Improvement of the Derjaguin-Broekhoff-de Boer theory for the capillary condensation/evaporation of nitrogen in spherical cavities and its application for the pore size analysis of silicas with ordered cagelike mesopores

In a previous work, we proposed an improvement of the Derjaguin-Broekhoff-de Boer (DBdB) theory for capillary condensation/evaporation in open-ended cylindrical mesopores. In this paper, we report a further extension of this approach to the capillary condensation/evaporation of nitrogen in siliceous spherical cavities. The main idea of this improvement is to employ the Gibbs-Tolman-Koenig-Buff equation to predict the variation of the surface tension in spherical mesopores. In addition, the statistical film thickness (the so-called t-curve), which is evaluated accurately on the basis of adsorption isotherms measured for MCM-41 materials, is used instead of the originally proposed t-curve to take into account the excess chemical potential due to the surface forces. It is shown that the aforementioned modifications of the original DBdB theory that was refined by Ravikovitch and Neimark have significant implications for the pore size analysis of cagelike mesoporous silicas. To verify the proposed improvement of the DBdB pore size analysis (IDBdB), two series of FDU-1 samples, which are well-defined cagelike mesoporous materials (composed of siliceous spherical cavities interconnected by short necks), were used for the evaluation of the pore size distributions (PSDs). The correlation between the spinodal condensation point in the spherical pores predicted by the nonlocal density functional theory (NDFT) developed by Ravikovitch and Neimark and that predicted by the IDBdB theory is very good in the whole range of mesopores. This feature is mirrored to the realistic PSD characterized by the bimodal structure of pores computed from the IDBdB theory. As in the case of open-ended cylindrical pores, the improvement of the classical DBdB theory preserves its simplicity and simultaneously ensures a significant improvement of the pore size analysis, which is confirmed by the independent estimation of the average pore size by the NDFT and the powder X-ray diffraction method.     

Thermodynamic verification of the gradient method for surface area estimation

We present thermodynamic verification of Nonaka's gradient method for surface area estimation. On the basis of calorimetric measurements and integral molar entropy calculations it is shown that the main assumption of this method, when used at around room temperature, is an approximation. The specific surface areas of Sterling MT graphitized carbon black, obtained on the basis of three methods are compared. It is shown that the gradient method may be used, for its operational convenience, in cases where an uncertainty of several per cent may be tolerated.     

Energetics of methane adsorption on microporous activated carbons

The influence of microporous carbon surface oxidation on energetics of methane adsorption at 308 K is discussed. Obtained adsorption heats and integral molar entropies of the adsorbate show that microporous carbon surface oxidation changes the methane adsorption process. This is probably resulted by the existence of an endothermic effect during adsorption in oxidized carbon micropores.     

Estimating the pore size distribution of activated carbons from adsorption data of different adsorbates by various methods

Experimental adsorption isotherms of four adsorbates (N2, Ar, C6H6, and CCl4) as well as adsorption enthalpy (C6H6 and CCl4) measured on two strictly microporous carbons are used to evaluate the porosity of adsorbents (i.e., pore size distributions (PSDs) and average pore diameter ( Lav )). The influence of the diameter of adsorbates ( dA) as well as of the temperature ( T ) is analyzed in order to explain the differences or similarities between the above-mentioned quantities for all systems. Proposed previously, the general relationships between the parameters of the Dubinin-Astakhov (DA) isotherm equation (the characteristic energy of adsorption ( E0 ) and the exponent of this equation ( n )) and the average slit-width of carbon micropores are investigated. Moreover, the thermodynamic verification of the Horvath-Kawazoe (HK) theory and the ND model is presented based on data of the adsorption and enthalpy of adsorption of benzene and carbon tetrachloride on two carbons. Finally, the pore diameters calculated from calorimetry data using the Everett and Powl method and those calculated applying the recently developed equations are compared. In our opinion the change of apparent PSD should be monitored by performing a series of isotherm measurements from high (equal and higher than room temperature) to low temperatures (ca. 77.5 K) as was presented in the current study. Moreover, the analysis of the experimental data leads to the conclusion that the entropy of C6H6 and CCl4 can approach to the values characteristic of quasi-solid (a partially ordered structure). Therefore, this behavior of the adsorbate should be taken into consideration in the theoretical assumptions of model and its thermodynamic verification.     

