N). RRDE is one of the few methods sufficient on its own for measuring unstable intermediates and reaction selectivity.

Protocol in catalyst measurement

A thin-film catalyst ink is drop-cast on the glassy-carbon disk; activity is reported, after iR correction and subtraction of the background (N₂-saturated), by normalising the kinetic current at a given potential to mass (A/mg) or ECSA (A/cm²). Half-wave potential and Tafel slope are the comparison criteria.