H.D. Do

A Model for water adsorption in activated carbon

In this paper we present a new model to describe the adsorption equilibrium of water in activated carbon. The model is based on the growth of the water cluster at the functional groups and the penetration of water clusters into the micropore in the form of pentamer, which has sufficiently high dispersion energy to remain in the micropore. This model is able to describe all possible behaviours of the water adsorption isotherm observed in the literature, ranging from type V for hydrophobic carbon to type IV for highly oxidised carbon. Testing of the model against a number of experimental data shows that the model is able to describe data well

Characterization of micro-mesoporous carbon media

A simple method to characterize the micro and mesoporous carbon media is discussed. In this method, the overall adsorption quantity is the sum of capacities of all pores (slit shape is assumed), in each of which the process of adsorption occurs in two sequential steps: the multi-layering followed by pore filling steps. The critical factor in these two steps is the enhancement of the pressure of occluded free molecules in the pore as well as the enhancement of the adsorption layer thickness. Both of these enhancements are due to the overlapping of the potential fields contributed by the two opposite walls. The classical BET and modified Kelvin equations are assumed to be applicable for the two steps mentioned above, with the allowance for the enhanced pore pressure, the enhanced adsorption energy and the enhanced BET constant,all of which vary with pore width. The method is then applied to data of many carbon samples of different sources to derive their respective pore size distributions, which are compared with those obtained from DFT analysis. Similar pore size distributions (PSDs) are observed although our method gives sharper distribution. Furthermore, we use our theory to analyze adsorption data of nitrogen at 77 K and that of benzene at 303 K (ambient temperature). The PSDs derived from these two different probe molecules are similar, with some small differences that could be attributed to the molecular properties, such as the collision diameter. Permeation characteristics of sub-critical fluids are also discussed in this paper

Adsorption of supercritical fluids in non-porous and porous carbons : Analysis of adsorbed phase volume and density

In this paper, we revisit the surface mass excess in adsorption studies and investigate the role of the volume of the adsorbed phase and its density in the analysis of supercritical gas adsorption in non-porous as well as microporous solids. For many supercritical fluids tested (krypton, argon, nitrogen, methane) on many different carbonaceous solids, it is found that the volume of the adsorbed phase is confined mostly to a geometrical volume having a thickness of up to a few molecular diameters. At high pressure the adsorbed phase density is also found to be very close to but never equal or greater than the liquid phase density

A new adsorption isotherm for heterogeneous adsorbent based on the isosteric heat as a function of loading

A new adsorption isotherm model is proposed in this paper for a heterogeneous solid. The basis of this isotherm equation is that the degree of heterogeneity is reflected through the variation of the isosteric heat of adsorption with respect to loading. This degree as well as the pattern of heterogeneity is assumed to be independent of adsorbate used. The influence of the adsorbate on the isotherm will be through the interaction energy at zero loading as well as parameters which reflect the way in which the adsorbate fits into the adsorption sites. The resulting isotherm equation is very general, and under certain conditions it reduces to many isotherms commonly used in the literature, such as the Langmuir, Langmuir-Freundlich, Toth, Fowler-Guggenheim and Nitta et al. equations. The new isotherm is tested with adsorption isotherm data of many adsorbates on various samples of activated carbon and zeolite, and the parameters extracted for these adsorbates shed some light on the system heterogeneity. Implications of this new isotherm are discussed in this paper.

Pore characterization of carbonaceous materials by DFT and GCMC simulations: A review

A review is given of the pore characterization of carbonaceous materials, including activated carbon, carbon fibres, carbon nanotubes, etc., using adsorption techniques. Since the pores of carbon media are mostly of molecular dimensions, the appropriate modern tools for the analysis of adsorption isotherms are grand canonical Monte Carlo (GCMC) simulations and density functional theory (DFT). These techniques are presented and applications of such tools in the derivation of pore-size distribution highlighted.

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 Hoffs 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.

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.

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.

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.

Surface diffusion of strong adsorbing vapours on porous carbon

Surface diffusion of strongly adsorbing hydrocarbon vapours on activated carbon was measured by using a constant molar flow method (D.D. Do, Dynamics of a semi-batch adsorber with constant molar supply rate: a method for studying adsorption rate of pure gas, Chem. Eng. Sci. 50 (1995) 549), where pure adsorbate is introduced into a semi-batch adsorber at a constant molar flow rate. The surface diffusivity was determined from the analysis of pressure response versus time, using a linear mathematical model developed earlier. To apply the linear theory over the non-linear range of the adsorption isotherm, we implement a differential increment method on the system which is initially equilibrated with some pre-determined loading. By conducting the experiments at different initial loadings, the surface diffusivity can be extracted as a function of loading. Propane, n-butane, n-hexane, benzene, and ethanol were used as diffusing adsorbate on a commercial activated carbon. It is found that the surface diffusivity of these strongly adsorbing vapours increases rapidly with loading, and the surface diffusion flux contributes significantly to the total flux and cannot be ignored. The surface diffusivity increases with temperature according to the Arrhenius law, and for the paraffins tested it decreases with the molecular weight of the adsorbate