Thermodynamic expressions for the Tolman length

Abstract

The Tolman length delta [TolmanJ. Chem. Phys. 17, 333 (1949)] measures the extent by which the surface tension of a small liquid drop deviates from its planar value. Despite increasing theoretical attention, debate continues on even the sign of Tolman's length for simple liquids. Recent thermodynamic treatments have proposed a relation between the Tolman length and the isothermal compressibility of the liquid at two-phase coexistence, delta approximately -kappa([script-l])sigma. Here, we review the derivation of this relation and show how it is related to earlier thermodynamic expressions. Its applicability is discussed in the context of the squared-gradient model for the liquid-vapor interface. It is found that the relation is semiquantitatively correct for this model unless one is too close to the critical point.

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

“…However, there is much about it that is still not understood, even for simple fluids. 3 The magnitude of the Tolman length has long been agreed upon to be 10%-20% of a molecular diameter. The sign of the Tolman length enjoys no such consensus.…”

“…Furthermore, it has also been shown that the Tolman length can be found from the planar limit of the difference between these two dividing surfaces, is not yet a consensus upon the sign of ␦. 3 Theoretical estimates using density functional theory ͑DFT͒ result in negative values for the Tolman length, [4][5][6][7][8] while computer simulations of planar interfaces give positive values for the Tolman length, via Eq. ͑6͒ below, [9][10][11] or were inconclusive.…”

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

“…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.…”

Pressure Tensor of Nanoscopic Liquid Drops

“…To compare with our result, in these expressions, we make the changes that we have introduced for ρ( r) in Equation (22) and r in Equation (23), and the result obtained is as follows:…”

“…The calculation of the microscopic expressions of the coefficients introduced in this model is a difficult task in the statistical physics of inhomogeneous fluids; although it has been made from different routes, it is still a subject of analysis and discussion [5,12,22]. We emphasize in this study calculating the microscopic expressions of the pressure difference between the two phases of a single and multicomponent system using the stress tensor in the mean field derived by Romero-Percus [23,24].…”