Computer simulation of argon adsorption on graphite surface from subcritical to supercritical conditions: the behavior of differential and integral molar enthalpies of adsorption

We investigate in detail the computer simulation of argon adsorption on a graphite surface over a very wide range of temperature, from below the triple point to well above the critical point. Adsorption over such a wide temperature range has not been reported previously in the form of adsorption isotherms and enthalpy change during adsorption. The adsorption isotherms can be classified broadly into four categories: below the triple point, the isotherms show stepwise character (a strict layering mechanism) with 2D condensation; type II (according to the IUPAC classification) is followed by isotherms at temperatures above the triple point and below the critical point and a sharp spike is seen for isotherms in the neighborhood of the critical point; and finally the typical behavior of a maximum is observed for isotherms above the critical point. For the isosteric heat, the heat curve (plotted against loading) remains finite for subcritical conditions but is infinite (singularity) at the maximum in excess loading for supercritical adsorption. For the latter case, a better representation of the energy change is the use of the integral molecular enthalpy because this does not exhibit a singularity as in the case of isosteric heat. We compare the differential and integral molecular enthalpies for the subcritical and supercritical adsorptions.

Monte Carlo optimization scheme to determine the physical properties of porous and nonporous solids

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.

New method to determine surface area and its energy distribution for nonporous solids: a computer simulation and experimental study

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.

On the existence of negative excess isotherms for argon adsorption on graphite surfaces and in graphitic pores under supercritical conditions at pressures up to 10,000 atm

In this paper, we consider in detail the computer simulation of argon adsorption on a graphite surface and inside graphitic slit pores under supercritical conditions. Experimental results in the literature for graphitic adsorbents show that excess isotherms pass through a maximum and then become negative at high pressures (even for adsorption on open surfaces) when a helium void volume is used in the calculation of the excess amount. Here we show that, by using the appropriate accessible volume (which is smaller than the helium void volume), the excess isotherms still have a maximum but are always positive. The existence and the magnitude of this maximum is because the rate of change of the adsorbed density is equal to that of the bulk gas, which has a large change in bulk gas density for a small variation in pressure for temperatures not far above the critical point. However for temperatures far above T(c), this change in the bulk gas density is no longer significant and the maximum in the surface excess density becomes less pronounced and even disappears at high enough temperatures. The positivity of the adsorption excess persists for all pressures up to 10,000 atm for adsorption on surfaces and in slit pores of all sizes. For adsorption on a surface, the surface excess density eventually reaches a plateau at high pressures as expected, because the change in the adsorbed phase is comparable to that of the bulk gas. Positive excess lends support to our physical argument that the adsorbed phase is denser than the bulk gas, and this is logical as the forces exerted by the pore walls should aid to the compression of the adsorbed phase.

On the Henry constant and isosteric heat at zero loading in gas phase adsorption

The Henry constant and the isosteric heat of adsorption at zero loading are commonly used as indicators of the strength of the affinity of an adsorbate for a solid adsorbent. It is assumed that (i) they are observable in practice, (ii) the Van Hoff's plot of the logarithm of the Henry constant versus the inverse of temperature is always linear and the slope is equal to the heat of adsorption, and (iii) the isosteric heat of adsorption at zero loading is either constant or weakly dependent on temperature. We show in this paper that none of these three points is necessarily correct, first because these variables might not be observable since they are outside the range of measurability; second that the linearity of the Van Hoff plot breaks down at very high temperature, and third that the isosteric heat versus loading is a strong function of temperature. We demonstrate these points using Monte Carlo integration and Monte Carlo simulation of adsorption of various gases on a graphite surface. Another issue concerning the Henry constant is related to the way the adsorption excess is defined. The most commonly used equation is the one that assumes that the void volume is the volume extended all the way to a boundary passing through the centres of the outermost solid atoms. With this definition the Henry constant can become negative at high temperatures. Although adsorption at these temperatures may not be practical because of the very low value of the Henry constant, it is more useful to define the Henry constant in such a way that it is always positive at all temperatures. Here we propose the use of the accessible volume; the volume probed by the adsorbate when it is in nonpositive regions of the potential, to calculate the Henry constant.

Prospective surveillance of women with a family history of breast cancer: auditing the risk threshold

To evaluate current guidelines criteria for inclusion of women in special ‘breast cancer family history’ surveillance programmes, records were reviewed of women referred to Scottish breast cancer family clinics between January 1994 and December 2003 but discharged as at ‘less than ‘moderate’ familial risk’. The Scottish Cancer Registry was then interrogated to determine subsequent age-specific incidence of breast cancer in this cohort and corresponding Scottish population figures. Among 2074 women, with an average follow-up of 4.0 years, 28 invasive breast cancers were recorded up to December 2003, where 14.4 were expected, a relative risk (RR) of 1.94. Eleven further breast cancers were recorded between January 2004 and February 2006 (ascertainment incomplete for this period). The overall RR for women in the study cohort exceeded the accepted ‘cutoff’ level (RR=1.7) for provision of special counselling and surveillance. The highest RR was found for the age group 45–59 years and this group also generated the majority of breast cancers. The National Institute for Clinical Excellence (‘NICE’) guidelines appear to be more accurate than those of the Scottish Intercollegiate Guidelines Network (‘SIGN’) in defining ‘moderate’ familial risk, and longer follow-up of this cohort could generate an evidence base for further modification of familial breast cancer services.

Anomalous transport in molecularly confined spaces

We develop a novel theory to predict the density dependence of the diffusivity of simple fluids in a molecularly sized nanopore with diffusely reflecting walls, incorporating nearest neighbor intermolecular interactions within the framework of the recent oscillator model of low density transport arising from this laboratory. It is shown that when the pore width is about two molecular diameters, at sufficiently high densities these interactions lead to a repulsive inner core, as a result of which the diffusing molecules undergo more frequent reflections at the wall. This leads to a reduction in diffusivity with increase in density, which is consistent with molecular dynamics simulation results, and contrasts with the behavior in larger pores where the transport coefficient has previously been shown to increase with increase in density due to viscouslike intermolecular interactions. At low densities the behavior is opposite, with the inner core becoming more attractive with increase in density, which can lead to an increase in diffusivity. The theory consistently explains molecular dynamics simulation results when the inhomogeneous pair distribution function of moving particles in the pore is axially periodic, suggesting concerted motion of neighboring molecules. It is also shown that a potential of mean force concept is inadequate for describing the influence of intermolecular interactions on transport.

High-pressure adsorption capacity and structure of CO2 in carbon slit pores: theory and simulation

We present new simulation results for the packing of single-center and three-center models of carbon dioxide at high pressure in carbon slit pores. The former shows a series of packing transitions that are well described by our density functional theory model developed earlier. In contrast, these transitions are absent for the three-center model. Analysis of the simulation results shows that alternations of flat-lying molecules and rotated molecules can occur as the pore width is increased. The presence or absence of quadrupoles has negligible effect on these high-density structures.