Phenol adsorption on closed carbon nanotubes

We present the results of systematic studies of phenol adsorption on closed commercially available, unmodified carbon nanotubes. Phenol adsorption is determined by the value of tube-specific surface area, the presence of small amount of surface groups influence adsorption only in very small amount. Phenol can be applied as a probe molecule for comparative analysis of tube surface areas. Tube curvature influences adsorption from solution, i.e., we observe increasing adsorption energy (and slower desorption process) with the decrease in tube curvature. This is in full accordance with molecular simulation results.     

How realistic is the pore size distribution calculated from adsorption isotherms if activated carbon is composed of fullerene-like fragments?

A plausible model for the structure of non-graphitizing carbon is one which consists of curved, fullerene-like fragments grouped together in a random arrangement. Although this model was proposed several years ago, there have been no attempts to calculate the properties of such a structure. Here, we determine the density, pore size distribution and adsorption properties of a model porous carbon constructed from fullerene-like elements. Using the method proposed recently by Bhattacharya and Gubbins (BG), which was tested in this study for ideal and defective carbon slits, the pore size distributions (PSDs) of the initial model and two related carbon models are calculated. The obtained PSD curves show that two structures are micro-mesoporous (with different ratio of micro/mesopores) and the third is strictly microporous. Using the grand canonical Monte Carlo (GCMC) method, adsorption isotherms of Ar (87 K) are simulated for all the structures. Finally PSD curves are calculated using the Horvath-Kawazoe, non-local density functional theory (NLDFT), Nguyen and Do, and Barrett-Joyner-Halenda (BJH) approaches, and compared with those predicted by the BG method. This is the first study in which different methods of calculation of PSDs for carbons from adsorption data can be really verified, since absolute (i.e. true) PSDs are obtained using the BG method. This is also the first study reporting the results of computer simulations of adsorption on fullerene-like carbon models.     

Porous structure of natural and modified clinoptilolites

The evaluation of the pore-size distribution (PSD) of natural and modified mesoporous zeolites, i.e., clinoptilolites is presented. We demonstrate the SEM results showing that the pores of fracture-type from 25-50 nm to 100 nm in size between clinoptilolite grains, as well as pores between crystal aggregates up to 500 nm in size are present in the studied material. The detailed distribution of pore sizes and tortuosity factor of the above-mentioned materials are determined from the adsorption-desorption isotherms of nitrogen measured volumetrically at 77 K. To obtain the reliable pore size distribution (PSD) of the above-mentioned materials both adsorption and desorption branches of the experimental hysteresis loop are described simultaneously by recently developed corrugated pore structure model (CPSM) of Androutsopoulos and Salmas. Evaluated pore size distributions are characterized by well-defined smooth peaks placed in the region of the mesoporosity. Moreover, the mean pore diameter calculated from the classical static measurement of nitrogen adsorption at 77 K correspond very well to the pore diameters from SEM, showing the applicability of the CPSM for characterization of the porosity of natural zeolites. We conclude that classical static adsorption measurements combined with the proper modeling of the capillary condensation/evaporation phenomena are a powerful method which can be applied for pore structure characterization of natural and modified clinoptilolites.     

Study of the selection mechanism of heavy metal (Pb2+, Cu2+, Ni2+, and Cd2+) adsorption on clinoptilolite

The study was carried out on the sorption of heavy metals (Ni2+, Cu2+, Pb2+, and Cd2+) under static conditions from single- and multicomponent aqueous solutions by raw and pretreated clinoptilolite. The sorption has an ion-exchange nature and consists of three stages, i.e., the adsorption on the surface of microcrystals, the inversion stage, and the moderate adsorption in the interior of the microcrystal. The finer clinoptilolite fractions sorb higher amounts of the metals due to relative enriching by the zeolite proper and higher cleavage. The slight difference between adsorption capacity of the clinoptilolite toward lead, copper, and cadmium from single- and multicomponent solutions may testify to individual sorption centers of the zeolite for each metal. The decrease of nickel adsorption from multicomponent solutions is probably caused by the propinquity of its sorption forms to the other metals and by competition. The maximum sorption capacity toward Cd2+ is determined as 4.22 mg/g at an initial concentration of 80 mg/L and toward Pb2+, Cu2+, and Ni2+ as 27.7, 25.76, and 13.03 mg/g at 800 mg/L. The sorption results fit well to the Langmuir and the Freundlich models. The second one is better for adsorption modeling at high metal concentrations.