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Faraday efficiency

Faradaic efficiency, also known as current efficiency, is a fundamental metric in electrochemistry that measures the fraction of electrical charge passed through an electrochemical cell that effectively contributes to the desired faradaic process, such as the formation of a specific product, relative to the total charge applied.^[1] It quantifies the selectivity and efficacy of an electrochemical reaction by comparing the actual amount of product generated to the theoretical amount predicted by the charge passed, typically expressed as a percentage.^[2] This efficiency is particularly critical in processes where side reactions or non-faradaic losses, like capacitive charging, can divert current from the intended transformation.^[3] The concept of faradaic efficiency is directly derived from Michael Faraday's laws of electrolysis, which establish the stoichiometric relationship between the quantity of electricity passed and the amount of substance chemically altered at an electrode.^[1] Mathematically, it is calculated as FE = (n × F × moles of product) / Q, where n is the number of electrons transferred per mole of product, F is the Faraday constant (approximately 96,485 C/mol), and Q is the total charge passed (in coulombs); this formula ensures alignment with Faraday's first law, which states that the mass of a substance altered is proportional to the charge passed.^[3] In ideal cases, faradaic efficiency approaches 100%, indicating complete utilization of charge for the target reaction, but real-world values are often lower due to competing processes.^[2] Faradaic efficiency plays a pivotal role in optimizing electrochemical technologies, including water electrolysis for hydrogen production, CO₂ reduction for sustainable fuels, metal electrowinning, and rechargeable batteries, where high efficiency directly impacts energy consumption, cost, and environmental footprint.^[4] For instance, in solid oxide electrolysis cells, achieving faradaic efficiencies above 95% is essential for industrial scalability, and recent advances in catalyst design and operating conditions have pushed efficiencies toward these benchmarks.^[4] Accurate measurement of faradaic efficiency requires precise quantification of products via techniques like gas chromatography or titration, alongside total charge integration, to account for potential discrepancies from incomplete collection or parasitic reactions.^[3]

Basic Concepts

Definition

Faraday efficiency, also known as current efficiency, is defined as the ratio of the charge utilized for the desired electrochemical reaction to the total charge passed through the electrochemical cell, expressing the selectivity toward the target product.^[3] This metric quantifies the fraction of the applied current that contributes to the formation of the intended species, distinguishing it from side reactions or non-productive processes.^[2] The quantitative expression for Faraday efficiency (η_F) is given by

\eta_F = \frac{n F N}{Q_\text{total}} \times 100\%

where n is the number of electrons transferred per mole of product, F is Faraday's constant (approximately 96,485 C/mol), N is the moles of the desired product, and Q_\text{total} is the total charge passed, typically calculated as the product of current and time.^[3] This formula derives from the theoretical yield expected under ideal conditions, allowing direct comparison between experimental outcomes and stoichiometric predictions. Faraday efficiency is crucial for evaluating the performance and selectivity of electrochemical processes, such as CO₂ reduction or nitrogen fixation, where high values (close to 100%) indicate minimal energy waste on competing pathways and are essential for scalable applications.^[2] It serves as a key indicator of catalyst efficacy, guiding optimization efforts to enhance resource utilization in sustainable energy technologies. The concept is grounded in Michael Faraday's laws of electrolysis, developed between 1832 and 1834.^[5]

Relation to Faraday's Laws

Faraday's first law of electrolysis states that the mass m of a substance altered at an electrode is directly proportional to the quantity of electricity Q transferred through the electrolyte. This relationship is mathematically expressed as

m = \frac{Q \cdot M}{n \cdot F},

where M is the molar mass of the substance, n is the stoichiometric number of electrons transferred per mole of substance (also known as the valence factor), and F is the Faraday constant, approximately 96,485 coulombs per mole, representing the charge of one mole of electrons.^[6] The quantity of electricity Q is given by Q = I \cdot t, with I denoting the current and t the time. This law, developed by Michael Faraday between 1832 and 1834 with the first law stated in 1832 and the second in 1833, provides the foundational quantitative basis for predicting the amount of material produced or consumed in an ideal electrolytic process.^[6] Faraday's second law complements the first by stating that, for a fixed quantity of electricity passed through different electrolytes, the masses of substances deposited or liberated at the electrodes are proportional to their chemical equivalent weights, defined as the molar mass divided by the number of electrons transferred per formula unit. This implies that the same charge Q produces amounts of different substances in the ratio of their equivalents, reinforcing the idea of a universal electrochemical equivalence tied to the electron.^[6] Faraday efficiency, denoted \eta_F, directly builds on these laws by quantifying the fraction of the total charge that contributes to the desired faradaic reaction as opposed to side processes. In ideal conditions, \eta_F = 1, meaning all electricity passed results in the exact mass or moles of product predicted by Faraday's laws, with no deviations from stoichiometry. Deviations where \eta_F < 1 signal inefficiencies, such as competing reactions or losses, where the actual yield falls short of the theoretical expectation.^[6] The actual yield of the electrolytic product can be derived from Faraday's first law, accounting for efficiency, as the number of moles of product:

