Communication: Nonexistence of a critical point within the Kirkwood superposition approximation

Piasecki, J.; Szymczak, Piotr; Kozak, John J.

doi:10.1063/1.4824388

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…Let us now see that Eq. ( 38) is incompatible with the existence of a critical point, i.e., the approximation (38) is incompatible with the exact relation (11) (with k = 2) near the critical point [2]. To that end, we start by assuming that a critical point does exist.…”

Section: Kirkwood's Superposition Approximationmentioning

confidence: 99%

“…A well-known example is the Kirkwood superposition (KSA) approximation discussed in Section 5. It turns out that this approximation applied to the exact hierarchy yields a closed equation for the pair correlation function inconsistent with a critical behaviour [2]. In Section 6 we present arguments suggesting the impossibility of describing criticality even within generalised superposition approximations (GSA) where higher order correlation functions are approximated in terms of the lower order ones.…”

Section: Introductionmentioning

confidence: 99%

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Multi-particle critical correlations

Santos

Piasecki

2015

Molecular Physics

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We study the role of multi-particle spatial correlations in the appearance of a liquid-vapour critical point. Our analysis is based on the exact infinite hierarchy of equations relating spatial integrals of $(k+1)$-particle correlations to the $k$-particle ones and their derivatives with respect to the density. Critical exponents corresponding to generalized compressibility equations resulting from the hierarchy are shown to grow linearly with the order of correlations. We prove that the critical behaviour requires taking into account correlation functions of arbitrary order. It is however only a necessary condition. Indeed, approximate closures of the hierarchy obtained by expressing higher order correlations in terms of lower order ones (Kirkwood's superposition approximation and its generalizations) turn out to be inconsistent with the critical behaviour.Comment: 14 pages, 1 figure; v2: minor change

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Section: Kirkwood's Superposition Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multi-particle critical correlations

Santos

Piasecki

2015

Molecular Physics

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Distribution Function Approach to the Stability of Fluid Phases

Kozak

Piasecki

Szymczak

2016

Advances in Chemical Physics

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Fourth Moment Sum Rule for the Charge Correlations of a Two-Component Classical Plasma

Alastuey

Fantoni

2016

J Stat Phys

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We consider an ionic fluid made with two species of mobile particles carrying either a positive or a negative charge. We derive a sum rule for the fourth moment of equilibrium charge correlations. Our method relies on the study of the system response to the potential created by a weak external charge distribution with slow spatial variations. The induced particle densities, and the resulting induced charge density, are then computed within density functional theory, where the free energy is expanded in powers of the density gradients. The comparison with the predictions of linear response theory provides a thermodynamical expression for the fourth moment of charge correlations, which involves the isothermal compressibility as well as suitably defined partial compressibilities. The familiar Stillinger-Lovett condition is also recovered as a by-product of our method, suggesting that the fourth moment sum rule should hold in any conducting phase. This is explicitly checked in the low density regime, within the Abe-Meeron diagrammatical expansions. Beyond its own interest, the fourth-moment sum rule should be useful for both analyzing and understanding recently observed behaviours near the ionic critical point.

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Communication: Nonexistence of a critical point within the Kirkwood superposition approximation

Cited by 3 publications

References 8 publications

Multi-particle critical correlations

Multi-particle critical correlations

Distribution Function Approach to the Stability of Fluid Phases

Fourth Moment Sum Rule for the Charge Correlations of a Two-Component Classical Plasma

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