Studies on adsorption energy distributions computation from adsorption isotherms by the ansatz method

Since the well-known adsorption integral equation (AIE) is an ill-posed problem, calculation of relevant energetic properties from gas and liquid adsorption isotherms on porous solids still remains a challenging field of research. There are two approaches for solving the AIE: (1) the numerical regularization method and (2) the fitting of the experimental adsorption data by functions possessing an analytical solution. Up to now the latter approach has been treated without consideration of the ill-posedness. The inclusion of ill-posedness in the approach leads to its specification which we call the ansatz method. By showing that a certain class of ansatz functions cannot be used for describing the total isotherms, we were urged to consider more general solutions being connected with the Stieltjes integrals. After applying a general inversion formula we can restrict the theoretically possible total isotherms and outline a feasible general ansatz.     

Configurational effects of templating on the adsorption isotherms of templated porous materials

The porosity and pore geometry of disordered materials can be influenced by employing a removable template during synthesis. A theoretical and simulation study is reported of the configurational effects of template size and density on the adsorption isotherms of templated porous materials. To isolate the configurational (entropic) contributions, the adsorbate, matrix and template components are modelled as hard spheres. The replica Ornstein-Zernike equations proposed by Zhang, L. and Van Tassel, P. R. (2000) J. chem Phys., 112, 3006 are used within the Percus-Yevick approximation to calculate adsorption isotherms for differently sized adsorbate and template components. These theoretical results are compared with results from Monte Carlo simulation. It is found that adsorption is most enhanced whenever the size of the template is equal to or slightly larger than that of the adsorbate. Also, for systems of constant matrix density or constant matrix plus template density, increasing the density of template enhances the adsorption.     

The crossing of N2 adsorption isotherms on CdCl2

The adsorption of N₂ at 77.7, 83.3 and 90.1 K has been obtained on a sample of CdCl₂ previously treated in vacuum at 150°C for 40 h. All adsorption isotherms, when plotted versus relative pressure, cross at a point near $\text{P}\text{P}{}_0$ = 0.15. The volume adsorbed at the crossing point is near the BET or point B monolayer volume. The crossing of the isotherms is related to the high surface homogeneity of the sample.     

Evaluation of the adsorption capacity of carbon nanofibers with the use of distribution functions

The sorption properties of carbon nanosystems are investigated using appropriate distribution functions. The adsorption capacities of carbon nanofibers for hydrogen are calculated in the singlet approximation under the assumption that adsorbent molecules elastically interact with walls. The optimum interplanar distances determined for carbon nanofibers are as follows: 0.39 ± 0.07 nm for the reduced density n ₀ = 0.15 and 0.46 ± 0.04 nm for the reduced density n ₀ = 0.3.     

Calculating surface tension isotherms and the adsorption of components in ternary Na-K-Cs alloys

The results from calculating the surface tension (ST) isotherms and adsorption coefficients for components (?? _i ^(N) ) of Na-K-Cs alloys obtained by means of graphic computations and using a semi-empirical formula are presented. Ternary alloys with compositions corresponding to sections of a concentration triangle directed toward vertices of sodium, potassium, and cesium are investigated. A comparison of the values for ST isotherms and adsorption (where i represents Na, Cs, and K), calculated using the above methods, demonstrates their satisfactory agreement among themselves and with the experimental data.     

Dielectric and adsorption isotherms of adsorbed krypton and xenon on boron nitride

We present simultaneous measurements of adsorption isotherms and dielectric isotherms for krypton and xenon on boron nitride. Dielectric measurements give a good characterization of monolayer formation and completion, and provide new information on the dielectric properties evolution from a two-dimensional system towards the bulk.     