\text{moles}_{\text{product, actual}} = \frac{I \cdot t \cdot \eta_F}{n \cdot F},

where I is the average current (in amperes), t is the electrolysis time (in seconds), \eta_F is the Faraday efficiency (dimensionless, between 0 and 1), n is the number of electrons per mole of product, and F is the Faraday constant. This equation shows how the laws provide the baseline for efficiency assessment: when \eta_F = 1, it reduces to the pure theoretical moles \frac{I \cdot t}{n \cdot F}, assuming complete utilization of charge for the target reaction.^[6]

Sources of Inefficiency

Faradaic Losses

Faradaic losses occur in electrochemical processes when a portion of the applied current is diverted to unintended side reactions rather than the desired faradaic process, thereby decreasing the overall Faraday efficiency. These losses arise specifically from charge-transfer events at the electrodes that compete with or bypass the primary reaction, leading to incomplete utilization of electrical energy for product formation.^[2] The primary mechanisms of Faradaic losses involve competing electrode reactions, where multiple redox processes occur simultaneously at the electrode surface due to overlapping potential windows. For instance, during cathodic metal deposition such as zinc or copper plating, the hydrogen evolution reaction (HER) competes with metal ion reduction, consuming protons and electrons without depositing the target metal and thus lowering efficiency.^[7] Another mechanism includes homogeneous reactions in the electrolyte that consume reactants or intermediates produced at the electrode, indirectly reducing the yield of the desired product relative to the total charge passed. For example, in CO₂ electroreduction on gold electrodes, a homogeneous reaction between CO₂ and OH⁻ can limit the local CO₂ concentration at high current densities, reducing Faradaic efficiency for CO due to increased hydrogen evolution.^[8] Impurity-induced side paths represent a third key mechanism, where trace contaminants catalyze parasitic redox cycles that shunt current from the main reaction; in copper electrowinning, iron impurities (Fe³⁺/Fe²⁺) cause losses through cathodic reduction of Fe³⁺ to Fe²⁺ and subsequent anodic re-oxidation, forming a non-productive shuttle without copper deposition.^[9] In industrial settings, these mechanisms can result in Faradaic losses equivalent to 5-20% of the total current, depending on process conditions; for copper electrowinning, typical current efficiencies of 90-95% imply 5-10% losses primarily from impurity-related side reactions and HER, while uncontrolled iron levels (e.g., >10 g/L) can exacerbate this to 20-50% reductions in efficiency.^[10]^[9] Faraday efficiency, defined as η_F = (actual moles of product × n × F) / total charge passed, where n is the number of electrons per product molecule and F is Faraday's constant, is directly diminished by such losses.^[2] Several factors influence the extent of Faradaic losses, including electrode potential, which determines the relative rates of competing reactions via their overpotentials—for instance, shifting potential to favor metal deposition over HER can improve efficiency by 10-15% in plating processes. Electrolyte composition plays a critical role by altering reactant concentrations and introducing or mitigating impurities; high chloride levels, for example, can enhance HER kinetics and increase losses in metal electrowinning. Temperature affects these losses by modulating reaction kinetics and overpotentials; in many electrowinning processes, elevated temperatures can reduce overpotentials for competing reactions like HER, potentially increasing losses unless optimized, though control can limit losses to under 5%.^[11]^[1]^[12]

