Differential theory of fluids below the critical temperature: Study of the Lennard-Jones fluid and of a model of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mrow><mml:mn>60</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Tau, M.; Parola, Alberto; Pini, Davide; Reatto, L.

doi:10.1103/physreve.52.2644

Cited by 64 publications

(54 citation statements)

References 20 publications

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“…On the other hand, the more cumbersome SCOZA technique can provide us with highly precise results for the phase boundaries and it remains accurate even near criticality [33]. The other concept is the hierarchical reference theory (HRT) [30,[34][35][36], that combines features of the renormalization group theory (RGT) and theoretical liquid-state approaches and allows to reproduce some critical exponents more precisely with respect to the MSA. For instance, the critical exponent β (which gives the curvature of the coexistence curve near the critical point) takes the values 7/20 and 0.345 within the SCOZA and HRT, respectively.…”

Section: Introductionmentioning

confidence: 99%

Ising fluids in an external magnetic field: An integral equation approach

et al. 2004

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The phase behavior of Ising spin fluids is studied in the presence of an external magnetic field with the integral equation method. The calculations are performed on the basis of a soft mean spherical approximation using an efficient algorithm for solving the coupled set of the Ornstein-Zernike equations, the closure relations, and the external field constraint. The phase diagrams are obtained in the whole thermodynamic space including the magnetic field H for a wide class of Ising fluid models with various ratios R for the strengths of magnetic to nonmagnetic Yukawa-like interactions. The influence of varying the inverse screening lengths z 1 and z 2 , corresponding to the magnetic and nonmagnetic Yukawa parts of the potential, is investigated too. It is shown that changes in R as well as in z 1 and z 2 can lead to different topologies of the phase diagrams. In particular, depending on the value of R, the critical temperature of the liquid-gas transition either decreases monotonically, behaves nonmonotonically, or increases monotonically with increasing H. The paraferro magnetic transition is also affected by changes in R and the screening lengths. At H = 0, the Ising fluid maps onto a simple model of a symmetric nonmagnetic binary mixture. For H → ∞, it reduces to a pure nonmagnetic 1 fluid. The results are compared with available simulations and the predictions of other theoretical methods. It is demonstrated, that the mean spherical approximation appears to be more accurate compared with mean field theory, especially for systems with short ranged attraction potentials (when z 1 and z 2 are large). In the Kac limit z 1 , z 2 → +0, both approaches tend to nearly the same results. PACS number(s): 64.70. Fx, 05.70.Fh, 75.50.Mm

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Section: Introductionmentioning

confidence: 99%

Ising fluids in an external magnetic field: An integral equation approach

et al. 2004

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“…The unusual aspects of the phase behavior have occasioned several studies on the C 60 model by means of refined theoretical tools, like for instance integral equation theories for the fluid phase [13,16], various density functional approximations [14,20,21], and the hierarchical reference theory [22]. Preliminary studies have been recently carried out, based on the Modified Hypernetted Chain approach (MHNC, [23]), solved under a global thermodynamic consistency constraint [24], and on the Self-Consistent Ornstein-Zernike Approximation (SCOZA [25,26,27]) [28].…”

Section: Introductionmentioning

confidence: 99%

Theoretical description of phase coexistence in modelC60

et al. 2003

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We have investigated the phase diagram of a pair interaction model of C60 fullerene [L. A. Girifalco, J. Phys. Chem. 96, 858 (1992)], in the framework provided by two integral equation theories of the liquid state, namely the Modified Hypernetted Chain (MHNC) implemented under a global thermodynamic consistency constraint, and the Self-Consistent Ornstein-Zernike Approximation (SCOZA), and by a Perturbation Theory (PT) with various degrees of refinement, for the free energy of the solid phase.We present an extended assessment of such theories as set against a recent Monte Carlo study of the same model [D. Costa, G. Pellicane, C. Caccamo, and M. C. Abramo, J. Chem. Phys. 118, 304 (2003)]. We have compared the theoretical predictions with the corresponding simulation results for several thermodynamic properties like the free energy, the pressure, and the internal energy. Then we have determined the phase diagram of the model, by using either the SCOZA, or the MHNC, or the PT predictions for one of the coexisting phases, and the simulation data for the other phase, in order to separately ascertain the accuracy of each theory. It turns out that the overall appearance of the phase portrait is reproduced fairly well by all theories, with remarkable accuracy as for the melting line and the solid-vapor equilibrium. All theories show a more or less pronounced discrepancy with the simulated fluid-solid coexistence pressure, above the triple point. The MHNC and SCOZA results for the liquid-vapor coexistence, as well as for the corresponding critical points, are quite accurate; the SCOZA tends to underestimate the density corresponding to the freezing line. All results are discussed in terms of the basic assumptions underlying each theory.We have selected the MHNC for the fluid and the first-order PT for the solid phase, as the most accurate tools to investigate the phase behavior of the model in terms of purely theoretical approaches. It emerges that the use of different procedures to characterize the fluid and the solid phases provides a semiquantitative reproduction of the thermodynamic properties of the C60 model at issue.The overall results appear as a robust benchmark for further theoretical investigations on higher order Cn>60 fullerenes, as well as on other fullerene-related materials, whose description can be based on a modelization similar to that adopted in this work.

