Surface tension of molecular liquids: Lattice gas approach

Abstract

The approach of global isomorphism between the fluid and the Ising model is applied to obtain an expression for the surface tension of the Lennard-Jones fluid on the basis of the information about the Ising model. This is done in a broad interval of temperatures along the phase coexistence, and is valid both in 2D and 3D. The relation between the critical amplitudes of the surface tension of the fluid and the Ising model is derived in the vicinity of the critical point. The obtained theoretical estimates agree well with the literature results for the surface tension. The methodology is demonstrated for the 2D LJ fluid on the basis of the exact solution of the 2D Ising model and is tested for the 3D LJ fluid. As a result, an expression for the surface tension without any fitting parameter is derived.

The Line of Ideal Isothermal Compressibility

“…The latter are the two parameters defining the Z-line, and we will consider them below. One more consequence of the Z-line linearity is the existence of isomorphism between lattice and continuous systems. − More details about the Z-line can be found in ref . Here, we only note that all abovementioned regularities were found in the liquid phase.…”

The Line of the Unit Compressibility Factor (Zeno-Line) for Crystal States

“…Thus, the linearity of the Z-line is some general property for many substances and systems. It allows us to find the other regularities, for instance, the isomorphism between lattice and continuous systems. − …”

Similarity Laws for the Lines of Ideal Free Energy and Chemical Potential in Supercritical Fluids

“…Presently it is used to generate new similarity relations. For instance, it is the isomorphism between lattice and continuous systems − or new Zeno-like states for the binodal. Besides, the Z-line is used to check both the reference and semiempirical equations of states (EOS’s).…”