Nonfaradaic Processes

Nonfaradaic processes in electrochemistry encompass currents that flow without direct electron transfer across the electrode-electrolyte interface to or from redox-active species, distinguishing them from Faradaic reactions that involve such charge transfer for product formation. These processes primarily arise from the capacitive charging of the electrical double layer at the interface, where ions accumulate to form a capacitor-like structure, storing charge electrostatically without chemical transformation. Additionally, they include reversible adsorption or desorption of ions and solvent molecules that do not lead to redox events.^[13]^[14] Key types of nonfaradaic processes include double-layer capacitance, where the electrode acts as one plate and the diffuse ion layer as the other, with typical capacitances ranging from 10 to 50 μF/cm² depending on the electrolyte and electrode material. Another type involves ion migration under the applied electric field, contributing to conduction without reaction, though this is often intertwined with ohmic effects. Pseudocapacitive behaviors, while involving fast surface redox, can mimic nonfaradaic currents in transient measurements due to their reversible, non-diffusional nature, but strictly, they entail electron transfer. Solvent interactions, such as orientation without decomposition, also fall under nonfaradaic contributions by altering the interfacial dipole without net charge transfer.^[13]^[14] These processes significantly impact Faradaic efficiency (η_F) by adding to the total current (I_total = I_Faradaic + I_nonfaradaic) without contributing to the desired product yield, thus lowering the fraction of charge effectively utilized for the target reaction. In dynamic conditions, such as high scan rates in cyclic voltammetry (e.g., >100 mV/s), the nonfaradaic charging current (i_c = C_dl * dv/dt) dominates, often comprising over 90% of the measured signal and masking Faradaic peaks, while at low current densities or steady-state potentials, it becomes negligible as the double layer charges rapidly. For instance, in plasma-electrolysis systems, nonfaradaic interface processes primarily drive the chemistry at the plasma-electrolyte interface, often resulting in negligible Faradaic efficiency for targeted products.^[15]^[14]^[16] In practical examples like supercapacitors, nonfaradaic processes account for nearly 100% of the current in electric double-layer capacitors, enabling high power density but zero Faradaic product formation, which highlights their role in energy storage rather than conversion. Mitigation strategies include steady-state techniques, such as chronoamperometry, where nonfaradaic currents decay exponentially (time constant τ = R_u * C_dl, often <1 s), isolating Faradaic contributions and improving η_F measurements to near 100% in controlled electrolysis. Unlike complementary Faradaic losses from side reactions, nonfaradaic processes are purely physical and reversible, avoiding permanent material changes.^[13]^[14]

Measurement and Analysis

Experimental Methods

Experimental methods for determining Faraday efficiency primarily involve direct quantification of electrodeposited or evolved products compared to the theoretical yield from the passed charge, or indirect analysis of reaction products using analytical techniques. In direct approaches, such as coulometric analysis in electrolysis cells, the mass of material deposited on the electrode is weighed before and after electrolysis to assess the efficiency of charge utilization for the desired faradaic process.^[17] This method is particularly useful for metal electrodeposition, where the actual mass gain is divided by the theoretical mass calculated from Faraday's laws, providing a straightforward measure of faradaic losses.^[18] Indirect methods rely on detecting and quantifying gaseous or liquid products post-electrolysis, often through chromatographic or spectroscopic tools to account for nonfaradaic or side reactions. For instance, in water electrolysis, gas chromatography (GC) with thermal conductivity detectors measures the volumes of evolved hydrogen and oxygen, enabling calculation of efficiency by comparing detected amounts to theoretical expectations.^[2] Spectroscopic techniques, such as nuclear magnetic resonance (NMR) or high-performance liquid chromatography (HPLC), monitor liquid-phase reactants and products, like in CO₂ reduction where formate or alcohols are quantified to evaluate selectivity.^[3] These methods are essential for systems producing volatile or soluble species, where direct mass measurement is impractical. Laboratory setups typically employ three-electrode configurations to isolate the working electrode's response and control applied potentials accurately, minimizing ohmic losses and ensuring reproducible conditions. The working electrode hosts the reaction of interest, a reference electrode (e.g., Ag/AgCl or saturated calomel) maintains a stable potential reference, and a counter electrode completes the circuit, all integrated with a potentiostat for precise current and potential monitoring.^[19] This configuration is standard in bulk electrolysis experiments, often conducted in H-cells to separate anodic and cathodic compartments and prevent product crossover.^[2] Challenges in these measurements include accounting for gas solubility in electrolytes, which can lead to underestimation of evolved gases if not purged or corrected for, as seen in aqueous systems where dissolved H₂ or O₂ affects volume-based quantifications.^[3] Volatile products may evaporate during sampling, requiring sealed setups and immediate analysis, while small flow rates demand high-precision instruments to detect minor losses. Industrial validation often follows harmonized protocols, such as those outlined in EU guidelines for low-temperature water electrolysers, which specify operating conditions like temperatures of 20–80°C, water flow rates ≥2 mL min⁻¹ cm⁻², and gas analysis via GC or mass spectrometry for accurate and standardized measurements.^[20]

