Contact: Jörg Weissmüller
High-school curricula and everyday experience teach us that the surface of a fluid exerts forces, measured by the "surface tension", on the underlying bulk phase. As early as 1800, Young and Laplace have quantified the resulting pressure in small droplets in the capillary equation that bears their name. Two hundred years later, amazingly, the transfer of this simple phenomenon from the fluid to a solid remains subject of discussion. Open issues relate to the definition of and distinction between the two relevant capillary parameters for solids, surface stress and surface tension. Furthermore, the empirical data base for surface stress in materials is slim. The mechanical balance equations that link the surface stress to the compensating stresses in the bulk are only partly understood, real microstructures with nontrivial geometry continuing to be a challenge. Fascinating issues, with practical relevance in micromechanical systems and energy storage materials, concern the coupling of surface-induced stress and chemistry.
J. Weissmüller and J.W. Cahn
Mean Stresses in Microstructures due to Interface Stresses: A Generalization of a Capillary Equation for Solids
Acta Mater. 45 (1997) 1899.
M.E. Gurtin, J. Weissmüller and F. Larché
A General Theory of Curved Deformable Interfaces in Solids at Equilibrium
Phil. Mag. A 78 (1998) 1093.
D. Kramer and J. Weissmüller
A Note on Surface Stress and Surface Tension and their Interrelation via Shuttleworth's Equation and the Lippmann Equation
Surf. Sci. 601 (2007) 3042.
J. Weissmüller and H.L. Duan
Cantilever Bending with Rough Surfaces
Phys. Rev. Lett. 101 (2008) 146102.
| || |
Capillary equations for solids.
Top, Gurtin's balance law for the local bulk stress immediately underneath a curved surface (general expression and explicit form for the special case of a spherical surface segment with radius R). Bottom, the generalized capillary equation for solids by Weissmüller and Cahn, connecting averages of the stress in the bulk and of the surface stress (tensor equation and scalar variant for the pressure).
Experimental data for surface stress, f, and surface tension, γ, versus the superficial charge density, q, for a 111-textured gold electrode in dilute perchloric acid. Measurement using substrate bending technique with laser detection.