Global isomorphism between the Lennard-Jones fluids and the Ising model

The Journal of Chemical Physics

2013

Self Cite

The relation between the critical compressibility factors Zc of the Lennard-Jones fluid and the Lattice Gas (Ising model) is derived within the global isomorphism approach. On this basis, we obtain the alternative form for the value of the critical compressibility factor which is different from widely used phenomenological Timmermans relation. The estimates for the critical pressure Pc and Zc of the Lennard-Jones fluid are obtained in case of two and three dimensions. The extension of the formalism is proposed to include the Pitzer's acentric factor into consideration.

Section: Introductionmentioning

confidence: 99%

The critical compressibility factor of fluids from the global isomorphism approach

The Journal of Chemical Physics

2013

Self Cite

“…where d is the dimension [15]. So that for LJ in 2D and 3D we have z ¼ 1=3 and z ¼ 1=2 correspondingly.…”

Section: The Relation Between the Thermodynamic Potentials Of The Flumentioning

confidence: 94%

“…Recently, simple geometrical formulation of the results on the Zeno line, the LRD and the triangle of liquid-gas states was proposed in [14] and developed in series of publications [15][16][17]. It is based on the fact that the lines of the phase equilibria determine the partitions for the space of thermodynamic states.…”

Section: ð3:5þmentioning

confidence: 98%

See 1 more Smart Citation

Global Isomorphism Approach: Main Results and Perspectives

Bulavin

Cheplak

Springer Proceedings in Physics

2015

In this chapter we review main results of the Global Isomorphism approach and discuss possible routes for further studies. The approach is based on the minimal geometric reformulation of the (approximate) linearities of the binodal diameter and the unit compressibility line (Batschinsky law). Explicit relations between the thermodynamic functions of the Lattice Gas model and the fluid within the framework of the approach proposed earlier in [V.L. Kulinskii, J. Phys. Chem. B 114 2852 (2010)] are discussed. On this basis we show that the critical compressibility factor of molecular fluids can be related with that of the lattice gas. We show how the associative properties of a fluid can be taken into account via the structure of the isomorphic lattice. Also we derive the relation between the entropies of a fluid and its lattice analog. The entropy of the fluid is decomposed into symmetrical and asymmetrical parts. We demonstrate that such decomposition is consistent with the basic Clausius-Clapeyron relation and the binodal asymmetry represented by the law of the rectilinear diameter.

“…Since its attractive part has asymptotic behavior ∼ −r −6 , it is possible to sow that z = D 6 (12) where D is the spatial dimension and 6 is the power the attractive part of the potential [21]. The relation between the parameter Φ 0 and the lattice gas interaction parameter ε in Eq.…”

Section: Global Isomorphism and The Zeno-linementioning

confidence: 99%

Surface tension of molecular liquids: Lattice gas approach

Maslechko

Glavatskiy

Journal of Molecular Liquids

2017

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.