GouyChapman

Gouy-Chapman refers to a theory of the diffuse part of the electrical double layer that forms at a charged surface in an electrolyte. It describes how mobile ions rearrange themselves to screen and balance the surface charge, treating ions as point charges in a continuous dielectric and applying statistical mechanics to predict ion distributions and electric potential.

The theory combines Poisson's equation with the Boltzmann distribution for mobile ions. For a symmetric 1:1 electrolyte with bulk concentration c0, the surface potential ψ0 and the surface charge density σ are related by σ = sqrt(8 ε ε0 kT c0) sinh(e ψ0 / 2kT), where ε is the dielectric constant, ε0 the vacuum permittivity, k the Boltzmann constant, T the temperature, and e the elementary charge. The electric potential ψ(x) decays away from the surface according to the Poisson-Boltzmann equation, describing a diffuse ion distribution in the interfacial region.

The differential capacitance of the diffuse layer follows from dσ/dψ0 and is given by C = sqrt(2 ε ε0 kT c0) cosh(e ψ0 / 2kT). In the low-potential limit, the capacitance is approximately constant, while at higher potentials it increases with ψ0. These relationships provide a framework for interpreting charging of interfaces and electrokinetic phenomena.

Historically, Louis Georges Gouy introduced the concept of a diffuse layer, with David L. Chapman extending it in the early 1910s. The Gouy-Chapman model is foundational in electrochemistry and colloid science and is often paired with the Stern model to account for a compact, non-diffuse layer at the surface (the Gouy-Chapman-Stern model). The theory assumes point ions and a mean-field approach, neglecting finite ion size, correlations, and specific adsorption.

Applications include interpretation of zeta potential measurements, electrokinetic effects, and the charging of colloidal particles and electrochemical interfaces.