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.

Molecular simulation of excess isotherm and excess enthalpy change in gas-phase adsorption.

We present a new approach to calculating excess isotherm and differential enthalpy of adsorption on surfaces or in confined spaces by the Monte Carlo molecular simulation method. The approach is very general and, most importantly, is unambiguous in its application to any configuration of solid structure (crystalline, graphite layer or disordered porous glass), to any type of fluid (simple or complex molecule), and to any operating conditions (subcritical or supercritical). The behavior of the adsorbed phase is studied using the partial molar energy of the simulation box. However, to characterize adsorption for comparison with experimental data, the isotherm is best described by the excess amount, and the enthalpy of adsorption is defined as the change in the total enthalpy of the simulation box with the change in the excess amount, keeping the total number (gas + adsorbed phases) constant. The excess quantities (capacity and energy) require a choice of a reference gaseous phase, which is defined as the adsorptive gas phase occupying the accessible volume and having a density equal to the bulk gas density. The accessible volume is defined as the mean volume space accessible to the center of mass of the adsorbate under consideration. With this choice, the excess isotherm passes through a maximum but always remains positive. This is in stark contrast to the literature where helium void volume is used (which is always greater than the accessible volume) and the resulting excess can be negative. Our definition of enthalpy change is equivalent to the difference between the partial molar enthalpy of the gas phase and the partial molar enthalpy of the adsorbed phase. There is no need to assume ideal gas or negligible molar volume of the adsorbed phase as is traditionally done in the literature. We illustrate this new approach with adsorption of argon, nitrogen, and carbon dioxide under subcritical and supercritical conditions.

Henry constant and isosteric heat at zero-loading for gas adsorption in carbon nanotubes.

The Henry constant and the isosteric heat of adsorption at zero loading in a carbon nanotube bundle are studied with Monte Carlo integration for the adsorption of gases over a range of temperatures. The spacing between nanotubes in a bundle is determined from the minimization of potential energy of interaction between these tubes. We study different tube configurations with bundles of 2, 3, 4 and 7 tubes. Depending on the configuration it is found that the spacing is of between 0.31 to 0.333 nm, and this falls within the range reported in the literature. The Henry constant has been carefully defined so that it will not become negative at high temperatures. This is done with the aid of accessible volume, rather than the usual absolute void volume. We show that linearity of the van't Hoff plot for the Henry constant is not strictly followed. Furthermore the slope of this plot is not equal to the isosteric heat of adsorption at zero loading, which is found to be a strong function of temperature. From the results we find that the Henry constant and the heat of adsorption depend on the tube configuration. In general the adsorption in the cusp interstices is strongest followed by that inside the tube and finally on the outer surface. However for very small tubes adsorption occurs inside the tube first. For molecules with orientation, the behaviour is even more interesting and the shape of the isosteric heat versus temperature depends on the degree of orientation, tube configuration and the domain of adsorption (interstices, inside the tube and on the outer surface).

A new method to determine pore size and its volume distribution of porous solids having known atomistic configuration.

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.

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.

On the anatomy of the adsorption heat versus loading as a function of temperature and adsorbate for a graphitic surface.

In this paper we review and classify the various patterns of isosteric heat versus loading for adsorption of gases on graphitised thermal carbon black at temperatures ranging from below the 3D triple point to temperatures above it, but less than the 3D critical point. We have identified the features of heat curve and highlighted the microscopic origin of these features. The patterns vary with temperature and with the relative strength of the fluid-fluid interaction and solid-fluid interaction. For simple adsorptives (by simple we meant there is no strong association between fluid particles), the heat curve is typified by fluid-fluid attraction and layering phenomena. For adsorptives showing strong association such as water, ammonia and methanol, the heat curve essentially begins below the condensation heat and then approaches it as loading is increased. This is mainly due to the strong hydrogen bonding in these fluids. A third group includes adsorptives such as benzene, where the heat curve is constant in the sub-monolayer coverage region (but is higher than the condensation heat) and then drops off to the condensation heat when higher layers are formed. The constant heat in the sub-monolayer region is due to the balance between the energy factor (from fluid-fluid interaction) and entropy factor (due to re-orientation of adsorbed molecules). Our proposed classification is supported by detailed GCMC simulations of various gases that have been reported in the literature, and we supplement these with new results for the adsorption of xenon on graphite to investigate in more detail the change in heat pattern with temperature. Xenon is chosen because of its high fluid-fluid interaction, allowing us to study the 2D-phase transition in the first as well as higher layers.

