Simulations slit pore

A7 Ethane/methane selectivity calculated from grand canonical Monte Carlo simulations of mixtures in slit IS at a temperature of 296 K. The selectivity is defined as the ratio of the mole fractions in the pore to the ratio of mole fractions in the bulk. H is the slit width defined in terms of the methane collision diameter (Tch,- (Figure awn from Crackncll R F, D Nicholson and N Quirke 1994. A Grand Canonical Monte Carlo Study ofLennard-s Mixtures in Slit Pores 2 Mixtures of Two-Centre Ethane with Methane. Molecular Simulation 13 161-175.)... 

The principal effect of the presence of a smooth wall, compared to a free surface, is the occurrence of a maximum in the density near the interface due to packing effects. The height of the first maximum in the density profile and the existence of additional maxima depend on the strength of the surface-water interactions. The thermodynamic state of the liquid in a slit pore, which has usually not been controlled in the simulations, also plays a role. If the two surfaces are too close to each other, the liquid responds by producing pronounced density oscillations. 

FIG. 3 Setup of simulation cell of confined electrolyte with periodic boundary conditions, (a) Electrolyte bound by two infinitely long charged plates, representing a slit pore, (b) Electrolyte in a cylindrical nanopore. 

Both a uniform bulk fluid and an inhomogeneous fluid were simulated. The latter was in the form of a slit pore, terminated in the -direction by uniform Lennard-Jones walls. The distance between the walls for a given number of atoms was chosen so that the uniform density in the center of the cell was equal to the nominal bulk density. The effective width of the slit pore used to calculate the volume of the subsystem was taken as the region where the density was nonzero. For the bulk fluid in all directions, and for the slit pore in the lateral directions, periodic boundary conditions and the minimum image convention were used. 

Figure 7 also shows results for the thermal conductivity obtained for the slit pore, where the simulation cell was terminated by uniform Lennard-Jones walls. The results are consistent with those obtained for a bulk system using periodic boundary conditions. This indicates that the density inhomogeneity induced by the walls has little effect on the thermal conductivity. 

Q. Y. Wang and J. K. Johnson, Molecular simulation of hydrogen adsorption in single-walled carbon nanotubes and idealized carbon slit pores,./ Chem. Phys., 110, 577-586 (1999). 

Figure 3. GCMC simulated Xe adsorption isotherms on a graphite slit pore at 300 K. Experimetal isotherms are also shown. w= 0.90 nm, w= l.OOnm 0 P5, O P10, P20...

Do DD, Nicholson D, and Do HD. Heat of adsorption and density distribution in slit pores with defective walls GCMC simulation studies and comparison with experimental data. Appl. Surf. Sci., 2007 253(13 SPEC. ISS.) 5580-5586. 

In relation to methane adsorption in active carbon, which as previously described is formed by slit pores (see Figure 2.21), several numerical simulations have revealed that the highest density of the adsorbed phase is achieved within slit pores of 1.12-1.14 nm of diameter [187,200], For slit pores of a width, L = 1.13 nm (see Figure 2.21), two facing methane molecule monolayers may be inserted between pore walls [203-205],... 

Monte Carlo Simulation for Distribution Equilibrium between Supercritical Fluid and Slit Pores... 

Because of its diatomic nature and permanent quadrupole moment, the physisorp-tion of nitrogen at 77 K presents special problems. The application of DFT is facilitated if the molecules are assumed to be spherical, which was the approach originally adopted by Seaton et al. (1989) and also by Lastoskie et al. (1993). The analytical procedures already outlined in Chapter 7 (Section 7.6) do not depend on the meniscus curvature and are in principle applicable to both capillary condensation and micropore filling. The non-local version of the mean field theory (NLDFT), which was used by Lastoskie, gave excellent agreement with computer simulation when applied to the carbon slit pore model. However, as pointed out earlier, these computational procedures are not entirely independent since they involve the same model parameters. 

Figure 2. Global phase diagram of a fluid in a slit pore of width (1.5 nm) from (a) simulations, and (b)...

This expression agrees rather well with the exact summation and gives the correct limiting form at large z which is an energy that varies as as calculated from the theory of dispersion interactions [10]. Although this potential is widely used in studies of structure in films adsorbed on a surface, it is even more popular in simulations of sorption in parallel-walled slit pores, some of which will be discussed below. 

A simulation study has been reported for methane at room temperature in parallel-walled slit pores with interaction potentials given by an equation of the form of equation (16) with parameters suitable for the methane graphite system. 

