Determination of the Transference Number of Homogeneous Anion Exchange Membranes: Principles, Method

The transference number (transport number) is the defining permselectivity metric for homogeneous anion exchange membranes, quantifying the fraction of the total electric current carried by counter-ions across the membrane. This article explains the measurement principle, sample requirements, the membrane potential (EMF), Hittorf, and electrodialysis-based test methods, calculation formulas, and typical applications of transference number determination for quality control, research, and certification in accredited third-party laboratories.

Technical Overview

Homogeneous anion exchange membranes are ion-exchange membranes in which cationic functional groups—typically quaternary ammonium or amine groups—are chemically anchored to and uniformly distributed within a continuous polymer matrix. Because there is no inert binder phase, these membranes combine low electrical resistance with high permselectivity, making them the preferred separator for electrodialysis, diffusion dialysis, and bipolar membrane electrodialysis processes.

The transference number, denoted t⁻ for an anion exchange membrane, is defined as the fraction of the total current passing through the membrane that is carried by counter-ions (anions). An ideal membrane with perfect Donnan exclusion would exhibit t⁻ = 1. In practice, co-ion leakage and water transport reduce this value; commercial homogeneous anion exchange membranes typically show t⁻ between 0.90 and 0.98 in dilute sodium chloride solution. The transference number is therefore the most direct indicator of membrane permselectivity, and it governs current efficiency, energy consumption, and product purity in electro-membrane processes.

The measured value depends on the membrane's fixed charge concentration (related to ion exchange capacity), swelling degree, and the supporting electrolyte concentration. Transference number determination is routinely performed during membrane research and development, production batch release, incoming inspection, and third-party verification in laboratories operating under quality frameworks such as ISO/IEC 17025, with reference to test practices published by standards organizations including ISO, IEC, ASTM, and Chinese national standards (GB/T) and related industry standards (HY/T) covering ion exchange membranes and electrodialysis equipment.

Testing Samples

Flat-Sheet Homogeneous Anion Exchange Membranes

Coupons cut from production sheets, typically with an effective test area of at least 5–7 cm² (for example, 3 cm × 3 cm or a circular disk). The sample thickness, appearance, and batch identification are recorded, and the membrane is free of pinholes, creases, and visible contamination.

Membranes in Different Counter-Ion Forms

The standard measurement is performed with the membrane in the chloride (Cl⁻) form. Membranes supplied in the OH⁻, SO₄²⁻, or other counter-ion forms are converted by conditioning in sodium chloride solution before testing, since the counter-ion species directly affects the measured transference number.

Specialty and Composite Membranes

Perfluorinated anion exchange membranes, hydrocarbon-based membranes, monovalent-selective anion membranes, the anion-exchange layer of bipolar membranes, and anion exchange membranes intended for alkaline water electrolyzers or fuel cells can also be evaluated, with the electrolyte and concentration adapted to the target application.

Testing Items

The core deliverable of the test is the membrane transference number, supported by the intermediate electrochemical quantities and conditioning data listed below.

• Counter-ion (anion) transference number t⁻ across the membrane — the primary reported parameter.
• Membrane potential (electromotive force) generated across the membrane separating two electrolyte solutions of different concentration.
• Apparent permselectivity P, calculated as the ratio of the measured membrane potential to the theoretical Nernst potential.
• Apparent transference number (current efficiency) derived from a laboratory electrodialysis stack test, reflecting performance under realistic operating conditions (optional, application-oriented).
• Supporting data: counter-ion form, membrane thickness, conditioning history, test electrolyte identity and concentrations, and temperature.

Testing Methods

Three complementary approaches are used: the membrane potential (EMF) method as the reference method, the Hittorf titration method as an absolute method, and the electrodialysis current-efficiency method for application-oriented evaluation.

Membrane Potential (Electromotive Force) Method — Reference Method

The conditioned membrane is clamped between two compartments of a thermostated glass cell maintained at 25.0 ± 0.5 °C. The compartments are filled with sodium chloride or potassium chloride solutions of different concentration, commonly 0.1 mol/L and 0.2 mol/L, and stirred to suppress concentration polarization. The potential difference across the membrane is measured with a matched pair of reference electrodes (Ag/AgCl or calomel with salt bridges) connected to a high-input-impedance electrometer, after subtracting the electrode asymmetry potential.

For a 1:1 electrolyte, the theoretical Nernst potential for a perfectly permselective membrane is E(theor) = (RT/F) × ln(a₂/a₁), which corresponds to approximately 16.3 mV for 0.1 and 0.2 mol/L sodium chloride at 25 °C when mean ionic activities are used. The permselectivity and transference number are then calculated as follows:

• P = E(measured) / E(theor)
• t⁻ = (1 + P) / 2

For example, a measured membrane potential of 15.2 mV against a theoretical value of 16.3 mV gives P ≈ 0.93 and t⁻ ≈ 0.965, indicating a high-permselectivity membrane.

