Gravity Effects near the Gas-Liquid Critical Point

Hohenberg, P. C.; Barmatz, M.

doi:10.1103/physreva.6.289

Cited by 140 publications

(39 citation statements)

References 26 publications

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“…Our model is similar to the linear parametric model by Schofield et al [47][48][49] and the local functional model by Upton et al 27,28,42,50 . The latter is composed of the free energy of the linear parametric model and the gradient free energy.…”

Section: Critical Behavior For T = Tcmentioning

confidence: 94%

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Casimir amplitudes and capillary condensation of near-critical fluids between parallel plates: Renormalized local functional theory

Okamoto

Ōnuki

2012

The Journal of Chemical Physics

120

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We investigate the critical behavior of a near-critical fluid confined between two parallel plates in contact with a reservoir by calculating the order parameter profile and the Casimir amplitudes (for the force density and for the grand potential). Our results are applicable to one-component fluids and binary mixtures. We assume that the walls absorb one of the fluid components selectively for binary mixtures. We propose a renormalized local functional theory accounting for the fluctuation effects. Analysis is performed in the plane of the temperature T and the order parameter in the reservoir ψ∞. Our theory is universal if the physical quantities are scaled appropriately. If the component favored by the walls is slightly poor in the reservoir, there appears a line of first-order phase transition of capillary condensation outside the bulk coexistence curve. The excess adsorption changes discontinuously between condensed and noncondensed states at the transition. With increasing T , the transition line ends at a capillary critical point T = T ca c slightly lower than the bulk critical temperature Tc. The Casimir amplitudes are larger than their critical-point values by 10-100 times at off-critical compositions near the capillary condensation line.

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Section: Critical Behavior For T = Tcmentioning

confidence: 94%

“…48,49 for detailed discussions on this model. It uses two parametric variables,r and θ, withr ≥ 0 and |θ| ≤ 1;r represents a distance to the critical point and θ an angle around it in the ψ-τ plane.…”

Section: Appendix A: Mechanical Equilibriummentioning

confidence: 99%

Casimir amplitudes and capillary condensation of near-critical fluids between parallel plates: Renormalized local functional theory

Okamoto

Ōnuki

2012

The Journal of Chemical Physics

120

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“…This length that scales inversely with the "gravitational constant" characterizing the gravitation-like potential and hence can be made arbitrarily large 33 , but the linear dimension of the simulated system in the z-direction in which this gravitation-like force acts must then be huge, also. A well-known case, where even the real gravitation potential on earth substantially disturbs the equation of state is a fluid very close to the gas-liquid critical point 40 , since there the correlation length of density fluctuations diverges, and critical fluctuations undisturbed by gravity can occur in the x, y-directions perpendicular to the gravitational force only 40 . Other cases, apart from critical points of second-order transitions, where large length scales arise that are potentially disturbed by the gravitation-like potential are associated with the formation of thick wetting layers at walls, for instance.…”

Section: Introductionmentioning

confidence: 99%

Equation of state for macromolecules of variable flexibility in good solvents: A comparison of techniques for Monte Carlo simulations of lattice models

Иванов

Spirin

et al. 2007

Phys. Rev. E

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The osmotic equation of state for the athermal bond fluctuation model on the simple cubic lattice is obtained from extensive Monte Carlo simulations. For short macromolecules (chain length N=20) we study the influence of various choices for the chain stiffness on the equation of state. Three techniques are applied and compared in order to critically assess their efficiency and accuracy: the "repulsive wall" method, the thermodynamic integration method (which rests on the feasibility of simulations in the grand canonical ensemble), and the recently advocated sedimentation equilibrium method, which records the density profile in an external (e.g. gravitation-like) field and infers, via a local density approximation, the equation of state from the hydrostatic equilibrium condition. We confirm the conclusion that the latter technique is far more efficient than the repulsive wall method, but we find that the thermodynamic integration method is similarly efficient as the sedimentation equilibrium method. For very stiff chains the onset of nematic order enforces the formation of an isotropic-nematic interface in the sedimentation equilibrium method leading to strong rounding effects and deviations from the true equation of state in the transition regime.

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“…A treatment of sedimentation in one-component systems based on the van der Waals equation of state was given by Baehr in 1954 [2,3]. Using the scalling approach to critical phenomena, Hohenberg and Barmatz [4] presented a comprehensive theory of gravitational effects in gases.…”

Section: Introductionmentioning

confidence: 99%

Sedimentation of dissolved macromolecules in the vicinity of the consolute point 1. Strictly binary systems and kinetic considerations

Ballauff

Wolf

1986

Colloid & Polymer Sci

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This paper analyzes the effect of gravity on polymer solutions near the consolute point. Calculations are carried out for monodisperse polystyrene in cyclohexane using the Flory=Huggins expression with a concentration-dependent interaction parameter for the free energy of mixing. Depending on molecular weight and distance to the demixing temperature, the influence of gravity leads to non-negligible gradients of the volume fraction in the one-phase region as well as in the two-phase region. In particular, the effect of gravity on the measurement of the coexistence curve in a finite sample is calculated explicitly.In contrast to theory, experiments show that the concentration remains constant throughout the sample over a period of days as long as the system is kept in the homogenous region. Pronounced concentration gradients, however, are established in the twophase region within approximately one day. These findings are discussed with respect to sedimentation kinetics in terms of the droplet model of critical fluids.

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Gravity Effects near the Gas-Liquid Critical Point

Cited by 140 publications

References 26 publications

Casimir amplitudes and capillary condensation of near-critical fluids between parallel plates: Renormalized local functional theory

Casimir amplitudes and capillary condensation of near-critical fluids between parallel plates: Renormalized local functional theory

Equation of state for macromolecules of variable flexibility in good solvents: A comparison of techniques for Monte Carlo simulations of lattice models

Sedimentation of dissolved macromolecules in the vicinity of the consolute point 1. Strictly binary systems and kinetic considerations

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