A Monte Carlo test of the Fisher–Nakanishi–Scaling theory for the capillary condensation critical point

Dillmann, O.; Janke, Wolfhard; Müller, Marcus; Binder, Kurt

doi:10.1063/1.1350574

Cited by 34 publications

(40 citation statements)

References 94 publications

(134 reference statements)

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“…This becomes most transparent for the case of an Ising magnet (or, equivalently, the lattice gas model), where in the bulk there is a symmetry between the coexisting "spin up" and "spin down" phases. However, in the thin film, this symmetry may be broken by a surface magnetic field H 1 [4,5,11,37,38]. While phase coexistence in the bulk occurs for bulk magnetic field H = 0, coexistence in the thin film now requires a nonzero bulk field (with a sign opposite to that of the surface field H 1 ).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…The scaling functionsf ± , where the signs refer to the sign of t, are discussed in more detail in Refs. [5,11]. Here, we only infer from Eq.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Of course, the smooth decrease of these "effective" values can only be taken as a very rough description of the theoretically expected crossover scaling scenario [8,9,10,11]. For the case of D = 5 and hard-wall boundary conditions, a more elaborate analysis is presented in Ref.…”

Section: Model and Simulation Techniquementioning

confidence: 99%

“…Here, we have assumed that the amplitudesÂ i are functions of the aspect ratio D/L; such a dependence can be motivated by finite size scaling arguments [10,11]. In view of the rather large error bars in δ L,cr in Fig.…”

Section: B Binodal and Coexistence Diametermentioning

confidence: 99%

“…Our work complements earlier work [27,28], based on Gibbs ensemble Monte Carlo, which focused on the non-critical regime of the phase diagram. In this work, also the critical regime is considered, in order to compare to theoretical predictions for the shift in critical parameters as function of the film thickness [5,11]. We consider a colloid-to-polymer size ratio q = σ p /σ c = 0.8, with σ c the colloid diameter and σ p the polymer diameter of gyration, since for this particular size ratio, accurate information on the bulk and interfacial properties is available [29,30].…”

Section: Introductionmentioning

confidence: 99%

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Phase diagram and structure of colloid-polymer mixtures confined between walls

et al. 2006

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The influence of confinement, due to flat parallel structureless walls, on phase separation in colloid-polymer mixtures, is investigated by means of grand-canonical Monte Carlo simulations. Ultra-thin films, with thicknesses between D = 3 − 10 colloid diameters, are studied. The AsakuraOosawa model [J. Chem. Phys. 22, 1255(1954] is used to describe the particle interactions. To simulate efficiently, a "cluster move" [J. Chem. Phys. 121, 3253 (2004)] is used in conjunction with successive umbrella sampling [J. Chem. Phys. 120, 10925 (2004)]. These techniques, when combined with finite size scaling, enable an accurate determination of the unmixing binodal. Our results show that the critical behavior of the confined mixture is described by "effective" critical exponents, which gradually develop from values near those of the two-dimensional Ising model, to those of the three-dimensional Ising model, as D increases. The scaling predictions of Fisher and Nakanishi [J. Chem. Phys. 75, 5875 (1981)] for the shift of the critical point are compatible with our simulation results. Surprisingly, however, the colloid packing fraction at criticality approaches its bulk (D → ∞) value non-monotonically, as D is increased. Far from the critical point, our results are compatible with the simple Kelvin equation, implying a shift of order 1/D in the coexistence colloid chemical potential. We also present density profiles and pair distribution functions for a number of state points on the binodal, and the influence of the colloid-wall interaction is studied.

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Section: Theoretical Backgroundmentioning

confidence: 99%

“…The scaling functionsf ± , where the signs refer to the sign of t, are discussed in more detail in Refs. [5,11]. Here, we only infer from Eq.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Model and Simulation Techniquementioning

confidence: 99%

Section: B Binodal and Coexistence Diametermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Phase diagram and structure of colloid-polymer mixtures confined between walls

et al. 2006

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Statistical Surface Thermodynamics

Patrykiejew

Sokołowski

Pizio

2016

Surface and Interface Science

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Modeling and Simulation of Structure, Thermodynamics, and Transport of Fluids in Molecular Confinements

Fritzsche¹,

Haberlandt²,

Vörtler³

2004

Molecules in Interaction With Surfaces and Interfaces

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Abstract. The theoretical understanding of the properties of molecular confined fluids is crucial for many applications in science and technology, which reach from molecules enclosed in porous media (zeolites) to aqueous phases at biological active interfaces (biomembranes). We discuss these complicated many-particle systems -which usually are to complex for an analytical statistical-mechanical treatment-by means of molecular simulation methods. We focus on advanced Monte Carlo techniques to study structure and thermodynamics of inhomogeneous fluids and on recent molecular dynamics methods to describe transport phenomena in microporous materials.The state of the art in the field is demonstrated by reviewing selected results of our recent computer simulations. We present both Monte Carlo studies of equilibrium properties of geometrically restricted fluids (such as spatial distribution functions, thermodynamic pressures and phase equilibria) and molecular dynamics studies of dynamical processes in nanoporous media, particularly diffusion of guest molecules in zeolites. The diffusion mechanism is analyzed in detail by computer simulations and theoretical analytical treatment as well.

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A Monte Carlo test of the Fisher–Nakanishi–Scaling theory for the capillary condensation critical point

Cited by 34 publications

References 94 publications

Phase diagram and structure of colloid-polymer mixtures confined between walls

Phase diagram and structure of colloid-polymer mixtures confined between walls

Statistical Surface Thermodynamics

Modeling and Simulation of Structure, Thermodynamics, and Transport of Fluids in Molecular Confinements

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