scholarly journals Molecular Dimerisation in a Multilayer Adsorption Phase on Homogeneous Surfaces of a Solid Adsorbent

2019 ◽  
Vol 67 (2) ◽  
pp. 59-68
Author(s):  
Jerzy K. Garbacz ◽  
Karol Karpiński ◽  
Mariusz Kozakiewicz
Keyword(s):  
Analytical Form ◽  
Langmuir Equation ◽  
Multilayer Adsorption ◽  
Approximation Characteristic ◽  
Adsorption Phase ◽  
Solid Adsorbent ◽  
Adsorption Equation ◽  
Boundary Properties ◽  
Theoretical Considerations

Abstract Continuing the discussion on the description of adsorbate-adsorbate association on homogeneous surfaces of solids, an attempt was made to formulate an analytical form of adsorption equation for a multilayer adsorption phase. The validity of Berezin’s and Kiselev’s assumptions concerning the independence of adsorption in further layers from the model of the phenomenon in the first of them was discussed. The fundamental validity of this assumption has been demonstrated, simultaneously ridding it of its arbitrary character. The main aim of the study was to demonstrate the possibility of formulating a description assuming molecule association in the entire adsorption phase (and not only in the first layer). Theoretical considerations are confined to the case of dimerisation in the concentration range thus warranting the approximation characteristic of the Berezin and Kiselev model. The obtained final adsorption equation exhibits physically acceptable boundary properties; with adequate assumptions it amounts to the Brunauer, Emmett and Teller equation, the equation formulated earlier by one of the authors of this paper or the Langmuir equation.

Continuous and Discontinuous Linear Approximation of the Window Spectrum by Least Squares Method

2011 ◽  
Vol 18 (3) ◽  
pp. 379-390 ◽  
Author(s):  
Józef Borkowski
Keyword(s):  
Least Squares ◽  
Linear Approximation ◽  
Least Squares Method ◽  
Analytical Form ◽  
Linear Functions ◽  
Approximation Solution ◽  
Approximation Accuracy ◽  
Approximation Characteristic ◽  
Zero Padding ◽  
Approximation Parameter

Continuous and Discontinuous Linear Approximation of the Window Spectrum by Least Squares Method This paper presents the general solution of the least-squares approximation of the frequency characteristic of the data window by linear functions combined with zero padding technique. The approximation characteristic can be discontinuous or continuous, what depends on the value of one approximation parameter. The approximation solution has an analytical form and therefore the results have universal character. The paper presents derived formulas, analysis of approximation accuracy, the exemplary characteristics and conclusions, which confirm high accuracy of the approximation. The presented solution is applicable to estimating methods, like the LIDFT method, visualizations, etc.

scholarly journals Phenomenological Variant of Quasi-Chemical Approximation in the Description of the Dimerisation of Adsorbate Molecules in a Multilayer Adsorption Phase on a Homogeneous Surface

2019 ◽  
Vol 68 (3) ◽  
pp. 33-40
Author(s):  
Jerzy K. Garbacz ◽  
Mariusz Kozakiewicz ◽  
Barbara Rymian
Keyword(s):  
Binding Sites ◽  
Gas Adsorption ◽  
Multilayer Adsorption ◽  
Homogeneous Surface ◽  
Adsorption Phase ◽  
Secondary Interactions ◽  
Fundamental Possibility ◽  
Layer Adsorption ◽  
Adsorption Complexes ◽  
Chemical Scheme

Abstract This article is related thematically to two of our earlier publications, which demonstrated full equivalence of statistical and phenomenological methods in the description of physical gas adsorption on the surface of a solid body, and the fundamental possibility of analytical solution of adsorbate-adsorbate association problems in the entire multi-layer adsorption phase. The quasi-chemical scheme of secondary interactions leading to the formation of horizontal multimolecular adsorption complexes has been elaborated. A new adsorption equation was formulated taking into account the dimerisation of adsorbed molecules in the whole adsorption phase, as well as the influence of topography of the binding sites of adsorbent surfaces on the form of this solution.

scholarly journals The equivalence of quasi-chemical and statistical description of adsorbate molecule association in a localised adsorption monolayer on a homogeneous solid surface

2018 ◽  
Vol 65 (4) ◽  
pp. 25-38
Author(s):  
Jerzy K. Garbacz ◽  
Mariusz Kozakiewicz
Keyword(s):  
Canonical Ensemble ◽  
Equilibrium Concentration ◽  
Critical Conditions ◽  
Homogeneous Surface ◽  
Adsorption Sites ◽  
Solid Adsorbent ◽  
Adsorption Equation ◽  
Correct Form ◽  
Adsorption Monolayer ◽  
Association Of Molecules

