Prediction of a structural transition in the hard disk fluid

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

doi:10.1063/1.3491039

Cited by 9 publications

(12 citation statements)

References 39 publications

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“…11 The results obtained in Ref. 10 are immediately relevant to the present study. From our analysis and complementary numerical studies, we found for hard discs that exponentially damped oscillations can occur only up to a packing fraction φ* ∼ 0.718, a value which is in agreement with the packing fraction φ ∼ 0.723 believed to characterize the transition from the ordered solid phase to a dense fluid phase, as inferred from Mak's Monte Carlo simulations.…”

Section: Introductionsupporting

confidence: 56%

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Stability of phases of a square-well fluid within superposition approximation

Piasecki

Szymczak

Kozak

2013

The Journal of Chemical Physics

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The analytic and numerical methods introduced previously to study the phase behavior of hard sphere fluids starting from the Yvon-Born-Green (YBG) equation under the Kirkwood superposition approximation (KSA) are adapted to the square-well fluid. We are able to show conclusively that the YBG equation under the KSA closure when applied to the square-well fluid: (i) predicts the existence of an absolute stability limit corresponding to freezing where undamped oscillations appear in the long-distance behavior of correlations, (ii) in accordance with earlier studies reveals the existence of a liquid-vapor transition by the appearance of a "near-critical region" where monotonically decaying correlations acquire very long range, although the system never loses stability.

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Section: Introductionsupporting

confidence: 56%

“…Recently, the authors of the present study have developed an analytic criterion to study the asymptotic decay of correlations in hard disk and hard sphere fluids 10 and in hypersphere fluids. 11 The results obtained in Ref.…”

Section: Introductionmentioning

confidence: 99%

Stability of phases of a square-well fluid within superposition approximation

Piasecki

Szymczak

Kozak

2013

The Journal of Chemical Physics

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“…4. (In our paper 18 we found at D = 3 the threshold value 34.81 for the parameter considered by Kirkwood. et al 20 , and equal to 2λ of the present paper).…”

Section: Iterative Solution Of the Integral Equationmentioning

confidence: 66%

Structural transitions in hypersphere fluids: Predictions of Kirkwood's approximation

Piasecki

Szymczak

Kozak

2011

The Journal of Chemical Physics

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We use an analytic criterion for vanishing of exponential damping of correlations developed previously (Piasecki et al, J. Chem. Phys., 133, 164507, 2010) to determine the threshold volume fractions for structural transitions in hard sphere systems in dimensions D=3,4,5 and 6, proceeding from the YBG hierarchy and using the Kirkwood superposition approximation. We conclude that the theory does predict phase transitions in qualitative agreement with numerical studies. We also derive, within the superposition approximation, the asymptotic form of the analytic condition for occurence of a structural transition in the D → ∞ limit .

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“…Here, the true values ofB 3 have been used, but we have checked that the curves are practically indistinguishable from those obtained ifB 3 is replaced byB app 3 as given in Eq. (17). While the mapping (21) does a good job for not too disparate mixtures (say, m 2 < 2 or, equivalently,B 2 > 1.5), it clearly fails for the mixtures B4-B8, even in the stable region.…”

Section: Assessment Of the Mappingmentioning

confidence: 99%

“…For more detailed information on these issues, see Refs. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Equation of state of polydisperse hard-disk mixtures in the high-density regime

et al. 2017

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A proposal to link the equation of state of a monocomponent hard-disk fluid to the equation of state of a polydisperse hard-disk mixture is presented. Event-driven molecular dynamics simulations are performed to obtain data for the compressibility factor of the monocomponent fluid and of 26 polydisperse mixtures with different size distributions. Those data are used to assess the proposal and to infer the values of the compressibility factor of the monocomponent hard-disk fluid in the metastable region from those of mixtures in the high-density region. The collapse of the curves for the different mixtures is excellent in the stable region. In the metastable regime, except for two mixtures in which crystallization is present, the outcome of the approach exhibits a rather good performance. The simulation results indicate that a (reduced) variance of the size distribution larger than about 0.01 is sufficient to avoid crystallization and explore the metastable fluid branch.

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Prediction of a structural transition in the hard disk fluid

Cited by 9 publications

References 39 publications

Stability of phases of a square-well fluid within superposition approximation

Stability of phases of a square-well fluid within superposition approximation

Structural transitions in hypersphere fluids: Predictions of Kirkwood's approximation

Equation of state of polydisperse hard-disk mixtures in the high-density regime

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