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“…Consequently, for the calculations reported below we resort to step sizes ∆Q pre-determined in a way analogous to that employed in earlier applications 6,19 ; still, monitoring and assessing suitable components of the solution vector in terms of ǫ # as described in sub-section III E of ref. 19 may yield a wealth of information on the numerical process and its evolution.…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…While applicability of hrt to a number of interesting systems, ranging from a lattice gas or Ising model 11 to various one-component fluids [6][7][8] even including three-body interactions 13,14 , internal degrees of freedom 15 , or non-hard-core reference systems 16 , was demonstrated early on, the main focus of research on hrt has since shifted to the richer phase behavior of binary systems [16][17][18] . Nevertheless, in the light of hrt's high promise and low penetration into the liquid physics community, further study and critical assessment of this theory seem worthwhile, even and foremost in the case of simple one-component fluids: indeed, it is in this comparatively simple setting that we may gain important insights into the numerical side of the theory, and barring special mechanisms relevant to some specific model system only, any problems uncovered here must be expected to haunt more advanced applications of hrt, too.…”

Section: Introductionmentioning

confidence: 99%

“…Asymptotically close to the critical point, on the other hand, renormalization group (rg) theory is the instrument of choice for describing the fluid; in general, however, rg approaches do not allow one to derive non-universal quantities from microscopic information only, i. e. from knowledge of the forces acting between the fluid's particles alone. One of the theories devised to bridge the conceptual gap between these complementary approaches is the Hierarchical Reference Theory (hrt) first put forward by Parola and Reatto [2][3][4][5][6][7][8][9][10][11][12][13] : In this theory the introduction of a cut-off wavenumber Q inspired by momentum space rg theory and, for every value of Q, of a renormalized potential v (Q) (r) means that only non-critical systems have to be considered at any stage of the calculation; consequently, integral equations may successfully be applied to every system with Q > 0, and critical behavior characterized by non-classical critical exponents is recovered only in the limit Q → 0.…”

Section: Introductionmentioning

confidence: 99%

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The hierarchical reference theory as applied to square well fluids of variable range

Reiner

Kahl

2002

The Journal of Chemical Physics

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Continuing our investigation into the numerical properties of the Hierarchical Reference Theory, we study the square well fluid of range λ from slightly above unity up to 3.6. After briefly touching upon the core condition and the related decoupling assumption necessary for numerical calculations, we shed some light on the way an inappropriate choice of the boundary condition imposed at high density may adversely affect the numerical results; we also discuss the problem of the partial differential equation becoming stiff for close-to-critical and sub-critical temperatures. While agreement of the theory's predictions with simulational and purely theoretical studies of the square well system is generally satisfactory for λ > ∼ 2, the combination of stiffness and the closure chosen is found to render the critical point numerically inaccessible in the current formulation of the theory for most of the systems with narrower wells. The mechanism responsible for some deficiencies is illuminated at least partially and allows us to conclude that the specific difficulties encountered for square wells are not likely to resurface for continuous potentials.

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Differential theory of fluids below the critical temperature: Study of the Lennard-Jones fluid and of a model ofC60

Cited by 64 publications

References 20 publications

Ising fluids in an external magnetic field: An integral equation approach

Ising fluids in an external magnetic field: An integral equation approach

Theoretical description of phase coexistence in modelC60

The hierarchical reference theory as applied to square well fluids of variable range

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