Calculation Techniques

The Faraday efficiency, denoted as η_F, is computed from experimental data by comparing the charge required to produce the observed amount of a specific product to the total charge passed through the electrochemical cell. The general formula is

\eta_F = \frac{n F \Delta N_p}{\int_0^t I(t) \, dt} \times 100\%

where n is the stoichiometric number of electrons transferred per mole of product, F is the Faraday constant (approximately 96,485 C/mol), ΔN_p is the measured change in moles of the product over the electrolysis time t, and the denominator represents the total charge Q_total obtained by integrating the current I(t) over time.^[3] This calculation assumes accurate quantification of the product via techniques such as gas chromatography for gases or nuclear magnetic resonance for liquids, with the integration typically performed on chronoamperometric data.^[3] To perform the step-by-step calculation, first acquire the current-time profile from the potentiostat during the experiment. Integrate this profile to determine Q_total, ensuring the baseline is corrected for any ohmic drop or noise. Next, independently measure the moles of product formed, accounting for any losses such as gas leakage or evaporation. Finally, apply the formula, using the appropriate n value derived from the reaction stoichiometry—for instance, n=2 for hydrogen evolution (2H^+ + 2e^- → H_2). The result yields η_F as a percentage, ideally approaching 100% for selective processes.^[3] When multiple products form, the total charge is apportioned based on their respective stoichiometries, with individual η_F values summing to approximately 100% if all faradaic processes are accounted for. For each product i, η_{F,i} = (n_i F N_{p,i}) / Q_total, where side reactions like competing reductions or evolutions are quantified separately to avoid overestimation. In the chlor-alkali process, for example, anodic chlorine evolution (2Cl^- → Cl_2 + 2e^-, n=2) competes with oxygen evolution (2H_2O → O_2 + 4H^+ + 4e^-, n=4); the η_F for Cl_2 is calculated from measured Cl_2 moles, while η_F for O_2 is derived analogously, with material balance adjustments for brine concentrations to refine cathodic caustic efficiency.^[3]^[21] Error analysis in η_F computation arises primarily from uncertainties in current integration and product quantification. Current measurements in electrochemical setups typically carry uncertainties of ±1-5%, stemming from instrument precision, temperature fluctuations, and noise in potentiostats, while product quantification errors can reach ±5-10% due to analytical method limitations like calibration inaccuracies or crossover effects. Statistical methods, such as least-squares fitting for integration baselines or propagation of uncertainties via the formula δ(η_F)/η_F ≈ √[(δI/I)^2 + (δN_p/N_p)^2 + (δn/n)^2], help quantify overall error, with recommendations to report standard deviations from at least three replicates for reliable assessment.^[3]^[22] Software tools facilitate data processing for η_F calculations. EC-Lab, developed by BioLogic, enables direct export of integrated charge from current-time curves during experiments like constant current electrolysis, with built-in functions for efficiency evaluation in battery and electrolysis modes. For post-processing, Origin software from OriginLab supports numerical integration of I-t data via its Mathematics: Integrate tool, allowing baseline subtraction and area calculation under the curve. As an example walkthrough with a hypothetical dataset: import a CSV file with columns for time (s) and current (A); select the range; apply integration to obtain Q_total (e.g., 1200 C over 3600 s); measure ΔN_p = 0.01 mol for a product with n=2; compute η_F ≈ 80% using the formula in Origin's Set Column Values dialog, verifying against manual trapezoidal rule for consistency.^[23]

Interconnections with Other Efficiencies

Voltage Efficiency

Voltage efficiency, denoted as \eta_V, quantifies the effectiveness of the applied electrical potential in driving an electrochemical reaction relative to the thermoneutral voltage required. It is defined as the ratio of the thermoneutral voltage E_\text{th}, which corresponds to the enthalpy change \Delta H of the reaction adjusted for conditions (e.g., approximately 1.48 V for water electrolysis), to the actual applied cell voltage E_\text{applied}:

