Thermodynamic consistency of energy and virial routes: An exact proof within the linearized Debye-Hückel theory

Journal of Chemical Physics

Volumn 131, Issue 18, 2009, Pages

  Santos, Andŕs ^a   Fantoni, Riccardo ^b   Giacometti, Achille ^c  

^a UNIVERSITY OF EXTREMADURA   (Spain)

^b NATIONAL INSTITUTE FOR THEORETICAL PHYSICS NITHEP   (South Africa)

^c CA' FOSCARI UNIVERSITY OF VENICE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ENERGY ROUTE; LIQUID STATE; THERMODYNAMIC CONSISTENCY;

LINEARIZATION;

EID: 72949085930     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3265991     Document Type: Article

References (21)

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10. This can be quickly established by starting from the definition of the Helmholtz free energy F=U-TS (S being the entropy), so that P=- (F/V) Β,N, Z=ρ [ (ΒF/N) /ρ] Β, and U= [ (ΒF) /Β] N,V. Equation then follows immediately.
11. In the nonlinear Debye-Hückel theory, the potential of mean force follows the relation -Β [ψ (r) -φ (r)] =w (r), where w̃ (k) is still given by Eq.. Note that within the LDH approximation, h (r) =f (r) +w (r) +w (r) f (r). Upon dropping the last nonlinear term, using the Ornstein-Zernike relation in k -space, h̃ (k) = c̃ (k) / [1-ρ c̃ (k)], and transforming back to real space, one finds c (r) =f (r). This can be further reduced to the MSA approximation (extended to all r) c (r) =-Βφ (r) for bounded potentials and high temperatures (see below).
12. Note that the LDH theory was originally devised for Coulomb potential where it is justified for distances larger than the Debye length (and sufficiently high temperatures). For bounded potentials (and again sufficiently high temperatures), the region of reliability is extended to all distances.
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14. See also B. M. Mladek, M. J. Fernaud, G. Kahl, and M. Neumann, Condens Matter Phys. 8, 135 (2005).
15. C. N. Likos, Phys. Rep. 0370-1573 348, 267 (2001). 10.1016/S0370-1573(00) 00141-1
16. 106 MC steps (one particle move per step). The pressure was determined from the virial equation through analysis of the pair correlation function at the singularities of the potential.
17. A. G. Schlijper, M. M. Telo de Gama, and P. G. Ferreira, J. Chem. Phys. 0021-9606 98, 1534 (1993). 10.1063/1.464269
18. The HNC closure can also be derived from a variational principle (see Ref.). The functional evaluated at its extremum is proportional to the excess Helmholtz free energy of the fluid and this ensures thermodynamic consistency between the virial and energy routes. In this context, see W. Olivares and D. A. McQuarrie, J. Chem. Phys. 0021-9606 65, 3604 (1976) 10.1063/1.433545;
19. R. Fantoni and G. Pastore, J. Chem. Phys. 0021-9606 119, 3810 (2003). 10.1063/1.1590642
20. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York, 1975).
21. In this respect, note that the Percus-Yevick theory, which retains all linear chains but only a subset of netted chains in the diagrammatic expansion of y (r), yields in general inconsistent energy and virial equations of state.