Appropriate volumes for adsorption isotherm studies: the absolute void volume, accessible pore volume and enclosing particle volume.

In adsorption studies the choice of an appropriate void volume in the calculation of the adsorption isotherm is very crucial. It is often taken to be the apparent volume as determined by the helium expansion experiments. Unfortunately this method has difficulties especially when dealing with microporous solids, in which adsorption of helium might become significant at ambient temperatures. The amount adsorbed is traditionally obtained as the excess amount and the term "excess" refers to the excess over the amount occupying the apparent volume that has the same density as the bulk gas density. This could give rise to the maximum in the plot of excess amount versus pressure under supercritical conditions, and in some cases giving negative excess. Such behavior is difficult to analyze because the excess amount is not amenable to any classical thermodynamic treatments. In this paper we will present a method to determine the absolute void volume, and in that sense this volume is independent of temperature and adsorbate. The volume that is accessible to the centers of gas molecules is also investigated, and it is called the accessible volume. This volume depends on the choice of adsorbate, and it is appropriate to use this volume to calculate the pore density because we can assess how dense the adsorbed phase is. In the quest to determine the "absolute" adsorption isotherm so that a thermodynamics analysis can be applied, it is necessary to introduce the concept of "enclosing" volume, which is essentially the volume that encloses all solid particles, including all void spaces in them. The amount adsorbed is defined by the number of molecules residing in this volume. Having these volumes, we can derive the geometrical accessible void volume inside the particle and the solid volume, from which the particle and solid densities can be calculated.

Modeling of adsorption on nongraphitized carbon surface: GCMC simulation studies and comparison with experimental data.

We model nongraphitized carbon black surfaces and investigate adsorption of argon on these surfaces by using the grand canonical Monte Carlo simulation. In this model, the nongraphitized surface is modeled as a stack of graphene layers with some carbon atoms of the top graphene layer being randomly removed. The percentage of the surface carbon atoms being removed and the effective size of the defect (created by the removal) are the key parameters to characterize the nongraphitized surface. The patterns of adsorption isotherm and isosteric heat are particularly studied, as a function of these surface parameters as well as pressure and temperature. It is shown that the adsorption isotherm shows a steplike behavior on a perfect graphite surface and becomes smoother on nongraphitized surfaces. Regarding the isosteric heat versus loading, we observe for the case of graphitized thermal carbon black the increase of heat in the submonolayer coverage and then a sharp decline in the heat when the second layer is starting to form, beyond which it increases slightly. On the other hand, the isosteric heat versus loading for a highly nongraphitized surface shows a general decline with respect to loading, which is due to the energetic heterogeneity of the surface. It is only when the fluid-fluid interaction is greater than the surface energetic factor that we see a minimum-maximum in the isosteric heat versus loading. These simulation results of isosteric heat agree well with the experimental results of graphitization of Spheron 6 (Polley, M. H.; Schaeffer, W. D.; Smith, W. R. J. Phys. Chem. 1953, 57, 469; Beebe, R. A.; Young, D. M. J. Phys. Chem. 1954, 58, 93). Adsorption isotherms and isosteric heat in pores whose walls have defects are also studied from the simulation, and the pattern of isotherm and isosteric heat could be used to identify the fingerprint of the surface.

Adsorption of carbon tetrachloride on graphitized thermal carbon black and in slit graphitic pores: five-site versus one-site potential models.

The performance of intermolecular potential models on the adsorption of carbon tetrachloride on graphitized thermal carbon black at various temperatures is investigated. This is made possible with the extensive experimental data of Machin and Ross(1), Avgul et al.,(2) and Pierce(3) that cover a wide range of temperatures. The description of all experimental data is only possible with the allowance for the surface mediation. If this were ignored, the grand canonical Monte Carlo (GCMC) simulation results would predict a two-dimensional (2D) transition even at high temperatures, while experimental data shows gradual change in adsorption density with pressure. In general, we find that the intermolecular interaction has to be reduced by 4% whenever particles are within the first layer close to the surface. We also find that this degree of surface mediation is independent of temperature. To understand the packing of carbon tetrachloride in slit pores, we compared the performance of the potential models that model carbon tetrachloride as either five interaction sites or one site. It was found that the five-site model performs better and describes the imperfect packing in small pores better. This is so because most of the strength of fluid-fluid interaction between two carbon tetrachloride molecules comes from the interactions among chlorine atoms. Methane, although having tetrahedral shape as carbon tetrachloride, can be effectively modeled as a pseudospherical particle because most of the interactions come from carbon-carbon interaction and hydrogen negligibly contributes to this.

