Electrochemical Analytical Methods

Overview and Basic Principles

Electrochemical analytical methods use electrical quantities (current, voltage, charge, conductivity) to obtain information about the composition of a sample. They are particularly useful for:

• Detecting and quantifying ions and redox‑active species
• Studying redox processes and electrode reactions
• Working in aqueous solutions and, often, in real samples (natural waters, biological fluids, industrial process streams)

All electrochemical methods involve:

• At least one indicator (working) electrode where the analytical reaction occurs
• Often a reference electrode with a well‑defined, stable potential
• Sometimes a counter (auxiliary) electrode to carry the current
• An electrolyte solution providing ionic conductivity

The measurable quantities are typically:

• An electric potential (voltage) between electrodes
• An electric current through the cell
• The charge passed during a controlled electrolysis
• The conductivity or resistance of the solution

In analytical use, the relation between signal and analyte amount or concentration is established via calibration (standard solutions, standard addition) or, in some methods, via directly proportional physical laws.

Potentiometric Methods

Principle

In potentiometry, the cell voltage (potential difference) between an indicator electrode and a reference electrode is measured at negligible current. The potential depends on the activity (closely related to concentration) of a specific ionic species.

The central relation is the Nernst equation; for a simple ion of charge $z$:

$$
E = E^\circ + \frac{RT}{zF} \ln a
$$

At constant temperature (e.g. $25^\circ\text{C}$), this simplifies to a linear dependence of $E$ on $\log a$. Here:

• $E$ = electrode potential
• $E^\circ$ = standard electrode potential (constant for a given electrode)
• $R$ = gas constant
• $T$ = temperature
• $F$ = Faraday constant
• $a$ = activity of the analyte ion
• $z$ = charge number of the ion

For analytical work, activity is usually treated as proportional to concentration in dilute solutions.

Electrode Types

Reference Electrodes

Reference electrodes maintain a constant, known potential. Common examples:

• Silver/silver chloride electrode (Ag/AgCl)
• Saturated calomel electrode (SCE)

Their potential should be stable over time and insensitive to the sample composition.

Indicator Electrodes

Indicator electrodes respond selectively (or semi‑selectively) to analyte ions:

• Ion‑selective electrodes (ISEs): membranes that respond mainly to one type of ion
• Glass electrode: mainly selective for $\text{H}^+$ (pH measurement)
• Fluoride, nitrate, calcium, potassium, etc. electrodes
• Metal electrodes: respond to their own metal ions or to redox systems at the surface
• For example, a silver electrode for $\text{Ag}^+$, a platinum electrode for redox couples

The potential of the indicator electrode follows a Nernst‑type behavior within a certain concentration range.

pH Measurement as a Key Application

The glass electrode is the most common ion‑selective electrode and is used for pH measurement. Features:

• Thin glass membrane sensitive to $\text{H}^+$ activity
• Potential difference across the membrane is proportional to pH
• Combined electrodes integrate glass and reference electrode in one body

The measured cell voltage is converted to pH via calibration with buffer solutions of known pH. The pH meter electronics apply the Nernst slope (ideally $\approx 59.16 \,\text{mV}$ per pH unit at $25^\circ\text{C}$).

Potentiometric Titrations

In potentiometric titrations, the cell potential is monitored while a titrant is added. Key aspects:

• The potential shows a characteristic jump near the equivalence point
• No indicator dye is needed; useful for colored or turbid solutions
• Common titrations: acid–base, redox, complexometric, precipitation

The equivalence point is obtained from the potential–volume curve (e.g. by finding the point of maximum slope or inflection).

Advantages and Limitations

Advantages:

• Non‑destructive (little to no current)
• Wide concentration range (especially for pH)
• Suitable for routine monitoring (e.g. pH in environmental and industrial samples)
• Relatively simple, robust instrumentation

Limitations:

• Requires stable reference electrode
• Selectivity can be limited (interference by similar ions)
• Calibration and temperature control are important
• For some ions, suitable ion‑selective electrodes may not exist or may be difficult to handle

Conductometric Methods

Principle

Conductometric methods measure the electrical conductivity of a solution, which arises from the movement of ions under an electric field. The measured quantity is:

• Conductance $G$ (inverse of resistance $R$): $G = \frac{1}{R}$
• Or specific conductivity (conductivity) $\kappa$ related to the solution’s ability to carry current

For a simple cell with electrode area $A$ and distance $l$:

$$
\kappa = G \cdot \frac{l}{A}
$$

The conductivity depends on:

• Concentration and charges of ions
• Mobility of ions (depends on solvent and temperature)
• Temperature (strong influence, typically compensated)

Analytical Use

Direct Conductivity Measurements

Common applications:

• Assessing total ion content in natural waters or industrial effluents
• Monitoring desalination or deionization processes
• Checking purity of solvents (e.g. high‑purity water)

The relationship between conductivity and concentration is often empirical and established by calibration.

