ABSTRACT
In this work the thermodynamic geometry (TG) of semiclassical fluids is analyzed. We present results for two models. The first one is a semiclassical hard-sphere (SCHS) fluid whose Helmholtz free energy is obtained from path-integral Monte Carlo simulations. It is found that, due to quantum contributions in the thermodynamic potential, the anomaly found in TG for the classical hard-sphere fluid related to the sign of the scalar curvature is now avoided in a considerable region of the thermodynamic space. The second model is a semiclassical square-well fluid, described by a SCHS repulsive interaction coupled with a classical attractive square-well contribution. The behavior of the semiclassical curvature scalar as a function of the thermal de Broglie wavelength λ_{B} is analyzed for several attractive-potential ranges. A description of the semiclassical R Widom lines, defined by the maxima of the curvature scalar, is also obtained and results are compared with the corresponding classical systems for different square-well ranges.
ABSTRACT
The statistical mechanics of a cloud of particles interacting via their gravitational potentials encounters some issues when the Boltzmann-Gibbs statistics is applied. In this work, we consider the alternative statistical framework of Tsallis and analyze the statistical and thermodynamical implications for a self-gravitating gas, obtaining analytical and convergent expressions for the equation of state and specific heat in the ensembles of constant temperature and constant energy. Although our results are comparable in both ensembles, it turns out that only in the ensemble of constant temperature do the thermodynamic quantities depend explicitly on the Tsallis parameter, indicating that the question of ensemble equivalence for Tsallis statistics must be further reviewed.
ABSTRACT
We have refined and improved the computational efficiency of the TriPOD technique, used to determine the accessible characteristics of porous solids with a known configuration of solid atoms. Instead of placing a probe molecule randomly, as described in the original version of the TriPOD method (Herrera et al., 2011), we implemented a scheme for dividing the porous solid into 3D-grids and computing the solid-fluid potential energies at these grid points. We illustrate the potential of this technique in determining the total pore volume, the surface area and the pore size distribution of various molecular models of porous carbons, ranging from simple pore models to a more complex simulated porous carbon model; the latter is constructed from a canonical Monte Carlo simulation of carbon microcrystallites of various sizes.
ABSTRACT
A new method, based on a Monte Carlo scheme, is developed to determine physical properties of nonporous and porous solids. In the case of nonporous solids, we calculate the surface area. This surface area is found as the sum of areas of patches of different surface energy on the solid, which is assumed to take a patchwise topology (i.e., adsorption sites of the same energy are grouped together in one patch). As a result of this assumption, we derive not only the surface area, but also the accessible volume and the surface energy distribution. In the case of porous solids, the optimization method is used to derive the surface area and the pore size distribution simultaneously. The derivation of these physical properties is based on adsorption data from a volumetric apparatus. We test this novel idea with the inversion problem of deriving surface areas of patches of different energies for a number of nonporous solids. The method is also tested with the derivation of the pore size distribution of some porous solid models. The results are very encouraging and demonstrate the great potential of this method as an alternative to the usual deterministic optimization algorithms which are known to be sensitive to the choice of the initial guess of the parameters. Since the geometrical parameters are physical quantities (i.e., only positive values are accepted), we also propose a scheme to enforce the positivity constraint of the solution.
ABSTRACT
We present in this article a new method to determine the "geometrical" surface area of nonporous solids. This method is based on the total number of molecules dosed into the adsorption cell and a knowledge of the distribution of molecules between the gas phase and the surface phase. By matching this experimental amount with the corresponding theoretical equation, we can derive not only the surface area but also its energy distribution and the void volume of the adsorption cell. The method avoids the limitations of other methods presented in the literature. The BET method, for example, involves unrealistic assumptions and necessitates the choice of a molecular projection area. Our method does not suffer from these assumptions or limitations and is self-consistent, from the measurement of adsorption data to the final analysis of the surface area. The novelties of the method are the following: (i) it is valid over the complete range of reduced pressure, (ii) it does not require a molecular projection area, (iii) beside the total surface area, we also derive its energy distribution, and (iv) the helium expansion method (or any equivalent method) is not required to determine the void volume.
ABSTRACT
A simple method, based on Monte Carlo integration, is presented to derive pore size and its volume distribution for porous solids having known configuration of solid atoms. Because pores do not have any particular shape, it is important that we define the pore size in an unambiguous manner and the volume associated with each pore size. The void volume that we adopt is the one that is accessible to the center of mass of the probe particle. We test this new method with porous solids having well defined pores such as graphitic slit pores and carbon nanotubes, and then apply it to obtain the pore volume distribution of complex solids such as disordered solids, rectangular pores, defected graphitic pores, metal organic framework and zeolite.
ABSTRACT
Grand canonical Monte Carlo simulation is used to study the adsorption of nitrogen at 77 K and ammonia at 240 K to represent weakly polar and polar molecules, respectively, on infinite and finite graphite surfaces. These graphite surfaces were modeled with different percentages of carbons removed (defects) from the top graphite layer. Increasing the number of defects increases the adsorption and the isosteric heat of nitrogen at low pressure. At moderate pressures the amount adsorbed is less due to the disruption in the packing of the nitrogen in the first layer. In contrast, the adsorption of ammonia at all pressures is reduced as the percentage of defects is increased. This is due to the disruption in ammonia bonding caused by the defects. The condensation-like step change in the ammonia isotherm on the perfect graphite surface is not observed for any of these surfaces with defects even for the case of only 10% defects. At high percentage of defects the adsorption isotherm is close to Henry law behavior for much of the pressure range. The adsorption on finite surfaces shows that the amount adsorbed for both molecules decreases compared with that of the infinite surfaces, resulting from interaction potentials with the surface and other fluid molecules at the edge. The decrease is much greater for the ammonia adsorption because the bonding between ammonia molecules is disrupted, meaning that the adsorption cannot follow the mechanism of condensation seen for the infinite surface.
