Virial series for inhomogeneous fluids applied to the Lennard-Jones wall-fluid surface tension at planar and curved walls

Abstract

We formulate a straightforward scheme of statistical mechanics for inhomogeneous systems that includes the virial series in powers of the activity for the grand free energy and density distributions. There, cluster integrals formulated for inhomogeneous systems play a main role. We center on second order terms that were analyzed in the case of hard-wall confinement, focusing in planar, spherical and cylindrical walls. Further analysis was devoted to the Lennard-Jones system and its generalization the 2k-k potential. For this interaction potentials the second cluster integral was evaluated analytically. We obtained the fluid-substrate surface tension at second order for the planar, spherical and cylindrical confinement. Spherical and cylindrical cases were analyzed using a series expansion in the radius including higher order terms. We detected a ln R −1 /R 2 dependence of the surface tension for the standard Lennard-Jones system confined by spherical and cylindrical walls, no matter if particles are inside or outside of the hard-walls. The analysis was extended to bending and Gaussian curvatures, where exact expressions were also obtained.

Bending and Gaussian rigidities of confined soft spheres from second-order virial series

“…Expressions (23,24,25) are formally identical to that obtained previously for different types of pair potentials which produce a different expression for C q (ε). [9] For short-range potentials, those with ν > 6, we found…”

“…Again, if we replace using the identity β q Γ (1 − q) → −qC q (0) these expressions coincide with those found recently for the Lennard-Jones fluid, but with a different definition for C q (0). [9] In Fig. 4 the bending rigidity constant k is presented as a function of temperature for different values of hardness parameter ν.…”

“…To evaluate τ 2 we adapt and simplify here the approach followed in Ref. [9]. Introducing the identity g (…”

“…Our results complement other recent works, showing that k = 0 for different fluids under different circumstances and suggesting that morphometric thermodynamics has to be used with caution. [7,9,45,[47][48][49] We think that arguments inducing to establish the absence of nonlinear terms in the free energy of fluids in thermodynamics and statistical mechanics should be revised at least when one recognizes that almost any real (finite-size) fluid system is in some sense confined. r > σ we obtain C m+1,ν = − 1 m+1 + 1 ν C q , where the first term on the right is the hard-core contribution and C q (ε) =ˆ1 ε y −(1+q) exp −βy − 1 dy , (B1)…”

“…Recently, new exact results based on virial series were obtained for confined hard spheres (HS), [6][7][8] square well, and even Lennard-Jones, systems. [9] This work aims to contribute in this direction by studying the physical properties of pure repulsive soft-spheres system confined by curved walls.…”