Depolarization Factor
Definition and meaning of Depolarization Factor in chemistry.
Depolarization factor (symbol L) is a dimensionless geometric parameter, ranging from 0 to 1, that describes how much the electric field inside a polarizable particle is reduced by the surface charges the particle itself induces when placed in a uniform external electric field.
In more detail
An ellipsoidal particle placed in a uniform field develops bound surface charge that creates its own internal field opposing the applied one; the depolarization factor quantifies this self-field for each principal axis. Because the three axis values (Lx, Ly, Lz) always sum to 1, particle shape alone determines them: a sphere gives L = 1/3 on every axis, a long needle approaches L = 0 along its length, and a thin disk approaches L = 1 perpendicular to its face. The factor depends only on shape, never on size or the dielectric constant, which makes it essential for calculating effective polarizability in models like the Clausius-Mossotti and Maxwell Garnett effective-medium theories used for colloids, composites, and nanoparticle optics.
Key facts
| Field | Physical Chemistry |
|---|---|
| Symbol | L (dimensionless, 0 ≤ L ≤ 1) |
| Sum rule | Lx + Ly + Lz = 1 |
| Sphere value | L = 1/3 along each axis |
A spherical dielectric particle has the same depolarization factor, L = 1/3, along all three axes (by symmetry, they must sum to 1). The internal field is then E_in = E_applied × 3/(ε_r + 2), the classic Clausius-Mossotti result, showing how the sphere's induced surface charge partially cancels the applied field.
Frequently asked questions
Does the depolarization factor depend on particle size or material?
No. It depends only on the particle's shape (aspect ratio), not on its size or dielectric constant.
Why must the three depolarization factors sum to one?
They arise from solving Laplace's equation for a uniformly polarized ellipsoid; the geometric partition of the induced field among the three principal axes is only self-consistent, matching the isotropic sphere limit, if Lx + Ly + Lz = 1.