\eta_V = \frac{E_\text{th}}{E_\text{applied}}

This metric, typically less than 1 in practical systems, reflects losses due to overpotentials that exceed the thermoneutral potential needed for the reaction.^[24] The interaction between voltage efficiency and Faraday efficiency (\eta_F) is critical, as deviations in \eta_V from unity introduce overpotentials that can shift reaction pathways toward undesired side reactions, thereby diminishing the fraction of current contributing to the target product in \eta_F. At elevated applied voltages, these overpotentials amplify competitive processes, such as hydrogen evolution during CO₂ reduction, leading to reduced selectivity and overall current efficiency. For example, in CO₂ electrocatalysis, increasing overpotentials for the primary reduction simultaneously boost those for the competing hydrogen evolution reaction, causing \eta_F for CO to peak and then decline as side products dominate.^[25]^[26] Key contributors to this interplay include activation overpotential, which arises from the kinetic barriers at the electrode surface and elevates the energy required to initiate the reaction, thereby promoting side reactions that consume charge without forming the desired species and lowering \eta_F. Concentration overpotential, stemming from mass transport limitations, creates depleted reactant zones near the electrode, exacerbating uneven current distribution and favoring alternative pathways under high current densities. These factors collectively degrade both \eta_V and \eta_F, particularly in systems where diffusion rates cannot match reaction kinetics.^[27]^[28] A representative case illustrates this effect in water electrolysis: the oxygen evolution reaction (OER) experiences lower \eta_V than the hydrogen evolution reaction (HER) due to inherently higher overpotentials (often 300–400 mV versus <100 mV for HER on efficient catalysts), resulting in kinetic biases that drive side reactions like peroxide formation, causing a 10–30% reduction in \eta_F for OER compared to near-unity values for HER.^[29]

Energy Efficiency

In electrochemical systems, overall energy efficiency (η_E) quantifies the fraction of electrical energy input converted into useful chemical energy output, such as the higher heating value (HHV) of produced hydrogen in water electrolysis. It is derived from the balance between input power (P_in = V_cell × I, where V_cell is the cell voltage and I is the current) and output energy (proportional to the actual moles of product formed times the theoretical energy per mole, ΔH). The theoretical minimum energy required is given by ΔG = n F E_rev (Gibbs free energy, with n as electrons transferred, F as Faraday's constant, and E_rev as reversible potential), but practical systems account for entropic contributions via ΔH ≈ 1.48 V for water splitting at standard conditions. Thus, η_E = (η_F × n F E_th × I × t) / (V_cell × I × t), simplifying to η_E = η_F × (E_th / V_cell) when thermal losses are negligible, where E_th ≈ ΔH / (n F) is the thermoneutral voltage and η_F is the Faraday efficiency.^[30] This formulation extends to η_E = η_F × η_V × η_aux, incorporating voltage efficiency (η_V = E_th / V_cell, capturing overpotentials) and auxiliary factors (η_aux), such as thermal management or balance-of-plant losses, which can reduce η_E by 5-10% in stack-level systems. Low η_F propagates inefficiencies multiplicatively; for instance, an η_F of 80% combined with η_V of 70% yields η_E ≈ 56% (ignoring η_aux), significantly elevating energy costs in processes like hydrogen production where electricity comprises over 50% of operational expenses.^[31] Graphical analyses often depict η_F versus cell voltage or current density, revealing trade-offs: at low voltages near E_rev (≈1.23 V), η_F approaches 100% due to minimal side reactions, but η_V suffers from high ohmic and kinetic losses, dropping η_E below 50%; as voltage rises to 1.8-2.0 V, η_F may decline to 80-90% from parasitic processes, yet η_V improves, optimizing η_E around 60-70% at intermediate currents (0.2-0.5 A/cm²). These plots, derived from Butler-Volmer kinetics (i = i_0 [exp(α_a F η / RT) - exp(-α_c F η / RT)], linking overpotential η to current density i via exchange current i_0 and transfer coefficients α), highlight how activation barriers limit η_V at low currents while mass transport reduces η_F at high ones.^[32]^[33] Optimization strategies focus on balancing current density to maximize η_E, targeting 0.3-1 A/cm² where kinetic overpotentials (from Butler-Volmer) are moderate and diffusion limitations are avoided, often yielding η_E > 65% in alkaline or PEM electrolyzers without excessive thermal dissipation. Electrode catalysts with high i_0 (e.g., Pt or Ni-based) minimize η_V losses, while flow designs mitigate concentration gradients affecting η_F, ensuring holistic efficiency gains.^[31]^[33]