Conductometric Titrations

In conductometric titrations, conductivity is recorded while a titrant is added. The curve of conductivity vs. titrant volume changes character at or near equivalence. Examples:

• Acid–base titrations: replacement of $\text{H}^+$ by less mobile $\text{Na}^+$ changes conductivity
• Precipitation titrations: removal of ions as a low‑solubility salt reduces conductivity until slight excess of titrant adds new ions
• Complexation titrations: formation of neutral complexes can reduce ionic strength

This approach is applicable even in colored or highly turbid solutions, where visual indicators fail.

Advantages and Limitations

Advantages:

• Simple, robust, inexpensive instruments
• No special electrodes for specific ions, only a conductivity cell
• Useful when only the total ionic content is needed
• Suitable for turbid or colored solutions

Limitations:

• Poor selectivity; cannot distinguish between different ions with similar mobilities
• Strong temperature dependence; requires compensation
• Typically used for higher concentrations (low concentrations give small signals)

Voltammetric and Polarographic Methods

General Principle

Voltammetric methods measure the current as a function of applied potential. A potential is applied between a working electrode and a reference electrode, and the resulting current is recorded.

Key features:

• The working electrode potential is controlled
• The current–potential curve (voltammogram) contains qualitative information (peak positions) and quantitative information (peak heights or areas)
• Electroactive species are oxidized or reduced at characteristic potentials

A simple relation often used in quantitative analysis is that, under controlled conditions, the limiting or peak current is proportional to concentration:

$$
i \propto c
$$

The exact form depends on the method and mass transport (diffusion, convection).

Electrode Types and Cell Setup

Typical arrangement:

• Working electrode: small area; made of inert materials (e.g. platinum, gold, glassy carbon) or specialized materials (e.g. mercury drops, modified electrodes)
• Reference electrode: e.g. Ag/AgCl or calomel
• Counter electrode: completes the circuit and carries the current

For analytical voltammetry, the working electrode is often polished or renewed between measurements to maintain reproducible surfaces.

Polarography and Dropping Mercury Electrode

Classical Polarography

In polarography, a dropping mercury electrode (DME) or static mercury drop electrode (SMDE) is used as the working electrode. Mercury offers:

• Highly reproducible, constantly renewed surface
• Wide cathodic potential window for reductions
• Formation of amalgams with many metals (facilitates their reduction)

In direct current (DC) polarography:

• A linearly varying potential is applied
• The current is measured as a function of potential
• The resulting wave‑shaped curve shows limiting currents for different species

The half‑wave potential $E_{1/2}$ is characteristic for a given redox couple and is used for qualitative identification. The limiting current is proportional to concentration and is used for quantification.

Differential Pulse and Other Pulse Methods

Pulse polarographic methods (e.g. differential pulse polarography, square‑wave polarography) superimpose small potential pulses on a base potential ramp. They provide:

• Significantly improved detection limits
• Better resolution of overlapping signals
• Enhanced signal‑to‑noise ratio

These are particularly used for trace metal analysis in environmental and biological samples.

Modern Voltammetric Techniques

Cyclic Voltammetry (CV)

In cyclic voltammetry:

• The potential is swept linearly in one direction and then reversed
• The current is recorded versus potential
• Forward and reverse scans reveal oxidation and reduction peaks

CV is widely used for:

• Investigating redox mechanisms
• Studying electron transfer kinetics
• Characterizing electroactive materials (e.g. battery materials, catalysts)

While CV is often qualitative or semi‑quantitative, it can be used analytically with suitable calibration.

Stripping Voltammetry

Stripping methods are highly sensitive:

1. Preconcentration step: The analyte is accumulated at the electrode (e.g. by reduction and deposition as a metal on a mercury or solid electrode, or by adsorption).
2. Stripping step: The potential is varied to re‑oxidize (or re‑reduce) the deposited species; the current during “stripping” is measured.

Common variants:

• Anodic stripping voltammetry (ASV): Metals are first reduced and plated, then oxidized (anodic peak) during the stripping scan.
• Cathodic stripping voltammetry (CSV): Preconcentrated oxidized species are reduced during stripping.
• Adsorptive stripping voltammetry (AdSV): Molecules are adsorbed, then oxidized or reduced.

