Statistical Mechanics of Surface Tension
スポンサーリンク
概要
- 論文の詳細を見る
It is shown that we can derive by a comparatively simple procedure the formula of surface tension in terms of distribution functions from purely statistical considerations. Surface tension is derived as the increase of free energy which accompanies the increase of unit area of the interface between the liquid and the vapor phases. The expression obtained is the same as MacLellan's: $\gamma{=}\frac{1}{2}\iiiint\frac{d\phi_{12}}{d\mbi{R}_{12}}\frac{x{_{12}}^{2}-z{_{12}}^{2}}{\mbi{R}_{12}}{\rho_{s}}^{(2)}(z,\mbi{R}_{12})dz_{1}dv_{12}$, where $\gamma$ is the surface tension, $\phi_{12}$ is the intermolecular potential and ${\rho_{s}}^{(2)}(z,\mbi{R}_{12})$ is the excess pair density reckoned relative to an arbitrary Gibbs dividing surface. The above expression can be transformed into the form given by Bakker, $\gamma{=}\int(p_{N}-p_{T})dz_{1}$, where $p_{N}(z_{1}){=}kT\rho^{(1)}(z_{1})-\frac{1}{2}\iiint dv_{12}\int_{z_{1}-z_{12}}^{z_{1}}\frac{d\phi_{12}}{d\mbi{R}_{12}}\frac{z_{12}}{\mbi{R}_{12}}\rho^{(2)}(\zeta,\mbi{R}_{12})d\zeta$, $p_{T}(z_{1}){=}kT\rho^{(1)}(z_{1})-\frac{1}{2}\iiint dv_{12}\frac{d\phi_{12}}{d\mbi{R}_{12}}\frac{x{_{12}}^{2}}{\mbi{R}_{12}}\rho^{(2)}(z_{1},\mbi{R}_{12})$. This result coincides with that of Kirkwood and Buff which was derived by calculating stressed directly. The assumption of density discontinuity, which is often made in the theory of surface tension, is examined closely.
- INSTITUTE OF PURE AND APPLIED PHYSICSの論文
- 1953-05-25
著者
-
Harasima Akira
Tokyo Institute Of Technology
-
Harasima Akira
Tokyo Institute of Technology, Oh-Okayama, Tokyo