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

Abstract

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.

Excess equimolar radius of liquid drops

“…Subsequent studies, however, have also found δ to be negligible or even equal to zero [20,63,76], positive and larger than σ [25,66], negative with −σ < δ < 0 [22,24,77] or negative and diverging (δ 0 = −∞) in the planar limit [78], while others have claimed that the sign of δ is curvature dependent itself [79,80]. Thereby, they have only proven the mutual inconsistency of their assumptions and methods, while nothing is truely known about δ and the dependence of the surface tension on curvature.…”

“…The most widespread implementation of this approach in terms of intermolecular pair potentials makes use of the Irving-Kirkwood (IK) [43] pressure tensor, which was first applied to (spherical) interfaces by Buff [13] and underlies the simulation studies of Vrabec et al [25] as well as those of van Giessen and Blokhuis [24]. Its normal component is given by [34,43] …”

“…In this way, the thermodynamics of liquid drops are discussed by following a new route that relies on the density profiles and bulk properties only, avoiding the intricacies of defining the pressure tensor or the change in the surface area as required by other approaches. The present method is related to the «direct determination» of δ 0 proposed by Nijmeijer et al [23], as recently applied by van Giessen and Blokhuis [24] on the basis of a representation of ϕR ρ over 1/R ρ with…”

“…Vrabec et al [25]. On account of this, numerous studies on nanoscopic liquid drops have been reported [18,24,25,[63][64][65][66][67]. The LJTS fluid can thus be regarded as a key benchmark for theoretical and simulation approaches to the problem of curved vapour-liquid interfaces.…”

“…For the surface tension in the zero-curvature limit, the values γ 0 (0.65 ε/k) = 0.680 ± 0.009, γ 0 (0.75 ε/k) = 0.493 ± 0.008, γ 0 (0.85 ε/k) = 0.317 ± 0.007 and γ 0 (0.95 ε/ k) = 0.158 ± 0.006 εσ −2 are taken from the correlation of Vrabec et al [25]; the error corresponds to the individual data points for γ 0 from the same source. In case of T = 0.9 ε/k, the higher precision of the computations of van Giessen and Blokhuis [24] is exploited, using the value γ 0 = 0.227 ± 0.002 εσ −2 obtained from a linear fit to data for the curved interface [24], cf. Fig.…”