These methods provide very low detection limits, making them important for trace analysis of heavy metals and certain organic complexes.

Advantages and Limitations

Advantages:

• High sensitivity (especially stripping methods)
• Multicomponent analysis is possible if peaks are separated in potential
• Information about redox properties and reaction mechanisms
• Flexible: different waveforms, electrodes, and preconcentration strategies

Limitations:

• More complex instrumentation than potentiometry or conductometry
• Electrode surface must be carefully controlled and maintained
• Matrix effects and interferences can be significant
• Mercury electrodes raise environmental and safety concerns; alternatives are increasingly used

Coulometric Methods

Principle

Coulometric methods quantify analytes by measuring the total electric charge passed during a complete electrochemical reaction of the analyte. The key relationship is Faraday’s law:

$$
Q = n z F
$$

with

• $Q$ = total charge passed
• $n$ = number of moles of analyte reacted
• $z$ = number of electrons transferred per analyte molecule or ion
• $F$ = Faraday constant

If all analyte molecules are converted at the electrode (100% current efficiency), the method can be absolute: no external standard is needed.

Coulometric Titrations

In coulometric titrations, the titrant is generated electrochemically in situ at an electrode. Example:

• Generate $\text{I}_2$ from $\text{I}^-$ by electrolysis and let it react with the analyte
• Monitor the end point (e.g. potentiometrically or amperometrically)

The amount of titrant produced is directly related to the charge passed. This allows precise determination of very small amounts of analyte.

Controlled‑Potential Coulometry

In controlled‑potential coulometry:

• The electrode potential is held constant at a value where the analyte is completely oxidized or reduced
• The current decays over time as the analyte concentration decreases
• The total charge is obtained by integrating current over time

With proper control of conditions and knowledge of $z$, the number of moles $n$ can be calculated directly.

Advantages and Limitations

Advantages:

• High accuracy; often an absolute method without external calibration
• Can determine very small quantities
• Useful for standardizing solutions and for high‑precision work

Limitations:

• Time‑consuming due to need for complete conversion
• Requires good control of current efficiency and side reactions
• More specialized and less common in routine laboratories than potentiometry or voltammetry

Amperometric Methods

Principle

Amperometric methods measure the current at a fixed potential (or a limited potential range), often as a function of time or titrant volume. Unlike voltammetry, the potential is usually held constant at a value where the analyte is limiting the current (diffusion‑controlled).

The measured current $i$ is proportional to the analyte concentration $c$ under diffusion control:

$$
i = k \, c
$$

where $k$ depends on electrode area, diffusion coefficients, and experimental conditions.

Amperometric Titrations

In amperometric titrations:

• The working electrode is held at a constant potential
• The current is recorded as titrant is added
• The current–volume curve shows a change in slope at the equivalence point

Applications include:

• Redox titrations (e.g. determination of halides, metal ions)
• Situations with strongly colored or opaque solutions where optical detection fails

Amperometric Sensors and Biosensors

Amperometry is widely used in electrochemical sensors, especially:

• Oxygen sensors: reduction of $\text{O}_2$ at a cathode; current proportional to dissolved oxygen concentration
• Glucose biosensors: enzymatic reaction produces an electroactive species (often $\text{H}_2\text{O}_2$) that is oxidized or reduced at the electrode; current proportional to glucose concentration

These are key tools in medical diagnostics and process monitoring.

Advantages and Limitations

Advantages:

• Sensitive and relatively rapid
• Suitable for flow‑through systems and on‑line monitoring
• Compatible with enzymatic and other recognition elements for selective detection

Limitations:

• Electrode fouling or poisoning can affect long‑term stability
• Potential interferences from other electroactive species
• Requires careful choice of potential to ensure selectivity

Selection and Practical Considerations

When choosing an electrochemical analytical method, important criteria include:

• Analyte type: ionic, redox‑active, metal, organic, etc.
• Concentration range: trace vs. major components
• Sample matrix: purity, color, turbidity, presence of interfering species
• Required accuracy and detection limit
• Available equipment and expertise
• Need for absolute vs. relative (calibrated) determinations

Typical choices:

• pH and simple ion determinations: potentiometry with ion‑selective electrodes
• Total ionic content / water purity: conductometry
• Trace metals and redox‑active species: voltammetry and stripping voltammetry
• High‑precision determinations and standardizations: coulometry
• On‑line and biosensing applications: amperometry

Calibration, validation with standards, and appropriate control of temperature, ionic strength, and electrode conditioning are crucial for reliable electrochemical analysis.