Adsorption of benzene on graphitized thermal carbon black: reduction of the quadrupole moment in the adsorbed phase.

The performance of intermolecular potential models on the adsorption of benzene on graphitized thermal carbon black at various temperatures is investigated. Two models contain only dispersive sites, whereas the other two models account explicitly for the dispersive and electrostatic sites. Using numerous data in the literature on benzene adsorption on graphitized thermal carbon black at various temperatures, we have found that the effect of surface mediation on interaction between adsorbed benzene molecules must be accounted for to describe correctly the adsorption isotherm as well as the isosteric heat. Among the two models with partial charges tested, the WSKS model of Wick et al. that has only six dispersive sites and three discrete partial charges is better than the very expensive all-atom model of Jorgensen and Severance. Adsorbed benzene molecules on graphitized thermal carbon black have a complex orientation with respect to distance from the surface and also with respect to loading. At low loadings, they adopt the parallel configuration relative to the graphene surface, whereas at higher loadings (still less than monolayer coverage) some molecules adopt a slant orientation to maximize the fluid-fluid interaction. For loadings in the multilayer region, the orientation of molecules in the first layer is influenced by the presence of molecules in the second layer. The data that are used in this article come from the work of Isirikyan and Kiselev, Pierotti and Smallwood, Pierce and Ewing, Belyakova, Kiselev, and Kovaleva, and Carrott et al.

Adsorption of argon from sub- to supercritical conditions on graphitized thermal carbon black and in graphitic slit pores: a grand canonical Monte Carlo simulation study.

In this paper we consider the adsorption of argon on the surface of graphitized thermal carbon black and in slit pores at temperatures ranging from subcritical to supercritical conditions by the method of grand canonical Monte Carlo simulation. Attention is paid to the variation of the adsorbed density when the temperature crosses the critical point. The behavior of the adsorbed density versus pressure (bulk density) shows interesting behavior at temperatures in the vicinity of and those above the critical point and also at extremely high pressures. Isotherms at temperatures greater than the critical temperature exhibit a clear maximum, and near the critical temperature this maximum is a very sharp spike. Under the supercritical conditions and very high pressure the excess of adsorbed density decreases towards zero value for a graphite surface, while for slit pores negative excess density is possible at extremely high pressures. For imperfect pores (defined as pores that cannot accommodate an integral number of parallel layers under moderate conditions) the pressure at which the excess pore density becomes negative is less than that for perfect pores, and this is due to the packing effect in those imperfect pores. However, at extremely high pressure molecules can be packed in parallel layers once chemical potential is great enough to overcome the repulsions among adsorbed molecules.

Adsorption of argon on homogeneous graphitized thermal carbon black and heterogeneous carbon surface.

In this paper we investigate the effects of surface mediation on the adsorption behavior of argon at different temperatures on homogeneous graphitized thermal carbon black and on heterogeneous nongraphitized carbon black surface. The grand canonical Monte Carlo (GCMC) simulation is used to study the adsorption, and its performance is tested against a number of experimental data on graphitized thermal carbon black (which is known to be highly homogeneous) that are available in the literature. The surface-mediation effect is shown to be essential in the correct description of the adsorption isotherm because without accounting for that effect the GCMC simulation results are always greater than the experimental data in the region where the monolayer is being completed. This is due to the overestimation of the fluid-fluid interaction between particles in the first layer close to the solid surface. It is the surface mediation that reduces this fluid-fluid interaction in the adsorbed layers, and therefore the GCMC simulation results accounting for this surface mediation that are presented in this paper result in a better description of the data. This surface mediation having been determined, the surface excess of argon on heterogeneous carbon surfaces having solid-fluid interaction energies different from the graphite can be readily obtained. Since the real heterogeneous carbon surface is not the same as the homogeneous graphite surface, it can be described by an area distribution in terms of the well depth of the solid-fluid energy. Assuming a patchwise topology of the surface with patches of uniform well depth of solid-fluid interaction, the adsorption on a real carbon surface can be determined as an integral of the local surface excess of each patch with respect to the differential area. When this is matched against the experimental data of a carbon surface, we can derive the area distribution versus energy and hence the geometrical surface area. This new approach will be illustrated with the adsorption of argon on a nongraphitized carbon at 87.3 and 77 K, and it is found that the GCMC surface area is different from the BET surface area by about 7%. Furthermore, the description of the isotherm in the region of BET validity of 0.06 to 0.2 is much better with our method than with the BET equation.