Evaluation of adsorption energy distribution of microporous materials by a multivariant identification

The applicability of new BET-like adsorption models (uLBET and LBET formulas) for the examination of microporous materials of irregular structure is discussed. The models are intended to handle the main effects of random pore geometry on the adsorption isotherm shape. They are based on a generalized BET theory and employ simple (but realistic) adsorption energy-pore geometry relationships. To overcome numerical problems inherent in fitting any more advanced adsorption model, a multivariant identification procedure is proposed with a subset of parameters being fixed in each variant. The reliability assessment of the system parameters evaluation is stressed. The paper outlines formal and numerical bounds for adsorption measurements-based identifiability of irregular porous structures. The LBET-type formulas are recommended for the examination of such materials, as a relatively simple alternative versus DFT-based techniques. Numerous simulation results and exemplary examinations of an empirical isotherm are discussed.     

Particle distribution from effective classical potential

We show that the method of effective classical partition functions can be extended to find an approximation to the temperature dependent particle distributions of quantum systems which are quite accurate, even at low temperature.     

Influence of the two-body potential on the radial distribution function of liquid 4He

The theoretical ground-state radial distribution function of liquid ⁴He appears to depend much more sensitively on the range of the assumed two-body potential than on its depth. Fairly good agreement with experiment is obtained by using realistic pair potentials.     

Application of the J-walking formalism to the test particle method: adsorption isotherms for atomic monolayers

By implementing the J-walking formalism within the test particle method, adsorption isotherms for various Lennard-Jones systems were constructed. The method decreases the uncertainties in the average thermodynamic values by approximately one order of magnitude and substantially increases the percentage insertion of the ghost particle. The adsorption isotherms showed that at low temperatures the amount of adsorbed material seems to be independent of the vapour pressure of the gas if attractive forces dominate the system. On the other hand, systems dominated by repulsive forces show the usual type B behaviour for adsorption isotherms. The equation of state is used to confirm these results.     

Sticky hard sphere potential—Evaluation of the structure function of liquids

The direct correlation function as obtained by Baxter for a sticky hard sphere potential, which is significant improvement over that of the hard sphere potential, has been used in the evaluation of the structure function of aluminium and lead. The values obtained by the present method are in good agreement with experiment.     

Canonical equilibrium distribution derived from Helmholtz potential

Plastino and Curado [A. Plastino, E.M.F. Curado, Phys. Rev. E 72 (2005) 047103] recently determined the equilibrium probability distribution for the canonical ensemble using only phenomenological thermodynamical laws as an alternative to the entropy maximization procedure of Jaynes. In the current paper we present another alternative derivation of the canonical equilibrium probability distribution, which is based on the definition of the Helmholtz free energy (and its being constant at the equilibrium) and the assumption of the uniqueness of the equilibrium probability distribution. Noting that this particular derivation is applicable for all trace-form entropies, we also apply it to the Tsallis entropy, showing that the Tsallis entropy yields genuine inverse power laws.     

Wetting transitions at triple points; A study based upon the analysis of stepwise adsorption isotherms

This adsorption isotherm study finds that ethylene adsorption on PbI₂ is limited to only a few layers at T<T_3t (the triple point temperature of bulk ethylene) but that almost unlimited adsorption can take place as T_3t, is approached. This behaviour is qualitatively identical to the behaviour of the ethylene/graphite system previously reported. In both cases wetting by ethylene is incomplete below T_3t since the adlayers formed have an orientational order which is in compatible with that which is found in the bulk solid ethylene. However, C₂H₄ shows a strong tendency to wetting somewhat below its bulk triple point temperature because it can form a liquid or at least an orientationally disordered solid film of limited thickness. The similarities and differences between these two systems are discussed. In addition, we discuss in general systems for which wetting is temperature dependent. The first part of this paper is devoted to outlining in detail how stepwise adsorption isotherms on powdered samples can be used to give information about wetting of the exposed basal face. The merits and limitations of this method are discussed in the context of the ethylene/PbI₂ example.     

First quantum correction to the radial distribution function for a fluid of non-analytic potential

Basis set expansion in molecules containing second-row atoms by inclusion of s and p-type gaussian functions centred on the bond axes is shown to be efficient and is compared with the addition of d-orbitals to the basis set, in the test molecule SO₂. Calculations on SO₂ and other molecules at MBS and double-zeta level have been carried out with wave-function polarization introduced by bond functions at various locations in the molecule. Some simple rules for basis set enhancement by this method are presented.