Pressure tensor of a spherical interface

Blokhuis, Edgar M.; Bedeaux, Dick

doi:10.1063/1.462992

Cited by 108 publications

(93 citation statements)

References 14 publications

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“…͑6͒ and ͑7͒, which is a consequence of the more general observation that the local pressure tensor route is always consistent with the virial route as long as the Irving-Kirkwood definition for the pressure tensor is used. 18 However, as mentioned above, the determination from simulations of ⌬p through Eq. ͑21͒, which results in the Tolman length being determined by Eq.…”

Section: The Local Pressure Tensormentioning

confidence: 99%

“…13 It should be emphasized that this route is identical to the virial route when the IrvingKirkwood definition for the local pressure tensor is used. 18 The difference between the normal and tangential components of the pressure tensor p N ͑r͒ − p T ͑r͒ can also be determined directly from the Irving-Kirkwood expression for the pressure tensor, which involves the pair density of the spherical interface s ͑2͒ ͑r 1 , r 2 ͒, 17,18 This is the equation which is used to determine ⌬p next to the determination of the individual bulk pressures. The limits on the integration are from deep in the liquid phase to deep in the vapor phase.…”

Section: The Local Pressure Tensormentioning

confidence: 99%

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Direct determination of the Tolman length from the bulk pressures of liquid drops via molecular dynamics simulations

Giessen

Blokhuis

2009

The Journal of Chemical Physics

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An expression for the difference in pressure between a liquid drop in equilibrium with its vapor ⌬p = p ᐉ − p v is derived from previous expressions for the components of the Irving-Kirkwood pressure tensor. This expression, as well as the bulk values of the pressure tensor, is then evaluated via molecular dynamics simulations of particles interacting through a truncated Lennard-Jones potential. We determine the Tolman length ␦ from the dependence of ⌬p on the equimolar radius. We determine the Tolman length to be ␦ = −0.10Ϯ 0.02 in units of the particle diameter. This is the first determination of the Tolman length for liquid droplets via the pressure tensor route through computer simulation that is negative, in contrast to all previous results from simulation, but in agreement with results from density functional theory. In addition, we study the planar liquid-vapor interface and observe a dependence of the physical properties of the system on the system size, as measured by the surface area.

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Section: The Local Pressure Tensormentioning

confidence: 99%

Section: The Local Pressure Tensormentioning

confidence: 99%

Direct determination of the Tolman length from the bulk pressures of liquid drops via molecular dynamics simulations

Giessen

Blokhuis

2009

The Journal of Chemical Physics

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“…Particularly, different possible definitions of P U produce different values of pressure tensor in inhomogeneous fluids. 9 In this work we adopt a pressure tensor definition extensively utilized in MD simulations, 36 the components of the pressure tensor for the two body system are…”

Section: Mechanical Equilibrium and Pressure Tensormentioning

confidence: 99%

“…9,11,12,33,43 It seems that the spherical symmetry is the simplest one, and then the principal subject of several works on curved interfaces but deviations from sphericity are also studied. 33 The suspended drop on its vapor, 9,10,19 the bubble of vapor on its liquid, the fluid in contact with a spherical convex substrates ͑or cavity in the liquid͒, 11,12,19,20 and the fluid confined in a spherical vessel or pore 11,18,40 are different systems in which the spherical inhomogeneity of the fluid is central, and currently, the study of these systems are converging to the analysis of the curvature dependence of physical magnitudes. 11 Particularly relevant for PW are such works on HS systems 12 and hard wall spherical substrates.…”

Section: Introductionmentioning

confidence: 99%

Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension

Urrutia

Szybisz

2010

Journal of Mathematical Physics

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Structures of hard-sphere fluids from a modified fundamental-measure theory J. Chem. Phys. 117, 10156 (2002) This work is devoted to the exact statistical mechanics treatment of simple inhomogeneous few-body systems. The system of two hard spheres ͑HSs͒ confined in a hard spherical pore is systematically analyzed in terms of its dimensionality D. The canonical partition function and the one-and two-body distribution functions are analytically evaluated and a scheme of iterative construction of the D + 1 system properties is presented. We analyze in detail both the effect of high confinement, when particles become caged, and the low density limit. Other confinement situations are also studied analytically and several relations between the two HSs in a spherical pore, two sticked HSs in a spherical pore, and two HSs on a spherical surface partition functions are traced. These relations make meaningful the limiting caging and low density behavior. Turning to the system of two HSs in a spherical pore, we also analytically evaluate the pressure tensor. The thermodynamic properties of the system are discussed. To accomplish this statement we purposely focus in the overall characteristics of the inhomogeneous fluid system, instead of concentrate in the peculiarities of a few-body system. Hence, we analyze the equation of state, the pressure at the wall, and the fluid-substrate surface tension. The consequences of new results about the spherically confined system of two HSs in D dimension on the confined many HS system are investigated. New constant coefficients involved in the low density limit properties of the open and closed systems of many HS in a spherical pore are obtained for arbitrary D. The complementary system of many HS which surrounds a HS ͑a cavity inside of a bulk HS system͒ is also discussed.

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“…The parameter C 0 measures the profile assymetry [21,22,23] and for the sharp-kink approximation used throughout this paper it is zero. The first non-vanishing corrections to the planar interface Hamiltonian are quadratic in inverse curvature radii.…”

Section: Local Hamiltonianmentioning

confidence: 99%

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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Pressure tensor of a spherical interface

Cited by 108 publications

References 14 publications

Direct determination of the Tolman length from the bulk pressures of liquid drops via molecular dynamics simulations

Direct determination of the Tolman length from the bulk pressures of liquid drops via molecular dynamics simulations

Statistical mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension

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

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