Evaluation of 1-site and 5-site models of methane on its adsorption on graphite and in graphitic slit pores.

In this paper, we evaluate the performance of the 1- and 5-site models of methane on the description of adsorption on graphite surfaces and in graphitic slit pores. These models have been known to perform well in the description of the fluid-phase behavior and vapor-liquid equilibria. Their performance in adsorption is evaluated in this work for nonporous graphitized thermal carbon black, and simulation results are compared with the experimental data of Avgul and Kiselev (Chemistry and Physics of Carbon; Dekker: New York, 1970; Vol. 6, p 1). On this nonporous surface, it is found that these models perform as well on isotherms at various temperatures as they do on the experimental isosteric heat for adsorption on a graphite surface. They are then tested for their performance in predicting the adsorption isotherms in graphitic slit pores, in which we would like to explore the effect of confinement on the molecule packing. Pore widths of 10 and 20 A are chosen in this investigation, and we also study the effects of temperature by choosing 90.7, 113, and 273 K. The first two are for subcritical conditions, with 90.7 K being the triple point of methane and 113 K being its boiling point. The last temperature is chosen to represent the supercritical condition so that we can investigate the performance of these models at extremely high pressures. We have found that for the case of slit pores investigated in this paper, although the two models yield comparable pore densities (provided the accessible pore width is used in the calculation of pore density), the number of particles predicted by the 1-site model is always greater than that predicted by the 5-site model, regardless of whether temperature is subcritical or supercritical. This is due to the packing effect in the confined space such that a methane molecule modeled as a spherical particle in the 1-site model would pack better than the fused five-sphere model in the case of the 5-site model. Because the 5-site model better describes the liquid- and solid-phase behavior, we would argue that the packing density in small pores is better described with a more detailed 5-site model, and care should be exercised when using the 1-site model to study adsorption in small pores.

Effects of potential models on the adsorption of ethane and ethylene on graphitized thermal carbon black. Study of two-dimensional critical temperature and isosteric heat versus loading.

Adsorption of ethylene and ethane on graphitized thermal carbon black and in slit pores whose walls are composed of graphene layers is studied in detail to investigate the packing efficiency, the two-dimensional critical temperature, and the variation of the isosteric heat of adsorption with loading and temperature. Here we used a Monte Carlo simulation method with a grand canonical Monte Carlo ensemble. A number of two-center Lennard-Jones (LJ) potential models are investigated to study the impact of the choice of potential models in the description of adsorption behavior. We chose two 2C-LJ potential models in our investigation of the (i) UA-TraPPE-LJ model of Martin and Siepmann for ethane and Wick et al. for ethylene and (ii) AUA4-LJ model of Ungerer et al. for ethane and Bourasseau et al. for ethylene. These models are used to study the adsorption of ethane and ethylene on graphitized thermal carbon black. It is found that the solid-fluid binary interaction parameter is a function of adsorbate and temperature, and the adsorption isotherms and heat of adsorption are well described by both the UA-TraPPE and AUA models, although the UA-TraPPE model performs slightly better. However, the local distributions predicted by these two models are slightly different. These two models are used to explore the two-dimensional condensation for the graphitized thermal carbon black, and these values are 110 K for ethylene and 120 K for ethane.

Effect of surface-perturbed intermolecular interaction on adsorption of simple gases on a graphitized carbon surface.

