Surface tension

The surface tension, $\gamma$, is a measure of the work required to create a surface.

Thermodynamics

In the Canonical ensemble the surface tension is formally given as:

$\gamma ={\frac {\partial A(N,V,T,{\mathcal {A}})}{\partial {\mathcal {A}}}}$;

where

• $N$ is the number of particles
• $V$ is the volume
• $T$ is the temperature
• ${\mathcal {A}}$ is the surface area
• $A$ is the Helmholtz energy function

Computer Simulation

A review on different techniques to compute surface (interface) tension can be found in the paper by Gloor et al.

Liquid-Vapour Interfaces of one component systems

Binder procedure

For given conditions of volume and temperature, the Helmholtz energy function is computed as a function of the number of molecules:

$A(N;V,T)$

The calculation is usually carried out using Monte Carlo simulation

If liquid-vapour equilibrium occurs, the plot of the chemical potential, $\mu \equiv (\partial A/\partial N)_{V,T}$, as a function of $N$ shows a loop.

Using basic thermodynamic procedures (Maxwell construction) it is possible to compute the densities of the two phases; $\rho _{v},\rho _{l}$

References

1. K. Binder "Monte Carlo calculation of the surface tension for two- and three-dimensional lattice-gas models", Physical Review A 25 pp. 1699 - 1709 (1982)

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