Transference Number

During battery operation, ions move through the electrolyte between the electrodes to carry charge and balance the flow of electrons through the external circuit. The electrolyte usually contains two types of charged particles:

• Positive ions (cations), like lithium ions in lithium-ion batteries

• Negative ions (anions), which typically come from the dissolved electrolyte salt

  
  

The main role of the anions is to help maintain charge balance inside the electrolyte, while the cations are typically the working ions that directly participate in the battery redox reactions. For example: in lithium-ion batteries the working ion is Li⁺, in sodium-ion batteries, it's Na⁺,  in zinc-ion batteries, it's Zn²⁺.  

The transference number (often written as t₊) describes the fraction of the total ionic current carried by a specific ion species. In batteries, the focus is usually on the working ion. 

For example, a lithium-ion transference number of 0.4 means that 40% of the ionic current is carried by lithium ions, while the remaining 60% is carried by the anions.

Why does it matter?

When the transference number is low, a larger fraction of ionic current is being carried by the anions rather than the working ions involved in the redox reactions. As current demand rises, the working ions are consumed at the electrode surface faster than they can be replenished from the bulk electrolyte. This leads to the development of concentration gradients between the electrode surface and the bulk electrolyte . 

A large concentration gradient increases the transport overpotential. Put simply, extra voltage is needed to drive ions through the electrolyte quickly enough to keep up with the electrochemical reactions occurring at the electrode surface. 

During charging, this increases the voltage required to charge the battery. During discharge, it lowers the delivered voltage. At very high currents, severe concentration gradients can even contribute to issues like lithium plating because lithium ions can become depleted near the electrode surface.

Increasing transference number

Most conventional lithium-ion electrolytes have lithium-ion transference numbers around 0.2 - 0.5. The two main factors contributing to low transference number are low working-ion mobility and low working-ion concentration. Countering these can help improve transference number. 

1. Working- ion mobility: Lithium ions are pretty small, so it is expected that they would move very quickly. However, lithium ions do not move around as bare ions inside electrolyte. Due to their high charge density, solvent molecules surround them and form what’s called a solvation shell. This effectively makes the lithium ion behave like a bulkier species, and slows its movement through the electrolyte. Reducing solvent interactions with the working ion can help improve mobility and increase the transference number. 

   
   

2. Working-ion concentration: Charge transport is partly a numbers game. The greater the proportion of working ions relative to other ions in the electrolyte, the larger the fraction of ionic current they can carry.

Measuring transference number

There are different ways to measure transference number, but one of the most commonly used methods is the Bruce-Vincent method. This method typically uses a symmetric cell to eliminate complications from having different electrode reactions occurring on each side of the cell:

 Working ion | Electrolyte | Working ion 

First, a small DC voltage is applied across the cell. Immediately after polarization, both the working ions and anions migrate in response to the electric field, producing an initial current (I₀). 

The working ions move in the direction of the field, and the anions move in the opposite direction. Because anions cannot participate in the electrode reactions, salt concentration gradients begin to build up in the electrolyte. 

Diffusion occurs in response to the concentration gradient and increasingly opposes the anion migration. Eventually, the diffusion and migration contributions for the anions nearly balance each other, causing the net anion flux to approach zero. At this point, the steady-state current (Iss) becomes more strongly dominated by working-ion transport. 

Electrochemical impedance spectroscopy (EIS) measurements are taken before and after polarization to account for changes in interfacial resistance. 

The Bruce–Vincent equation is then used to estimate the lithium-ion transference number:

Where: I₀ = initial current, Iₛₛ = steady-state current, R₀ = interfacial resistance before polarization, Rₛₛ = interfacial resistance after polarization, ΔV = applied DC voltage

Conceptually, the method compares the initial current, where both ions contribute to charge transport, to the steady-state current, where concentration polarization suppresses most of the net anion contribution and working-ion transport carries more of the current. 

In conclusion,

A high transference number alone does not automatically mean an electrolyte is great overall, but it is an important transport property because it affects how efficiently ions move through the cell during operation.

As batteries are pushed toward faster charging and higher power operation, managing ion transport limitations becomes increasingly important, which is why transference number continues to be an active area of electrolyte research.