Quantum Theory of Surface Energy and Tension
Abstract
The surface energy ${E}_{S}$ of a system of interacting particles is ${E}_{S}=\ensuremath{\int}{\ensuremath{-}\ensuremath{\infty}}^{\ensuremath{\infty}}dz{\ensuremath{\epsilon}(z)\ensuremath{-}{\ensuremath{\epsilon}}_{B}[\frac{\ensuremath{\rho}(z)}{{\ensuremath{\rho}}_{B}}]}$, where $\ensuremath{\epsilon}(z)$ and $\ensuremath{\rho}(z)$ are the energy and particle densities along the axis normal to the surface. ${\ensuremath{\epsilon}}_{B}$ and ${\ensuremath{\rho}}_{B}$ are the corresponding quantities in the bulk. Alternatively one may formulate an exact expression for the surface tension defined as $\ensuremath{\gamma}={(\frac{\ensuremath{\partial}F}{\ensuremath{\partial}S})}_{V}$, with the result that $\ensuremath{\gamma}=\ensuremath{\int}{\ensuremath{-}\ensuremath{\infty}}^{\ensuremath{\infty}}\mathrm{dz}\left\{2[{t}_{z}(z)\ensuremath{-}{t}_{\ensuremath{\perp}}(z)]+\frac{1}{4}\ensuremath{\int}d\mathrm{r}({r}^{2}\ensuremath{-}3{{r}_{z}}^{2})\frac{1}{r}\frac{\mathrm{dv}}{\mathrm{dr}}{\ensuremath{\rho}}^{(2)}(z, z+{r}_{z})\right\}.$ ${t}_{i}(z)$ are the components of the average kinetic energy density and ${\ensuremath{\rho}}^{(2)}({r}_{1}, {r}_{2})$ is the pair distribution function. In the ground state $\ensuremath{\gamma}={E}_{S}$. We have applied these formulas to liquid ${\mathrm{He}}^{4}$ and ${\mathrm{He}}^{3}$ assuming that ${\ensuremath{\rho}}^{(2)}=\ensuremath{\rho}(z)\ifmmode\times\else\texttimes\fi{}\ensuremath{\rho}(z+{r}_{z}){g}_{B}(r)$. The bulk radial…
Read the paper
Related studies
- Chaos and quantum thermalization
- The Dalton quantum chemistry program system
- Cord Blood Leptin and Adiponectin as Predictors of Adiposity in Children at 3 Years of Age: A Prospective Cohort Study
- Quantitative metabolomics by H-NMR and LC-MS/MS confirms altered metabolic pathways in diabetes
- Stable adiabatic quantum batteries
- A novel self-lipid antigen targets human T cells against CD1c(+) leukemias
Go deeper in Evidence Hub
Evidence Hub adds a study data sheet (design, sample size, evidence level, key numbers), an AI summary and a chat grounded in the paper's text.