The discovery of periodic mesoporous MCM-41 and related molecular sieves has attracted significant attention from a fundamental as well as applied perspective. They possess well-defined cylindrical/hexagonal mesopores with a simple geometry, tailored pore size, and reproducible surface properties. Hence, there is an ever-growing scientific interest in the challenges posed by their processing and characterization and by the refinement of various sorption models. Further, MCM-41-based materials are currently under intense investigation with respect to their utility as adsorbents, catalysts, supports, ion-exchangers, and molecular hosts. In this article, we provide a critical review of the developments in these areas with particular emphasis on adsorption characteristics, progress in controlling the pore sizes, and a comparison of pore size distributions using traditional and newer models. The model proposed by the authors for adsorption isotherms and criticalities in capillary condensation and hysteresis is found to explain unusual adsorption behavior in these materials while providing a convenient characterization tool.

MCM-41 materials of six different pore diameters were prepared and characterized using X-ray diffraction, transmission electron microscopy, helium pycnometry, small-angle neutron scattering, and gas adsorption (argon at 77.4 and 87.4 K, nitrogen and oxygen at 77.4 K, and carbon dioxide at 194.6 K). A recent molecular continuum model of the authors, previously used for adsorption of nitrogen at 77.4 K, was applied here for adsorption of argon, oxygen, and carbon dioxide. While model predictions of single-pore adsorption isotherms for argon and oxygen are in satisfactory agreement with experimental data, significant deviation was found for carbon dioxide, most likely due to its high quadrupole moment. Predictions of critical pore diameter, below which reversible condensation occurs, were possible by the model and found to be consistent with experimental estimates, for the adsorption of the various gases. On the other hand, existing models such as the Barrett−Joyner−Halenda (BJH), Saito−Foley, and Dubinin−Astakhov models were found to be inadequate, either predicting an incorrect pore diameter or not correlating the isotherms adequately. The wall structure of MCM-41 appears to be close to that of amorphous silica, as inferred from our skeletal density measurements.

The present work deals with the study of palladium-silver (PdAg) and palladium-gold (PdAu) binary alloys over a broad range of temperatures and alloy compositions using density functional theory (DFT) to find possible conditions where the solubility of hydrogen (H) is significantly higher than that of pure palladium (Pd). Several alloy structures, such as Pd(100-x)Ag(x) with x = 14.81, 25.93, 37.04, and 48.51, Pd(100-x)Aux with x = 14.81, 25.93, and 37.04, and Pd(100-x)Cu(x) with x = 25.93 and 48.51 were considered. The lattice constants of these structures were optimized using DFT, and relaxed structures were used for the estimation of binding energy. It was found that the solubility of H in PdAg is higher than pure Pd with a maximum at approximately 30% Ag at 456 K. Also, the solubility of PdAu alloys was higher than pure Pd with a maximum at about 20% Au with a solubility 12 times higher than that of pure Pd. It was found that for a 3.7% H concentration in a PdAg alloy, a cell expansion of 0.15-0.2% occurs, which if ignored may affect the individual binding energy of the O-site by approximately 3.56% and may affect the predicted solubility by approximately 11.8%.

In this article, a new hybrid model for estimating the pore size distribution of micro-and mesoporous materials is developed, and tested with the adsorption data of nitrogen, oxygen, and argon on ordered mesoporous materials reported in the literature. For the micropore region, the model uses the Dubinin-Rudushkevich (DR) isotherm with the Chen-Yang modification. A recent isotherm model of the authors for nonporous materials, which uses a continuum-mechanical model for the multilayer region and the Unilan model for the submonolayer region, has been extended for adsorption in mesopores. The experimental data is inverted using regularization to obtain the pore size distribution. The present model was found to be successful in predicting the pore size distribution of pure as well as binary physical mixtures of MCM-41 synthesized with different templates, with results in agreement with those from the XRD method and nonlocal density functional theory. It was found that various other recent methods, as well as the classical Broekhoff and de Boer method, underpredict the pore diameter of MCM-41. The present model has been successfully applied to MCM-48, SBA's, CMK, KIT, HMS, FSM, MTS, mesoporous fly ash, and a large number of other regular mesoporous materials.

The present work investigates both the diffusivity and permeability of hydrogen (H) in palladium-silver (PdAg) and palladium-gold (PdAu) alloys over a 400-1200 K temperature range for Pd(100-X)M(X), M=Ag or Au and X=0%-48% using density functional theory (DFT) and kinetic Monte Carlo simulations (KMC). DFT has been employed to obtain octahedral (O)-, tetrahedral (T)-, and transition state (TS)- site energetics as a function of local alloy composition for several PdAg and PdAu alloys with compositions in supercells of X=14.18%, 25.93%, 37.07%, and 48.15% with the nearest (NNs) and next nearest neighbors (NNNs) varied over the entire range of compositions. The estimates were then used to obtain a model relating the O, T, and TS energies of a given site with NN(X), NNN(X), and the lattice constant. The first passage approach combined with KMC simulations was used for the H diffusion coefficient predictions. It was found that the diffusion coefficient of H in PdAg alloy decreases with increasing Ag and increases with increasing temperature, matching closely with the experimental results reported in the literature. The calculated permeabilities of H in these novel binary alloys obtained from both diffusivity and solubility predictions were found to have a maximum at approximately 20% Ag and approximately 12% Au, which agree well with experimental predictions. Specifically, the permeability of H in PdAg alloy with approximately 20% Ag at 456 K is three to four times that of pure Pd, while the PdAu alloy at 12% Au is four to five times that of pure Pd at 456 K.