Surface tension

The surface tension, $\gamma$, is a measure of the work required to create a surface. In the Canonical ensemble: two phases;

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

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

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, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu \equiv (\partial A/\partial N)_{V,T} } , as a function of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N } shows a loop.

Using basic thermodynamic procedures (Maxwell construction) it is possible to compute the densities of the two phases; Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_v, \rho_l }

• Explicit interface

References

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