Practical Applications

Industrial Electrolysis

Industrial electrolysis encompasses large-scale electrochemical processes where Faraday efficiency plays a critical role in determining the viability and cost-effectiveness of production. In these operations, Faraday efficiency quantifies the fraction of electrical current effectively utilized for the desired faradaic reactions, such as the generation of chlorine in the chlor-alkali process or aluminum reduction in the Hall-Héroult method. High Faraday efficiency minimizes wasteful side reactions, reduces energy consumption, and enhances overall process sustainability, as deviations from 100% efficiency lead to increased operational costs and environmental burdens. Optimization strategies in industrial settings focus on electrode design, electrolyte management, and operational parameters to achieve efficiencies typically exceeding 90% in mature technologies.^[34]^[35] Prominent examples include the chlor-alkali process, which produces chlorine, hydrogen, and sodium hydroxide from brine electrolysis, and the Hall-Héroult process for primary aluminum production. In modern membrane-based chlor-alkali cells, Faraday efficiency for chlorine evolution often surpasses 95%, reflecting the selective oxidation of chloride ions at the anode while suppressing competing oxygen evolution.^[34] This high efficiency is achieved through ion-exchange membranes that prevent hydroxyl ion crossover, thereby maintaining a stable anolyte pH and minimizing parasitic reactions. In contrast, the Hall-Héroult process operates in a molten cryolite-alumina electrolyte with carbon anodes, yielding Faraday efficiencies of 92-96% for aluminum deposition, primarily limited by back-diffusion of metal and the occurrence of anode effects—transient events where alumina depletion causes non-wetting of the anode surface, leading to perfluorocarbon emissions and reduced current utilization.^[35]^[36] Scaling industrial electrolysis introduces unique challenges to Faraday efficiency, including uneven current distribution across large electrodes, which promotes localized overpotentials and side reactions such as gas evolution or metal dissolution. These effects exacerbate losses in high-current-density environments, where mass transport limitations amplify inefficiencies. Historically, the chlor-alkali industry saw significant advancements with the adoption of membrane cells in the 1970s, which elevated Faraday efficiency from around 70-92% in earlier mercury and diaphragm technologies to over 95% in contemporary ion-exchange membrane systems, driven by reduced ohmic losses and improved selectivity.^[37]^[38] In aluminum production, anode effects further compound scaling issues, periodically dropping efficiency below 90% until alumina feeding is adjusted, underscoring the need for precise process control in electrolytic pots handling thousands of amperes.^[39] To mitigate these challenges, industrial strategies emphasize catalyst coatings and current density optimization. Dimensionally stable anodes (DSAs) coated with ruthenium or iridium oxides in chlor-alkali cells suppress oxygen evolution side reactions, enhancing chlorine selectivity and boosting Faraday efficiency by up to 5-10% compared to uncoated alternatives.^[40] Similarly, in aluminum electrolysis, research into inert anode coatings aims to eliminate carbon consumption and anode effects, potentially raising efficiency toward 98%, with pilot tests as of 2025 showing promising results.^[41] Current density control, typically maintained at 0.2-0.5 A/cm², balances reaction kinetics with mass transport; exceeding this range increases overpotentials and side reactions, while lower densities underutilize capacity, both eroding Faraday efficiency.^[42] These approaches, informed by seminal developments like DSA introduction in the 1960s and membrane innovations, have become standard for achieving reliable performance in commercial plants.^[34] The economic ramifications of Faraday efficiency in industrial electrolysis are profound, as even marginal improvements translate to substantial savings given the energy-intensive nature of these processes. For instance, a 1% increase in efficiency can reduce annual energy costs by tens of millions of dollars across global production scales, where chlor-alkali facilities consume approximately 150 TWh yearly and aluminum smelters around 950 TWh as of 2024; this stems from the direct proportionality between current efficiency and the electricity required per unit of product, per Faraday's laws.^[43]^[44] Such gains not only lower operational expenses but also enhance competitiveness by minimizing byproduct formation and extending equipment life, underscoring the incentive for ongoing R&D in electrode materials and cell design.^[39]