In this paper, we investigate the effect of the solid surface on the fluid-fluid intermolecular potential energy. This modified fluid-fluid interaction energy due to the inducement of a solid surface is used in the grand canonical Monte Carlo (GCMC) simulation of various noble gases, nitrogen, and methane on graphitized thermal carbon black. This effect is such that the effective interaction potential energy between two particles close to surface is less than the potential energy if the solid substrate is not present. With this modification the GCMC simulation results agree extremely well with the experimental data over a wide range of pressures while the simulation results with the unmodified potential energy give rise to a shoulder near the neighborhood of monolayer coverage and the significant overprediction of the second and higher layer coverages. In particular the unmodified GCMC results exhibit very sharp change in those higher layers while the experimental data have a much gradual change in the uptake. We will illustrate this theory with adsorption data of argon, xenon, neon, nitrogen, and methane on graphitized thermal carbon black.

Adsorption of ethylene on graphitized thermal carbon black and in slit pores: a computer simulation study.

In this paper, we studied vapor-liquid equilibria (VLE) and adsorption of ethylene on graphitized thermal carbon black and in slit pores whose walls are composed of graphene layers. Simple models of a one-center Lennard-Jones (LJ) potential and a two-center united atom (UA)-LJ potential are investigated to study the impact of the choice of potential models in the description of VLE and adsorption behavior. Here, we used a Monte Carlo simulation method with grand canonical Monte Carlo (GCMC) and Gibbs ensemble Monte Carlo ensembles. The one-center potential model cannot describe adequately the VLE over the practical range of temperature from the triple point to the critical point. On the other hand, the two-center potential model (Wick et al. J. Phys. Chem. B 2000, 104, 8008-8016) performs well in the description of VLE (saturated vapor and liquid densities and vapor pressure) over the wide range of temperature. This UA-LJ model is then used in the study of adsorption of ethylene on graphitized thermal carbon black and in slit pores. Agreement between the GCMC simulation results and the experimental data on graphitized thermal carbon black for moderate temperatures is excellent, demonstrating that the potential of the GCMC method and the proper choice of potential model are essential to investigate adsorption. For slit pores of various sizes, we have found that the behavior of ethylene exhibits a number of features that are not manifested in the study of spherical LJ particles. In particular, the singlet density distribution versus distance across the pore and the angle between the molecular axis and the z direction provide rich information about the way molecules arrange themselves when the pore width is varied. Such an arrangement has been found to be very sensitive to the pore width.

X-ray structure and crystal lattice interactions of the taxol side-chain methyl ester.

A colorless, parallelepiped crystal of methyl (2R,3S)-N-benzoyl-3-phenylisoserinate belonging to the space group P2(1) with a = 5.414(4), b = 7.813(1), c = 17.802(7) A, beta = 90.87(4) degrees, Z = 2, V = 752.9 A3, Dcalc = 1.32 g cm-3, and mu calc = 1.02 cm-1 was selected and the structure solved using direct methods. Refinement led to a final R = 0.079 for 819 [Fo greater than or equal to 5 sigma (Fo)] reflections. Intermolecular hydrogen-bonding interactions are prevalent in the crystal lattice of this compound.

Platelet activating factor antagonist design. 2. X-ray structure of dimethyl 2,3,4,5-tetrahydro-5 beta-(3,4-methylenedioxyphenyl)-2-oxo-3 beta-(3,4,5-trimethoxybenzoyl)-3 alpha,4 alpha-furandicarboxylate.

C25H24O12, Mr = 516.46, triclinic, P-1, a = 8.780 (3), b = 11.298 (4), c = 13.271 (6) A, alpha = 71.77 (4), beta = 70.31 (3), gamma = 72.66 (3) degrees, V = 1189 A3, Z = 2, Dx = 1.44 g cm-3, lambda (Mo K alpha) = 0.71073 A, mu = 0.74 cm-1, F(000) = 540, T = 293 K, final R = 0.046 for 2495 observed [Fo greater than or equal to 5 sigma (Fo)] reflections. The observed structure reveals a trans disposition for the methoxycarbonyl and aryl substituents at positions 4 and 5 of the heterocycle and a cis-3,4-bis(methoxycarbonyl) relationship. There is no crystallographically imposed symmetry. Several intermolecular van der Waals interactions occur in the cell lattice of this compound.