Continuum Theory of Negative Surface Energy: Resolving the Paradox in Quantum Dots and Nanostructures

Abstract

Calvin et al. [1] recently reported a result that sounds thermodynamically forbidden: semiconductor

quantum dots with negative surface energy. If creating surface area lowers a system’s free energy,

why do these materials not spontaneously subdivide into oblivion? As Calvin et al. qualitatively

recognized, this paradox vanishes because a ligand-capped nanocrystal is not a pristine solid-vacuum

boundary, but a chemically open system where favorable ligand adsorption can drive the scalar

surface excess negative. In this work, we formalize this physical distinction by extending the theory

of continuum surface mechanics to account for chemically open, ligand-decorated surfaces. Our

framework decouples the scalar calorimetric excess from its mechanical derivatives, illustrating that

an apparent negative surface energy implies neither negative surface stress nor mechanical instability.

Furthermore, this open-system formulation predicts fundamental chemo-mechanical phenomena:

ligand relaxation softens tangent surface moduli, and adsorption-stress Maxwell relations explicitly

link lattice strain to ligand coverage. Applying this theory, we demonstrate that nanostructure

behavior is governed by the derivatives of the open-system interfacial free energy and finite-size

corrections rather than the scalar energy alone. Open-system residual stress dictates lattice strain;

favorable chemical interfacial energy drives core/shell wetting by overpowering positive elastic

mismatch; and geometric regularizations, such as curvature, thermodynamically arrest runaway

subdivision.