Abstract The analysis of Berezin and Kiselev’s concept assuming linear association of molecules in a localised adsorption monolayer on the homogeneous surface of a solid adsorbent was carried out. An inconsistency due to the lack of consideration of equilibrium concentration of free adsorption sites in the formulation of the expression for the association constant has been pointed out. It was shown that the correct form of this function leads to the final adsorption equation being identical to the specific case of the Fowler-Guggenheim equation. The obtained result has been generalised to cases of branched adsorbateadsorbate associations. A new adsorption equation limiting the association to at most the dimers has been introduced. Critical conditions for the two-dimensional condensation of the adsorption layer were determined. By applying the formalism of canonical ensemble, full equivalence of the phenomenological and statistical methods was demonstrated in the description of the intermolecular interactions in the localised adsorption monolayer.

Metal Microstructures in Advanced CMOS Devices

1996 ◽  
Vol 54 ◽  
pp. 358-359
Author(s):  
L. M. Gignac ◽  
K. P. Rodbell
Keyword(s):  
Grain Boundaries ◽  
Semiconductor Device ◽  
Chemical Vapor ◽  
Microstructural Characterization ◽  
Metal Films ◽  
Thin Metal ◽  
Electrical Performance ◽  
Thin Metal Films ◽  
Chemical Vapor Deposited ◽  
Boundary Properties

As advanced semiconductor device features shrink, grain boundaries and interfaces become increasingly more important to the properties of thin metal films. With film thicknesses decreasing to the range of 10 nm and the corresponding features also decreasing to sub-micrometer sizes, interface and grain boundary properties become dominant. In this regime the details of the surfaces and grain boundaries dictate the interactions between film layers and the subsequent electrical properties. Therefore it is necessary to accurately characterize these materials on the proper length scale in order to first understand and then to improve the device effectiveness. In this talk we will examine the importance of microstructural characterization of thin metal films used in semiconductor devices and show how microstructure can influence the electrical performance. Specifically, we will review Co and Ti silicides for silicon contact and gate conductor applications, Ti/TiN liner films used for adhesion and diffusion barriers in chemical vapor deposited (CVD) tungsten vertical wiring (vias) and Ti/AlCu/Ti-TiN films used as planar interconnect metal lines.

On the influence of specimen thickness in TEM images of super-conducting vortices

1996 ◽  
Vol 54 ◽  
pp. 724-725
Author(s):  
J. Bonevich ◽  
D. Capacci ◽  
G. Pozzi ◽  
K. Harada ◽  
H. Kasai ◽  
...  
Keyword(s):  
Flux Line ◽  
Analytical Form ◽  
Realistic Model ◽  
Electron Holography ◽  
Specimen Thickness ◽  
Flux Tubes ◽  
Analytical Expression ◽  
Flux Lines ◽  
Normal Core ◽  
Two Parameters

The successful observation of superconducting flux lines (fluxons) in thin specimens both in conventional and high Tc superconductors by means of Lorentz and electron holography methods has presented several problems concerning the interpretation of the experimental results. The first approach has been to model the fluxon as a bundle of flux tubes perpendicular to the specimen surface (for which the electron optical phase shift has been found in analytical form) with a magnetic flux distribution given by the London model, which corresponds to a flux line having an infinitely small normal core. In addition to being described by an analytical expression, this model has the advantage that a single parameter, the London penetration depth, completely characterizes the superconducting fluxon. The obtained results have shown that the most relevant features of the experimental data are well interpreted by this model. However, Clem has proposed another more realistic model for the fluxon core that removes the unphysical limitation of the infinitely small normal core and has the advantage of being described by an analytical expression depending on two parameters (the coherence length and the London depth).

The Biological Clock and Sleep in the Elderly

2006 ◽  
Vol 19 (1) ◽  
pp. 45-51 ◽  
Author(s):  
Myriam Juda ◽  
Mirjam Münch ◽  
Anna Wirz-Justice ◽  
Martha Merrow ◽  
Till Roenneberg
Keyword(s):  
Circadian Rhythms ◽  
Biological Clock ◽  
The Elderly ◽  
Early Morning ◽  
Behavioral Changes ◽  
Older Age ◽  
Age Related ◽  
Theoretical Considerations ◽  
Sleep Difficulties ◽  
Circadian Biology

Abstract: Among many other changes, older age is characterized by advanced sleep-wake cycles, changes in the amplitude of various circadian rhythms, as well as reduced entrainment to zeitgebers. These features reveal themselves through early morning awakenings, sleep difficulties at night, and a re-emergence of daytime napping. This review summarizes the observations concerning the biological clock and sleep in the elderly and discusses the documented and theoretical considerations behind these age-related behavioral changes, especially with respect to circadian biology.

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