Van der Waals equation for the description of monolayer formation on arbitrary surfaces

The van der Waals equation is well known for the description of two-dimensional monolayers. The formation of a monolayer is the result of a compromise between the process of self-organization on the surface and the probabilities of spatial configurations of adsorbate molecules near the surface. The main reasons for the geometric heterogeneity of the monolayer are the geometric disorder and the energy inhomogeneity of the surface profile. A monolayer is a statistically related system and its symmetry causes correlations of processes at different spatial scales. The classical van der Waals equation is written for the two-dimensional, completely symmetric Euclidean space. In the general case, the geometry of the monolayer must be defined for the Euclidean space of fractional dimension (fractal space) with symmetry breaking. In this case, the application of the classical van der Waals equation is limited. Considering the fractal nature of the monolayer–solid interface, a quasi-two-dimensional van der Waals equation is developed. The application of the equation to experimental data of an activated carbon is shown

Analytical equation for the mesopore size distribution function of open cylindrical capillaries

For the characterization of porous structures, besides the specific surface area, the pore size distribution is of special interest. In this paper, the pore size distribution of mesoporous structures is calculated from the adsorption branch of the hysteresis loop, whereby only loops of type H1 are considered. The modeling is done only for cylindrical capillaries and the calculation of the pore size distribution is done by a combination of the percolation theory and the theory of capillary condensation. By applying percolation theory to the adsorption process, the pressure dependence of pore filling during capillary condensation is described. Because of a lack of strictly theoretically based equations for the adsorption process by capillary condensation, a mathematical adaptation to measured data is done by the Bernoulli equation. This is proposed by the authors for the first time for a description of adsorption–desorption processes. Thus a new, strictly thermodynamic method to calculate the mesopore size distribution is gained. As an example, the pore size distribution is calculated. The results coincide well with other evaluation methods

Non-Arrhenius form of the Henry adsorption on inhomogeneous substrates: The effect of frozen disorder

Usually, when considering sub-monolayer adsorption at different temperatures T, the logarithm of the Henry constant is represented as (Formula presented.) with some constant “heat of adsorption” U0 > 0. However, such Arrhenius-type form has a clear base only for an ideal translational-invariant crystal substrate. In more real situation, e.g. for a structurally disordered substrate, the “heat of adsorption” will be some random function of two-dimensional coordinates characterized by some distribution function of its different values. Starting from general principles of the theory of Gaussian fluctuations, we show that the adsorption at the substrate with bulk inhomogeneous structure leads to expression (Formula presented.) with some fluctuation quantity Δ. A possibility to observe such “non-Arrhenius” additive seems most favorable at rather low temperatures for substrates modeled by substitutional solid solutions. The theoretical predictions are illustrated by comparison with the experimental data obtained for some disordered adsorbents

Adsorption Hysteresis in Open Slit-like Micropores

Adsorption hysteresis in the low-pressure range is only rarely described in the literature. To optimise, for example, heat storage technologies, a deeper understanding of the low-pressure hysteresis (LPH) process is necessary. Here, two thermodynamically based approaches are further developed for analysing the LPH within the framework of thermodynamically irreversible processes and fractal geometry. With both methods developed, it is possible to obtain the description of the adsorption and desorption branches with high accuracy. Within the framework of the two thermodynamic models of the hysteresis loop, generalised equations are obtained with the control parameter in the form of the degree of irreversibility. This is done by taking the adsorption of water on alumina as an example. It is shown that the fractal dimension of the adsorption process is larger than the fractal dimension of the desorption branch, meaning that the phase state of the adsorbate is more symmetric during the adsorption step than in the desorption process

Fractal characteristics of microporous adsorbents

The traditional version of the theory of volume filling of micropores was used for the estimation of the fractal dimension of microporous solids. For this purpose, the Dubinin’s integral equation was solved for infinite and limited integration limits. The results were applied to the adsorption of nitrogen (T = 78 K) on coal samples and Davisil F silica and to the adsorption of water (Т = 293 К) on lunar soil sample and on rice starch. The traditional version of the theory of volume filling of micropores was used for the estimation of the fractal dimension of microporous solids. For this purpose, the Dubinin’s integral equation was solved for infinite and limited integration limits. The results were applied to the adsorption of nitrogen (T = 78 K) on coal samples and Davisil F silica and to the adsorption of water (Т = 293 К) on lunar soil sample and on rice starch. The traditional version of the theory of volume filling of micropores was used for the estimation of the fractal dimension of microporous solids. For this purpose, the Dubinin’s integral equation was solved for infinite and limited integration limits. The results were applied to the adsorption of nitrogen (T = 78 K) on coal samples and Davisil F silica and to the adsorption of water (Т = 293 К) on lunar soil sample and on rice starch

Long-Term Behavior of Fuel Vapor Retaining Systems for Pure (E0) and Blended Fuels (E10) Part 2: Regeneration with Nitrogen of 70% Relative Humidity

In gasoline-driven vehicles, fuel vapor retaining systems are used to prevent the emission of hydrocarbons from the fuel tank into the atmosphere. In this paper, which is Part 2 of our publication, measurements of regeneration processes of the activated carbon by flushing it with humid nitrogen gas of 70% relative humidity are represented. Using purge air with high relative humidities, representing realistic conditions, it can be observed that water is accumulated in the activated carbon. For ethanol-containing fuel blends, additional accumulation of ethanol in the carbon occurs, decreasing the adsorption capacity of the carbon for standard fuel’s components considerably. State-of-the-art testing procedures use purge air with about 50% relative humidity for the regeneration of the activated carbon filters. As this often does not represent real operation conditions, the working limits of the fuel vapor retaining systems could not be identified up to now. Furthermore, the determination of the butane working capacity as a quality parameter of the fuel vapor retaining systems is also based on the assumption of relatively low air humidity. Consequently, a new quality criterion has to be established