Figure 1. The dependence of the average gas-solid potential energy for methane in a gr hitic slit pore upon position within the pore is shown for three values of the pore filling 0.040 (solid line), 0.059 (short dashes) and 0.077 (long dashes). Also given is the z-dependence of the simulated chemical potential IkT for these three densities in a pore of width 14.8 A From. Ref [22], Sep. ScL and Tech. 27 (1992), 1837-1856.

Figure 2. Simulated isotherms for methane-in carbon slit pores of varying widths are shown here. The number of adsorbed molecules per unit area of pore wall is plotted as a function of the pressure times the Henry s constant, which gives the single straight line shown for the limiting low pressme parts of the isotherms. Pore widths in A are shown on the Figure. From Ref. [22], Sep. Sci. and Tech. 27 (1992), 1837-1856.

Phase diagrams for strongly polar molecules in adsorbed films are still in the process of development even for the films on the basal plane of graphite [35]. These systems are made more complex because of the interplay of dipolar forces and molecular shape in determining preferred orientations relative to the surface and to neighboring molecules. A simulation of Stockmayer molecules (Lennard-Jones atoms with ideal dipoles attached) adsorbed on a featureless slit pore at low temperature [46] has shown that the dipoles tend to lie parallel to the surface in... 

The Gibbs-ensemble procedure lias also been employed to estimate adsorptionisothemis for simple systems. The approach is illustrated- by calculations for a straight cylindrical pore where both fluid/fluid and fluid/adsorbent molecular interactions can be represented by tlie Lemiard-Jones potential-energy function [Eq. (16.1)]. Simulation calculations have also been made for isothemis of methane and ethane adsorbed on a model carbonaceous slit pore. Isosteric heats of adsorption liave also been calculated. ... 

Figure 3 Comparison of PSDs obtained using the Dubinin-Stoeckli (DS), Horvalh-Kawazoe (HK), and density fitnctional theory (DFT) methods to interpret an isotherm generated from molecular simulation of nitrogen adsorption in a model carbon that has an Gaussian distribution of slit pore widths (18]. Results are shown for mean pore widths of 8.9 A (left) and 16.9 A (right).

Classical methods, like DS and HK, show shortcomings in the determination of MSD due to the assumptions involved in their formulation of the adsorption process Dubinin equation does not show linearity in the Dubinin plot for single slit pores and Horvath-Kawazoe equation assumes that at a given pressure a pore is either completely filled or completely empty, which is contrary to the behavior observed in computer simulations Resulting MSD are shifted respect to those obtained by Monte Carlo simulations, by amounts that vary with the actual distribution, and too small micropores are predicted... 

In this paper, a modified HK method is presented which accounts for spatial variations in the density profile of a fluid (argon) adsorbed within a carbon slit pore. We compare the pore width/filling pressure correlations predicted by the original HK method, the modified HK method, and methods based upon statistical thermodynamics (density functional theory and Monte Carlo molecular simulation). The inclusion of the density profile weighting in the HK adsorption energy calculation improves the agreement between the HK model and the predictions of the statistical thermodynamics methods. Although the modified Horvath-Kawazoe adsorption model lacks the quantitative accuracy of the statistical thermodynamics approaches, it is numerically convenient for ease of application, and it has a sounder molecular basis than analytic adsorption models derived from the Kelvin equation. 

The principal drawback of the DFT method is that it is computationally intensive relative to the classical adsorption models, although it is still much less compute-intensive than full Monte Carlo molecular simulation. A semianalytic adsorption model that retains computational efficiency while accounting for gas-solid potential interactions in micropores was originally proposed by Horvath and Kawazoe [12], In the Horvath-Kawazoe or HK method, a pore filling correlation is obtained by calculating the mean heat of adsorption (/> required to transfer an adsorbate molecule from the gas phase to the condensed phase in a slit pore of width // ... 

Salamacha and coworkers304 306 have carried out a series of studies on Lennard-Jones fluids confined to nanoscopic slit pores made from parallel planes of face centred cubic crystals. Grand canonical and canonical ensemble MC simulations have been used to determine the structure and phase behaviour as the width of the pore and the strength of the fluid-wall interactions were varied. The pore widths were small accommodating 2 to 5 layers of fluid molecules.304,305 The strength of the fluid-wall interaction is linked to the degree of corrugation of the surface, and it is found that the structure of the... 

Wongkoblap et al.307 study Lennard-Jones fluids in finite pores, and compare their results with Grand canonical ensemble simulations of infinite pores. Slit pores of 3 finite layers of hexagonally arranged carbon atoms were constructed. They compare the efficiency of Gibbs ensemble simulations (where only the pore is modelled) with Canonical ensemble simulations where the pore is situated in a cubic cell with the bulk fluid, and find that while the results are mostly the same, the Gibbs ensemble method is more efficient. However, the meniscus is only able to be modelled in the canonical ensemble. 

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