For decades, battery researchers have treated one particular electrical signature as a near-direct window into what happens inside an electrode particle. When a battery’s overpotential—the extra voltage required to drive a reaction—grows in proportion to the square root of time, the behavior is commonly interpreted as evidence that lithium ions are slowly diffusing through a solid material. From that response, scientists calculate lithium chemical diffusion coefficients, numbers that are then used to compare electrode materials and predict how quickly batteries can charge and discharge. A new study now warns that this interpretation may be far less secure than assumed.
Writing in Nature Energy, researchers report that square-root-of-time overpotentials can emerge from mechanisms that do not involve solid-state diffusion at all. Their experiments focused on particles of lithium nickel manganese cobalt oxide, commonly known as NMC111 and represented chemically as LixNi1/3Mn1/3Co1/3O2. This layered oxide is widely used as a model cathode material and is closely related to compositions found in commercial lithium-ion batteries. The team found that changing the liquid electrolyte altered the apparent diffusion-related overpotential, even when the electrodes were sufficiently thin that conventional explanations based on long transport pathways became difficult to sustain.
The finding strikes at a widely used shortcut in battery electroanalysis. In a simplified diffusion model, a sudden change in current or voltage creates a concentration gradient within a solid particle. Lithium must then redistribute through the crystal, and the resulting voltage response can display a characteristic dependence on the square root of time. Because the mathematical form is associated with Fickian diffusion, researchers often fit the response to diffusion equations and extract a chemical diffusion coefficient. The coefficient is intended to describe how rapidly lithium moves through the active solid, but the new work shows that the same mathematical appearance can arise from the electrical architecture surrounding the particle.
Overpotential is not produced by a single process. It can include contributions from lithium transport through the electrolyte, charge-transfer reactions at interfaces, electronic resistance, and changes in the chemical potential of lithium inside the electrode. These processes can overlap in time, making it difficult to identify the origin of a voltage signal from its shape alone. If altering the electrolyte changes the supposed solid-state diffusion response, the signal may contain a substantial contribution from the liquid phase or from interfaces rather than reflecting lithium movement through the NMC crystal itself.
The researchers provide a physical explanation involving pores that penetrate agglomerated particles. Battery electrode powders are often made from secondary particles, which are clusters of smaller primary particles. When liquid electrolyte enters the spaces inside these agglomerates, the pores can become electrochemically active pathways. The electrolyte within them stores chemical charge and couples different regions of the particle assembly. Instead of behaving like a simple, isolated solid sphere, the agglomerate can act as a distributed network of resistive and capacitive elements.
This arrangement is known as a transmission line. In electrochemistry, a transmission-line model describes a system in which resistance and capacitance are spread continuously through a structure rather than concentrated at one interface. Electrolyte-filled pores provide ionic resistance, while the surfaces of the active material provide chemical capacitance, a voltage-dependent ability to store lithium-related charge. When these elements are connected throughout a porous network, the combined response can resemble the gradual relaxation expected from diffusion. Crucially, the resulting square-root-of-time behavior can appear even if no lithium is diffusing through the solid particles.
The distinction matters because a diffusion-like voltage curve can produce misleading numerical results. Fitting such a response with a solid-state diffusion model may yield an apparent diffusion coefficient that actually reflects pore geometry, electrolyte conductivity, interfacial charge storage, or charge-transfer kinetics. Small changes in solvent, salt, additives, or electrolyte composition could then be interpreted incorrectly as changes in lithium mobility inside the crystal. The authors argue that this may help explain why reported lithium diffusivities for similar battery materials span more than four orders of magnitude.
Their observations also challenge the belief that using thin electrodes automatically isolates particle-scale diffusion. Thin electrodes reduce the distance through which ions must travel across the electrode and can minimize some macroscopic transport limitations. Yet electrolyte can still penetrate the internal pores of an agglomerated particle, creating a distributed electrochemical network at the particle level. The study therefore suggests that even carefully designed experiments may retain non-diffusive contributions capable of imitating the classic diffusion signature.
The consequences extend beyond one cathode chemistry or one measurement method. Apparent charge-transfer resistances may also be affected when porous structures and electrolyte-filled pathways are treated as simple interfaces. If researchers assign every slow voltage relaxation to transport through the solid, they may misjudge which material properties limit power density, energy density, fast charging, and low-temperature performance. A material could appear to have unusually rapid or unusually sluggish lithium diffusion when the dominant factor is actually the electrolyte-filled architecture around its active surfaces.
The researchers are not arguing that solid-state diffusion is unimportant, but that its presence must be demonstrated rather than presumed from a square-root-of-time response. More discriminating experiments could vary electrolyte composition, particle size, porosity, agglomerate structure, temperature, and electrode thickness while comparing the results with coupled electrochemical models. Independent measurements may also be needed to separate chemical diffusion from ionic resistance, interfacial kinetics, and distributed chemical capacitance. By identifying the physical origin of each overpotential contribution, battery scientists may be able to replace a convenient mathematical diagnosis with a more reliable picture of how real electrodes operate—and revisit a large body of reported diffusion coefficients and charge-transfer values in the process.
Subject of Research: Non-diffusion mechanisms that produce diffusion-like overpotentials in battery particles, including electrolyte-penetrated pores and transmission-line chemical capacitance.
Article Title: Diffusion-like overpotentials from non-diffusion mechanisms in battery particles
Article References: Kapate, N., Pathak, S., Kweon, H. et al. Diffusion-like overpotentials from non-diffusion mechanisms in battery particles. Nature Energy (2026). https://doi.org/10.1038/s41560-026-02118-2
Image Credits: AI Generated
DOI: https://doi.org/10.1038/s41560-026-02118-2
Keywords: lithium-ion batteries, overpotential, solid-state diffusion, chemical diffusion coefficient, NMC111, electrolyte, porous particles, transmission line, chemical capacitance, charge-transfer resistance