Water Electrolysis and CO₂ Reduction

Water electrolysis for hydrogen production is a key application where high Faraday efficiency is essential for efficient renewable energy storage. In proton exchange membrane (PEM) electrolyzers, Faraday efficiencies for hydrogen evolution often exceed 95-99%, limited by crossover and recombination losses. Recent advances in catalyst design, such as non-precious metal oxides, have pushed efficiencies toward 100% at industrial scales, reducing energy penalties in green hydrogen production.^[4] Electrochemical CO₂ reduction to fuels and chemicals relies on selective faradaic processes at copper-based electrodes, with efficiencies for specific products like ethylene reaching 60-80% in flow cells. Challenges include competing hydrogen evolution, but tandem catalyst systems and optimized electrolytes have improved overall Faraday efficiency to over 90% for C2+ products as of 2025, advancing carbon capture and utilization technologies.^[2]

Electrochemical Energy Storage

In electrochemical energy storage devices, particularly rechargeable batteries, Faraday efficiency—also known as Coulombic efficiency—measures the fraction of electrical charge that contributes to the desired Faradaic redox reactions at the electrodes, as opposed to parasitic side reactions. It is calculated as the ratio of the total charge extracted during discharge to the total charge input during the preceding charge cycle, reflecting the reversibility of ion intercalation or plating/stripping processes. High Faraday efficiency is critical for long-term performance, as deviations indicate irreversible capacity loss due to solid electrolyte interphase (SEI) formation, electrolyte decomposition, or dendrite growth, which diminish the available active material over cycles. In lithium-ion batteries, typical values exceed 99% under optimal conditions, enabling hundreds to thousands of cycles with minimal degradation.^[45] For advanced systems like lithium-metal batteries, achieving Faraday efficiencies above 99.9% is necessary to realize their high theoretical energy density (over 1000 Wh/kg), as lower values lead to rapid lithium inventory loss and safety risks from dendrite penetration. Seminal studies highlight that electrolyte composition plays a pivotal role; for instance, localized high-concentration electrolytes (LHCEs) have demonstrated Coulombic efficiencies up to 99.6% over 500 cycles by stabilizing the SEI and suppressing dead lithium formation. Recent advances as of 2025, including artificial SEI designs and novel electrolytes, have achieved up to 99.9999% CE, enabling over 1600 cycles with minimal fade and supporting practical EV applications.^[46]^[47]^[48] In contrast, conventional carbonate-based electrolytes often yield efficiencies below 98% due to uneven lithium deposition, underscoring the need for tailored interfaces to minimize parasitic reactions. These efficiencies directly influence practical energy storage metrics, with even a 0.01% per-cycle loss compounding to significant capacity fade after 1000 cycles.^[46] In pseudocapacitive supercapacitors, which incorporate Faradaic charge storage via surface redox reactions, Faraday efficiency assesses the selectivity and completeness of these processes, typically aiming for near-100% to maximize energy density without compromising power delivery. Materials like transition metal oxides (e.g., MnO₂) exhibit efficiencies around 95-98% in hybrid devices, where inefficiencies arise from incomplete ion adsorption or competing hydrogen evolution. However, unlike batteries, supercapacitors prioritize rapid charge-discharge over long-term cycling, so Faraday efficiency is secondary to overall capacitance retention. Emerging redox-active electrolytes further enhance this efficiency, boosting specific energy to over 30 Wh/kg while maintaining high rate capability. In flow batteries, such as vanadium redox systems, Faraday efficiency tracks the utilization of active species, often exceeding 95% with membrane optimizations to prevent crossover losses.^[49]

