Critical-point and coexistence-curve properties of the Lennard-Jones fluid: A finite-size scaling study

Wilding, Nigel B.

doi:10.1103/physreve.52.602

Cited by 437 publications

(534 citation statements)

References 61 publications

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“…Once one has ␤ c ͑L͒ and the corresponding ␤⌬ c ͑L͒, using the appropriate reweighting strategies one can compute at those conditions the system size dependent pseudocritical quantities c ͑L͒, x c ͑L͒, and ␦x c ͑L͒. These quantities are expected to fulfill for not too small systems 42,44 …”

Section: Analysis Of the Simulation Resultsmentioning

confidence: 99%

“…It can be seen that as the system size increases, the shape of these distributions approaches the universal curve. 42 According to finite-size scaling procedures, 42,44 the following asymptotic behavior is expected for ␤ c ͑N͒:…”

Section: Analysis Of the Simulation Resultsmentioning

confidence: 99%

“…For ␤ Ͼ ␤ c ͑␤p͒ the composition of the two phases at equilibrium will be given by The quantity G 4 ͑N͒, defined through the second and fourth moments of the mole fraction probability distribution at ͑␤⌬ e ͒, is closely related to the reduced fourth order cumulant of the distribution. 36,41,42 The behavior of G 4 ͑N͒ with the system size is expected to fulfill 36,42 lim…”

Section: Analysis Of the Simulation Resultsmentioning

confidence: 99%

“…42,43 For systems with critical behavior belonging to the three dimensional ͑3D͒ Ising universality class that are simulated on cubic boxes with PBC, we have 43 G c Ϸ 0.698.…”

Section: Analysis Of the Simulation Resultsmentioning

confidence: 99%

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Demixing in binary mixtures of apolar and dipolar hard spheres

Almarza

Lomba

Martín

et al. 2008

The Journal of Chemical Physics

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We study the demixing transition of mixtures of equal size hard spheres and dipolar hard spheres using computer simulation and integral equation theories. Calculations are carried out at constant pressure, and it is found that there is a strong correlation between the total density and the composition. The critical temperature and the critical total density are found to increase with pressure. The critical mole fraction of the dipolar component on the contrary decreases as pressure is augmented. These qualitative trends are reproduced by the theoretical approaches that on the other hand overestimate by far the value of the critical temperature. Interestingly, the critical parameters for the liquid-vapor equilibrium extrapolated from the mixture results in the limit of vanishing neutral hard sphere concentration agree rather well with recent estimates based on the extrapolation of charged hard dumbbell phase equilibria when dumbbell elongation shrinks to zero ͓G. Ganzenmüller and P.

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Section: Analysis Of the Simulation Resultsmentioning

confidence: 99%

Section: Analysis Of the Simulation Resultsmentioning

confidence: 99%

Section: Analysis Of the Simulation Resultsmentioning

confidence: 99%

“…42,43 For systems with critical behavior belonging to the three dimensional ͑3D͒ Ising universality class that are simulated on cubic boxes with PBC, we have 43 G c Ϸ 0.698.…”

Section: Analysis Of the Simulation Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Demixing in binary mixtures of apolar and dipolar hard spheres

Almarza

Lomba

Martín

et al. 2008

The Journal of Chemical Physics

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“…The critical temperature was taken as T C = 1/4w = 1.1876, and density as ρ C = 0.3197σ −3 (ref. 27). We fixed the density, and varied the temperature.…”

Section: Monte Carlo Simulationmentioning

confidence: 99%

Bridging length scales in colloidal liquids and interfaces from near-critical divergence to single particles

