A Conjecture Concerning the Symmetries of Planar Nets and the Hard disk Freezing Transition

Kozak, John J.; Brzezinski, Jacek; Rice, Stuart A.

doi:10.1021/jp806287e

Cited by 14 publications

(15 citation statements)

References 32 publications

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“…The values of κ(ξ) predicted with the use of Eq. (38) are in good agreement with the decay of the amplitude of H(x) determined by the iterative solution of integral equation (19). Plotting the absolute value of H(x) on a logarithmic plot, and fitting it by the single mode αe κ ′ x , we obtain values of κ ′ which are slightly below those obtained by solving Eq.…”

Section: A Breakdown Of the Methods Used For Attractive Interactionssupporting

confidence: 83%

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Prediction of a structural transition in the hard disk fluid

Piasecki

Szymczak

Kozak

2010

The Journal of Chemical Physics

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Starting from the second equilibrium equation in the BBGKY hierarchy under the Kirkwood superposition closure, we implement a new method for studying the asymptotic decay of correlations in the hard disk fluid in the high density regime. From our analysis and complementary numerical studies, we find that exponentially damped oscillations can occur only up to a packing fraction η * ∼ 0.718, a value which is in substantial agreement with the packing fraction, η ∼ 0.723, believed to characterize the transition from the ordered solid phase to a dense fluid phase, as inferred from Phys. 18, 1040Phys. 18, (1950]. Finally, we show that our method confirms the absence of any structural transition in hard rods for the entire range of densities below close packing.

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Section: A Breakdown Of the Methods Used For Attractive Interactionssupporting

confidence: 83%

“…3 is the fact that the root becomes purely imaginary at A = A * ≈ 15.1. This point can be made more precise by analyzing when the equation (38) (38) implies the condition…”

Section: A Breakdown Of the Methods Used For Attractive Interactionsmentioning

confidence: 99%

Prediction of a structural transition in the hard disk fluid

Piasecki

Szymczak

Kozak

2010

The Journal of Chemical Physics

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“…However, one very general class of first order phase transitions is purely entropy driven. One of such systems, namely non-interacting hard disks in two-dimensions, has been studied extensively theoretically in the last decades-and is still not fully understood [61][62][63][64][65]. This system can be seen as a simplified model of our system of adsorbed CuPc molecules (an even more accurate description are non-interacting hard squares, which is, however, less frequently studied [64,66]).…”

Section: Details Of the Phase Transformationmentioning

confidence: 99%

Towards functionalization of graphene:in situstudy of the nucleation of copper-phtalocyanine on graphene

2016

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Molecular films present an elegant way for the uniform functionalization or doping of graphene. Here, we present an in situ study on the initial growth of copper phthalocyanine (CuPc) on epitaxial graphene on Ir(111). We followed the growth up to a closed monolayer with low energy electron microscopy and selected area electron diffraction (μLEED). The molecules coexist on graphene in a disordered phase without long-range order and an ordered crystalline phase. The local topography of the graphene substrate plays an important role in the nucleation process of the crystalline phase. Graphene flakes on Ir(111) feature regions that are under more tensile stress than others. We observe that the CuPc molecules form ordered domains initially on those graphene regions that are closest to the fully relaxed lattice. We attribute this effect to a stronger influence of the underlying Ir(111) substrate for molecules adsorbed on those relaxed regions. OPEN ACCESS RECEIVED

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“…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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A Conjecture Concerning the Symmetries of Planar Nets and the Hard disk Freezing Transition

Cited by 14 publications

References 32 publications

Prediction of a structural transition in the hard disk fluid

Prediction of a structural transition in the hard disk fluid

Towards functionalization of graphene:in situstudy of the nucleation of copper-phtalocyanine on graphene

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

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