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A generalized current efficiency equation was derived from material balance considerations to estimate the caustic current efficiency in ion exchange chlor.
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Reliable reporting of Faradaic efficiencies for electrocatalysis research
Mar 1, 2023 · Here, we highlight measurements of Faradaic efficiency to support claims of electrocatalyst activity, selectivity, and stability.Missing: Fe2+ | Show results with:Fe2+
[22]
Origin Help - Integrate - OriginLab
To Use Integration Tool. Create a new worksheet with input data. Highlight the selected data. Select Analysis: Mathematics: Integrate from the Origin menu to ...Missing: current- electrochemistry
[23]
Voltage Efficiency - an overview | ScienceDirect Topics
Voltage efficiency is defined as the ratio between the theoretical decomposition potential and the operational voltage of a reactor, indicating the ...
[24]
Overpotentials and Faraday Efficiencies in CO 2 Electrocatalysis ...
Feb 22, 2016 · We consider the overpotentials for the reduction of CO2 and HER as well as the Faraday efficiencies for the formation of CO and H2. As major ...
[25]
Interplay of Homogeneous Reactions, Mass Transport, and Kinetics ...
As overpotential is increased, CO faradaic efficiency reaches a maximal value (near 90%) because CO production is controlled by an electron transfer rate ...
[26]
Effects of activation overpotential in photoelectrochemical cells ...
This work analyzes the impact of on solar-to-fuel efficiency ( ) and H 2 production rate (HPR). This work also discusses choosing appropriate photo-absorbing ...
[27]
Concentration Overpotential - an overview | ScienceDirect Topics
The concentration overpotential, also denoted as the diffusion overpotential, models the resistance due to the mass transfer within the cell.<|separator|>
[28]
A comprehensive review on the electrochemical parameters and ...
Jan 26, 2023 · Assuming a 100% faradaic efficiency, the theoretical volume of gas can be calculated using the Faraday's second law, based on the current ...
[29]
[PDF] Electrical Efficiency of Electrolytic Hydrogen Production
Apr 1, 2012 · Common industrial electrolyzers have a nominal hydrogen production efficiency of around 70%. High power dissipation value is the most ...<|control11|><|separator|>
[30]
Mathematical-Programming-Based Optimization of Alkaline Water ...
Feb 28, 2025 · This work reports the simultaneous optimization of operating conditions and cell dimensions in an alkaline water electrolysis cell to maximize ...
[31]
Comparison of cell voltage, faradaic and energy efficiencies as...
Download scientific diagram | Comparison of cell voltage, faradaic and energy efficiencies as functions of current density at two electrolyte membrane ...
[32]
A concise model for evaluating water electrolysis - ScienceDirect
To solve the Butler–Volmer equation, two parameters of exchange current density for the anode and the cathode are required to describe the electrode activities.
[33]
[PDF] Advanced Chlor-Alkali Technology - eere.energy.gov
current efficiency above 96% at standard industrial current densities (≤ 0.4 A/cm2). This matches or exceeds the current norms for conventional membrane cells.
[34]
Energy and Exergy Analyses of Different Aluminum Reduction ...
Since the typical current efficiency of Hall–Heroult technology is 90%, attention should be paid to reduce the voltages of Hall–Heroult components. Table 1.
[35]
Aluminum Electrolysis - an overview | ScienceDirect Topics
The onset of the anode effect in Hall–Héroult aluminum cells is primarily due to the depletion of the oxygen-containing ionic species at the surface of ...
[36]
[PDF] Revisiting Chlor-Alkali Electrolyzers: from Materials to Devices
Chlor-alkali industry has been upgraded from mercury, diaphragm electrolytic cell, to ion exchange membrane (IEM) electrolytic cells. However, several ...<|separator|>
[37]
Journey of electrochemical chlorine production: From brine to ...
Current development of the membrane-based CA process benefits from the first ion-exchange membrane invention in the 1970s [18,19]. It is still widely used in ...
[38]
[PDF] U.S. Aluminum Production Energy Requirements - ACEEE
Alcoa obtained 90% current efficiency at 9.26 kWh/kg Al, 40% more efficient than a Hall-Héroult cell. The prototype plant was eventually shutdown because of the ...
[39]
On the electrolysis of dilute chloride solutions - Academia.edu
The Ti/RuO₂·2SnO₂ electrode demonstrates superior Faradic efficiency for active chlorine compared to Ti/Pt. Chlorate and perchlorate presence primarily results ...
[40]
[PDF] Hydrogen and Fuel Cells - DTU Research Database
By design, current alkaline electrolysis cell can hardly operate at very low current density. ... Operating current density (A/cm2). 0.2–0.5. 0.1–1. 0–2.
[41]
Caustic Soda Production, Energy Efficiency, and Electrolyzers
Sep 15, 2021 · This indicates that if all methods had similar efficiencies, EDBM and DE would use less energy to produce NaOH than the chlor-alkali processes.
[42]
BU-808c: Coulombic and Energy Efficiency with the Battery
Voltaic efficiency is another way to measure battery efficiency, which represents the ratio of the average discharge voltage to the average charge voltage.
[43]
https://www.sciencedirect.com/science/article/abs/pii/S0926337325005867
[44]
Efficient faradaic supercapacitor energy storage using redox-active ...
New redox-active CMPs (Py-BDT, Py-Ph-BDT) enable rapid charge transport, outstanding faradaic energy storage, and a 38.21 Wh kg-1 energy density.