2007

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Boiling and condensation are among the best recognized phase transitions of condensed matter. Approaching the critical point, a liquid becomes indistinguishable from its vapour, the interfacial thickness diverges and the system is dominated by long-wavelength density fluctuations 1 . Long wavelength usually means hundreds of particle diameters, but here we consider the limits of this assumption, using a mesoscopic analogue of simple liquids, a colloid-polymer mixture 2,3 . We simultaneously visualize both the colloidal particles and near-critical density fluctuations, and reveal particle-level images of the critical clusters and liquid-gas interface. Surprisingly, we find that critical scaling does not break down until the correlation length approaches the size of the constituent particles, where there is a smooth transition to non-critical classical behaviour. Our results could provide a framework for unifying the disparate particle and correlation length scales, and bring new insight into the nature of the liquid-gas interface and the limit of the critical regime.Among the simplest pictures of two different phases is that of a magnet, whose sites can only point up or down, and do so depending solely on their neighbours. This Ising model in fact describes a general class of phase transitions 1 , from the original ferromagnetic transition in magnets to phase separation in alloys, binary liquids, emulsions and polymers, and the liquidgas transition in simple liquids and colloid-polymer mixtures. Although we shall consider the latter two cases, this work has implications for many systems that belong to the same universality class. Close to the critical point, many physical properties such as the bulk correlation length, ξ B , are described by simple scaling, such as ξ B = ξ 0 B ε −ν , where ξ 0 B is the bare correlation length (or critical amplitude) and ε = (T − T C )/T C is a reduced temperature where T is the temperature and T C is the critical temperature. The critical exponent ν = 0.5 according to mean-field theory, and very close to the critical point there is a crossover to ν = 0.63, 'three-dimensional (3D) Ising universality' 4 . We shall refer to the entire scaling regime, both mean field and 3D Ising as the critical region. Although criticality is well understood, the point at which it breaks down has so far received relatively little attention. Conventional theory of critical phenomena assumes a large separation in length scales, that is, that the correlation length is decoupled from other length scales. This length-scale separation lies at the heart of critical universality, implying that the microscopic details are irrelevant. Whereas length-scale coupling has been considered in complex fluids with much longer length scales, such as polymer 5 and ionic 6 solutions, we consider here a more general limit: the case that the correlation length approaches that of the constituent particles. Although it is difficult to approach this limit experimentally in molecular systems, a colloidpolymer mixture provides...

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Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

Müller¹

1999

Macromol. Theory Simul.

106

113

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SUMMARY: Computer simulation studies on the miscibility behavior and single chain properties in binary polymer blends are reviewed. We consider blends of various architectures in order to identify important architectural parameters on a coarse grained level and study their qualitative consequences for the miscibility behavior. The phase diagram, the relation between the exchange chemical potential and the composition, and the intermolecular pair correlation functions for symmetric blends of linear chains, blends of cyclic polymers, blends with an asymmetry in cohesive energies, blends with different chain lengths, blends with distinct monomer shapes, and blends with a stiffness disparity between the components are discussed. For strictly symmetric blends the Flory-Huggins theory becomes quantitatively correct in the long chain length limit, when the v parameter is identified via the intermolecular pair correlation function. For small chain lengths composition fluctuations are important. They manifest themselves in 3D Ising behavior at the critical point and an upward parabolic curvature of the v parameter from small-angle neutron scattering close to the critical point. The ratio between the mean field estimate and the true critical temperature decreases like v p aqb 3 for long chain lengths. The chain conformations in the minority phase of a symmetric blend shrink as to reduce the number of energeticaly unfavorable interactions. Scaling arguments, detailed self-consistent field calculations and Monte Carlo simulations of chains with up to 512 effective segments agree that the conformational changes decrease around the critical point like 1a N p . Other mechanisms for a composition dependence of the single chain conformations in asymmetric blends are discussed. If the constituents of the blends have non-additive monomer shapes, one has a large positive chain-length-independent entropic contribution to the v parameter. In this case the blend phase separates upon heating at a lower critical solution temperature. Upon increasing the chain length the critical temperature approaches a finite value from above. For blends with a stiffness disparity an entropic contribution of the v parameter of the order 10 -3 is measured with high accuracy. Also the enthalpic contribution increases, because a back folding of the stiffer component is suppressed and the stiffer chains possess more intermolecular contacts. Two aspects of the single chain dynamics in blends are discussed: (a) The dynamics of short non-entangled chains in a binary blend are studied via dynamic Monte Carlo simulations. There is hardly any coupling between the chain dynamics and the thermodynamic state of the mixture. Above the critical temperatures both the translational diffusion and the relaxation of the chain conformations are independent of the temperature. (b) Irreversible reactions of a small fraction of reactive polymers at a strongly segregated interface in a symmetric binary polymer blend are investigated. End-functionalized homopolymers of different...

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Critical-point and coexistence-curve properties of the Lennard-Jones fluid: A finite-size scaling study

Cited by 437 publications

References 61 publications

Demixing in binary mixtures of apolar and dipolar hard spheres

Demixing in binary mixtures of apolar and dipolar hard spheres

Bridging length scales in colloidal liquids and interfaces from near-critical divergence to single particles

Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

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