Chemical binding energy and electrostatic potential combine additively in the electron electrochemical potential:
[ \tilde{\mu}{e^-}=\mu{e^-}+z_{e^-}q\Phi ] where (\mu_{e^-}) is the electron’s chemical potential, (z_{e^-}=-1), (q) is the elementary charge, and (\Phi) is the relevant inner electrostatic potential. Thus, for an electron, (\tilde{\mu}{e^-}=\mu{e^-}-q\Phi); the chemical term describes the material-dependent electronic energy, while the electrostatic term describes the energy shift caused by electric potentials.

The electrochemical potential is the electron’s complete thermodynamic energy accounting for both chemical environment and electric field. In battery materials, changes in composition, doping, charge state, and interfacial charge can therefore shift the electron energy and determine electron-transfer driving forces.

What the Electrochemical Potential Represents

The chemical contribution

The chemical potential, (\mu_{e^-}), describes how the electron energy changes with the material’s chemical and electronic state.

It reflects effects such as:

• Chemical bonding and electron binding
• Electrode composition and lithiation state
• Alloying and phase changes
• Electronic structure and density of states
• Doping and carrier concentration

A thermodynamic activity formulation can be written as:

[ \mu_{e^-}=\mu_{e^-}^{\circ}+RT\ln(a_{e^-}) ]

where (\mu_{e^-}^{\circ}) is a reference chemical potential and (a_{e^-}) is the electron activity.

The electrostatic contribution

The electrostatic term is:

[ z_{e^-}q\Phi=-q\Phi ]

because the electron has charge (-q). A positive increase in electrostatic potential therefore lowers the electron’s electrostatic energy under this convention.

The sign is important: electrons respond oppositely to positively charged particles. Confusing electron charge with the magnitude of elementary charge is a common source of incorrect energy shifts.

How the Potentials Are Combined

Inner potential, outer potential, and surface dipole

The inner electrostatic potential is often separated conceptually into:

[ \Phi=\Psi+\chi ]

Here:

• (\Psi) is the outer electrostatic potential, associated primarily with macroscopic electric fields and excess charge.
• (\chi) is the surface dipole potential, arising from the charge distribution across the solid–vacuum or solid–electrolyte boundary.

Substitution gives:

[ \tilde{\mu}_{e^-}

\mu_{e^-} -q(\Psi+\chi) ]

or, if the chemical potential is expanded using activity,

[ \tilde{\mu}_{e^-}

\mu_{e^-}^{\circ} +RT\ln(a_{e^-}) -q(\Psi+\chi) ]

This last form avoids double counting. If (\mu_{e^-}) already includes the (RT\ln(a_{e^-})) term, that term should not be added again.

Why both terms are needed

Two materials can have different electron energies for two independent reasons.

One may have different chemical binding or electronic structure, producing a different (\mu_{e^-}). It may also have a different electrostatic environment, producing a different (\Phi).

The measurable or thermodynamically relevant electron-transfer tendency depends on their combined value, not on either contribution alone.

Application to Battery Materials Characterization

Metals and alloy electrodes

In an idealized pure metal, the electron activity is often treated as approximately constant, so composition-dependent changes in the chemical term may be small.

In alloy electrodes, however, changes in composition can substantially modify the electron chemical potential. The relevant energy can shift as the electrode absorbs or releases lithium, sodium, or other electroactive species.

Semiconductors and active electrode materials

In semiconductors and many battery electrodes, doping, defects, carrier concentration, and phase composition can strongly change the electron chemical potential.

The electron energy may therefore vary with position inside a particle or electrode, particularly when local composition and charge density are nonuniform.

Solid electrolyte interfaces

At a solid electrolyte interface, charge redistribution creates electrostatic fields and interfacial dipoles.

The resulting change in (\Phi), combined with changes in the chemical term, determines band bending, contact potential differences, and the energetic barrier for electron transfer.

Charging and discharging

During charging or discharging, the electrode composition and electronic state evolve.

The electrochemical potential tracks the resulting change in electron energy and provides the relevant thermodynamic quantity for evaluating whether electron transfer is favorable across an interface.

How Measurements Relate to the Components

Contact potential differences

When two materials are brought into electrical contact, electrons redistribute until their electrochemical potentials reach equilibrium.

The resulting contact potential difference is therefore related to differences in the combined chemical and electrostatic contributions. It should not automatically be interpreted as a direct measurement of chemical binding energy alone.

Work function and surface-sensitive measurements

Surface-sensitive techniques can respond to the electron energy relative to a vacuum reference. In such cases, the surface dipole contribution (\chi) can be important.

The measured work function, for example, reflects both the bulk electronic chemical potential and the surface electrostatic dipole. Surface contamination, reconstruction, and termination can therefore alter the result.

Bulk and interfacial interpretation

A bulk electrochemical potential and a surface-referenced electron energy are related but not identical observables.

Careful interpretation requires specifying the reference state, the location of the potential, and whether the measurement is sensitive to bulk composition, surface dipoles, or interfacial charge.

Understanding the Trade-offs

Chemical energy is not always directly measurable

The chemical contribution is often inferred from thermodynamic data, electronic-structure calculations, spectroscopy, or composition-dependent equilibrium measurements.

It is generally difficult to isolate it experimentally from electrostatic and interfacial contributions without a defined reference and an appropriate model.

Electrostatic potential is reference-dependent

Absolute electrostatic potentials are not directly meaningful without specifying a reference. Potential differences are physically observable, while the zero of potential can be shifted by convention.

Comparisons between calculations and experiments must therefore use compatible energy and potential references.

Electron activity is not always simple

Treating (a_{e^-}\approx 1) can be a useful approximation for some metals, but it is not universally valid for semiconductors, mixed-valence oxides, alloys, or partially occupied battery electrodes.

In these materials, carrier concentration, density of states, defects, and phase transitions can all influence the chemical potential.

Surface dipoles can complicate bulk conclusions

A change in measured electron energy may originate from the bulk chemical state, the surface dipole, or interfacial charge redistribution.

Attributing the entire shift to chemical binding energy without separating these effects can lead to incorrect conclusions about battery reaction mechanisms.

Making the Right Choice for Your Goal

The most useful interpretation depends on whether you are analyzing bulk thermodynamics, electronic structure, or an interface.

• If your primary focus is bulk electrode thermodynamics: Track the composition- and temperature-dependent electron chemical potential, using (\mu_{e^-}=\mu_{e^-}^{\circ}+RT\ln(a_{e^-})) where an activity description is appropriate.
• If your primary focus is interfacial charge transfer: Evaluate the full electrochemical potential, including the electrostatic potential and any interfacial dipole.
• If your primary focus is spectroscopy or work-function measurements: Define the energy reference explicitly and account for surface dipoles rather than treating the measurement as a direct bulk chemical-potential measurement.
• If your primary focus is charging and discharging behavior: Compare electrochemical-potential changes between the relevant electrode and electrolyte states to identify electron-transfer driving forces.

Understanding the electrochemical potential as the sum of chemical and electrostatic contributions provides the correct framework for interpreting electron energies throughout battery materials and interfaces.

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