ABSTRACT
We show that a simple model consisting of a binary hard-sphere mixture in a narrow cylindrical pore can lead to strong size selectivity by considering a situation where each species of the mixture sees a different radius of the cylinder. Two mechanisms are proposed to explain the observed results depending on the radius of the cylinder: for large radii the selectivity is driven by an enhancement of the depletion forces at the cylinder walls whereas for the narrowest cylinders excluded-volume effects lead to a shift of the effective chemical potential of the particles in the pore.
ABSTRACT
Two density functional theories, the fundamental measures theory of Rosenfeld [Phys. Rev. Lett. 63, 980 (1989)] and a subsequent approximation by Tarazona [Phys. Rev. Lett. 84, 694 (2000)] are applied to the study of the hard-sphere fluid in two situations: the cylindrical pore and the spherical cavity. The results are compared with those obtained with grand canonical ensemble Monte Carlo simulations. The differences between both theories are evaluated and interpreted in the terms of the dimensional crossover from three to one and zero dimensions.
Subject(s)
Chemistry, Physical/methods , Nanotechnology/methods , Algorithms , Fourier Analysis , Hardness , Models, Statistical , Models, Theoretical , Monte Carlo Method , Surface PropertiesABSTRACT
We examine the microscopic structure of a hard-sphere fluid confined to a small cylindrical pore by means of Monte Carlo simulation. In order to analyze finite-size effects, the simulations are carried out in the framework of different statistical mechanics ensembles. We find that the size effects are specially relevant in the canonical ensemble where noticeable differences are found with the results in the grand canonical ensemble (GCE) and the isothermal isobaric ensemble (IIE) which, in most situations, remain very close to the infinite system results. A customary series expansion in terms of fluctuations of either the number of particles (GCE) or the inverse volume (IIE) allows us to connect with the results of the canonical ensemble.
ABSTRACT
When thermodynamic properties of a pure substance are transformed to reduced form by using both critical- and triple-point values, the corresponding experimental data along the whole liquid-vapor coexistence curve can be correlated with a very simple analytical expression that interpolates between the behavior near the triple and the critical points. The leading terms of this expression contain only two parameters: the critical exponent and the slope at the triple point. For a given thermodynamic property, the critical exponent has a universal character but the slope at the triple point can vary significantly from one substance to another. However, for certain thermodynamic properties including the difference of coexisting densities, the enthalpy of vaporization, and the surface tension of the saturated liquid, one finds that the slope at the triple point also has a nearly universal value for a wide class of fluids. These thermodynamic properties thus show a corresponding apparently universal behavior along the whole coexistence curve.
ABSTRACT
We present a density functional theory for inhomogeneous fluids at constant external pressure. The theory is formulated for a volume-dependent density, n(r,V), defined as the conjugate variable of a generalized external potential, nu(r,V), that conveys the information on the pressure. An exact expression for the isothermal-isobaric free-energy density functional is obtained in terms of the corresponding canonical ensemble functional. As an application we consider a hard-sphere system in a spherical pore with fluctuating radius. In general we obtain very good agreement with simulation. However, in some situations a peak develops in the center of the cavity and the agreement between theory and simulation becomes worse. This happens for systems where the number of particles is close to the magic numbers N=13, 55, and 147.
