GibbsThomson

Gibbs-Thomson, also known as the Gibbs-Thomson equation or Thomson equation, describes how interfacial curvature and surface tension modify thermodynamic properties that govern phase equilibrium. It arises from the combination of Gibbs free energy considerations with capillarity and is named for Josiah Willard Gibbs and William Thomson (Lord Kelvin).

For a curved interface with radius of curvature r, the difference in chemical potential between the curved interface and a flat interface is Δμ = μ(r) − μ(∞) = 2 γ V_m / r, where γ is the interfacial tension and V_m is the molar volume of the phase. This relation implies that small, highly curved interfaces have higher chemical potentials than flat ones.

A common consequence is a curvature-dependent vapor pressure over a droplet. The equilibrium vapor pressure p(r) over a droplet of radius r relates to the flat-surface pressure p_eq by p(r) = p_eq exp(2 γ V_m / (r R_g T)), where R_g is the gas constant and T is temperature. For small curvature, p(r) ≈ p_eq [1 + 2 γ V_m / (r R_g T)]. Thus, smaller droplets require higher vapor pressures to remain in equilibrium.

The Gibbs-Thomson effect is a key factor in nucleation, condensation, crystal growth, and Ostwald ripening, influencing the stability and growth rates of tiny droplets or particles in clouds, aerosols, and solidifying materials.

Limitations include assumptions of constant γ, spherical geometry, and single-component systems. At very small radii, γ itself may depend on curvature, and non-equilibrium effects can become important. The relation is widely used in materials science, atmospheric science, and physical chemistry to understand finite-size and capillarity phenomena.