Interfacial properties of liquid-vapor interfaces with planar, spherical, and cylindrical geometries in mean field

Segovia-López, José G.; Romero-Rochı́n, Vı́ctor

doi:10.1103/physreve.73.021601

Phys. Rev. E

2006

DOI: 10.1103/physreve.73.021601

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Interfacial properties of liquid-vapor interfaces with planar, spherical, and cylindrical geometries in mean field

José G. Segovia-López

Vı́ctor Romero-Rochı́n

Abstract: Following the route of the stress tensor we study the free energy of a fluid liquid-vapor interface in the van der Waals approximation for planar, cylindrical and spherical interfaces. By performing a systematic expansion in powers of the inverse of the curvature radii, and appropriately defining the Gibbs dividing surface, we find unambiguous expressions for the surface tension, the spontaneous curvature, the bending rigidity and the Gaussian rigidity.

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Cited by 4 publications

References 29 publications

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Effective Hamiltonian for a liquid–gas interface fluctuating around a corrugated cylindrical substrate in the presence of van der Waals interactions

Dutka

Napiórkowski

2009

Physica A: Statistical Mechanics and its Applications

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We investigate liquid layers adsorbed at spherical and corrugated cylindrical substrates. The effective Hamiltonians for the liquid-gas interfaces fluctuating in the presence of such curved substrates are derived via the mean-field density functional theory. Their structure is compared with the Helfrich Hamiltonian which is parametrized by the bending and Gaussian rigidity coefficients. For long-ranged interparticle interactions of van der Waals type these coefficients turn out to be non-universal functions of interfacial curvatures; their form varies from one interface to another. We discuss implications of the structure of these functions on the effective Hamiltonian.

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Effective Hamiltonian for a liquid–gas interface fluctuating around a corrugated cylindrical substrate in the presence of van der Waals interactions

Dutka

Napiórkowski

2009

Physica A: Statistical Mechanics and its Applications

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Effective Hamiltonian of liquid-vapor curved interfaces in mean field

Segovia-López

Zamora

Santiago

2011

The Journal of Chemical Physics

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We analyze a one-component simple fluid in a liquid-vapor coexistence state, which forms an arbitrarily curved interface. By using an approach based on density functional theory, we obtain an exact and simple expression for the grand potential at the level of mean field approximation that depends on the density profile and the short-range interaction potential. By introducing the step-function approximation for the density profile, and using general geometric arguments, we expand the grand potential in powers of the principal curvatures of the surface and find consistency with the Helfrich phenomenological model in the second order approximation.

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Applications of computational geometry to the molecular simulation of interfaces

Usabiaga

Duque

2009

Phys. Rev. E

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The identification of the interfacial molecules in fluid-fluid equilibrium is a long-standing problem in the area of simulation. We here propose a new point of view, making use of concepts taken from the field of computational geometry, where the definition of the "shape" of a set of point is a well-known problem. In particular, we employ the α-shape construction which, applied to the positions of the molecules, selects a shape and identifies its boundary points, which we will take to define our interfacial molecules. A single parameter needs to be fixed (the "α" of the α-shape), and several proposals are examined, all leading to very similar choices. Results of this methodology are evaluated against previous proposals, and seen to be reasonable.

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Interfacial properties of liquid-vapor interfaces with planar, spherical, and cylindrical geometries in mean field

Cited by 4 publications

References 29 publications

Effective Hamiltonian for a liquid–gas interface fluctuating around a corrugated cylindrical substrate in the presence of van der Waals interactions

Effective Hamiltonian for a liquid–gas interface fluctuating around a corrugated cylindrical substrate in the presence of van der Waals interactions

Effective Hamiltonian of liquid-vapor curved interfaces in mean field

Applications of computational geometry to the molecular simulation of interfaces

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