Virial series for inhomogeneous fluids applied to the Lennard-Jones wall-fluid surface tension at planar and curved walls
arXiv:1603.02885 · doi:10.1063/1.4947587
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 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.
arXiv comment15 pages, 6 figures
References in corpus (18)
- Logarithmic Finite-Size Effects on Interfacial Free Energies: Phenomenological Theory and Monte Carlo Studies
- Non-analytic curvature contributions to solvation free energies: influence of drying
- Density Functional Theory of a Curved Liquid-Vapour Interface: Evaluation of the rigidity constants
- The Complete Jamming Landscape of Confined Hard Discs
- Wetting at Curved Substrates: Non-Analytic Behavior of Interfacial Properties
- Determination of the origin and magnitude of logarithmic finite-size effects on interfacial tension: Role of interfacial fluctuations and domain breathing
- Bending rigidity and higher order curvature terms for the hard-sphere fluid near a curved wall
- The existence of a bending rigidity for a hard sphere liquid near a curved hard wall: Helfrich or Hadwiger?
- Corresponding states law for a generalized Lennard-Jones potential
- Deriving the Rosenfeld Functional from the Virial Expansion
- The effective colloid interaction in the Asakura-Oosawa model. Assessment of non-pairwise terms from the virial expansion
- Two hard spheres in a pore: Exact Statistical Mechanics for different shaped cavities
- Implications of interface conventions for morphometric thermodynamics
- Statistical Mechanics of Two Hard Spheres in a Spherical Pore, Exact Analytic Results in D Dimension
- Virial coefficients and demixing in the Asakura-Oosawa model
- Fourth virial coefficient of additive hard-sphere mixtures in the Percus-Yevick and hypernetted-chain approximations
- Fluids confined in wedges and by edges: From cluster integrals to thermodynamic properties referred to different regions
- Fluids confined in wedges and by edges: virial series for the line-thermodynamic properties of hard spheres