Hittorf (Direct Titration) Method

A known quantity of electricity is passed through a two- or three-compartment cell containing the test membrane. The anion content of each compartment is determined before and after electrolysis, typically by argentometric titration of chloride. Applying Faraday's law, the charge attributable to anion transport yields the transference number directly, with an optional correction for electroosmotic water transport. This absolute method is mainly used to validate the membrane potential method.

Electrodialysis Current-Efficiency Method

A small laboratory electrodialysis stack is assembled with the test membrane, and a defined feed solution is desalinated under constant current. The concentration change, monitored by conductivity or titration, is compared with the total charge passed to obtain the apparent transference number. This method captures the influence of hydrodynamics and stack design on real-world performance.

Quality Control and Reporting

Prior to measurement, samples are conditioned, for example 24 hours in 0.5 mol/L sodium chloride solution, followed by equilibration in the test solution. Measurements are performed at least in triplicate. The test report should state the electrolyte, concentrations, temperature, membrane counter-ion form, individual and mean transference numbers, and measurement uncertainty. Testing can be carried out by manufacturers' laboratories or by accredited third-party laboratories following recognized electrochemical practices published by standards bodies such as ISO, IEC, ASTM, and the GB/T and HY/T standard series for ion exchange membranes and electrodialysis.

Applications

Transference number data underpin the selection, qualification, and quality assurance of homogeneous anion exchange membranes across the water, chemical, food, and energy sectors.

• Electrodialysis desalination of brackish water and production of edible salt from seawater or concentrated brine, where high t⁻ directly reduces specific energy consumption.
• Food and pharmaceutical processing, including whey demineralization, juice deacidification, and amino acid purification.
• Industrial wastewater treatment and resource recovery: removal or recovery of heavy metals, fluoride, nitrate, and cyanide; regeneration of spent acids and alkalis.
• Bipolar membrane electrodialysis for in-situ acid and base generation and salt splitting, where the anion layer's permselectivity limits process efficiency.
• Salinity-gradient energy harvesting by reverse electrodialysis (RED).
• Anion exchange membranes for alkaline electrolyzers and fuel cells, where faithful hydroxide transport affects cell voltage and efficiency.
• Research and development benchmarking, production batch release by membrane manufacturers, incoming inspection by equipment OEMs, and independent verification in accredited third-party laboratories.

FAQ

What transference number indicates a high-quality homogeneous anion exchange membrane?

A value of t⁻ ≥ 0.95 measured in 0.1/0.2 mol/L sodium chloride at 25 °C is considered excellent. Values between 0.90 and 0.95 are acceptable for many electrodialysis duties, while values below 0.90 usually indicate co-ion leakage, excessive swelling, surface fouling, or membrane defects. The acceptance threshold ultimately depends on the application.

Why is the chloride form used as the standard test condition?

The chloride ion is chemically stable, has well-characterized activity coefficients, is easily quantified by titration, and is the dominant anion in most electrodialysis feeds. Membranes in other counter-ion forms can be tested after ion-exchange conditioning, but the results are not directly comparable with chloride-form data.

How do homogeneous membranes compare with heterogeneous membranes?

Because the ion-exchange groups are uniformly distributed in a continuous phase, homogeneous membranes generally achieve higher transference numbers (typically 0.93–0.98) and lower area resistance than heterogeneous, binder-based membranes (commonly 0.85–0.93), owing to stronger and more uniform Donnan exclusion.

What factors can bias the measurement?

Common error sources include concentration polarization from inadequate stirring, reference electrode asymmetry, liquid junction potentials, temperature drift, neglect of activity coefficients, incomplete conversion of the counter-ion form, and membrane surface fouling. Standardized cell geometry, matched reference electrodes, and strict temperature control minimize these effects.

Can the test be performed in electrolytes other than sodium chloride?

Yes. The method is applicable to potassium chloride, sodium sulfate, hydrochloric acid, sodium hydroxide, and other systems, provided the theoretical Nernst potential is recalculated with the appropriate activities and valences. The report must always specify the electrolyte and its concentrations.

What is the typical turnaround time?

Conditioning and measurement typically require 2–5 working days, with a full test report, including replicate data and uncertainty, generally issued within 5–10 working days. Samples should be shipped flat or in sealed, moisture-protected packaging to prevent drying, folding, and microbial contamination.