p18 J Phys Chem C 115 (2011) 20628–20638 SI (original) (raw)
Related papers
As the understanding of any physical phenomenon progresses, existing theories are extended or modified until a new theory is developed which better explains experimental observations. Often, change comes after research in the underlying science reveals weaknesses in the current theoretical model. Breaking away from a traditional view can lead to a more elegant description of the phenomenon, but doing so is likely to require the total revision of a representative model to which many have become accustomed. A familiar example of changing viewpoint after extending a traditional theoretical model to its limit is the evolution of atomic theory. Rutherford introduced the classical "planetary" model of electron orbits. Bohr extended Rutherford's model to account for the emission line spectra of hydrogen. Sommerfeld extended Bohr's model to explain the observed fine structure of the spectra, but further extensions to the classical theory failed to explain the spectra of other atomic species; the model had reached its practical limit. Only after the shift to wave mechanics with the applications of Schrodinger's wave equation were certain problems solved pertaining to atomic and molecular structure. As with the above example of the evolution of the atomic model, a similar evolution is taking place in the theory of fluids particularly as applied to the solid-fluid interface and, more specifically, in the instance of physical adsorption. Currently in this field, as in other branches of science, the computational method ("the third physics" 1 ) is providing an additional investigative approach in conjunction with traditional theoretical and experimental methods.
In this paper, scanning electron microscopy (SEM) images of carbon samples were analysed, and some textural characteristics were obtained and compared with those determined using mercury porosimetry data. Fractal dimensions were calculated from both mercury porosimetry and SEM images as methods for characterising the porous distribution (heterogeneity) of the samples. Lacunarity is easily determined from SEM images as a measure of the degree of heterogeneity of a porous surface. A relationship between the lacunarity and the fractal dimensions calculated using both methods is shown. Pore-size distributions were also determined from the analysis of SEM images. We show that the analysis of SEM images is a valuable complement to mercury porosimetry measurements and a useful tool for the characterisation of porous surfaces. This method offers the possibility of evaluating the features of porous materials and comparing the results to those obtained using mercury intrusion analysis.
Capillary condensation in MMS and pore structure characterization
Microporous and Mesoporous Materials, 2001
Phenomena of capillary condensation and desorption in siliceous mesoporous molecular sieves (MMS) with cylindrical channels are studied by means of the non-local density functional theory (NLDFT). The results are compared with macroscopic thermodynamic approaches based on Kelvin±Cohan (KC) and Derjaguin±Broekho±de Boer (DBdB) equations. We show that: The KC equations, which constitute the basis of the traditional BJH method for the pore size distribution analysis, are in error even in pores as large as 20 nm. The DBdB equations with consistently determined thickness of the adsorbed layer (disjoining pressure isotherm) can be justi®ed for pores wider than %7 nm in diameter. As the pore size decreases, the macroscopic arguments become less accurate, and the NLDFT and DBdB results dier signi®cantly in pores smaller than %4 nm. The adsorption±desorption isotherms predicted by NLDFT are found to be in quantitative agreement with the experimental nitrogen (77 K) and argon (87 K) isotherms on MCM-41 type materials with pores larger than 5 nm. Therewith, the experimental desorption branch corresponds to the equilibrium capillary condensation/evaporation transition. The experimental adsorption branch corresponds to the spontaneous spinodal condensation, which occurs at the limit of stability of adsorption ®lms. The NLDFT method has been developed for the calculation of pore size distributions from both the adsorption and desorption isotherms.
Adsorption of water on Grace Silica Gel 127B at low and high pressure
Adsorption, 2011
An application of the original Dubinin-Radushkevitch equation modified with based on Polanyi theory, which taking into consideration the self-associating molecules in heterogeneous microporous structures at low and high uptake was presented. The Polanyi-Dubinin models were applied to predicting the behavior of water adsorption on Grace Silica Gel 127B at pressures not yet reported in the literature. The heat of adsorption, differential entropy, henry ratio was obtained from adsorption isotherm. The resulting extensions are experimentally and analytically presented. The coefficient of multiple correlation (R 2 ) between the thermogravimetric measurements and the MDR equation was 0.9924, which is 8.13% better than the best Dubinin-Astakhov fit.
Journal of Colloid and Interface Science, 1998
sorption isotherms, (1) which is illustrated in Fig. 1. Type Adsorption at fluid-solid interfaces is considered in the frame-I isotherms are characteristic of microporous adsorbents. work of a lattice with boundaries. Using ideas proposed by S. Types II and III describe adsorption on macroporous adsor-Ono and S. Kondo (in ''Molecular Theory of Surface Tension in bents with strong and weak adsorbate-adsorbent interac-Liquids'' (S. Flü gge, Ed.), Encyclopedia of Physics, Vol. 10, p. tions respectively. Types IV and V represent adsorption iso-134. Springer-Verlag, Berlin, 1960), a lattice model is derived, therms with hysteresis. In addition to the five types of isoboth rigorously and phenomenologically, and applied to macro-, therms identified by BDDT, the IUPAC classification meso-, and microporous adsorbents by imposing different boundincludes a sixth isotherm (Type VI) which has steps. All of ary conditions. It is shown that this lattice theory can predict the entire spectrum of behavior observed when gases, liquids, or these types of isotherms have been observed in numerous supercritical fluids adsorb on solid surfaces. In particular, it is able experiments (3) and have been analyzed theoretically (see, to predict steps in the isotherms, scaling behavior near saturation for example, (4, 5)). conditions, supercritical behavior, and adsorption hysteresis. It is However, the IUPAC classification has two deficiencies: shown that there is a profound analogy in the adsorption behavior it is incomplete and it gives the incorrect impression that of a one-component gas to that of a binary liquid mixture. This adsorption isotherms are always monotonic functions of analysis leads to a new classification of physisorption isotherms pressure. To illustrate these points, consider the following for fluid/solid equilibria. ᭧ 1998 Academic Press experimental isotherms.
Effects of adsorption on equilibrium crystal shape: A zero-temperature calculation
Physical review. B, Condensed matter
&as adsorption at a crystal surface changes the interfacial free energy and, therefore, modifies the corresponding equilibrium crystal shape (ECS). A simple lattice-gas model of the adsorption process, including both adatom-adatom and adatorncrystal-atom interactions, allows this shape change to be computed explicitly at zero temperature. The dependence of the ECS on the adsorbed-gas chemical potential is calculated for cubic crystals (sc, bcc, fcc) with a variety of crystal-atomcrystal-atom interactions. Adsorption changes the ECS both by causing the appearance of new facets and by altering the relative areas of existing facets. The shape-change systernatics is given in terms of ECS phase diagrams.
Isothermal adsorption models: mini-focused observations
Journal of Petroleum Research and Studies
Adsorption is kinetically time-dependence controlled retention/ release mobility as a natural phenomenon in base and applicable in industry or in science. It is well-studied and modulated by known Langmuir, Temkin, Freundlich, and other models to describe how it occurred and explains kinetic- thermodynamic material behaviour. Linear and/ or non- linear expressions may take place according to the theoretical base of these models to conclude the layer formation, uniformity besides reaction reversibility, and favourability from kinetic- thermodynamic principles. Coefficient of determination (R2) is a mean variation of data or a degree of proper or fitting as mostly used in kinetic and isotherm literatures. In adsorption investigations, experimental physical- chemical conditions and error sources are the main influenced factors, for example, at surface coverage (or inhibition efficiency) in corrosion treatments or adsorption capacity in pollution subject. Linearity variation will govern...